From 74b247577714b3d72b569ab8d7c7ae82d20f92dc Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=A7=9C=E5=86=AC=E8=87=B4?= Date: Mon, 2 May 2016 23:39:14 +0800 Subject: [PATCH] Added files via GitHub desktop --- Adjust_profile_position.m | 77 + Adjust_profile_velocity.m | 79 + CTM_to_Euler.m | 28 + Calculate_errors_NED.m | 51 + ECEF_to_ECI.m | 47 + ECEF_to_NED.m | 85 + ECI_to_ECEF.m | 47 + Euler_to_CTM.m | 42 + GNSS_Demo_1.m | 86 + GNSS_Demo_2.m | 108 + GNSS_Demo_3.m | 108 + GNSS_Demo_4.m | 108 + GNSS_Demo_5.m | 108 + GNSS_Demo_6.m | 105 + GNSS_KF_Epoch.m | 146 + GNSS_Kalman_Filter.m | 253 + GNSS_LS_position_velocity.m | 149 + GNSS_Least_Squares.m | 214 + Generate_GNSS_measurements.m | 109 + Gravitation_ECI.m | 42 + Gravity_ECEF.m | 47 + Gravity_NED.m | 43 + IMU_model.m | 79 + INS_GNSS_Demo_1.m | 155 + INS_GNSS_Demo_10.m | 155 + INS_GNSS_Demo_11.m | 155 + INS_GNSS_Demo_12.m | 155 + INS_GNSS_Demo_2.m | 155 + INS_GNSS_Demo_3.m | 147 + INS_GNSS_Demo_4.m | 147 + INS_GNSS_Demo_5.m | 155 + INS_GNSS_Demo_6.m | 155 + INS_GNSS_Demo_7.m | 157 + INS_GNSS_Demo_8.m | 157 + INS_GNSS_Demo_9.m | 155 + Inertial_Demo_1ECEF.m | 89 + Inertial_Demo_1ECI.m | 98 + Inertial_Demo_1NED.m | 89 + Inertial_Demo_2.m | 89 + Inertial_Demo_3.m | 89 + Inertial_Demo_4.m | 89 + Inertial_Demo_5.m | 89 + Inertial_Demo_6.m | 89 + Inertial_Demo_7.m | 88 + Inertial_navigation_ECEF.m | 181 + Inertial_navigation_ECI.m | 190 + Inertial_navigation_NED.m | 177 + Initialize_GNSS_KF.m | 50 + Initialize_GNSS_biases.m | 66 + Initialize_LC_P_matrix.m | 34 + Initialize_NED.m | 50 + Initialize_NED_attitude.m | 27 + Initialize_TC_P_matrix.m | 38 + Interpolate_profile.m | 95 + Kinematics_ECEF.m | 90 + Kinematics_ECI.m | 76 + Kinematics_NED.m | 101 + LC_KF_Epoch.m | 128 + License.txt | 24 + Loosely_coupled_INS_GNSS.m | 338 + NED_to_ECEF.m | 57 + Nav_equations_ECEF.m | 87 + Nav_equations_ECI.m | 74 + Nav_equations_NED.m | 113 + Plot_errors.m | 91 + Plot_profile.m | 94 + Profile_0.csv | 6001 ++++ Profile_1.csv | 6001 ++++ Profile_2.csv | 17501 +++++++++++ Profile_3.csv | 41801 +++++++++++++++++++++++++ Profile_4.csv | 30001 ++++++++++++++++++ Radii_of_curvature.m | 33 + Read_profile.m | 53 + Satellite_positions_and_velocities.m | 75 + Skew_symmetric.m | 23 + Smooth_profile_velocity.m | 70 + TC_KF_Epoch.m | 184 + Tightly_coupled_INS_GNSS.m | 336 + Update_curvilinear_position.m | 47 + Velocity_from_curvilinear.m | 46 + Write_errors.m | 38 + Write_profile.m | 39 + pv_ECEF_to_NED.m | 80 + pv_NED_to_ECEF.m | 52 + 84 files changed, 109380 insertions(+) create mode 100644 Adjust_profile_position.m create mode 100644 Adjust_profile_velocity.m create mode 100644 CTM_to_Euler.m create mode 100644 Calculate_errors_NED.m create mode 100644 ECEF_to_ECI.m create mode 100644 ECEF_to_NED.m create mode 100644 ECI_to_ECEF.m create mode 100644 Euler_to_CTM.m create mode 100644 GNSS_Demo_1.m create mode 100644 GNSS_Demo_2.m create mode 100644 GNSS_Demo_3.m create mode 100644 GNSS_Demo_4.m create mode 100644 GNSS_Demo_5.m create mode 100644 GNSS_Demo_6.m create mode 100644 GNSS_KF_Epoch.m create mode 100644 GNSS_Kalman_Filter.m create mode 100644 GNSS_LS_position_velocity.m create mode 100644 GNSS_Least_Squares.m create mode 100644 Generate_GNSS_measurements.m create mode 100644 Gravitation_ECI.m create mode 100644 Gravity_ECEF.m create mode 100644 Gravity_NED.m create mode 100644 IMU_model.m create mode 100644 INS_GNSS_Demo_1.m create mode 100644 INS_GNSS_Demo_10.m create mode 100644 INS_GNSS_Demo_11.m create mode 100644 INS_GNSS_Demo_12.m create mode 100644 INS_GNSS_Demo_2.m create mode 100644 INS_GNSS_Demo_3.m create mode 100644 INS_GNSS_Demo_4.m create mode 100644 INS_GNSS_Demo_5.m create mode 100644 INS_GNSS_Demo_6.m create mode 100644 INS_GNSS_Demo_7.m create mode 100644 INS_GNSS_Demo_8.m create mode 100644 INS_GNSS_Demo_9.m create mode 100644 Inertial_Demo_1ECEF.m create mode 100644 Inertial_Demo_1ECI.m create mode 100644 Inertial_Demo_1NED.m create mode 100644 Inertial_Demo_2.m create mode 100644 Inertial_Demo_3.m create mode 100644 Inertial_Demo_4.m create mode 100644 Inertial_Demo_5.m create mode 100644 Inertial_Demo_6.m create mode 100644 Inertial_Demo_7.m create mode 100644 Inertial_navigation_ECEF.m create mode 100644 Inertial_navigation_ECI.m create mode 100644 Inertial_navigation_NED.m create mode 100644 Initialize_GNSS_KF.m create mode 100644 Initialize_GNSS_biases.m create mode 100644 Initialize_LC_P_matrix.m create mode 100644 Initialize_NED.m create mode 100644 Initialize_NED_attitude.m create mode 100644 Initialize_TC_P_matrix.m create mode 100644 Interpolate_profile.m create mode 100644 Kinematics_ECEF.m create mode 100644 Kinematics_ECI.m create mode 100644 Kinematics_NED.m create mode 100644 LC_KF_Epoch.m create mode 100644 License.txt create mode 100644 Loosely_coupled_INS_GNSS.m create mode 100644 NED_to_ECEF.m create mode 100644 Nav_equations_ECEF.m create mode 100644 Nav_equations_ECI.m create mode 100644 Nav_equations_NED.m create mode 100644 Plot_errors.m create mode 100644 Plot_profile.m create mode 100644 Profile_0.csv create mode 100644 Profile_1.csv create mode 100644 Profile_2.csv create mode 100644 Profile_3.csv create mode 100644 Profile_4.csv create mode 100644 Radii_of_curvature.m create mode 100644 Read_profile.m create mode 100644 Satellite_positions_and_velocities.m create mode 100644 Skew_symmetric.m create mode 100644 Smooth_profile_velocity.m create mode 100644 TC_KF_Epoch.m create mode 100644 Tightly_coupled_INS_GNSS.m create mode 100644 Update_curvilinear_position.m create mode 100644 Velocity_from_curvilinear.m create mode 100644 Write_errors.m create mode 100644 Write_profile.m create mode 100644 pv_ECEF_to_NED.m create mode 100644 pv_NED_to_ECEF.m diff --git a/Adjust_profile_position.m b/Adjust_profile_position.m new file mode 100644 index 0000000..2a7df5a --- /dev/null +++ b/Adjust_profile_position.m @@ -0,0 +1,77 @@ +function Adjust_profile_position(in_filename,out_filename) +%Adjust_profile_position - Adjusts the position in a motion profile file to +% make it consistent with the velocity +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 2/4/2012 by Paul Groves +% +% Inputs +% in_filename Name of inpit file, e.g. 'In_profile.csv' +% out_filename Name of inpit file, e.g. 'Out_profile.csv' + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Parameters +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; + + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(in_filename); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Initialize navigation solution +old_time = in_profile(1,1); +old_L_b = in_profile(1,2); +old_lambda_b = in_profile(1,3); +old_h_b = in_profile(1,4); +old_v_eb_n = in_profile(1,5:7)'; +old_eul_nb = in_profile(1,8:10)'; +out_profile(1,:) = in_profile(1,:); + +% Main loop +for epoch = 2:no_epochs + + % Input data from profile + time = in_profile(epoch,1); + v_eb_n = in_profile(epoch,5:7)'; + eul_nb = in_profile(epoch,8:10)'; + + % Time interval + tor_i = time - old_time; + + % Update position + [L_b,lambda_b,h_b]= Update_curvilinear_position(tor_i,old_L_b,... + old_lambda_b,old_h_b,old_v_eb_n,v_eb_n); + + % Generate output profile record + out_profile(epoch,1) = time; + out_profile(epoch,2) = L_b; + out_profile(epoch,3) = lambda_b; + out_profile(epoch,4) = h_b; + out_profile(epoch,5:7) = v_eb_n'; + out_profile(epoch,8:10) = eul_nb'; + + % Reset old values + old_time = time; + old_L_b = L_b; + old_lambda_b = lambda_b; + old_h_b = h_b; + old_v_eb_n = v_eb_n; + old_eul_nb = eul_nb; + +end %epoch + +% Write output profile +Write_profile(out_filename,out_profile); + +% Ends \ No newline at end of file diff --git a/Adjust_profile_velocity.m b/Adjust_profile_velocity.m new file mode 100644 index 0000000..a0dbe9c --- /dev/null +++ b/Adjust_profile_velocity.m @@ -0,0 +1,79 @@ +function Adjust_profile_velocity(in_filename,out_filename) +%Adjust_profile_velocity - Adjusts the velocity in a motion profile file to +% make it consistent with the position +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 2/4/2012 by Paul Groves +% +% Inputs +% in_filename Name of inpit file, e.g. 'In_profile.csv' +% out_filename Name of inpit file, e.g. 'Out_profile.csv' + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Parameters +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; + + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(in_filename); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Initialize navigation solution +old_time = in_profile(1,1); +old_L_b = in_profile(1,2); +old_lambda_b = in_profile(1,3); +old_h_b = in_profile(1,4); +old_v_eb_n = in_profile(1,5:7)'; +old_eul_nb = in_profile(1,8:10)'; +out_profile(1,:) = in_profile(1,:); + +% Main loop +for epoch = 2:no_epochs + + % Input data from profile + time = in_profile(epoch,1); + L_b = in_profile(epoch,2); + lambda_b = in_profile(epoch,3); + h_b = in_profile(epoch,4); + eul_nb = in_profile(epoch,8:10)'; + + % Time interval + tor_i = time - old_time; + + % Update velocity + v_eb_n = Velocity_from_curvilinear(tor_i,old_L_b,... + old_lambda_b,old_h_b,old_v_eb_n,L_b,lambda_b,h_b); + + % Generate output profile record + out_profile(epoch,1) = time; + out_profile(epoch,2) = L_b; + out_profile(epoch,3) = lambda_b; + out_profile(epoch,4) = h_b; + out_profile(epoch,5:7) = v_eb_n'; + out_profile(epoch,8:10) = eul_nb'; + + % Reset old values + old_time = time; + old_L_b = L_b; + old_lambda_b = lambda_b; + old_h_b = h_b; + old_v_eb_n = v_eb_n; + old_eul_nb = eul_nb; + +end %epoch + +% Write output profile +Write_profile(out_filename,out_profile); + +% Ends \ No newline at end of file diff --git a/CTM_to_Euler.m b/CTM_to_Euler.m new file mode 100644 index 0000000..faa5c16 --- /dev/null +++ b/CTM_to_Euler.m @@ -0,0 +1,28 @@ +function eul = CTM_to_Euler(C) +%CTM_to_Euler - Converts a coordinate transformation matrix to the +%corresponding set of Euler angles% +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 1/4/2012 by Paul Groves +% +% Inputs: +% C coordinate transformation matrix describing transformation from +% beta to alpha +% +% Outputs: +% eul Euler angles describing rotation from beta to alpha in the +% order roll, pitch, yaw(rad) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Calculate Euler angles using (2.23) +eul(1,1) = atan2(C(2,3),C(3,3)); % roll +eul(2,1) = - asin(C(1,3)); % pitch +eul(3,1) = atan2(C(1,2),C(1,1)); % yaw + +% Ends \ No newline at end of file diff --git a/Calculate_errors_NED.m b/Calculate_errors_NED.m new file mode 100644 index 0000000..2c4308d --- /dev/null +++ b/Calculate_errors_NED.m @@ -0,0 +1,51 @@ +function [delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n,true_L_b,... + true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n) +%Calculate_errors_NED - Calculates the position, velocity, and attitude +% errors of a NED navigation solution. +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 3/4/2012 by Paul Groves +% +% Inputs: +% est_L_b latitude solution (rad) +% est_lambda_b longitude solution (rad) +% est_h_b height solution (m) +% est_v_eb_n velocity solution of body frame w.r.t. ECEF frame, +% resolved along north, east, and down (m/s) +% est_C_b_n body-to-NED coordinate transformation matrix solution +% true_L_b true latitude (rad) +% true_lambda_b true longitude (rad) +% true_h_b true height (m) +% true_v_eb_n true velocity of body frame w.r.t. ECEF frame, resolved +% along north, east, and down (m/s) +% C_b_n true body-to-NED coordinate transformation matrix +% +% Outputs: +% delta_r_eb_n position error resolved along NED (m) +% delta_v_eb_n velocity error resolved along NED (m/s) +% delta_eul_nb_n attitude error as NED Euler angles (rad) +% These are expressed about north, east, and down + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Position error calculation, using (2.119) +[R_N,R_E] = Radii_of_curvature(true_L_b); +delta_r_eb_n(1) = (est_L_b - true_L_b) * (R_N + true_h_b); +delta_r_eb_n(2) = (est_lambda_b - true_lambda_b) * (R_E + true_h_b) *... + cos(true_L_b); +delta_r_eb_n(3) = -(est_h_b - true_h_b); + +% Velocity error calculation +delta_v_eb_n = est_v_eb_n - true_v_eb_n; + +% Attitude error calculation, using (5.109) and (5.111) +delta_C_b_n = est_C_b_n * true_C_b_n'; +delta_eul_nb_n = -CTM_to_Euler(delta_C_b_n); + +% Ends \ No newline at end of file diff --git a/ECEF_to_ECI.m b/ECEF_to_ECI.m new file mode 100644 index 0000000..f766539 --- /dev/null +++ b/ECEF_to_ECI.m @@ -0,0 +1,47 @@ +function [r_ib_i,v_ib_i,C_b_i] = ECEF_to_ECI(t,r_eb_e,v_eb_e,C_b_e) +%ECEF_to_ECI - Converts position, velocity, and attitude from ECEF- to +%ECI-frame referenced and resolved +%地心地固坐标系转换到地心惯性坐标系 +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 2/4/2012 by Paul Groves +% +% Inputs: +% t time (s) +% r_eb_e Cartesian position of body frame w.r.t. ECEF frame, resolved +% along ECEF-frame axes (m) +% v_eb_e velocity of body frame w.r.t. ECEF frame, resolved along +% ECEF-frame axes (m/s) +% C_b_e body-to-ECEF-frame coordinate transformation matrix +% +% Outputs: +% r_ib_i Cartesian position of body frame w.r.t. ECI frame, resolved +% along ECI-frame axes (m) +% v_ib_i velocity of body frame w.r.t. ECI frame, resolved along +% ECI-frame axes (m/s) +% C_b_i body-to-ECI-frame coordinate transformation matrix + +% Parameters +omega_ie = 7.292115E-5; % Earth rotation rate (rad/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Calculate ECEF to ECI coordinate transformation matrix using (2.145) +C_e_i = [cos(omega_ie * t), -sin(omega_ie * t), 0;... + sin(omega_ie * t), cos(omega_ie * t), 0;... + 0, 0, 1]; + +% Transform position using (2.146) +r_ib_i = C_e_i * r_eb_e; + +% Transform velocity using (2.145) +v_ib_i = C_e_i * (v_eb_e + omega_ie * [-r_eb_e(2);r_eb_e(1);0]); + +% Transform attitude using (2.15) +C_b_i = C_e_i * C_b_e; + +% Ends \ No newline at end of file diff --git a/ECEF_to_NED.m b/ECEF_to_NED.m new file mode 100644 index 0000000..046615c --- /dev/null +++ b/ECEF_to_NED.m @@ -0,0 +1,85 @@ +function [L_b,lambda_b,h_b,v_eb_n,C_b_n] = ECEF_to_NED(r_eb_e,v_eb_e,C_b_e) +%ECEF_to_NED - Converts Cartesian to curvilinear position, velocity +%resolving axes from ECEF to NED and attitude from ECEF- to NED-referenced +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 2/4/2012 by Paul Groves +% +% Inputs: +% r_eb_e Cartesian position of body frame w.r.t. ECEF frame, resolved +% along ECEF-frame axes (m) +% v_eb_e velocity of body frame w.r.t. ECEF frame, resolved along +% ECEF-frame axes (m/s) +% C_b_e body-to-ECEF-frame coordinate transformation matrix +% +% Outputs: +% L_b latitude (rad) +% lambda_b longitude (rad) +% h_b height (m) +% v_eb_n velocity of body frame w.r.t. ECEF frame, resolved along +% north, east, and down (m/s) +% C_b_n body-to-NED coordinate transformation matrix + +% Parameters +R_0 = 6378137; %WGS84 Equatorial radius in meters +e = 0.0818191908425; %WGS84 eccentricity + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Convert position using Borkowski closed-form exact solution +% From (2.113) +lambda_b = atan2(r_eb_e(2),r_eb_e(1)); + +% From (C.29) and (C.30) +k1 = sqrt(1 - e^2) * abs (r_eb_e(3)); +k2 = e^2 * R_0; +beta = sqrt(r_eb_e(1)^2 + r_eb_e(2)^2); +E = (k1 - k2) / beta; +F = (k1 + k2) / beta; + +% From (C.31) +P = 4/3 * (E*F + 1); + +% From (C.32) +Q = 2 * (E^2 - F^2); + +% From (C.33) +D = P^3 + Q^2; + +% From (C.34) +V = (sqrt(D) - Q)^(1/3) - (sqrt(D) + Q)^(1/3); + +% From (C.35) +G = 0.5 * (sqrt(E^2 + V) + E); + +% From (C.36) +T = sqrt(G^2 + (F - V * G) / (2 * G - E)) - G; + +% From (C.37) +L_b = sign(r_eb_e(3)) * atan((1 - T^2) / (2 * T * sqrt (1 - e^2))); + +% From (C.38) +h_b = (beta - R_0 * T) * cos(L_b) +... + (r_eb_e(3) - sign(r_eb_e(3)) * R_0 * sqrt(1 - e^2)) * sin (L_b); + +% Calculate ECEF to NED coordinate transformation matrix using (2.150) +cos_lat = cos(L_b); +sin_lat = sin(L_b); +cos_long = cos(lambda_b); +sin_long = sin(lambda_b); +C_e_n = [-sin_lat * cos_long, -sin_lat * sin_long, cos_lat;... + -sin_long, cos_long, 0;... + -cos_lat * cos_long, -cos_lat * sin_long, -sin_lat]; + +% Transform velocity using (2.73) +v_eb_n = C_e_n * v_eb_e; + +% Transform attitude using (2.15) +C_b_n = C_e_n * C_b_e; + +% Ends \ No newline at end of file diff --git a/ECI_to_ECEF.m b/ECI_to_ECEF.m new file mode 100644 index 0000000..438c27d --- /dev/null +++ b/ECI_to_ECEF.m @@ -0,0 +1,47 @@ +function [r_eb_e,v_eb_e,C_b_e] = ECI_to_ECEF(t,r_ib_i,v_ib_i,C_b_i) +%ECI_to_ECEF - Converts position, velocity, and attitude from ECI- to +%ECEF-frame referenced and resolved +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 2/4/2012 by Paul Groves +% +% Inputs: +% t time (s) +% r_ib_i Cartesian position of body frame w.r.t. ECI frame, resolved +% along ECI-frame axes (m) +% v_ib_i velocity of body frame w.r.t. ECI frame, resolved along +% ECI-frame axes (m/s) +% C_b_i body-to-ECI-frame coordinate transformation matrix +% +% Outputs: +% r_eb_e Cartesian position of body frame w.r.t. ECEF frame, resolved +% along ECEF-frame axes (m) +% v_eb_e velocity of body frame w.r.t. ECEF frame, resolved along +% ECEF-frame axes (m/s) +% C_b_e body-to-ECEF-frame coordinate transformation matrix + +% Parameters +omega_ie = 7.292115E-5; % Earth rotation rate (rad/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Calculate ECI to ECEF coordinate transformation matrix using (2.145) +C_i_e = [cos(omega_ie * t), sin(omega_ie * t), 0;... + -sin(omega_ie * t), cos(omega_ie * t), 0;... + 0, 0, 1]; + +% Transform position using (2.146) +r_eb_e = C_i_e * r_ib_i; + +% Transform velocity using (2.145) +v_eb_e = C_i_e * (v_ib_i - omega_ie * [-r_ib_i(2);r_ib_i(1);0]); + +% Transform attitude using (2.15) +C_b_e = C_i_e * C_b_i; + +% Ends \ No newline at end of file diff --git a/Euler_to_CTM.m b/Euler_to_CTM.m new file mode 100644 index 0000000..958b748 --- /dev/null +++ b/Euler_to_CTM.m @@ -0,0 +1,42 @@ +function C = Euler_to_CTM(eul) +%Euler_to_CTM - Converts a set of Euler angles to the corresponding +%coordinate transformation matrix 把欧拉角转换为相应的坐标转换矩阵 P.35 +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 1/4/2012 by Paul Groves +% +% Inputs: +% eul Euler angles describing rotation from beta to alpha in the +% order roll, pitch, yaw(rad) +% +% Outputs: +% C coordinate transformation matrix describing transformation from +% beta to alpha + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Precalculate sines and cosines of the Euler angles +sin_phi = sin(eul(1)); +cos_phi = cos(eul(1)); +sin_theta = sin(eul(2)); +cos_theta = cos(eul(2)); +sin_psi = sin(eul(3)); +cos_psi = cos(eul(3)); + +% Calculate coordinate transformation matrix using (2.22) +C(1,1) = cos_theta * cos_psi; +C(1,2) = cos_theta * sin_psi; +C(1,3) = -sin_theta; +C(2,1) = -cos_phi * sin_psi + sin_phi * sin_theta * cos_psi; +C(2,2) = cos_phi * cos_psi + sin_phi * sin_theta * sin_psi; +C(2,3) = sin_phi * cos_theta; +C(3,1) = sin_phi * sin_psi + cos_phi * sin_theta * cos_psi; +C(3,2) = -sin_phi * cos_psi + cos_phi * sin_theta * sin_psi; +C(3,3) = cos_phi * cos_theta; + +% Ends \ No newline at end of file diff --git a/GNSS_Demo_1.m b/GNSS_Demo_1.m new file mode 100644 index 0000000..b0eb62c --- /dev/null +++ b/GNSS_Demo_1.m @@ -0,0 +1,86 @@ +%GNSS_Demo_1 +%SCRIPT Stand-alone GNSS demo with least-squares solution: +% Profile_1 (60s artificial car motion with two 90 deg turns) +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 11/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_1.csv'; +% Output motion profile and error filenames +output_profile_name = 'GNSS_Demo_1_Profile.csv'; +output_errors_name = 'GNSS_Demo_1_Errors.csv'; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 1; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +% RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors,out_clock] = GNSS_Least_Squares(in_profile,... + no_epochs,GNSS_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/GNSS_Demo_2.m b/GNSS_Demo_2.m new file mode 100644 index 0000000..e53c57e --- /dev/null +++ b/GNSS_Demo_2.m @@ -0,0 +1,108 @@ +%GNSS_Demo_2 +%SCRIPT Stand-alone GNSS demo with Kalman filter solution: +% Profile_1 (60s artificial car motion with two 90 deg turns) +% +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 12/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_1.csv'; +% Output motion profile and error filenames +output_profile_name = 'GNSS_Demo_2_Profile.csv'; +output_errors_name = 'GNSS_Demo_2_Errors.csv'; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 1; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial position uncertainty per axis (m) +GNSS_KF_config.init_pos_unc = 10; +% Initial velocity uncertainty per axis (m/s) +GNSS_KF_config.init_vel_unc = 0.1; +% Initial clock offset uncertainty per axis (m) +GNSS_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +GNSS_KF_config.init_clock_drift_unc = 0.1; + +% Acceleration PSD per axis (m^2/s^3) +GNSS_KF_config.accel_PSD = 10; +% Receiver clock frequency-drift PSD (m^2/s^3) +GNSS_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +GNSS_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +GNSS_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +GNSS_KF_config.range_rate_SD = 0.05; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors,out_clock,out_KF_SD] = GNSS_Kalman_Filter(... + in_profile,no_epochs,GNSS_config,GNSS_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/GNSS_Demo_3.m b/GNSS_Demo_3.m new file mode 100644 index 0000000..2f5d317 --- /dev/null +++ b/GNSS_Demo_3.m @@ -0,0 +1,108 @@ +%GNSS_Demo_3 +%SCRIPT Stand-alone GNSS demo with Kalman filter solution: +% Profile_0 (60s stationary and level) +% +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 12/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_0.csv'; +% Output motion profile and error filenames +output_profile_name = 'GNSS_Demo_3_Profile.csv'; +output_errors_name = 'GNSS_Demo_3_Errors.csv'; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 1; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial position uncertainty per axis (m) +GNSS_KF_config.init_pos_unc = 10; +% Initial velocity uncertainty per axis (m/s) +GNSS_KF_config.init_vel_unc = 0.1; +% Initial clock offset uncertainty per axis (m) +GNSS_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +GNSS_KF_config.init_clock_drift_unc = 0.1; + +% Acceleration PSD per axis (m^2/s^3) +GNSS_KF_config.accel_PSD = 0.01; +% Receiver clock frequency-drift PSD (m^2/s^3) +GNSS_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +GNSS_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +GNSS_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +GNSS_KF_config.range_rate_SD = 0.05; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors,out_clock,out_KF_SD] = GNSS_Kalman_Filter(... + in_profile,no_epochs,GNSS_config,GNSS_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/GNSS_Demo_4.m b/GNSS_Demo_4.m new file mode 100644 index 0000000..2810455 --- /dev/null +++ b/GNSS_Demo_4.m @@ -0,0 +1,108 @@ +%GNSS_Demo_4 +%SCRIPT Stand-alone GNSS demo with Kalman filter solution: +% Profile_2 (175s car) +% +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 27/5/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_2.csv'; +% Output motion profile and error filenames +output_profile_name = 'GNSS_Demo_4_Profile.csv'; +output_errors_name = 'GNSS_Demo_4_Errors.csv'; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 1; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial position uncertainty per axis (m) +GNSS_KF_config.init_pos_unc = 10; +% Initial velocity uncertainty per axis (m/s) +GNSS_KF_config.init_vel_unc = 0.1; +% Initial clock offset uncertainty per axis (m) +GNSS_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +GNSS_KF_config.init_clock_drift_unc = 0.1; + +% Acceleration PSD per axis (m^2/s^3) +GNSS_KF_config.accel_PSD = 10; +% Receiver clock frequency-drift PSD (m^2/s^3) +GNSS_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +GNSS_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +GNSS_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +GNSS_KF_config.range_rate_SD = 0.05; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors,out_clock,out_KF_SD] = GNSS_Kalman_Filter(... + in_profile,no_epochs,GNSS_config,GNSS_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/GNSS_Demo_5.m b/GNSS_Demo_5.m new file mode 100644 index 0000000..24efb7a --- /dev/null +++ b/GNSS_Demo_5.m @@ -0,0 +1,108 @@ +%GNSS_Demo_5 +%SCRIPT Stand-alone GNSS demo with Kalman filter solution: +% Profile_3 (418s aircraft) +% +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 27/5/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_3.csv'; +% Output motion profile and error filenames +output_profile_name = 'GNSS_Demo_5_Profile.csv'; +output_errors_name = 'GNSS_Demo_5_Errors.csv'; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 1; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial position uncertainty per axis (m) +GNSS_KF_config.init_pos_unc = 10; +% Initial velocity uncertainty per axis (m/s) +GNSS_KF_config.init_vel_unc = 0.1; +% Initial clock offset uncertainty per axis (m) +GNSS_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +GNSS_KF_config.init_clock_drift_unc = 0.1; + +% Acceleration PSD per axis (m^2/s^3) +GNSS_KF_config.accel_PSD = 10; +% Receiver clock frequency-drift PSD (m^2/s^3) +GNSS_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +GNSS_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +GNSS_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +GNSS_KF_config.range_rate_SD = 0.05; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors,out_clock,out_KF_SD] = GNSS_Kalman_Filter(... + in_profile,no_epochs,GNSS_config,GNSS_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/GNSS_Demo_6.m b/GNSS_Demo_6.m new file mode 100644 index 0000000..5454385 --- /dev/null +++ b/GNSS_Demo_6.m @@ -0,0 +1,105 @@ +%GNSS_Demo_6 +%SCRIPT Stand-alone GNSS demo with Kalman filter solution: +% Profile_4 (300s boat) +% +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 27/5/12 by Paul Groves + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_4.csv'; +% Output motion profile and error filenames +output_profile_name = 'GNSS_Demo_6_Profile.csv'; +output_errors_name = 'GNSS_Demo_6_Errors.csv'; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 1; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial position uncertainty per axis (m) +GNSS_KF_config.init_pos_unc = 10; +% Initial velocity uncertainty per axis (m/s) +GNSS_KF_config.init_vel_unc = 0.1; +% Initial clock offset uncertainty per axis (m) +GNSS_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +GNSS_KF_config.init_clock_drift_unc = 0.1; + +% Acceleration PSD per axis (m^2/s^3) +GNSS_KF_config.accel_PSD = 10; +% Receiver clock frequency-drift PSD (m^2/s^3) +GNSS_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +GNSS_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +GNSS_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +GNSS_KF_config.range_rate_SD = 0.05; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors,out_clock,out_KF_SD] = GNSS_Kalman_Filter(... + in_profile,no_epochs,GNSS_config,GNSS_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/GNSS_KF_Epoch.m b/GNSS_KF_Epoch.m new file mode 100644 index 0000000..8b52b5d --- /dev/null +++ b/GNSS_KF_Epoch.m @@ -0,0 +1,146 @@ +function [x_est_new,P_matrix_new] = GNSS_KF_Epoch(GNSS_measurements,... + no_meas,tor_s,x_est_old,P_matrix_old,GNSS_KF_config) +%GNSS_KF_Epoch - Implements one cycle of the GNSS extended Kalman filter +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 12/4/2012 by Paul Groves +% +% Inputs: +% GNSS_measurements GNSS measurement data: +% Column 1 Pseudo-range measurements (m) +% Column 2 Pseudo-range rate measurements (m/s) +% Columns 3-5 Satellite ECEF position (m) +% Columns 6-8 Satellite ECEF velocity (m/s) +% no_meas Number of satellites for which measurements are +% supplied +% tor_s propagation interval (s) +% x_est_old previous Kalman filter state estimates +% P_matrix_old previous Kalman filter error covariance matrix +% GNSS_KF_config +% .accel_PSD Acceleration PSD per axis (m^2/s^3) +% .clock_freq_PSD Receiver clock frequency-drift PSD (m^2/s^3) +% .clock_phase_PSD Receiver clock phase-drift PSD (m^2/s) +% .pseudo_range_SD Pseudo-range measurement noise SD (m) +% .range_rate_SD Pseudo-range rate measurement noise SD (m/s) +% +% Outputs: +% x_est_new updated Kalman filter state estimates +% Rows 1-3 estimated ECEF user position (m) +% Rows 4-6 estimated ECEF user velocity (m/s) +% Row 7 estimated receiver clock offset (m) +% Row 8 estimated receiver clock drift (m/s) +% P_matrix_new updated Kalman filter error covariance matrix + + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants (sone of these could be changed to inputs at a later date) +c = 299792458; % Speed of light in m/s +omega_ie = 7.292115E-5; % Earth rotation rate in rad/s + +% Begins + +% SYSTEM PROPAGATION PHASE + +% 1. Determine transition matrix using (9.147) and (9.150) +Phi_matrix = eye(8); +Phi_matrix(1,4) = tor_s; +Phi_matrix(2,5) = tor_s; +Phi_matrix(3,6) = tor_s; +Phi_matrix(7,8) = tor_s; + +% 2. Determine system noise covariance matrix using (9.152) +Q_matrix = zeros(8); +Q_matrix(1:3,1:3) = eye(3) * GNSS_KF_config.accel_PSD * tor_s^3 / 3; +Q_matrix(1:3,4:6) = eye(3) * GNSS_KF_config.accel_PSD * tor_s^2 / 2; +Q_matrix(4:6,1:3) = eye(3) * GNSS_KF_config.accel_PSD * tor_s^2 / 2; +Q_matrix(4:6,4:6) = eye(3) * GNSS_KF_config.accel_PSD * tor_s; +Q_matrix(7,7) = (GNSS_KF_config.clock_freq_PSD * tor_s^3 / 3) +... + GNSS_KF_config.clock_phase_PSD * tor_s; +Q_matrix(7,8) = GNSS_KF_config.clock_freq_PSD * tor_s^2 / 2; +Q_matrix(8,7) = GNSS_KF_config.clock_freq_PSD * tor_s^2 / 2; +Q_matrix(8,8) = GNSS_KF_config.clock_freq_PSD * tor_s; + +% 3. Propagate state estimates using (3.14) +x_est_propagated = Phi_matrix * x_est_old; + +% 4. Propagate state estimation error covariance matrix using (3.15) +P_matrix_propagated = Phi_matrix * P_matrix_old * Phi_matrix' + Q_matrix; + +% MEASUREMENT UPDATE PHASE + +% Skew symmetric matrix of Earth rate +Omega_ie = Skew_symmetric([0,0,omega_ie]); + +u_as_e_T = zeros(no_meas,3); +pred_meas = zeros(no_meas,2); + +% Loop measurements +for j = 1:no_meas + + % Predict approx range + delta_r = GNSS_measurements(j,3:5)' - x_est_propagated(1:3); + approx_range = sqrt(delta_r' * delta_r); + + % Calculate frame rotation during signal transit time using (8.36) + C_e_I = [1, omega_ie * approx_range / c, 0;... + -omega_ie * approx_range / c, 1, 0;... + 0, 0, 1]; + + % Predict pseudo-range using (9.165) + delta_r = C_e_I * GNSS_measurements(j,3:5)' - x_est_propagated(1:3); + range = sqrt(delta_r' * delta_r); + pred_meas(j,1) = range + x_est_propagated(7); + + % Predict line of sight + u_as_e_T(j,1:3) = delta_r' / range; + + % Predict pseudo-range rate using (9.165) + range_rate = u_as_e_T(j,1:3) * (C_e_I * (GNSS_measurements(j,6:8)' +... + Omega_ie * GNSS_measurements(j,3:5)') - (x_est_propagated(4:6) +... + Omega_ie * x_est_propagated(1:3))); + pred_meas(j,2) = range_rate + x_est_propagated(8); + +end % for j + +% 5. Set-up measurement matrix using (9.163) +H_matrix(1:no_meas,1:3) = -u_as_e_T(1:no_meas,1:3); +H_matrix(1:no_meas,4:6) = zeros(no_meas,3); +H_matrix(1:no_meas,7) = ones(no_meas,1); +H_matrix(1:no_meas,8) = zeros(no_meas,1); +H_matrix((no_meas + 1):(2 * no_meas),1:3) = zeros(no_meas,3); +H_matrix((no_meas + 1):(2 * no_meas),4:6) = -u_as_e_T(1:no_meas,1:3); +H_matrix((no_meas + 1):(2 * no_meas),7) = zeros(no_meas,1); +H_matrix((no_meas + 1):(2 * no_meas),8) = ones(no_meas,1); + +% 6. Set-up measurement noise covariance matrix assuming all measurements +% are independent and have equal variance for a given measurement type +R_matrix(1:no_meas,1:no_meas) = eye(no_meas) *... + GNSS_KF_config.pseudo_range_SD^2; +R_matrix(1:no_meas,(no_meas + 1):(2 * no_meas)) =... + zeros(no_meas); +R_matrix((no_meas + 1):(2 * no_meas),1:no_meas) =... + zeros(no_meas); +R_matrix((no_meas + 1):(2 * no_meas),(no_meas + 1):(2 * no_meas)) =... + eye(no_meas) * GNSS_KF_config.range_rate_SD^2; + +% 7. Calculate Kalman gain using (3.21) +K_matrix = P_matrix_propagated * H_matrix' * inv(H_matrix *... + P_matrix_propagated * H_matrix' + R_matrix); + +% 8. Formulate measurement innovations using (3.88) +delta_z(1:no_meas,1) = GNSS_measurements(1:no_meas,1) -... + pred_meas(1:no_meas,1); +delta_z((no_meas + 1):(2 * no_meas),1) = GNSS_measurements(1:no_meas,2) -... + pred_meas(1:no_meas,2); + +% 9. Update state estimates using (3.24) +x_est_new = x_est_propagated + K_matrix * delta_z; + +% 10. Update state estimation error covariance matrix using (3.25) +P_matrix_new = (eye(8) - K_matrix * H_matrix) * P_matrix_propagated; + +% Ends \ No newline at end of file diff --git a/GNSS_Kalman_Filter.m b/GNSS_Kalman_Filter.m new file mode 100644 index 0000000..5f23f8f --- /dev/null +++ b/GNSS_Kalman_Filter.m @@ -0,0 +1,253 @@ +function [out_profile,out_errors,out_clock,out_KF_SD] = GNSS_Kalman_Filter(... + in_profile,no_epochs,GNSS_config,GNSS_KF_config) +%GNSS_Kalman_Filter - Simulates stand-alone GNSS using an Extended Kalman +%filter positioning algorithm +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 11/4/2012 by Paul Groves +% +% Inputs: +% in_profile True motion profile array +% no_epochs Number of epochs of profile data +% GNSS_config +% .epoch_interval Interval between GNSS epochs (s) +% .init_est_r_ea_e Initial estimated position (m; ECEF) +% .no_sat Number of satellites in constellation +% .r_os Orbital radius of satellites (m) +% .inclination Inclination angle of satellites (deg) +% .const_delta_lambda Longitude offset of constellation (deg) +% .const_delta_t Timing offset of constellation (s) +% .mask_angle Mask angle (deg) +% .SIS_err_SD Signal in space error SD (m) +% .zenith_iono_err_SD Zenith ionosphere error SD (m) +% .zenith_trop_err_SD Zenith troposphere error SD (m) +% .code_track_err_SD Code tracking error SD (m) +% .rate_track_err_SD Range rate tracking error SD (m/s) +% .rx_clock_offset Receiver clock offset at time=0 (m) +% .rx_clock_drift Receiver clock drift at time=0 (m/s) +% GNSS_KF_config +% .init_pos_unc Initial position uncertainty per axis (m) +% .init_vel_unc Initial velocity uncertainty per axis (m/s) +% .init_clock_offset_unc Initial clock offset uncertainty per axis (m) +% .init_clock_drift_unc Initial clock drift uncertainty per axis (m/s) +% .accel_PSD Acceleration PSD per axis (m^2/s^3) +% .clock_freq_PSD Receiver clock frequency-drift PSD (m^2/s^3) +% .clock_phase_PSD Receiver clock phase-drift PSD (m^2/s) +% .pseudo_range_SD Pseudo-range measurement noise SD (m) +% .range_rate_SD Pseudo-range rate measurement noise SD (m/s) +% +% Outputs: +% out_profile Navigation solution as a motion profile array +% out_errors Navigation solution error array +% out_clock Receiver clock estimate array +% out_KF_SD Output Kalman filter state uncertainties +% +% Format of motion profiles: +% Column 1: time (sec) +% Column 2: latitude (rad) +% Column 3: longitude (rad) +% Column 4: height (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll angle of body w.r.t NED (rad) +% Column 9: pitch angle of body w.r.t NED (rad) +% Column 10: yaw angle of body w.r.t NED (rad) +% +% Format of error array: +% Column 1: time (sec) +% Column 2: north position error (m) +% Column 3: east position error (m) +% Column 4: down position error (m) +% Column 5: north velocity error (m/s) +% Column 6: east velocity error (m/s) +% Column 7: down velocity (error m/s) +% Column 8: NOT USED (attitude error about north (rad)) +% Column 9: NOT USED (attitude error about east (rad)) +% Column 10: NOT USED (attitude error about down = heading error (rad)) +% +% Format of receiver clock array: +% Column 1: time (sec) +% Column 2: estimated clock offset (m) +% Column 3: estimated clock drift (m/s) +% +% Format of KF state uncertainties array: +% Column 1: time (sec) +% Column 2: X position uncertainty (m) +% Column 3: Y position uncertainty (m) +% Column 4: Z position uncertainty (m) +% Column 5: X velocity uncertainty (m/s) +% Column 6: Y velocity uncertainty (m/s) +% Column 7: Z velocity uncertainty (m/s) +% Column 8: clock offset uncertainty (m) +% Column 9: clock drift uncertainty (m/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Initialize true navigation solution +old_time = in_profile(1,1); +true_L_b = in_profile(1,2); +true_lambda_b = in_profile(1,3); +true_h_b = in_profile(1,4); +true_v_eb_n = in_profile(1,5:7)'; +true_eul_nb = in_profile(1,8:10)'; +true_C_b_n = Euler_to_CTM(true_eul_nb)'; +[true_r_eb_e,true_v_eb_e] =... + pv_NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n); + +time_last_GNSS = old_time; +GNSS_epoch = 1; + +% Determine satellite positions and velocities +[sat_r_es_e,sat_v_es_e] = Satellite_positions_and_velocities(old_time,... + GNSS_config); + +% Initialize the GNSS biases. Note that these are assumed constant throughout +% the simulation and are based on the initial elevation angles. Therefore, +% this function is unsuited to simulations longer than about 30 min. +GNSS_biases = Initialize_GNSS_biases(sat_r_es_e,true_r_eb_e,true_L_b,... + true_lambda_b,GNSS_config); + +% Generate GNSS measurements +[GNSS_measurements,no_GNSS_meas] = Generate_GNSS_measurements(old_time,... + sat_r_es_e,sat_v_es_e,true_r_eb_e,true_L_b,true_lambda_b,true_v_eb_e,... + GNSS_biases,GNSS_config); + +% Determine Least-squares GNSS position solution +[est_r_eb_e,est_v_eb_e,est_clock] = GNSS_LS_position_velocity(... + GNSS_measurements,no_GNSS_meas,GNSS_config.init_est_r_ea_e,[0;0;0]); + +% Initialize Kalman filter +[x_est,P_matrix] = Initialize_GNSS_KF(est_r_eb_e,est_v_eb_e,est_clock,... + GNSS_KF_config); + +est_C_b_n = true_C_b_n; % This sets the attitude errors to zero + + +[est_L_b,est_lambda_b,est_h_b,est_v_eb_n] =... + pv_ECEF_to_NED(x_est(1:3),x_est(4:6)); + +% Generate output profile record +out_profile(1,1) = old_time; +out_profile(1,2) = est_L_b; +out_profile(1,3) = est_lambda_b; +out_profile(1,4) = est_h_b; +out_profile(1,5:7) = est_v_eb_n'; +out_profile(1,8:10) = CTM_to_Euler(est_C_b_n')'; + +% Determine errors and generate output record +[delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n,true_L_b,... + true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); +out_errors(1,1) = old_time; +out_errors(1,2:4) = delta_r_eb_n'; +out_errors(1,5:7) = delta_v_eb_n'; +out_errors(1,8:10) = [0;0;0]; + +% Generate clock output record +out_clock(1,1) = old_time; +out_clock(1,2:3) = x_est(7:8); + +% Generate KF uncertainty record +out_KF_SD(1,1) = old_time; +for i =1:8 + out_KF_SD(1,i+1) = sqrt(P_matrix(i,i)); +end % for i + +% Progress bar +dots = '....................'; +bars = '||||||||||||||||||||'; +rewind = '\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b'; +fprintf(strcat('Processing: ',dots)); +progress_mark = 0; +progress_epoch = 0; + +% Main loop +for epoch = 2:no_epochs + + % Update progress bar + if (epoch - progress_epoch) > (no_epochs/20) + progress_mark = progress_mark + 1; + progress_epoch = epoch; + fprintf(strcat(rewind,bars(1:progress_mark),... + dots(1:(20 - progress_mark)))); + end % if epoch + + % Input time from motion profile + time = in_profile(epoch,1); + + % Determine whether to update GNSS simulation + if (time - time_last_GNSS) >= GNSS_config.epoch_interval + GNSS_epoch = GNSS_epoch + 1; + tor_s = time - time_last_GNSS; % KF time interval + time_last_GNSS = time; + + % Input data from motion profile + true_L_b = in_profile(epoch,2); + true_lambda_b = in_profile(epoch,3); + true_h_b = in_profile(epoch,4); + true_v_eb_n = in_profile(epoch,5:7)'; + true_eul_nb = in_profile(epoch,8:10)'; + true_C_b_n = Euler_to_CTM(true_eul_nb)'; + [true_r_eb_e,true_v_eb_e] =... + pv_NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n); + + % Determine satellite positions and velocities + [sat_r_es_e,sat_v_es_e] = Satellite_positions_and_velocities(time,... + GNSS_config); + + % Generate GNSS measurements + [GNSS_measurements,no_GNSS_meas] = Generate_GNSS_measurements(... + time,sat_r_es_e,sat_v_es_e,true_r_eb_e,true_L_b,true_lambda_b,... + true_v_eb_e,GNSS_biases,GNSS_config); + + % Update GNSS position solution + [x_est,P_matrix] = GNSS_KF_Epoch(GNSS_measurements,no_GNSS_meas,... + tor_s,x_est,P_matrix,GNSS_KF_config); + [est_L_b,est_lambda_b,est_h_b,est_v_eb_n] =... + pv_ECEF_to_NED(x_est(1:3),x_est(4:6)); + + est_C_b_n = true_C_b_n; % This sets the attitude errors to zero + + % Generate output profile record + out_profile(GNSS_epoch,1) = time; + out_profile(GNSS_epoch,2) = est_L_b; + out_profile(GNSS_epoch,3) = est_lambda_b; + out_profile(GNSS_epoch,4) = est_h_b; + out_profile(GNSS_epoch,5:7) = est_v_eb_n'; + out_profile(GNSS_epoch,8:10) = CTM_to_Euler(est_C_b_n')'; + + % Determine errors and generate output record + [delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n,true_L_b,... + true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + out_errors(GNSS_epoch,1) = time; + out_errors(GNSS_epoch,2:4) = delta_r_eb_n'; + out_errors(GNSS_epoch,5:7) = delta_v_eb_n'; + out_errors(GNSS_epoch,8:10) = [0;0;0]; + + % Generate clock output record + out_clock(GNSS_epoch,1) = time; + out_clock(GNSS_epoch,2:3) = x_est(7:8); + + % Generate KF uncertainty record + out_KF_SD(GNSS_epoch,1) = time; + for i =1:8 + out_KF_SD(GNSS_epoch,i+1) = sqrt(P_matrix(i,i)); + end % for i + + % Reset old values + old_time = time; + end % if time + +end %epoch + +% Complete progress bar +fprintf(strcat(rewind,bars,'\n')); + +% Ends \ No newline at end of file diff --git a/GNSS_LS_position_velocity.m b/GNSS_LS_position_velocity.m new file mode 100644 index 0000000..4bcb05d --- /dev/null +++ b/GNSS_LS_position_velocity.m @@ -0,0 +1,149 @@ +function [est_r_ea_e,est_v_ea_e,est_clock] = GNSS_LS_position_velocity(... + GNSS_measurements,no_GNSS_meas,predicted_r_ea_e,predicted_v_ea_e) +%GNSS_LS_position_velocity - Calculates position, velocity, clock offset, +%and clock drift using unweighted iterated least squares. Separate +%calculations are implemented for position and clock offset and for +%velocity and clock drift +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 11/4/2012 by Paul Groves +% +% Inputs: +% GNSS_measurements GNSS measurement data: +% Column 1 Pseudo-range measurements (m) +% Column 2 Pseudo-range rate measurements (m/s) +% Columns 3-5 Satellite ECEF position (m) +% Columns 6-8 Satellite ECEF velocity (m/s) +% no_GNSS_meas Number of satellites for which measurements are +% supplied +% predicted_r_ea_e prior predicted ECEF user position (m) +% predicted_v_ea_e prior predicted ECEF user velocity (m/s) +% +% Outputs: +% est_r_ea_e estimated ECEF user position (m) +% est_v_ea_e estimated ECEF user velocity (m/s) +% est_clock estimated receiver clock offset (m) and drift (m/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants (sone of these could be changed to inputs at a later date) +c = 299792458; % Speed of light in m/s +omega_ie = 7.292115E-5; % Earth rotation rate in rad/s + +% Begins + +% POSITION AND CLOCK OFFSET + +% Setup predicted state +x_pred(1:3,1) = predicted_r_ea_e; +x_pred(4,1) = 0; +test_convergence = 1; + +% Repeat until convergence +while test_convergence>0.0001 + + % Loop measurements + for j = 1:no_GNSS_meas + + % Predict approx range + delta_r = GNSS_measurements(j,3:5)' - x_pred(1:3); + approx_range = sqrt(delta_r' * delta_r); + + % Calculate frame rotation during signal transit time using (8.36) + C_e_I = [1, omega_ie * approx_range / c, 0;... + -omega_ie * approx_range / c, 1, 0;... + 0, 0, 1]; + + % Predict pseudo-range using (9.143) + delta_r = C_e_I * GNSS_measurements(j,3:5)' - x_pred(1:3); + range = sqrt(delta_r' * delta_r); + pred_meas(j,1) = range + x_pred(4); + + % Predict line of sight and deploy in measurement matrix, (9.144) + H_matrix (j,1:3) = - delta_r' / range; + H_matrix (j,4) = 1; + + end % for j + + % Unweighted least-squares solution, (9.35)/(9.141) + x_est = x_pred + inv(H_matrix(1:no_GNSS_meas,:)' *... + H_matrix(1:no_GNSS_meas,:)) * H_matrix(1:no_GNSS_meas,:)' *... + (GNSS_measurements(1:no_GNSS_meas,1) - pred_meas(1:no_GNSS_meas)); + + % Test convergence + test_convergence = sqrt((x_est - x_pred)' * (x_est - x_pred)); + + % Set predictions to estimates for next iteration + x_pred = x_est; + +end % while + +% Set outputs to estimates +est_r_ea_e(1:3,1) = x_est(1:3); +est_clock(1) = x_est(4); + +% VELOCITY AND CLOCK DRIFT + +% Skew symmetric matrix of Earth rate +Omega_ie = Skew_symmetric([0,0,omega_ie]); + +% Setup predicted state +x_pred(1:3,1) = predicted_v_ea_e; +x_pred(4,1) = 0; +test_convergence = 1; + +% Repeat until convergence +while test_convergence>0.0001 + + % Loop measurements + for j = 1:no_GNSS_meas + + % Predict approx range + delta_r = GNSS_measurements(j,3:5)' - est_r_ea_e; + approx_range = sqrt(delta_r' * delta_r); + + % Calculate frame rotation during signal transit time using (8.36) + C_e_I = [1, omega_ie * approx_range / c, 0;... + -omega_ie * approx_range / c, 1, 0;... + 0, 0, 1]; + + % Calculate range using (8.35) + delta_r = C_e_I * GNSS_measurements(j,3:5)' - est_r_ea_e; + range = sqrt(delta_r' * delta_r); + + % Calculate line of sight using (8.41) + u_as_e = delta_r / range; + + % Predict pseudo-range rate using (9.143) + range_rate = u_as_e' * (C_e_I * (GNSS_measurements(j,6:8)' +... + Omega_ie * GNSS_measurements(j,3:5)') - (x_pred(1:3) +... + Omega_ie * est_r_ea_e)); + pred_meas(j,1) = range_rate + x_pred(4); + + % Predict line of sight and deploy in measurement matrix, (9.144) + H_matrix (j,1:3) = - u_as_e'; + H_matrix (j,4) = 1; + + end % for j + + % Unweighted least-squares solution, (9.35)/(9.141) + x_est = x_pred + inv(H_matrix(1:no_GNSS_meas,:)' *... + H_matrix(1:no_GNSS_meas,:)) * H_matrix(1:no_GNSS_meas,:)' *... + (GNSS_measurements(1:no_GNSS_meas,2) - pred_meas(1:no_GNSS_meas)); + + % Test convergence + test_convergence = sqrt((x_est - x_pred)' * (x_est - x_pred)); + + % Set predictions to estimates for next iteration + x_pred = x_est; + +end % while + +% Set outputs to estimates +est_v_ea_e(1:3,1) = x_est(1:3); +est_clock(2) = x_est(4); + +% Ends \ No newline at end of file diff --git a/GNSS_Least_Squares.m b/GNSS_Least_Squares.m new file mode 100644 index 0000000..41061fd --- /dev/null +++ b/GNSS_Least_Squares.m @@ -0,0 +1,214 @@ +function [out_profile,out_errors,out_clock] = GNSS_Least_Squares(in_profile,... + no_epochs,GNSS_config) +%GNSS_Least_Squares - Simulates stand-alone GNSS using a least-squares +%positioning algorithm +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 11/4/2012 by Paul Groves +% +% Inputs: +% in_profile True motion profile array +% no_epochs Number of epochs of profile data +% GNSS_config +% .epoch_interval Interval between GNSS epochs (s) +% .init_est_r_ea_e Initial estimated position (m; ECEF) +% .no_sat Number of satellites in constellation +% .r_os Orbital radius of satellites (m) +% .inclination Inclination angle of satellites (deg) +% .const_delta_lambda Longitude offset of constellation (deg) +% .const_delta_t Timing offset of constellation (s) +% .mask_angle Mask angle (deg) +% .SIS_err_SD Signal in space error SD (m) +% .zenith_iono_err_SD Zenith ionosphere error SD (m) +% .zenith_trop_err_SD Zenith troposphere error SD (m) +% .code_track_err_SD Code tracking error SD (m) +% .rate_track_err_SD Range rate tracking error SD (m/s) +% .rx_clock_offset Receiver clock offset at time=0 (m) +% .rx_clock_drift Receiver clock drift at time=0 (m/s) +% +% Outputs: +% out_profile Navigation solution as a motion profile array +% out_errors Navigation solution error array +% out_clock Receiver clock estimate array +% +% Format of motion profiles: +% Column 1: time (sec) +% Column 2: latitude (rad) +% Column 3: longitude (rad) +% Column 4: height (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll angle of body w.r.t NED (rad) +% Column 9: pitch angle of body w.r.t NED (rad) +% Column 10: yaw angle of body w.r.t NED (rad) +% +% Format of error array: +% Column 1: time (sec) +% Column 2: north position error (m) +% Column 3: east position error (m) +% Column 4: down position error (m) +% Column 5: north velocity error (m/s) +% Column 6: east velocity error (m/s) +% Column 7: down velocity error (m/s) +% Column 8: NOT USED (attitude error about north (rad)) +% Column 9: NOT USED (attitude error about east (rad)) +% Column 10: NOT USED (attitude error about down = heading error (rad)) +% +% Format of receiver clock array: +% Column 1: time (sec) +% Column 2: estimated clock offset (m) +% Column 3: estimated clock drift (m/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Initialize true navigation solution +old_time = in_profile(1,1); +true_L_b = in_profile(1,2); +true_lambda_b = in_profile(1,3); +true_h_b = in_profile(1,4); +true_v_eb_n = in_profile(1,5:7)'; +true_eul_nb = in_profile(1,8:10)'; +true_C_b_n = Euler_to_CTM(true_eul_nb)'; +[true_r_eb_e,true_v_eb_e] =... + pv_NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n); + +time_last_GNSS = old_time; +GNSS_epoch = 1; + +% Determine satellite positions and velocities +[sat_r_es_e,sat_v_es_e] = Satellite_positions_and_velocities(old_time,... + GNSS_config); + +% Initialize the GNSS biases. Note that these are assumed constant throughout +% the simulation and are based on the initial elevation angles. Therefore, +% this function is unsuited to simulations longer than about 30 min. +GNSS_biases = Initialize_GNSS_biases(sat_r_es_e,true_r_eb_e,true_L_b,... + true_lambda_b,GNSS_config); + +% Generate GNSS measurements +[GNSS_measurements,no_GNSS_meas] = Generate_GNSS_measurements(old_time,... + sat_r_es_e,sat_v_es_e,true_r_eb_e,true_L_b,true_lambda_b,true_v_eb_e,... + GNSS_biases,GNSS_config); + +% Determine GNSS position solution +[est_r_eb_e,est_v_eb_e,est_clock] = GNSS_LS_position_velocity(... + GNSS_measurements,no_GNSS_meas,GNSS_config.init_est_r_ea_e,[0;0;0]); + +est_C_b_n = true_C_b_n; % This sets the attitude errors to zero + + +[est_L_b,est_lambda_b,est_h_b,est_v_eb_n] =... + pv_ECEF_to_NED(est_r_eb_e,est_v_eb_e); + +% Generate output profile record +out_profile(1,1) = old_time; +out_profile(1,2) = est_L_b; +out_profile(1,3) = est_lambda_b; +out_profile(1,4) = est_h_b; +out_profile(1,5:7) = est_v_eb_n'; +out_profile(1,8:10) = CTM_to_Euler(est_C_b_n')'; + +% Determine errors and generate output record +[delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n,true_L_b,... + true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); +out_errors(1,1) = old_time; +out_errors(1,2:4) = delta_r_eb_n'; +out_errors(1,5:7) = delta_v_eb_n'; +out_errors(1,8:10) = [0;0;0]; + +% Generate clock output record +out_clock(1,1) = old_time; +out_clock(1,2:3) = est_clock(1:2); + +% Progress bar +dots = '....................'; +bars = '||||||||||||||||||||'; +rewind = '\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b'; +fprintf(strcat('Processing: ',dots)); +progress_mark = 0; +progress_epoch = 0; + +% Main loop +for epoch = 2:no_epochs + + % Update progress bar + if (epoch - progress_epoch) > (no_epochs/20) + progress_mark = progress_mark + 1; + progress_epoch = epoch; + fprintf(strcat(rewind,bars(1:progress_mark),... + dots(1:(20 - progress_mark)))); + end % if epoch + + % Input time from motion profile + time = in_profile(epoch,1); + + % Determine whether to update GNSS simulation + if (time - time_last_GNSS) >= GNSS_config.epoch_interval + GNSS_epoch = GNSS_epoch + 1; + time_last_GNSS = time; + + % Input data from motion profile + true_L_b = in_profile(epoch,2); + true_lambda_b = in_profile(epoch,3); + true_h_b = in_profile(epoch,4); + true_v_eb_n = in_profile(epoch,5:7)'; + true_eul_nb = in_profile(epoch,8:10)'; + true_C_b_n = Euler_to_CTM(true_eul_nb)'; + [true_r_eb_e,true_v_eb_e] =... + pv_NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n); + + % Determine satellite positions and velocities + [sat_r_es_e,sat_v_es_e] = Satellite_positions_and_velocities(time,... + GNSS_config); + + % Generate GNSS measurements + [GNSS_measurements,no_GNSS_meas] = Generate_GNSS_measurements(... + time,sat_r_es_e,sat_v_es_e,true_r_eb_e,true_L_b,true_lambda_b,... + true_v_eb_e,GNSS_biases,GNSS_config); + + % Determine GNSS position solution + [est_r_eb_e,est_v_eb_e,est_clock] = GNSS_LS_position_velocity(... + GNSS_measurements,no_GNSS_meas,est_r_eb_e,est_v_eb_e); + [est_L_b,est_lambda_b,est_h_b,est_v_eb_n] =... + pv_ECEF_to_NED(est_r_eb_e,est_v_eb_e); + + est_C_b_n = true_C_b_n; % This sets the attitude errors to zero + + % Generate output profile record + out_profile(GNSS_epoch,1) = time; + out_profile(GNSS_epoch,2) = est_L_b; + out_profile(GNSS_epoch,3) = est_lambda_b; + out_profile(GNSS_epoch,4) = est_h_b; + out_profile(GNSS_epoch,5:7) = est_v_eb_n'; + out_profile(GNSS_epoch,8:10) = CTM_to_Euler(est_C_b_n')'; + + % Determine errors and generate output record + [delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n,true_L_b,... + true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + out_errors(GNSS_epoch,1) = time; + out_errors(GNSS_epoch,2:4) = delta_r_eb_n'; + out_errors(GNSS_epoch,5:7) = delta_v_eb_n'; + out_errors(GNSS_epoch,8:10) = [0;0;0]; + + % Generate clock output record + out_clock(GNSS_epoch,1) = time; + out_clock(GNSS_epoch,2:3) = est_clock(1:2); + + % Reset old values + old_time = time; + end % if time + +end %epoch + +% Complete progress bar +fprintf(strcat(rewind,bars,'\n')); + +% Ends \ No newline at end of file diff --git a/Generate_GNSS_measurements.m b/Generate_GNSS_measurements.m new file mode 100644 index 0000000..d2e582f --- /dev/null +++ b/Generate_GNSS_measurements.m @@ -0,0 +1,109 @@ +function [GNSS_measurements,no_GNSS_meas] = Generate_GNSS_measurements(... + time, sat_r_es_e,sat_v_es_e,r_ea_e,L_a,lambda_a,v_ea_e,... + GNSS_biases,GNSS_config) +%Generate_GNSS_measurements - Generates a set of pseudo-range and pseudo- +%range rate measurements for all satellites above the elevation mask angle +%and adds satellite positions and velocities to the datesets. +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 11/4/2012 by Paul Groves +% +% Inputs: +% time Current simulation time +% sat_r_es_e (no_sat x 3) ECEF satellite positions (m) +% sat_v_es_e (no_sat x 3) ECEF satellite velocities (m/s) +% r_ea_e ECEF user position (m) +% L_a user latitude (rad) +% lambda_a user longitude (rad) +% v_ea_e ECEF user velocity (m/s) +% GNSS_biases (no_sat) Bias-like GNSS range errors (m) +% GNSS_config +% .no_sat Number of satellites in constellation +% .mask_angle Mask angle (deg) +% .code_track_err_SD Code tracking error SD (m) +% .rate_track_err_SD Range rate tracking error SD (m/s) +% .rx_clock_offset Receiver clock offset at time=0 (m) +% .rx_clock_drift Receiver clock drift at time=0 (m/s) +% +% Outputs: +% GNSS_measurements GNSS measurement data: +% Column 1 Pseudo-range measurements (m) +% Column 2 Pseudo-range rate measurements (m/s) +% Columns 3-5 Satellite ECEF position (m) +% Columns 6-8 Satellite ECEF velocity (m/s) +% no_GNSS_meas Number of satellites for which measurements are +% supplied + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants (sone of these could be changed to inputs at a later date) +c = 299792458; % Speed of light in m/s +omega_ie = 7.292115E-5; % Earth rotation rate in rad/s + +% Begins +no_GNSS_meas = 0; + +% Calculate ECEF to NED coordinate transformation matrix using (2.150) +cos_lat = cos(L_a); +sin_lat = sin(L_a); +cos_long = cos(lambda_a); +sin_long = sin(lambda_a); +C_e_n = [-sin_lat * cos_long, -sin_lat * sin_long, cos_lat;... + -sin_long, cos_long, 0;... + -cos_lat * cos_long, -cos_lat * sin_long, -sin_lat]; + +% Skew symmetric matrix of Earth rate +Omega_ie = Skew_symmetric([0,0,omega_ie]); + +% Loop satellites +for j = 1:GNSS_config.no_sat + + % Determine ECEF line-of-sight vector using (8.41) + delta_r = sat_r_es_e(j,1:3)' - r_ea_e; + approx_range = sqrt(delta_r' * delta_r); + u_as_e = delta_r / approx_range; + + % Convert line-of-sight vector to NED using (8.39) and determine + % elevation using (8.57) + elevation = -asin(C_e_n(3,:) * u_as_e); + + % Determine if satellite is above the masking angle + if (elevation >= degtorad(GNSS_config.mask_angle)); + + % Increment number of measurements + no_GNSS_meas = no_GNSS_meas + 1; + + % Calculate frame rotation during signal transit time using (8.36) + C_e_I = [1, omega_ie * approx_range / c, 0;... + -omega_ie * approx_range / c, 1, 0;... + 0, 0, 1]; + + % Calculate range using (8.35) + delta_r = C_e_I * sat_r_es_e(j,1:3)' - r_ea_e; + range = sqrt(delta_r' * delta_r); + + % Calculate range rate using (8.44) + range_rate = u_as_e' * (C_e_I * (sat_v_es_e(j,1:3)' + Omega_ie *... + sat_r_es_e(j,1:3)') - (v_ea_e + Omega_ie * r_ea_e)); + + % Calculate pseudo-range measurement + GNSS_measurements(no_GNSS_meas,1) = range + GNSS_biases(j) +... + GNSS_config.rx_clock_offset + GNSS_config.rx_clock_drift *... + time + GNSS_config.code_track_err_SD * randn; + + % Calculate pseudo-range rate measurement + GNSS_measurements(no_GNSS_meas,2) = range_rate +... + GNSS_config.rx_clock_drift + GNSS_config.rate_track_err_SD *... + randn; + + % Append satellite position and velocity to output data + GNSS_measurements(no_GNSS_meas,3:5) = sat_r_es_e(j,1:3); + GNSS_measurements(no_GNSS_meas,6:8) = sat_v_es_e(j,1:3); + + end % elevation +end % for j + +% Ends \ No newline at end of file diff --git a/Gravitation_ECI.m b/Gravitation_ECI.m new file mode 100644 index 0000000..b281293 --- /dev/null +++ b/Gravitation_ECI.m @@ -0,0 +1,42 @@ +function gamma = Gravitation_ECI(r_ib_i) +%Gravitation_ECI - Calculates gravitational acceleration resolved about +%ECI-frame axes +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. + +% This function created 1/4/2012 by Paul Groves +% +% Inputs: +% r_ib_i Cartesian position of body frame w.r.t. ECI frame, resolved +% about ECI-frame axes (m) +% Outputs: +% gamma Acceleration due to gravitational force (m/s^2) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +%Parameters +R_0 = 6378137; %WGS84 Equatorial radius in meters +mu = 3.986004418E14; %WGS84 Earth gravitational constant (m^3 s^-2) +J_2 = 1.082627E-3; %WGS84 Earth's second gravitational constant + +% Begins + +% Calculate distance from center of the Earth +mag_r = sqrt(r_ib_i' * r_ib_i); + +% If the input position is 0,0,0, produce a dummy output +if mag_r==0 + gamma = [0;0;0]; + +% Calculate gravitational acceleration using (2.141) +else + z_scale = 5 * (r_ib_i(3) / mag_r)^2; + gamma = -mu / mag_r^3 *(r_ib_i + 1.5 * J_2 * (R_0 / mag_r)^2 *... + [(1 - z_scale) * r_ib_i(1); (1 - z_scale) * r_ib_i(2);... + (3 - z_scale) * r_ib_i(3)]); + +end % if + +% Ends \ No newline at end of file diff --git a/Gravity_ECEF.m b/Gravity_ECEF.m new file mode 100644 index 0000000..a3c8d44 --- /dev/null +++ b/Gravity_ECEF.m @@ -0,0 +1,47 @@ +function g = Gravity_ECEF(r_eb_e) +%Gravitation_ECI - Calculates acceleration due to gravity resolved about +%ECEF-frame +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 1/4/2012 by Paul Groves +% +% Inputs: +% r_eb_e Cartesian position of body frame w.r.t. ECEF frame, resolved +% about ECEF-frame axes (m) +% Outputs: +% g Acceleration due to gravity (m/s^2) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +%Parameters +R_0 = 6378137; %WGS84 Equatorial radius in meters +mu = 3.986004418E14; %WGS84 Earth gravitational constant (m^3 s^-2) +J_2 = 1.082627E-3; %WGS84 Earth's second gravitational constant +omega_ie = 7.292115E-5; % Earth rotation rate (rad/s) + +% Begins + +% Calculate distance from center of the Earth +mag_r = sqrt(r_eb_e' * r_eb_e); + +% If the input position is 0,0,0, produce a dummy output +if mag_r==0 + g = [0;0;0]; + +% Calculate gravitational acceleration using (2.142) +else + z_scale = 5 * (r_eb_e(3) / mag_r)^2; + gamma = -mu / mag_r^3 *(r_eb_e + 1.5 * J_2 * (R_0 / mag_r)^2 *... + [(1 - z_scale) * r_eb_e(1); (1 - z_scale) * r_eb_e(2);... + (3 - z_scale) * r_eb_e(3)]); + + % Add centripetal acceleration using (2.133) + g(1:2,1) = gamma(1:2) + omega_ie^2 * r_eb_e(1:2); + g(3) = gamma(3); + +end % if + +% Ends \ No newline at end of file diff --git a/Gravity_NED.m b/Gravity_NED.m new file mode 100644 index 0000000..ce8ac48 --- /dev/null +++ b/Gravity_NED.m @@ -0,0 +1,43 @@ +function g = Gravity_NED(L_b,h_b) +%Gravity_ECEF - Calculates acceleration due to gravity resolved about +%north, east, and down +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 2/4/2012 by Paul Groves +% +% Inputs: +% L_b latitude (rad) +% h_b height (m) +% Outputs: +% g Acceleration due to gravity (m/s^2) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Parameters +R_0 = 6378137; %WGS84 Equatorial radius in meters +R_P = 6356752.31425; %WGS84 Polar radius in meters +e = 0.0818191908425; %WGS84 eccentricity +f = 1 / 298.257223563; %WGS84 flattening +mu = 3.986004418E14; %WGS84 Earth gravitational constant (m^3 s^-2) +omega_ie = 7.292115E-5; % Earth rotation rate (rad/s) + +% Begins + +% Calculate surface gravity using the Somigliana model, (2.134) +sinsqL = sin(L_b)^2; +g_0 = 9.7803253359 * (1 + 0.001931853 * sinsqL) / sqrt(1 - e^2 * sinsqL); + +% Calculate north gravity using (2.140) +g(1,1) = -8.08E-9 * h_b * sin(2 * L_b); + +% East gravity is zero +g(2,1) = 0; + +% Calculate down gravity using (2.139) +g(3,1) = g_0 * (1 - (2 / R_0) * (1 + f * (1 - 2 * sinsqL) +... + (omega_ie^2 * R_0^2 * R_P / mu)) * h_b + (3 * h_b^2 / R_0^2)); + +% Ends \ No newline at end of file diff --git a/IMU_model.m b/IMU_model.m new file mode 100644 index 0000000..25372cf --- /dev/null +++ b/IMU_model.m @@ -0,0 +1,79 @@ +function [meas_f_ib_b,meas_omega_ib_b,quant_residuals] = IMU_model(tor_i,... + true_f_ib_b,true_omega_ib_b,IMU_errors,old_quant_residuals) +%IMU_model - Simulates an inertial measurement unit (IMU body axes used +%throughout this function) +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 3/4/2012 by Paul Groves +% +% Inputs: +% tor_i time interval between epochs (s) +% true_f_ib_b true specific force of body frame w.r.t. ECEF frame, resolved +% along body-frame axes, averaged over time interval (m/s^2) +% true_omega_ib_b true angular rate of body frame w.r.t. ECEF frame, resolved +% about body-frame axes, averaged over time interval (rad/s) +% IMU_errors +% .delta_r_eb_n position error resolved along NED (m) +% .b_a Accelerometer biases (m/s^2) +% .b_g Gyro biases (rad/s) +% .M_a Accelerometer scale factor and cross coupling errors +% .M_g Gyro scale factor and cross coupling errors +% .G_g Gyro g-dependent biases (rad-sec/m) +% .accel_noise_root_PSD Accelerometer noise root PSD (m s^-1.5) +% .gyro_noise_root_PSD Gyro noise root PSD (rad s^-0.5) +% .accel_quant_level Accelerometer quantization level (m/s^2) +% .gyro_quant_level Gyro quantization level (rad/s) +% old_quant_residuals residuals of previous output quantization process +% +% Outputs: +% meas_f_ib_b output specific force of body frame w.r.t. ECEF frame, resolved +% along body-frame axes, averaged over time interval (m/s^2) +% meas_omega_ib_b output angular rate of body frame w.r.t. ECEF frame, resolved +% about body-frame axes, averaged over time interval (rad/s) +% quant_residuals residuals of output quantization process + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Generate noise +if tor_i>0 + accel_noise = randn(3,1) * IMU_errors.accel_noise_root_PSD / sqrt(tor_i); + gyro_noise = randn(3,1) * IMU_errors.gyro_noise_root_PSD / sqrt(tor_i); +else + accel_noise = [0;0;0]; + gyro_noise = [0;0;0]; +end %if tor_i + +% Calculate accelerometer and gyro outputs using (4.16) and (4.17) +uq_f_ib_b = IMU_errors.b_a + (eye(3) + IMU_errors.M_a) * true_f_ib_b +... + accel_noise; +uq_omega_ib_b = IMU_errors.b_g + (eye(3) + IMU_errors.M_g) *... + true_omega_ib_b + IMU_errors.G_g * true_f_ib_b + gyro_noise; + +% Quantize accelerometer outputs +if IMU_errors.accel_quant_level>0 + meas_f_ib_b = IMU_errors.accel_quant_level * round((uq_f_ib_b +... + old_quant_residuals(1:3)) / IMU_errors.accel_quant_level); + quant_residuals(1:3,1) = uq_f_ib_b + old_quant_residuals(1:3) -... + meas_f_ib_b; +else + meas_f_ib_b = uq_f_ib_b; + quant_residuals(1:3,1) = [0;0;0]; +end %if IMU_errors.accel_quant_level + +% Quantize gyro outputs +if IMU_errors.gyro_quant_level>0 + meas_omega_ib_b = IMU_errors.gyro_quant_level * round((uq_omega_ib_b +... + old_quant_residuals(4:6)) / IMU_errors.gyro_quant_level); + quant_residuals(4:6,1) = uq_omega_ib_b + old_quant_residuals(4:6) -... + meas_omega_ib_b; +else + meas_omega_ib_b = uq_omega_ib_b; + quant_residuals(4:6,1) = [0;0;0]; +end %if IMU_errors.gyro_quant_level + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_1.m b/INS_GNSS_Demo_1.m new file mode 100644 index 0000000..ac9899e --- /dev/null +++ b/INS_GNSS_Demo_1.m @@ -0,0 +1,155 @@ +%INS_GNSS_Demo_1 +%SCRIPT Tightly coupled INS/GNSS demo: +% Profile_1 (60s artificial car motion with two 90 deg turns) +% Tactical-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 12/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_1.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_1_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_1_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +TC_KF_config.init_att_unc = degtorad(1); +% Initial velocity uncertainty per axis (m/s) +TC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +TC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +TC_KF_config.init_b_a_unc = 1000 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +TC_KF_config.init_b_g_unc = 10 * deg_to_rad / 3600; +% Initial clock offset uncertainty per axis (m) +TC_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +TC_KF_config.init_clock_drift_unc = 0.1; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +TC_KF_config.gyro_noise_PSD = (0.02 * deg_to_rad / 60)^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +TC_KF_config.accel_noise_PSD = (200 *... + micro_g_to_meters_per_second_squared)^2; +% Accelerometer bias random walk PSD (m^2 s^-5) +TC_KF_config.accel_bias_PSD = 1.0E-7; +% Gyro bias random walk PSD (rad^2 s^-3) +TC_KF_config.gyro_bias_PSD = 2.0E-12; +% Receiver clock frequency-drift PSD (m^2/s^3) +TC_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +TC_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +TC_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +TC_KF_config.range_rate_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,TC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_10.m b/INS_GNSS_Demo_10.m new file mode 100644 index 0000000..080988d --- /dev/null +++ b/INS_GNSS_Demo_10.m @@ -0,0 +1,155 @@ +%INS_GNSS_Demo_10 +%SCRIPT Tightly coupled INS/GNSS demo: +% Profile_3 (418s aircraft) +% Tactical-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 27/5/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_3.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_10_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_10_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +TC_KF_config.init_att_unc = degtorad(1); +% Initial velocity uncertainty per axis (m/s) +TC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +TC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +TC_KF_config.init_b_a_unc = 1000 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +TC_KF_config.init_b_g_unc = 10 * deg_to_rad / 3600; +% Initial clock offset uncertainty per axis (m) +TC_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +TC_KF_config.init_clock_drift_unc = 0.1; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +TC_KF_config.gyro_noise_PSD = (0.02 * deg_to_rad / 60)^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +TC_KF_config.accel_noise_PSD = (200 *... + micro_g_to_meters_per_second_squared)^2; +% Accelerometer bias random walk PSD (m^2 s^-5) +TC_KF_config.accel_bias_PSD = 1.0E-7; +% Gyro bias random walk PSD (rad^2 s^-3) +TC_KF_config.gyro_bias_PSD = 2.0E-12; +% Receiver clock frequency-drift PSD (m^2/s^3) +TC_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +TC_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +TC_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +TC_KF_config.range_rate_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,TC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_11.m b/INS_GNSS_Demo_11.m new file mode 100644 index 0000000..398f86f --- /dev/null +++ b/INS_GNSS_Demo_11.m @@ -0,0 +1,155 @@ +%INS_GNSS_Demo_11 +%SCRIPT Tightly coupled INS/GNSS demo: +% Profile_4 (300s boat) +% Tactical-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 27/5/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_4.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_11_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_11_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +TC_KF_config.init_att_unc = degtorad(1); +% Initial velocity uncertainty per axis (m/s) +TC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +TC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +TC_KF_config.init_b_a_unc = 1000 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +TC_KF_config.init_b_g_unc = 10 * deg_to_rad / 3600; +% Initial clock offset uncertainty per axis (m) +TC_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +TC_KF_config.init_clock_drift_unc = 0.1; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +TC_KF_config.gyro_noise_PSD = (0.02 * deg_to_rad / 60)^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +TC_KF_config.accel_noise_PSD = (200 *... + micro_g_to_meters_per_second_squared)^2; +% Accelerometer bias random walk PSD (m^2 s^-5) +TC_KF_config.accel_bias_PSD = 1.0E-7; +% Gyro bias random walk PSD (rad^2 s^-3) +TC_KF_config.gyro_bias_PSD = 2.0E-12; +% Receiver clock frequency-drift PSD (m^2/s^3) +TC_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +TC_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +TC_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +TC_KF_config.range_rate_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,TC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_12.m b/INS_GNSS_Demo_12.m new file mode 100644 index 0000000..182f478 --- /dev/null +++ b/INS_GNSS_Demo_12.m @@ -0,0 +1,155 @@ +%INS_GNSS_Demo_12 +%SCRIPT Tightly coupled INS/GNSS demo: +% Profile_3 (418s aircraft) +% Aviation-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 27/5/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_3.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_12_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_12_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.01;0.008;0.01]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [30;-45;26] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-0.0009;0.0013;-0.0008] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [100, -120, 80;... + -60, -120, 100;... + -100, 40, 90] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [8, -120, 100;... + 0, -6, -60;... + 0, 0, -7] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0, 0, 0;... + 0, 0, 0;... + 0, 0, 0] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 20 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.002 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 5E-5; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 1E-6; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +TC_KF_config.init_att_unc = degtorad(0.01); +% Initial velocity uncertainty per axis (m/s) +TC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +TC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +TC_KF_config.init_b_a_unc = 30 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +TC_KF_config.init_b_g_unc = 0.001 * deg_to_rad / 3600; +% Initial clock offset uncertainty per axis (m) +TC_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +TC_KF_config.init_clock_drift_unc = 0.1; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +TC_KF_config.gyro_noise_PSD = (0.004 * deg_to_rad / 60)^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +TC_KF_config.accel_noise_PSD = (40 *... + micro_g_to_meters_per_second_squared)^2; +% Accelerometer bias random walk PSD (m^2 s^-5) +TC_KF_config.accel_bias_PSD = 3.0E-9; +% Gyro bias random walk PSD (rad^2 s^-3) +TC_KF_config.gyro_bias_PSD = 2.0E-16; +% Receiver clock frequency-drift PSD (m^2/s^3) +TC_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +TC_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +TC_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +TC_KF_config.range_rate_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,TC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_2.m b/INS_GNSS_Demo_2.m new file mode 100644 index 0000000..371c771 --- /dev/null +++ b/INS_GNSS_Demo_2.m @@ -0,0 +1,155 @@ +%INS_GNSS_Demo_2 +%SCRIPT Tightly coupled INS/GNSS demo: +% Profile_0 (Stationary) +% Tactical-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 12/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_0.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_2_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_2_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +TC_KF_config.init_att_unc = degtorad(1); +% Initial velocity uncertainty per axis (m/s) +TC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +TC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +TC_KF_config.init_b_a_unc = 1000 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +TC_KF_config.init_b_g_unc = 10 * deg_to_rad / 3600; +% Initial clock offset uncertainty per axis (m) +TC_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +TC_KF_config.init_clock_drift_unc = 0.1; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +TC_KF_config.gyro_noise_PSD = (0.02 * deg_to_rad / 60)^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +TC_KF_config.accel_noise_PSD = (200 *... + micro_g_to_meters_per_second_squared)^2; +% Accelerometer bias random walk PSD (m^2 s^-5) +TC_KF_config.accel_bias_PSD = 1.0E-7; +% Gyro bias random walk PSD (rad^2 s^-3) +TC_KF_config.gyro_bias_PSD = 2.0E-12; +% Receiver clock frequency-drift PSD (m^2/s^3) +TC_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +TC_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +TC_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +TC_KF_config.range_rate_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,TC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_3.m b/INS_GNSS_Demo_3.m new file mode 100644 index 0000000..3c694c4 --- /dev/null +++ b/INS_GNSS_Demo_3.m @@ -0,0 +1,147 @@ +%INS_GNSS_Demo_3 +%SCRIPT Loosely coupled INS/GNSS demo: +% Profile_1 (60s artificial car motion with two 90 deg turns) +% Tactical-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 12/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_1.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_3_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_3_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +LC_KF_config.init_att_unc = degtorad(1); +% Initial velocity uncertainty per axis (m/s) +LC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +LC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +LC_KF_config.init_b_a_unc = 1000 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +LC_KF_config.init_b_g_unc = 10 * deg_to_rad / 3600; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +LC_KF_config.gyro_noise_PSD = (0.02 * deg_to_rad / 60)^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +LC_KF_config.accel_noise_PSD = (200 *... + micro_g_to_meters_per_second_squared)^2; +% Accelerometer bias random walk PSD (m^2 s^-5) +LC_KF_config.accel_bias_PSD = 1.0E-7; +% Gyro bias random walk PSD (rad^2 s^-3) +LC_KF_config.gyro_bias_PSD = 2.0E-12; + +% Position measurement noise SD per axis (m) +LC_KF_config.pos_meas_SD = 2.5; +% Velocity measurement noise SD per axis (m/s) +LC_KF_config.vel_meas_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Loosely_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,LC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_4.m b/INS_GNSS_Demo_4.m new file mode 100644 index 0000000..9615e75 --- /dev/null +++ b/INS_GNSS_Demo_4.m @@ -0,0 +1,147 @@ +%INS_GNSS_Demo_4 +%SCRIPT Loosely coupled INS/GNSS demo: +% Profile_0 (Stationary) +% Tactical-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 12/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_0.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_4_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_4_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +LC_KF_config.init_att_unc = degtorad(1); +% Initial velocity uncertainty per axis (m/s) +LC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +LC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +LC_KF_config.init_b_a_unc = 1000 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +LC_KF_config.init_b_g_unc = 10 * deg_to_rad / 3600; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +LC_KF_config.gyro_noise_PSD = (0.02 * deg_to_rad / 60)^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +LC_KF_config.accel_noise_PSD = (200 *... + micro_g_to_meters_per_second_squared)^2; +% Accelerometer bias random walk PSD (m^2 s^-5) +LC_KF_config.accel_bias_PSD = 1.0E-7; +% Gyro bias random walk PSD (rad^2 s^-3) +LC_KF_config.gyro_bias_PSD = 2.0E-12; + +% Position measurement noise SD per axis (m) +LC_KF_config.pos_meas_SD = 2.5; +% Velocity measurement noise SD per axis (m/s) +LC_KF_config.vel_meas_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Loosely_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,LC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_5.m b/INS_GNSS_Demo_5.m new file mode 100644 index 0000000..f97b7d5 --- /dev/null +++ b/INS_GNSS_Demo_5.m @@ -0,0 +1,155 @@ +%INS_GNSS_Demo_5 +%SCRIPT Tightly coupled INS/GNSS demo: +% Profile_1 (60s artificial car motion with two 90 deg turns) +% Aviation-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 13/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_1.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_5_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_5_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.01;0.008;0.01]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [30;-45;26] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-0.0009;0.0013;-0.0008] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [100, -120, 80;... + -60, -120, 100;... + -100, 40, 90] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [8, -120, 100;... + 0, -6, -60;... + 0, 0, -7] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0, 0, 0;... + 0, 0, 0;... + 0, 0, 0] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 20 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.002 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 5E-5; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 1E-6; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +TC_KF_config.init_att_unc = degtorad(0.01); +% Initial velocity uncertainty per axis (m/s) +TC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +TC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +TC_KF_config.init_b_a_unc = 30 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +TC_KF_config.init_b_g_unc = 0.001 * deg_to_rad / 3600; +% Initial clock offset uncertainty per axis (m) +TC_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +TC_KF_config.init_clock_drift_unc = 0.1; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +TC_KF_config.gyro_noise_PSD = (0.004 * deg_to_rad / 60)^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +TC_KF_config.accel_noise_PSD = (40 *... + micro_g_to_meters_per_second_squared)^2; +% Accelerometer bias random walk PSD (m^2 s^-5) +TC_KF_config.accel_bias_PSD = 3.0E-9; +% Gyro bias random walk PSD (rad^2 s^-3) +TC_KF_config.gyro_bias_PSD = 2.0E-16; +% Receiver clock frequency-drift PSD (m^2/s^3) +TC_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +TC_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +TC_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +TC_KF_config.range_rate_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,TC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_6.m b/INS_GNSS_Demo_6.m new file mode 100644 index 0000000..db38c08 --- /dev/null +++ b/INS_GNSS_Demo_6.m @@ -0,0 +1,155 @@ +%INS_GNSS_Demo_6 +%SCRIPT Tightly coupled INS/GNSS demo: +% Profile_0 (Stationary) +% Aviation-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 13/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_0.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_6_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_6_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.01;0.008;0.01]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [30;-45;26] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-0.0009;0.0013;-0.0008] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [100, -120, 80;... + -60, -120, 100;... + -100, 40, 90] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [8, -120, 100;... + 0, -6, -60;... + 0, 0, -7] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0, 0, 0;... + 0, 0, 0;... + 0, 0, 0] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 20 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.002 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 5E-5; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 1E-6; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +TC_KF_config.init_att_unc = degtorad(0.01); +% Initial velocity uncertainty per axis (m/s) +TC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +TC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +TC_KF_config.init_b_a_unc = 30 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +TC_KF_config.init_b_g_unc = 0.001 * deg_to_rad / 3600; +% Initial clock offset uncertainty per axis (m) +TC_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +TC_KF_config.init_clock_drift_unc = 0.1; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +TC_KF_config.gyro_noise_PSD = (0.004 * deg_to_rad / 60)^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +TC_KF_config.accel_noise_PSD = (40 *... + micro_g_to_meters_per_second_squared)^2; +% Accelerometer bias random walk PSD (m^2 s^-5) +TC_KF_config.accel_bias_PSD = 3.0E-9; +% Gyro bias random walk PSD (rad^2 s^-3) +TC_KF_config.gyro_bias_PSD = 2.0E-16; +% Receiver clock frequency-drift PSD (m^2/s^3) +TC_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +TC_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +TC_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +TC_KF_config.range_rate_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,TC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_7.m b/INS_GNSS_Demo_7.m new file mode 100644 index 0000000..7bad06f --- /dev/null +++ b/INS_GNSS_Demo_7.m @@ -0,0 +1,157 @@ +%INS_GNSS_Demo_7 +%SCRIPT Tightly coupled INS/GNSS demo: +% Profile_1 (60s artificial car motion with two 90 deg turns) +% Consumer-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 12/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_1.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_7_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_7_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.5;0.4;2]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [9000;-13000;8000] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-180;260;-160] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [50000, -15000, 10000;... + -7500, -60000, 12500;... + -12500, 5000, 20000] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [40000, -14000, 12500;... + 0, -30000, -7500;... + 0, 0, -17500] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [90, -110, -60;... + -50, 190, -160;... + 30, 110, -130] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 1000 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 1 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-1; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-3; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +TC_KF_config.init_att_unc = degtorad(2); +% Initial velocity uncertainty per axis (m/s) +TC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +TC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +TC_KF_config.init_b_a_unc = 10000 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +TC_KF_config.init_b_g_unc = 200 * deg_to_rad / 3600; +% Initial clock offset uncertainty per axis (m) +TC_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +TC_KF_config.init_clock_drift_unc = 0.1; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +TC_KF_config.gyro_noise_PSD = 0.01^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +TC_KF_config.accel_noise_PSD = 0.2^2; +% NOTE: A large noise PSD is modeled to account for the scale-factor and +% cross-coupling errors that are not directly included in the Kalman filter +% model +% Accelerometer bias random walk PSD (m^2 s^-5) +TC_KF_config.accel_bias_PSD = 1.0E-5; +% Gyro bias random walk PSD (rad^2 s^-3) +TC_KF_config.gyro_bias_PSD = 4.0E-11; +% Receiver clock frequency-drift PSD (m^2/s^3) +TC_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +TC_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +TC_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +TC_KF_config.range_rate_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,TC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_8.m b/INS_GNSS_Demo_8.m new file mode 100644 index 0000000..2853164 --- /dev/null +++ b/INS_GNSS_Demo_8.m @@ -0,0 +1,157 @@ +%INS_GNSS_Demo_8 +%SCRIPT Tightly coupled INS/GNSS demo: +% Profile_0 (Stationary) +% Consumer-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 12/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_0.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_8_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_8_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.5;0.4;2]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [9000;-13000;8000] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-180;260;-160] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [50000, -15000, 10000;... + -7500, -60000, 12500;... + -12500, 5000, 20000] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [40000, -14000, 12500;... + 0, -30000, -7500;... + 0, 0, -17500] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [90, -110, -60;... + -50, 190, -160;... + 30, 110, -130] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 1000 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 1 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-1; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-3; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +TC_KF_config.init_att_unc = degtorad(2); +% Initial velocity uncertainty per axis (m/s) +TC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +TC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +TC_KF_config.init_b_a_unc = 10000 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +TC_KF_config.init_b_g_unc = 200 * deg_to_rad / 3600; +% Initial clock offset uncertainty per axis (m) +TC_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +TC_KF_config.init_clock_drift_unc = 0.1; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +TC_KF_config.gyro_noise_PSD = 0.01^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +TC_KF_config.accel_noise_PSD = 0.2^2; +% NOTE: A large noise PSD is modeled to account for the scale-factor and +% cross-coupling errors that are not directly included in the Kalman filter +% model +% Accelerometer bias random walk PSD (m^2 s^-5) +TC_KF_config.accel_bias_PSD = 1.0E-5; +% Gyro bias random walk PSD (rad^2 s^-3) +TC_KF_config.gyro_bias_PSD = 4.0E-11; +% Receiver clock frequency-drift PSD (m^2/s^3) +TC_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +TC_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +TC_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +TC_KF_config.range_rate_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,TC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/INS_GNSS_Demo_9.m b/INS_GNSS_Demo_9.m new file mode 100644 index 0000000..cf3f34b --- /dev/null +++ b/INS_GNSS_Demo_9.m @@ -0,0 +1,155 @@ +%INS_GNSS_Demo_9 +%SCRIPT Tightly coupled INS/GNSS demo: +% Profile_2 (175s car) +% Tactical-grade IMU +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 27/5/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_2.csv'; +% Output motion profile and error filenames +output_profile_name = 'INS_GNSS_Demo_9_Profile.csv'; +output_errors_name = 'INS_GNSS_Demo_9_Errors.csv'; + +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Interval between GNSS epochs (s) +GNSS_config.epoch_interval = 0.5; + +% Initial estimated position (m; ECEF) +GNSS_config.init_est_r_ea_e = [0;0;0]; + +% Number of satellites in constellation +GNSS_config.no_sat = 30; +% Orbital radius of satellites (m) +GNSS_config.r_os = 2.656175E7; +% Inclination angle of satellites (deg) +GNSS_config.inclination = 55; +% Longitude offset of constellation (deg) +GNSS_config.const_delta_lambda = 0; +% Timing offset of constellation (s) +GNSS_config.const_delta_t = 0; + +% Mask angle (deg) +GNSS_config.mask_angle = 10; +% Signal in space error SD (m) *Give residual where corrections are applied +GNSS_config.SIS_err_SD = 1; +% Zenith ionosphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_iono_err_SD = 2; +% Zenith troposphere error SD (m) *Give residual where corrections are applied +GNSS_config.zenith_trop_err_SD = 0.2; +% Code tracking error SD (m) *Can extend to account for multipath +GNSS_config.code_track_err_SD = 1; +% Range rate tracking error SD (m/s) *Can extend to account for multipath +GNSS_config.rate_track_err_SD = 0.02; +% Receiver clock offset at time=0 (m); +GNSS_config.rx_clock_offset = 10000; +% Receiver clock drift at time=0 (m/s); +GNSS_config.rx_clock_drift = 100; + +% Initial attitude uncertainty per axis (deg, converted to rad) +TC_KF_config.init_att_unc = degtorad(1); +% Initial velocity uncertainty per axis (m/s) +TC_KF_config.init_vel_unc = 0.1; +% Initial position uncertainty per axis (m) +TC_KF_config.init_pos_unc = 10; +% Initial accelerometer bias uncertainty per instrument (micro-g, converted +% to m/s^2) +TC_KF_config.init_b_a_unc = 1000 * micro_g_to_meters_per_second_squared; +% Initial gyro bias uncertainty per instrument (deg/hour, converted to rad/sec) +TC_KF_config.init_b_g_unc = 10 * deg_to_rad / 3600; +% Initial clock offset uncertainty per axis (m) +TC_KF_config.init_clock_offset_unc = 10; +% Initial clock drift uncertainty per axis (m/s) +TC_KF_config.init_clock_drift_unc = 0.1; + +% Gyro noise PSD (deg^2 per hour, converted to rad^2/s) +TC_KF_config.gyro_noise_PSD = (0.02 * deg_to_rad / 60)^2; +% Accelerometer noise PSD (micro-g^2 per Hz, converted to m^2 s^-3) +TC_KF_config.accel_noise_PSD = (200 *... + micro_g_to_meters_per_second_squared)^2; +% Accelerometer bias random walk PSD (m^2 s^-5) +TC_KF_config.accel_bias_PSD = 1.0E-7; +% Gyro bias random walk PSD (rad^2 s^-3) +TC_KF_config.gyro_bias_PSD = 2.0E-12; +% Receiver clock frequency-drift PSD (m^2/s^3) +TC_KF_config.clock_freq_PSD = 1; +% Receiver clock phase-drift PSD (m^2/s) +TC_KF_config.clock_phase_PSD = 1; + +% Pseudo-range measurement noise SD (m) +TC_KF_config.pseudo_range_SD = 2.5; +% Pseudo-range rate measurement noise SD (m/s) +TC_KF_config.range_rate_SD = 0.1; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Tightly coupled ECEF Inertial navigation and GNSS integrated navigation +% simulation +[out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors... + ,IMU_errors,GNSS_config,TC_KF_config); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/Inertial_Demo_1ECEF.m b/Inertial_Demo_1ECEF.m new file mode 100644 index 0000000..a72fae8 --- /dev/null +++ b/Inertial_Demo_1ECEF.m @@ -0,0 +1,89 @@ +%Inertial_Demo_1ECEF +%SCRIPT Inertial navigation demonstration: +% Profile_1 (60s artificial car motion with two 90 deg turns) +% ECEF-frame inertial navigation equations +% Tactical-grade IMU error model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 3/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_1.csv'; +% Output motion profile and error filenames +output_profile_name = 'Inertial_Demo_1ECEF_Profile.csv'; +output_errors_name = 'Inertial_Demo_1ECEF_Errors.csv'; + +% Position initialization error (m; N,E,D) +initialization_errors.delta_r_eb_n = [4;2;3]; +% Velocity initialization error (m/s; N,E,D) +initialization_errors.delta_v_eb_n = [0.05;-0.05;0.1]; +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +% RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% ECEF Inertial navigation simulation +[out_profile,out_errors] = Inertial_navigation_ECEF(in_profile,no_epochs,... + initialization_errors,IMU_errors); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/Inertial_Demo_1ECI.m b/Inertial_Demo_1ECI.m new file mode 100644 index 0000000..7caf411 --- /dev/null +++ b/Inertial_Demo_1ECI.m @@ -0,0 +1,98 @@ +%Inertial_Demo_1ECI +%SCRIPT Inertial navigation demonstration: +% Profile_1 (60s artificial car motion with two 90 deg turns) +% ECI-frame inertial navigation equations +% Tactical-grade IMU error model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 3/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details +clear all; +clc; +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_1.csv'; +% Output motion profile and error filenames +output_profile_name = 'Inertial_Demo_1ECI_Profile.csv'; +output_errors_name = 'Inertial_Demo_1ECI_Errors.csv'; + +% Position initialization error (m; N,E,D)位置初始误差 +initialization_errors.delta_r_eb_n = [4;2;3]; + +%===========可以改，只影响第一个历元的误差。Apr.30,2016 17:10===========% +% initialization_errors.delta_r_eb_n = [0;0;0];% +%===========可以改，只影响第一个历元的误差。Apr.30,2016 17:10===========% + +% Velocity initialization error (m/s; N,E,D)速度初始误差 +initialization_errors.delta_v_eb_n = [0.05;-0.05;0.1]; +% Attitude initialization error (deg, converted to rad; @N,E,D)姿态初始误差 +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes)加速度计零偏 +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes)陀螺仪零偏 P.133 +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes)加速度计比例因子和交叉耦合误差 +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes)陀螺仪比例因子和交叉耦合误差 P.135 +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body +% axes)陀螺仪g相关零偏 P.139 +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +% 加速度计随机噪声的功率密度方根 +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5)陀螺仪随机 +% 噪声的功率密度方根 P.138 +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2)量化因子的数量级 +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s)量化因子的数量级 P.138 +IMU_errors.gyro_quant_level = 2E-4; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +% RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file开始读取文件 +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file 判断读取文件是否有错误 +if ~ok + return; +end %if + +% ECI Inertial navigation simulation 开始惯导仿真 +[out_profile,out_errors] = Inertial_navigation_ECI(in_profile,no_epochs,... + initialization_errors,IMU_errors); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/Inertial_Demo_1NED.m b/Inertial_Demo_1NED.m new file mode 100644 index 0000000..fdd0380 --- /dev/null +++ b/Inertial_Demo_1NED.m @@ -0,0 +1,89 @@ +%Inertial_Demo_1NED +%SCRIPT Inertial navigation demonstration: +% Profile_1 (60s artificial car motion with two 90 deg turns) +% Local-navigation-frame inertial navigation equations +% Tactical-grade IMU error model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 3/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_1.csv'; +% Output motion profile and error filenames +output_profile_name = 'Inertial_Demo_1NED_Profile.csv'; +output_errors_name = 'Inertial_Demo_1NED_Errors.csv'; + +% Position initialization error (m; N,E,D) +initialization_errors.delta_r_eb_n = [4;2;3]; +% Velocity initialization error (m/s; N,E,D) +initialization_errors.delta_v_eb_n = [0.05;-0.05;0.1]; +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors] = Inertial_navigation_NED(in_profile,no_epochs,... + initialization_errors,IMU_errors); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/Inertial_Demo_2.m b/Inertial_Demo_2.m new file mode 100644 index 0000000..072a6cb --- /dev/null +++ b/Inertial_Demo_2.m @@ -0,0 +1,89 @@ +%Inertial_Demo_2 +%SCRIPT Inertial navigation demonstration: +% Profile_1 (60s artificial car motion with two 90 deg turns) +% Local-navigation-frame inertial navigation equations +% Aviation-grade IMU error model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 4/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_1.csv'; +% Output motion profile and error filenames +output_profile_name = 'Inertial_Demo_2_Profile.csv'; +output_errors_name = 'Inertial_Demo_2_Errors.csv'; + +% Position initialization error (m; N,E,D) +initialization_errors.delta_r_eb_n = [4;2;3]; +% Velocity initialization error (m/s; N,E,D) +initialization_errors.delta_v_eb_n = [0.05;-0.05;0.1]; +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.01;0.008;0.01]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [30;-45;26] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-0.0009;0.0013;-0.0008] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [100, -120, 80;... + -60, -120, 100;... + -100, 40, 90] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [8, -120, 100;... + 0, -6, -60;... + 0, 0, -7] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0, 0, 0;... + 0, 0, 0;... + 0, 0, 0] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 20 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.002 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 5E-5; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 1E-6; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors] = Inertial_navigation_NED(in_profile,no_epochs,... + initialization_errors,IMU_errors); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/Inertial_Demo_3.m b/Inertial_Demo_3.m new file mode 100644 index 0000000..6bcaed8 --- /dev/null +++ b/Inertial_Demo_3.m @@ -0,0 +1,89 @@ +%Inertial_Demo_3 +%SCRIPT Inertial navigation demonstration: +% Profile_1 (60s artificial car motion with two 90 deg turns) +% Local-navigation-frame inertial navigation equations +% Consumer-grade IMU error model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 4/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_1.csv'; +% Output motion profile and error filenames +output_profile_name = 'Inertial_Demo_3_Profile.csv'; +output_errors_name = 'Inertial_Demo_3_Errors.csv'; + +% Position initialization error (m; N,E,D) +initialization_errors.delta_r_eb_n = [4;2;3]; +% Velocity initialization error (m/s; N,E,D) +initialization_errors.delta_v_eb_n = [0.05;-0.05;0.1]; +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.5;0.4;2]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [9000;-13000;8000] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-180;260;-160] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [50000, -15000, 10000;... + -7500, -60000, 12500;... + -12500, 5000, 20000] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [40000, -14000, 12500;... + 0, -30000, -7500;... + 0, 0, -17500] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [90, -110, -60;... + -50, 190, -160;... + 30, 110, -130] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 1000 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 1 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-1; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-3; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors] = Inertial_navigation_NED(in_profile,no_epochs,... + initialization_errors,IMU_errors); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/Inertial_Demo_4.m b/Inertial_Demo_4.m new file mode 100644 index 0000000..49e8783 --- /dev/null +++ b/Inertial_Demo_4.m @@ -0,0 +1,89 @@ +%Inertial_Demo_4 +%SCRIPT Inertial navigation demonstration: +% Profile_0 (60s stationary and level) +% Local-navigation-frame inertial navigation equations +% Tactical-grade IMU error model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 4/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_0.csv'; +% Output motion profile and error filenames +output_profile_name = 'Inertial_Demo_4_Profile.csv'; +output_errors_name = 'Inertial_Demo_4_Errors.csv'; + +% Position initialization error (m; N,E,D) +initialization_errors.delta_r_eb_n = [4;2;3]; +% Velocity initialization error (m/s; N,E,D) +initialization_errors.delta_v_eb_n = [0.05;-0.05;0.1]; +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors] = Inertial_navigation_NED(in_profile,no_epochs,... + initialization_errors,IMU_errors); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/Inertial_Demo_5.m b/Inertial_Demo_5.m new file mode 100644 index 0000000..bfd579b --- /dev/null +++ b/Inertial_Demo_5.m @@ -0,0 +1,89 @@ +%Inertial_Demo_5 +%SCRIPT Inertial navigation demonstration: +% Profile_2 (175s car) +% Local-navigation-frame inertial navigation equations +% Tactical-grade IMU error model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 27/5/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_2.csv'; +% Output motion profile and error filenames +output_profile_name = 'Inertial_Demo_5_Profile.csv'; +output_errors_name = 'Inertial_Demo_5_Errors.csv'; + +% Position initialization error (m; N,E,D) +initialization_errors.delta_r_eb_n = [4;2;3]; +% Velocity initialization error (m/s; N,E,D) +initialization_errors.delta_v_eb_n = [0.05;-0.05;0.1]; +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors] = Inertial_navigation_NED(in_profile,no_epochs,... + initialization_errors,IMU_errors); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/Inertial_Demo_6.m b/Inertial_Demo_6.m new file mode 100644 index 0000000..085e1b0 --- /dev/null +++ b/Inertial_Demo_6.m @@ -0,0 +1,89 @@ +%Inertial_Demo_6 +%SCRIPT Inertial navigation demonstration: +% Profile_3 (418s aircraft) +% Local-navigation-frame inertial navigation equations +% Aviation-grade IMU error model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 27/5/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_3.csv'; +% Output motion profile and error filenames +output_profile_name = 'Inertial_Demo_6_Profile.csv'; +output_errors_name = 'Inertial_Demo_6_Errors.csv'; + +% Position initialization error (m; N,E,D) +initialization_errors.delta_r_eb_n = [4;2;3]; +% Velocity initialization error (m/s; N,E,D) +initialization_errors.delta_v_eb_n = [0.05;-0.05;0.1]; +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.01;0.008;0.01]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [30;-45;26] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-0.0009;0.0013;-0.0008] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [100, -120, 80;... + -60, -120, 100;... + -100, 40, 90] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [8, -120, 100;... + 0, -6, -60;... + 0, 0, -7] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0, 0, 0;... + 0, 0, 0;... + 0, 0, 0] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 20 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.002 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 5E-5; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 1E-6; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors] = Inertial_navigation_NED(in_profile,no_epochs,... + initialization_errors,IMU_errors); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/Inertial_Demo_7.m b/Inertial_Demo_7.m new file mode 100644 index 0000000..95f5b3c --- /dev/null +++ b/Inertial_Demo_7.m @@ -0,0 +1,88 @@ +%Inertial_Demo_7 +%SCRIPT Inertial navigation demonstration: +% Profile_4 (300s boat) +% Local-navigation-frame inertial navigation equations +% Tactical-grade IMU error model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% Created 27/5/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; +micro_g_to_meters_per_second_squared = 9.80665E-6; + +% CONFIGURATION +% Input truth motion profile filename +input_profile_name = 'Profile_4.csv'; +% Output motion profile and error filenames +output_profile_name = 'Inertial_Demo_7_Profile.csv'; +output_errors_name = 'Inertial_Demo_7_Errors.csv'; + +% Position initialization error (m; N,E,D) +initialization_errors.delta_r_eb_n = [4;2;3]; +% Velocity initialization error (m/s; N,E,D) +initialization_errors.delta_v_eb_n = [0.05;-0.05;0.1]; +% Attitude initialization error (deg, converted to rad; @N,E,D) +initialization_errors.delta_eul_nb_n = [-0.05;0.04;1]*deg_to_rad; % rad + +% Accelerometer biases (micro-g, converted to m/s^2; body axes) +IMU_errors.b_a = [900;-1300;800] * micro_g_to_meters_per_second_squared; +% Gyro biases (deg/hour, converted to rad/sec; body axes) +IMU_errors.b_g = [-9;13;-8] * deg_to_rad / 3600; +% Accelerometer scale factor and cross coupling errors (ppm, converted to +% unitless; body axes) +IMU_errors.M_a = [500, -300, 200;... + -150, -600, 250;... + -250, 100, 450] * 1E-6; +% Gyro scale factor and cross coupling errors (ppm, converted to unitless; +% body axes) +IMU_errors.M_g = [400, -300, 250;... + 0, -300, -150;... + 0, 0, -350] * 1E-6; +% Gyro g-dependent biases (deg/hour/g, converted to rad-sec/m; body axes) +IMU_errors.G_g = [0.9, -1.1, -0.6;... + -0.5, 1.9, -1.6;... + 0.3, 1.1, -1.3] * deg_to_rad / (3600 * 9.80665); +% Accelerometer noise root PSD (micro-g per root Hz, converted to m s^-1.5) +IMU_errors.accel_noise_root_PSD = 100 *... + micro_g_to_meters_per_second_squared; +% Gyro noise root PSD (deg per root hour, converted to rad s^-0.5) +IMU_errors.gyro_noise_root_PSD = 0.01 * deg_to_rad / 60; +% Accelerometer quantization level (m/s^2) +IMU_errors.accel_quant_level = 1E-2; +% Gyro quantization level (rad/s) +IMU_errors.gyro_quant_level = 2E-4; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence (may not work in Octave). +RandStream.setDefaultStream(RandStream('mt19937ar','seed',1)); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% NED Inertial navigation simulation +[out_profile,out_errors] = Inertial_navigation_NED(in_profile,no_epochs,... + initialization_errors,IMU_errors); + +% Plot the input motion profile and the errors (may not work in Octave). +close all; +Plot_profile(in_profile); +Plot_errors(out_errors); + +% Write output profile and errors file +Write_profile(output_profile_name,out_profile); +Write_errors(output_errors_name,out_errors); + +% Ends \ No newline at end of file diff --git a/Inertial_navigation_ECEF.m b/Inertial_navigation_ECEF.m new file mode 100644 index 0000000..092d1ac --- /dev/null +++ b/Inertial_navigation_ECEF.m @@ -0,0 +1,181 @@ +function [out_profile,out_errors] = Inertial_navigation_ECEF(in_profile,... + no_epochs,initialization_errors,IMU_errors) +%Inertial_navigation_ECEF - Simulates inertial navigation using ECEF +% navigation equations and kinematic model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 3/4/2012 by Paul Groves +% +% Inputs: +% in_profile True motion profile array +% no_epochs Number of epochs of profile data +% initialization_errors +% .delta_r_eb_n position error resolved along NED (m) +% .delta_v_eb_n velocity error resolved along NED (m/s) +% .delta_eul_nb_n attitude error as NED Euler angles (rad) +% IMU_errors +% .delta_r_eb_n position error resolved along NED (m) +% .b_a Accelerometer biases (m/s^2) +% .b_g Gyro biases (rad/s) +% .M_a Accelerometer scale factor and cross coupling errors +% .M_g Gyro scale factor and cross coupling errors +% .G_g Gyro g-dependent biases (rad-sec/m) +% .accel_noise_root_PSD Accelerometer noise root PSD (m s^-1.5) +% .gyro_noise_root_PSD Gyro noise root PSD (rad s^-0.5) +% .accel_quant_level Accelerometer quantization level (m/s^2) +% .gyro_quant_level Gyro quantization level (rad/s) +% +% Outputs: +% out_profile Navigation solution as a motion profile array +% out_errors Navigation solution error array +% +% Format of motion profiles: +% Column 1: time (sec) +% Column 2: latitude (rad) +% Column 3: longitude (rad) +% Column 4: height (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll angle of body w.r.t NED (rad) +% Column 9: pitch angle of body w.r.t NED (rad) +% Column 10: yaw angle of body w.r.t NED (rad) +% +% Format of error array: +% Column 1: time (sec) +% Column 2: north position error (m) +% Column 3: east position error (m) +% Column 4: down position error (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: attitude error about north (rad) +% Column 9: attitude error about east (rad) +% Column 10: attitude error about down = heading error (rad) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Initialize true navigation solution +old_time = in_profile(1,1); +true_L_b = in_profile(1,2); +true_lambda_b = in_profile(1,3); +true_h_b = in_profile(1,4); +true_v_eb_n = in_profile(1,5:7)'; +true_eul_nb = in_profile(1,8:10)'; +true_C_b_n = Euler_to_CTM(true_eul_nb)'; +[old_true_r_eb_e,old_true_v_eb_e,old_true_C_b_e] =... + NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + +% Initialize estimated navigation solution +[old_est_L_b,old_est_lambda_b,old_est_h_b,old_est_v_eb_n,old_est_C_b_n] =... + Initialize_NED(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n,... + initialization_errors); + +% Initialize output profile record and errors record +out_profile = zeros(no_epochs,10); +out_errors = zeros(no_epochs,10); + +% Generate output profile record +out_profile(1,1) = old_time; +out_profile(1,2) = old_est_L_b; +out_profile(1,3) = old_est_lambda_b; +out_profile(1,4) = old_est_h_b; +out_profile(1,5:7) = old_est_v_eb_n'; +out_profile(1,8:10) = CTM_to_Euler(old_est_C_b_n')'; + +out_errors(1,1) = old_time; +out_errors(1,2:4) = initialization_errors.delta_r_eb_n'; +out_errors(1,5:7) = initialization_errors.delta_v_eb_n'; +out_errors(1,8:10) = initialization_errors.delta_eul_nb_n'; +[old_est_r_eb_e,old_est_v_eb_e,old_est_C_b_e] = NED_to_ECEF(old_est_L_b,... + old_est_lambda_b,old_est_h_b,old_est_v_eb_n,old_est_C_b_n); + +% Initialize IMU quantization residuals +quant_residuals = [0;0;0;0;0;0]; + +% Progress bar +dots = '....................'; +bars = '||||||||||||||||||||'; +rewind = '\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b'; +fprintf(strcat('Processing: ',dots)); +progress_mark = 0; +progress_epoch = 0; + +% Main loop +for epoch = 2:no_epochs + + % Update progress bar + if (epoch - progress_epoch) > (no_epochs/20) + progress_mark = progress_mark + 1; + progress_epoch = epoch; + fprintf(strcat(rewind,bars(1:progress_mark),... + dots(1:(20 - progress_mark)))); + end % if epoch + + % Input data from motion profile + time = in_profile(epoch,1); + true_L_b = in_profile(epoch,2); + true_lambda_b = in_profile(epoch,3); + true_h_b = in_profile(epoch,4); + true_v_eb_n = in_profile(epoch,5:7)'; + true_eul_nb = in_profile(epoch,8:10)'; + true_C_b_n = Euler_to_CTM(true_eul_nb)'; + [true_r_eb_e,true_v_eb_e,true_C_b_e] =... + NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + + % Time interval + tor_i = time - old_time; + + % Calculate specific force and angular rate + [true_f_ib_b,true_omega_ib_b] = Kinematics_ECEF(tor_i,true_C_b_e,... + old_true_C_b_e,true_v_eb_e,old_true_v_eb_e,old_true_r_eb_e); + + % Simulate IMU errors + [meas_f_ib_b,meas_omega_ib_b,quant_residuals] = IMU_model(tor_i,... + true_f_ib_b,true_omega_ib_b,IMU_errors,quant_residuals); + + % Update estimated navigation solution + [est_r_eb_e,est_v_eb_e,est_C_b_e] = Nav_equations_ECEF(tor_i,... + old_est_r_eb_e,old_est_v_eb_e,old_est_C_b_e,meas_f_ib_b,... + meas_omega_ib_b); + + [est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n] =... + ECEF_to_NED(est_r_eb_e,est_v_eb_e,est_C_b_e); + + % Generate output profile record + out_profile(epoch,1) = time; + out_profile(epoch,2) = est_L_b; + out_profile(epoch,3) = est_lambda_b; + out_profile(epoch,4) = est_h_b; + out_profile(epoch,5:7) = est_v_eb_n'; + out_profile(epoch,8:10) = CTM_to_Euler(est_C_b_n')'; + + % Determine errors and generate output record + [delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n,true_L_b,... + true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + out_errors(epoch,1) = time; + out_errors(epoch,2:4) = delta_r_eb_n'; + out_errors(epoch,5:7) = delta_v_eb_n'; + out_errors(epoch,8:10) = delta_eul_nb_n'; + + % Reset old values + old_time = time; + old_true_r_eb_e = true_r_eb_e; + old_true_v_eb_e = true_v_eb_e; + old_true_C_b_e = true_C_b_e; + old_est_r_eb_e = est_r_eb_e; + old_est_v_eb_e = est_v_eb_e; + old_est_C_b_e = est_C_b_e; + +end %epoch + +% Complete progress bar +fprintf(strcat(rewind,bars,'\n')); + +% Ends \ No newline at end of file diff --git a/Inertial_navigation_ECI.m b/Inertial_navigation_ECI.m new file mode 100644 index 0000000..84287d1 --- /dev/null +++ b/Inertial_navigation_ECI.m @@ -0,0 +1,190 @@ +function [out_profile,out_errors] = Inertial_navigation_ECI(in_profile,... + no_epochs,initialization_errors,IMU_errors) +%Inertial_navigation_ECI - Simulates inertial navigation using ECI +% navigation equations and kinematic model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 3/4/2012 by Paul Groves +% +% Inputs: +% in_profile True motion profile array +% no_epochs Number of epochs of profile data +% initialization_errors +% .delta_r_eb_n position error resolved along NED (m) +% .delta_v_eb_n velocity error resolved along NED (m/s) +% .delta_eul_nb_n attitude error as NED Euler angles (rad) +% IMU_errors +% .delta_r_eb_n position error resolved along NED (m) +% .b_a Accelerometer biases (m/s^2) +% .b_g Gyro biases (rad/s) +% .M_a Accelerometer scale factor and cross coupling errors +% .M_g Gyro scale factor and cross coupling errors +% .G_g Gyro g-dependent biases (rad-sec/m) +% .accel_noise_root_PSD Accelerometer noise root PSD (m s^-1.5) +% .gyro_noise_root_PSD Gyro noise root PSD (rad s^-0.5) +% .accel_quant_level Accelerometer quantization level (m/s^2) +% .gyro_quant_level Gyro quantization level (rad/s) +% +% Outputs: +% out_profile Navigation solution as a motion profile array +% out_errors Navigation solution error array +% +% Format of motion profiles: +% Column 1: time (sec) +% Column 2: latitude (rad)纬度 +% Column 3: longitude (rad)经度 +% Column 4: height (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll angle of body w.r.t NED (rad) +% Column 9: pitch angle of body w.r.t NED (rad) +% Column 10: yaw angle of body w.r.t NED (rad) +% +% Format of error array: +% Column 1: time (sec) +% Column 2: north position error (m) +% Column 3: east position error (m) +% Column 4: down position error (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: attitude error about north (rad) +% Column 9: attitude error about east (rad) +% Column 10: attitude error about down = heading error (rad) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Initialize true navigation solution 初始化，输入读取到的参数，使用第一个历元 +old_time = in_profile(1,1); +true_L_b = in_profile(1,2);%纬度 +true_lambda_b = in_profile(1,3);%经度 +true_h_b = in_profile(1,4); +true_v_eb_n = in_profile(1,5:7)'; +true_eul_nb = in_profile(1,8:10)'; +true_C_b_n = Euler_to_CTM(true_eul_nb)';%坐标转换矩阵 +[true_r_eb_e,true_v_eb_e,true_C_b_e] =... + NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); +[old_true_r_ib_i,old_true_v_ib_i,old_true_C_b_i] =... + ECEF_to_ECI(old_time,true_r_eb_e,true_v_eb_e,true_C_b_e); + +% Initialize estimated navigation solution +[old_est_L_b,old_est_lambda_b,old_est_h_b,old_est_v_eb_n,old_est_C_b_n] =... + Initialize_NED(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n,... + initialization_errors); + +% Initialize output profile record and errors record +out_profile = zeros(no_epochs,10); +out_errors = zeros(no_epochs,10); + +% Generate output profile record +out_profile(1,1) = old_time; +out_profile(1,2) = old_est_L_b; +out_profile(1,3) = old_est_lambda_b; +out_profile(1,4) = old_est_h_b; +out_profile(1,5:7) = old_est_v_eb_n'; +out_profile(1,8:10) = CTM_to_Euler(old_est_C_b_n')'; + +out_errors(1,1) = old_time; +out_errors(1,2:4) = initialization_errors.delta_r_eb_n'; +out_errors(1,5:7) = initialization_errors.delta_v_eb_n'; +out_errors(1,8:10) = initialization_errors.delta_eul_nb_n'; +[old_est_r_eb_e,old_est_v_eb_e,old_est_C_b_e] = NED_to_ECEF(old_est_L_b,... + old_est_lambda_b,old_est_h_b,old_est_v_eb_n,old_est_C_b_n); +[old_est_r_ib_i,old_est_v_ib_i,old_est_C_b_i] =... + ECEF_to_ECI(old_time,old_est_r_eb_e,old_est_v_eb_e,old_est_C_b_e); + +% Initialize IMU quantization residuals +quant_residuals = [0;0;0;0;0;0]; + +% Progress bar 进度条，可以不要 +dots = '....................'; +bars = '||||||||||||||||||||'; +rewind = '\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b'; +fprintf(strcat('Processing: ',dots)); +progress_mark = 0; +progress_epoch = 0; + +% Main loop +for epoch = 2:no_epochs + + % Update progress bar 更新进度条，没用 + if (epoch - progress_epoch) > (no_epochs/20) + progress_mark = progress_mark + 1; + progress_epoch = epoch; + fprintf(strcat(rewind,bars(1:progress_mark),... + dots(1:(20 - progress_mark)))); + end % if epoch + + % Input data from motion profile + time = in_profile(epoch,1); + true_L_b = in_profile(epoch,2); + true_lambda_b = in_profile(epoch,3); + true_h_b = in_profile(epoch,4); + true_v_eb_n = in_profile(epoch,5:7)'; + true_eul_nb = in_profile(epoch,8:10)'; + true_C_b_n = Euler_to_CTM(true_eul_nb)'; + [true_r_eb_e,true_v_eb_e,true_C_b_e] =... + NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + [true_r_ib_i,true_v_ib_i,true_C_b_i] =... + ECEF_to_ECI(time,true_r_eb_e,true_v_eb_e,true_C_b_e); + + % Time interval + tor_i = time - old_time; + + % Calculate specific force and angular rate + + [true_f_ib_b,true_omega_ib_b] = Kinematics_ECI(tor_i,true_C_b_i,... + old_true_C_b_i,true_v_ib_i,old_true_v_ib_i,old_true_r_ib_i); + + % Simulate IMU errors + [meas_f_ib_b,meas_omega_ib_b,quant_residuals] = IMU_model(tor_i,... + true_f_ib_b,true_omega_ib_b,IMU_errors,quant_residuals); + + % Update estimated navigation solution + [est_r_ib_i,est_v_ib_i,est_C_b_i] = Nav_equations_ECI(tor_i,... + old_est_r_ib_i,old_est_v_ib_i,old_est_C_b_i,meas_f_ib_b,... + meas_omega_ib_b); + + [est_r_eb_e,est_v_eb_e,est_C_b_e] =... + ECI_to_ECEF(time,est_r_ib_i,est_v_ib_i,est_C_b_i); + [est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n] =... + ECEF_to_NED(est_r_eb_e,est_v_eb_e,est_C_b_e); + + % Generate output profile record + out_profile(epoch,1) = time; + out_profile(epoch,2) = est_L_b; + out_profile(epoch,3) = est_lambda_b; + out_profile(epoch,4) = est_h_b; + out_profile(epoch,5:7) = est_v_eb_n'; + out_profile(epoch,8:10) = CTM_to_Euler(est_C_b_n')'; + + % Determine errors and generate output record + [delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n,true_L_b,... + true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + out_errors(epoch,1) = time; + out_errors(epoch,2:4) = delta_r_eb_n'; + out_errors(epoch,5:7) = delta_v_eb_n'; + out_errors(epoch,8:10) = delta_eul_nb_n'; + + % Reset old values + old_time = time; + old_true_r_ib_i = true_r_ib_i; + old_true_v_ib_i = true_v_ib_i; + old_true_C_b_i = true_C_b_i; + old_est_r_ib_i = est_r_ib_i; + old_est_v_ib_i = est_v_ib_i; + old_est_C_b_i = est_C_b_i; + +end %epoch + +% Complete progress bar +fprintf(strcat(rewind,bars,'\n')); + +% Ends \ No newline at end of file diff --git a/Inertial_navigation_NED.m b/Inertial_navigation_NED.m new file mode 100644 index 0000000..29bb464 --- /dev/null +++ b/Inertial_navigation_NED.m @@ -0,0 +1,177 @@ +function [out_profile,out_errors] = Inertial_navigation_NED(in_profile,... + no_epochs,initialization_errors,IMU_errors) +%Inertial_navigation_NED - Simulates inertial navigation using local +%navigation frame (NED) navigation equations and kinematic model +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 3/4/2012 by Paul Groves +% +% Inputs: +% in_profile True motion profile array +% no_epochs Number of epochs of profile data +% initialization_errors +% .delta_r_eb_n position error resolved along NED (m) +% .delta_v_eb_n velocity error resolved along NED (m/s) +% .delta_eul_nb_n attitude error as NED Euler angles (rad) +% IMU_errors +% .delta_r_eb_n position error resolved along NED (m) +% .b_a Accelerometer biases (m/s^2) +% .b_g Gyro biases (rad/s) +% .M_a Accelerometer scale factor and cross coupling errors +% .M_g Gyro scale factor and cross coupling errors +% .G_g Gyro g-dependent biases (rad-sec/m) +% .accel_noise_root_PSD Accelerometer noise root PSD (m s^-1.5) +% .gyro_noise_root_PSD Gyro noise root PSD (rad s^-0.5) +% .accel_quant_level Accelerometer quantization level (m/s^2) +% .gyro_quant_level Gyro quantization level (rad/s) +% +% Outputs: +% out_profile Navigation solution as a motion profile array +% out_errors Navigation solution error array +% +% Format of motion profiles: +% Column 1: time (sec) +% Column 2: latitude (rad) +% Column 3: longitude (rad) +% Column 4: height (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll angle of body w.r.t NED (rad) +% Column 9: pitch angle of body w.r.t NED (rad) +% Column 10: yaw angle of body w.r.t NED (rad) +% +% Format of error array: +% Column 1: time (sec) +% Column 2: north position error (m) +% Column 3: east position error (m) +% Column 4: down position error (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: attitude error about north (rad) +% Column 9: attitude error about east (rad) +% Column 10: attitude error about down = heading error (rad) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Initialize true navigation solution +old_time = in_profile(1,1); +old_true_L_b = in_profile(1,2); +old_true_lambda_b = in_profile(1,3); +old_true_h_b = in_profile(1,4); +old_true_v_eb_n = in_profile(1,5:7)'; +old_true_eul_nb = in_profile(1,8:10)'; +old_true_C_b_n = Euler_to_CTM(old_true_eul_nb)'; + +% Initialize estimated navigation solution +[old_est_L_b,old_est_lambda_b,old_est_h_b,old_est_v_eb_n,old_est_C_b_n] =... + Initialize_NED(old_true_L_b,old_true_lambda_b,old_true_h_b,... + old_true_v_eb_n,old_true_C_b_n,initialization_errors); + +% Initialize output profile record and errors record +out_profile = zeros(no_epochs,10); +out_errors = zeros(no_epochs,10); + +% Generate output profile record +out_profile(1,1) = old_time; +out_profile(1,2) = old_est_L_b; +out_profile(1,3) = old_est_lambda_b; +out_profile(1,4) = old_est_h_b; +out_profile(1,5:7) = old_est_v_eb_n'; +out_profile(1,8:10) = CTM_to_Euler(old_est_C_b_n')'; + +out_errors(1,1) = old_time; +out_errors(1,2:4) = initialization_errors.delta_r_eb_n'; +out_errors(1,5:7) = initialization_errors.delta_v_eb_n'; +out_errors(1,8:10) = initialization_errors.delta_eul_nb_n'; + +% Initialize IMU quantization residuals +quant_residuals = [0;0;0;0;0;0]; + +% Progress bar +dots = '....................'; +bars = '||||||||||||||||||||'; +rewind = '\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b'; +fprintf(strcat('Processing: ',dots)); +progress_mark = 0; +progress_epoch = 0; + +% Main loop +for epoch = 2:no_epochs + + % Update progress bar + if (epoch - progress_epoch) > (no_epochs/20) + progress_mark = progress_mark + 1; + progress_epoch = epoch; + fprintf(strcat(rewind,bars(1:progress_mark),... + dots(1:(20 - progress_mark)))); + end % if epoch + + % Input data from motion profile + time = in_profile(epoch,1); + true_L_b = in_profile(epoch,2); + true_lambda_b = in_profile(epoch,3); + true_h_b = in_profile(epoch,4); + true_v_eb_n = in_profile(epoch,5:7)'; + true_eul_nb = in_profile(epoch,8:10)'; + true_C_b_n = Euler_to_CTM(true_eul_nb)'; + + % Time interval + tor_i = time - old_time; + + % Calculate true specific force and angular rate + [true_f_ib_b,true_omega_ib_b] = Kinematics_NED(tor_i,true_C_b_n,... + old_true_C_b_n,true_v_eb_n,old_true_v_eb_n,true_L_b,true_h_b,... + old_true_L_b,old_true_h_b); + + % Simulate IMU errors + [meas_f_ib_b,meas_omega_ib_b,quant_residuals] = IMU_model(tor_i,... + true_f_ib_b,true_omega_ib_b,IMU_errors,quant_residuals); + + % Update estimated navigation solution + [est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n] = ... + Nav_equations_NED(tor_i,old_est_L_b,old_est_lambda_b,old_est_h_b,... + old_est_v_eb_n,old_est_C_b_n,meas_f_ib_b,meas_omega_ib_b); + + % Generate output profile record + out_profile(epoch,1) = time; + out_profile(epoch,2) = est_L_b; + out_profile(epoch,3) = est_lambda_b; + out_profile(epoch,4) = est_h_b; + out_profile(epoch,5:7) = est_v_eb_n'; + out_profile(epoch,8:10) = CTM_to_Euler(est_C_b_n')'; + + % Determine errors and generate output record + [delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n,true_L_b,... + true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + out_errors(epoch,1) = time; + out_errors(epoch,2:4) = delta_r_eb_n'; + out_errors(epoch,5:7) = delta_v_eb_n'; + out_errors(epoch,8:10) = delta_eul_nb_n'; + + % Reset old values + old_time = time; + old_true_L_b = true_L_b; + old_true_lambda_b = true_lambda_b; + old_true_h_b = true_h_b; + old_true_v_eb_n = true_v_eb_n; + old_true_C_b_n = true_C_b_n; + old_est_L_b = est_L_b; + old_est_lambda_b = est_lambda_b; + old_est_h_b = est_h_b; + old_est_v_eb_n = est_v_eb_n; + old_est_C_b_n = est_C_b_n; + +end %epoch + +% Complete progress bar +fprintf(strcat(rewind,bars,'\n')); + +% Ends \ No newline at end of file diff --git a/Initialize_GNSS_KF.m b/Initialize_GNSS_KF.m new file mode 100644 index 0000000..0c10cac --- /dev/null +++ b/Initialize_GNSS_KF.m @@ -0,0 +1,50 @@ +function [x_est,P_matrix] = Initialize_GNSS_KF(est_r_ea_e,est_v_ea_e,... + est_clock,GNSS_KF_config) +%Initialize_GNSS_KF - Initializes the GNSS EKF state estimates and error +%covariance matrix +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 11/4/2012 by Paul Groves +% +% Inputs: +% est_r_ea_e estimated ECEF user position (m) +% est_v_ea_e estimated ECEF user velocity (m/s) +% est_clock estimated receiver clock offset (m) and drift (m/s) +% GNSS_KF_config +% .init_pos_unc Initial position uncertainty per axis (m) +% .init_vel_unc Initial velocity uncertainty per axis (m/s) +% .init_clock_offset_unc Initial clock offset uncertainty per axis (m) +% .init_clock_drift_unc Initial clock drift uncertainty per axis (m/s) +% +% Outputs: +% x_est Kalman filter estimates: +% Rows 1-3 estimated ECEF user position (m) +% Rows 4-6 estimated ECEF user velocity (m/s) +% Row 7 estimated receiver clock offset (m) +% Row 8 estimated receiver clock drift (m/s) +% P_matrix state estimation error covariance matrix + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Initialize state estimates +x_est(1:3,1) = est_r_ea_e; +x_est(4:6,1) = est_v_ea_e; +x_est(7:8,1) = est_clock'; + +% Initialize error covariance matrix +P_matrix = zeros(8); +P_matrix(1,1) = GNSS_KF_config.init_pos_unc^2; +P_matrix(2,2) = GNSS_KF_config.init_pos_unc^2; +P_matrix(3,3) = GNSS_KF_config.init_pos_unc^2; +P_matrix(4,4) = GNSS_KF_config.init_vel_unc^2; +P_matrix(5,5) = GNSS_KF_config.init_vel_unc^2; +P_matrix(6,6) = GNSS_KF_config.init_vel_unc^2; +P_matrix(7,7) = GNSS_KF_config.init_clock_offset_unc^2; +P_matrix(8,8) = GNSS_KF_config.init_clock_drift_unc^2; + +% Ends \ No newline at end of file diff --git a/Initialize_GNSS_biases.m b/Initialize_GNSS_biases.m new file mode 100644 index 0000000..7513a0b --- /dev/null +++ b/Initialize_GNSS_biases.m @@ -0,0 +1,66 @@ +function GNSS_biases = Initialize_GNSS_biases(sat_r_es_e,r_ea_e,L_a,... + lambda_a,GNSS_config) +%Initialize_GNSS_biases - Initializes the GNSS range errors due to signal +%in space, ionosphere and troposphere errors based on the elevation angles. +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 11/4/2012 by Paul Groves +% +% Inputs: +% sat_r_es_e (no_sat x 3) ECEF satellite positions (m) +% r_ea_e ECEF user position (m) +% L_a user latitude (rad) +% lambda_a user longitude (rad) +% GNSS_config +% .no_sat Number of satellites in constellation +% .mask_angle Mask angle (deg) +% .SIS_err_SD Signal in space error SD (m) +% .zenith_iono_err_SD Zenith ionosphere error SD (m) +% .zenith_trop_err_SD Zenith troposphere error SD (m) +% +% Outputs: +% GNSS_biases (no_sat) Bias-like GNSS range errors + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Calculate ECEF to NED coordinate transformation matrix using (2.150) +cos_lat = cos(L_a); +sin_lat = sin(L_a); +cos_long = cos(lambda_a); +sin_long = sin(lambda_a); +C_e_n = [-sin_lat * cos_long, -sin_lat * sin_long, cos_lat;... + -sin_long, cos_long, 0;... + -cos_lat * cos_long, -cos_lat * sin_long, -sin_lat]; + +% Loop satellites +for j = 1:GNSS_config.no_sat + + % Determine ECEF line-of-sight vector using (8.41) + delta_r = sat_r_es_e(j,1:3)' - r_ea_e; + u_as_e = delta_r / sqrt(delta_r' * delta_r); + + % Convert line-of-sight vector to NED using (8.39) and determine + % elevation using (8.57) + elevation = -asin(C_e_n(3,:) * u_as_e); + + % Limit the minimum elevation angle to the masking angle + elevation = max(elevation,degtorad(GNSS_config.mask_angle)); + + % Calculate ionosphere and troposphere error SDs using (9.79) and (9.80) + iono_SD = GNSS_config.zenith_iono_err_SD / sqrt(1 - 0.899 *... + cos(elevation)^2); + trop_SD = GNSS_config.zenith_trop_err_SD / sqrt(1 - 0.998 *... + cos(elevation)^2); + + % Determine range bias + GNSS_biases(j) = GNSS_config.SIS_err_SD*randn + iono_SD*randn +... + trop_SD*randn; + +end % for j + +% Ends \ No newline at end of file diff --git a/Initialize_LC_P_matrix.m b/Initialize_LC_P_matrix.m new file mode 100644 index 0000000..1b75a15 --- /dev/null +++ b/Initialize_LC_P_matrix.m @@ -0,0 +1,34 @@ +function P_matrix = Initialize_LC_P_matrix(LC_KF_config) +%Initialize_LC_P_matrix - Initializes the loosely coupled INS/GNSS KF +%error covariance matrix +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 12/4/2012 by Paul Groves +% +% Inputs: +% TC_KF_config +% .init_att_unc Initial attitude uncertainty per axis (rad) +% .init_vel_unc Initial velocity uncertainty per axis (m/s) +% .init_pos_unc Initial position uncertainty per axis (m) +% .init_b_a_unc Initial accel. bias uncertainty (m/s^2) +% .init_b_g_unc Initial gyro. bias uncertainty (rad/s) +% +% Outputs: +% P_matrix state estimation error covariance matrix + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Initialize error covariance matrix +P_matrix = zeros(15); +P_matrix(1:3,1:3) = eye(3) * LC_KF_config.init_att_unc^2; +P_matrix(4:6,4:6) = eye(3) * LC_KF_config.init_vel_unc^2; +P_matrix(7:9,7:9) = eye(3) * LC_KF_config.init_pos_unc^2; +P_matrix(10:12,10:12) = eye(3) * LC_KF_config.init_b_a_unc^2; +P_matrix(13:15,13:15) = eye(3) * LC_KF_config.init_b_g_unc^2; + +% Ends \ No newline at end of file diff --git a/Initialize_NED.m b/Initialize_NED.m new file mode 100644 index 0000000..a22ac92 --- /dev/null +++ b/Initialize_NED.m @@ -0,0 +1,50 @@ +function [est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n] =... + Initialize_NED(L_b,lambda_b,h_b,v_eb_n,C_b_n,initialization_errors) +%Initialize_NED - Initializes the curvilinear position, velocity, and +%attitude solution by adding errors to the truth. +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 3/4/2012 by Paul Groves +% +% Inputs: +% L_b true latitude (rad) +% lambda_b true longitude (rad) +% h_b true height (m) +% v_eb_n true velocity of body frame w.r.t. ECEF frame, resolved +% along north, east, and down (m/s) +% C_b_n true body-to-NED coordinate transformation matrix +% initialization_errors +% .delta_r_eb_n position error resolved along NED (m) +% .delta_v_eb_n velocity error resolved along NED (m/s) +% .delta_eul_nb_n attitude error as NED Euler angles (rad) +% +% Outputs: +% est_L_b latitude solution (rad) +% est_lambda_b longitude solution (rad) +% est_h_b height solution (m) +% est_v_eb_n velocity solution of body frame w.r.t. ECEF frame, +% resolved along north, east, and down (m/s) +% est_C_b_n body-to-NED coordinate transformation matrix solution + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Position initialization, using (2.119) +[R_N,R_E] = Radii_of_curvature(L_b); +est_L_b = L_b + initialization_errors.delta_r_eb_n(1) / (R_N + h_b); +est_lambda_b = lambda_b + initialization_errors.delta_r_eb_n(2) /... + ((R_E + h_b) * cos(L_b)); +est_h_b = h_b - initialization_errors.delta_r_eb_n(3); + +% Velocity initialization +est_v_eb_n = v_eb_n + initialization_errors.delta_v_eb_n; + +% Attitude initialization, using (5.109) and (5.111) +delta_C_b_n = Euler_to_CTM(-initialization_errors.delta_eul_nb_n); +est_C_b_n = delta_C_b_n * C_b_n; + +% Ends \ No newline at end of file diff --git a/Initialize_NED_attitude.m b/Initialize_NED_attitude.m new file mode 100644 index 0000000..6e32b6a --- /dev/null +++ b/Initialize_NED_attitude.m @@ -0,0 +1,27 @@ +function est_C_b_n = Initialize_NED_attitude(C_b_n,initialization_errors) +%Initialize_NED_attitude - Initializes the attitude solution by adding +%errors to the truth. +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 12/4/2012 by Paul Groves +% +% Inputs: +% C_b_n true body-to-NED coordinate transformation matrix +% initialization_errors +% .delta_eul_nb_n attitude error as NED Euler angles (rad) +% +% Outputs: +% est_C_b_n body-to-NED coordinate transformation matrix solution + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Attitude initialization, using (5.109) and (5.111) +delta_C_b_n = Euler_to_CTM(-initialization_errors.delta_eul_nb_n); +est_C_b_n = delta_C_b_n * C_b_n; + +% Ends \ No newline at end of file diff --git a/Initialize_TC_P_matrix.m b/Initialize_TC_P_matrix.m new file mode 100644 index 0000000..cbae62d --- /dev/null +++ b/Initialize_TC_P_matrix.m @@ -0,0 +1,38 @@ +function P_matrix = Initialize_TC_P_matrix(TC_KF_config) +%Initialize_TC_P_matrix - Initializes the tightly coupled INS/GNSS EKF +%error covariance matrix +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 12/4/2012 by Paul Groves +% +% Inputs: +% TC_KF_config +% .init_att_unc Initial attitude uncertainty per axis (rad) +% .init_vel_unc Initial velocity uncertainty per axis (m/s) +% .init_pos_unc Initial position uncertainty per axis (m) +% .init_b_a_unc Initial accel. bias uncertainty (m/s^2) +% .init_b_g_unc Initial gyro. bias uncertainty (rad/s) +% .init_clock_offset_unc Initial clock offset uncertainty per axis (m) +% .init_clock_drift_unc Initial clock drift uncertainty per axis (m/s) +% +% Outputs: +% P_matrix state estimation error covariance matrix + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Initialize error covariance matrix +P_matrix = zeros(17); +P_matrix(1:3,1:3) = eye(3) * TC_KF_config.init_att_unc^2; +P_matrix(4:6,4:6) = eye(3) * TC_KF_config.init_vel_unc^2; +P_matrix(7:9,7:9) = eye(3) * TC_KF_config.init_pos_unc^2; +P_matrix(10:12,10:12) = eye(3) * TC_KF_config.init_b_a_unc^2; +P_matrix(13:15,13:15) = eye(3) * TC_KF_config.init_b_g_unc^2; +P_matrix(16,16) = TC_KF_config.init_clock_offset_unc^2; +P_matrix(17,17) = TC_KF_config.init_clock_drift_unc^2; + +% Ends \ No newline at end of file diff --git a/Interpolate_profile.m b/Interpolate_profile.m new file mode 100644 index 0000000..c44bff7 --- /dev/null +++ b/Interpolate_profile.m @@ -0,0 +1,95 @@ +function Interpolate_profile(input_profile_name,output_profile_name) +%Interpolate_profile - Interpolating .csv motion profiles: +% +% Inputs +% input_profile_name Input motion profile filename +% output_profile_name Output motion profile filename +% +% Created 3/4/12 by Paul Groves + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% CONFIGURATION +% Jitter standard deviation on interpolated velocity (m/s) +Velocity_jitter = 0.001; +% Jitter standard deviation on interpolated attitude (rad) +Attitude_jitter = 0.00002; + +% Seeding of the random number generator for reproducability. Change +% this value for a different random number sequence. +rng(1); + +% Begins + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(input_profile_name); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% Initialize true navigation solution +old_time = in_profile(1,1); +old_true_L_b = in_profile(1,2); +old_true_lambda_b = in_profile(1,3); +old_true_h_b = in_profile(1,4); +old_true_v_eb_n = in_profile(1,5:7)'; +old_true_eul_nb = in_profile(1,8:10)'; + +out_profile(1,:)=in_profile(1,:); + +% Main loop +for epoch = 2:no_epochs + + % Input data from motion profile + time = in_profile(epoch,1); + true_L_b = in_profile(epoch,2); + true_lambda_b = in_profile(epoch,3); + true_h_b = in_profile(epoch,4); + true_v_eb_n = in_profile(epoch,5:7)'; + true_eul_nb = in_profile(epoch,8:10)'; + + % Time interval + tor_i = time - old_time; + + % Interpolate + inter_L_b = 0.5 * (true_L_b + old_true_L_b); + inter_lambda_b = 0.5 * (true_lambda_b + old_true_lambda_b); + inter_h_b = 0.5 * (true_h_b + old_true_h_b); + inter_v_eb_n = 0.5 * (true_v_eb_n + old_true_v_eb_n) +... + randn(3,1) * Velocity_jitter; + inter_eul_nb = 0.5 * (true_eul_nb + old_true_eul_nb) +... + randn(3,1) * Attitude_jitter; + + % Generate output profile records + epoch1 = 2 * epoch -2; + epoch2 = 2 * epoch -1; + out_profile(epoch1,1) = 0.5* (time + old_time); + out_profile(epoch1,2) = inter_L_b; + out_profile(epoch1,3) = inter_lambda_b; + out_profile(epoch1,4) = inter_h_b; + out_profile(epoch1,5:7) = inter_v_eb_n'; + out_profile(epoch1,8:10) = inter_eul_nb'; + out_profile(epoch2,1) = time; + out_profile(epoch2,2) = true_L_b; + out_profile(epoch2,3) = true_lambda_b; + out_profile(epoch2,4) = true_h_b; + out_profile(epoch2,5:7) = true_v_eb_n'; + out_profile(epoch2,8:10) = true_eul_nb'; + + % Reset old values + old_time = time; + old_true_L_b = true_L_b; + old_true_lambda_b = true_lambda_b; + old_true_h_b = true_h_b; + old_true_v_eb_n = true_v_eb_n; + old_true_eul_nb = true_eul_nb; + +end %epoch + +% Write output profile +Write_profile(output_profile_name,out_profile); + +% Ends \ No newline at end of file diff --git a/Kinematics_ECEF.m b/Kinematics_ECEF.m new file mode 100644 index 0000000..daf8a4c --- /dev/null +++ b/Kinematics_ECEF.m @@ -0,0 +1,90 @@ +function [f_ib_b,omega_ib_b] = Kinematics_ECEF(tor_i,C_b_e,... + old_C_b_e,v_eb_e,old_v_eb_e,r_eb_e) +%Kinematics_ECEF - calculates specific force and angular rate from input +%w.r.t and resolved along ECEF-frame axes +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 1/4/2012 by Paul Groves +% +% Inputs: +% tor_i time interval between epochs (s) +% C_b_e body-to-ECEF-frame coordinate transformation matrix +% old_C_b_e previous body-to-ECEF-frame coordinate transformation matrix +% v_eb_e velocity of body frame w.r.t. ECEF frame, resolved along +% ECEF-frame axes (m/s) +% old_v_eb_e previous velocity of body frame w.r.t. ECEF frame, resolved +% along ECEF-frame axes (m/s) +% r_eb_e Cartesian position of body frame w.r.t. ECEF frame, resolved +% along ECEF-frame axes (m) +% Outputs: +% f_ib_b specific force of body frame w.r.t. ECEF frame, resolved +% along body-frame axes, averaged over time interval (m/s^2) +% omega_ib_b angular rate of body frame w.r.t. ECEF frame, resolved +% about body-frame axes, averaged over time interval (rad/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Parameters +omega_ie = 7.292115E-5; % Earth rotation rate (rad/s) + +% Begins + +if tor_i > 0 + + % From (2.145) determine the Earth rotation over the update interval + % C_Earth = C_e_i' * old_C_e_i + alpha_ie = omega_ie * tor_i; + C_Earth = [cos(alpha_ie), sin(alpha_ie), 0;... + -sin(alpha_ie), cos(alpha_ie), 0;... + 0, 0, 1]; + + % Obtain coordinate transformation matrix from the old attitude (w.r.t. + % an inertial frame) to the new + C_old_new = C_b_e' * C_Earth * old_C_b_e; + + % Calculate the approximate angular rate w.r.t. an inertial frame + alpha_ib_b(1,1) = 0.5 * (C_old_new(2,3) - C_old_new(3,2)); + alpha_ib_b(2,1) = 0.5 * (C_old_new(3,1) - C_old_new(1,3)); + alpha_ib_b(3,1) = 0.5 * (C_old_new(1,2) - C_old_new(2,1)); + + % Calculate and apply the scaling factor + temp = acos(0.5 * (C_old_new(1,1) + C_old_new(2,2) + C_old_new(3,3)... + - 1.0)); + if temp>2e-5 %scaling is 1 if temp is less than this + alpha_ib_b = alpha_ib_b * temp/sin(temp); + end %if temp + + % Calculate the angular rate + omega_ib_b = alpha_ib_b / tor_i; + + % Calculate the specific force resolved about ECEF-frame axes + % From (5.36), + f_ib_e = ((v_eb_e - old_v_eb_e) / tor_i) - Gravity_ECEF(r_eb_e)... + + 2 * Skew_symmetric([0;0;omega_ie]) * old_v_eb_e; + + % Calculate the average body-to-ECEF-frame coordinate transformation + % matrix over the update interval using (5.84) and (5.85) + mag_alpha = sqrt(alpha_ib_b' * alpha_ib_b); + Alpha_ib_b = Skew_symmetric(alpha_ib_b); + if mag_alpha>1.E-8 + ave_C_b_e = old_C_b_e * (eye(3) + (1 - cos(mag_alpha)) /mag_alpha^2 ... + * Alpha_ib_b + (1 - sin(mag_alpha) / mag_alpha) / mag_alpha^2 ... + * Alpha_ib_b * Alpha_ib_b) - 0.5 * ... + Skew_symmetric([0;0;alpha_ie]) * old_C_b_e; + else + ave_C_b_e = old_C_b_e -... + 0.5 * Skew_symmetric([0;0;alpha_ie]) * old_C_b_e; + end %if mag_alpha + + % Transform specific force to body-frame resolving axes using (5.81) + f_ib_b = inv(ave_C_b_e) * f_ib_e; + +else + % If time interval is zero, set angular rate and specific force to zero + omega_ib_b = [0;0;0]; + f_ib_b = [0;0;0]; +end %if tor_i +% Ends \ No newline at end of file diff --git a/Kinematics_ECI.m b/Kinematics_ECI.m new file mode 100644 index 0000000..84d5709 --- /dev/null +++ b/Kinematics_ECI.m @@ -0,0 +1,76 @@ +function [f_ib_b,omega_ib_b] = Kinematics_ECI(tor_i,C_b_i,... + old_C_b_i,v_ib_i,old_v_ib_i,r_ib_i); +%Kinematics_ECI - calculates specific force and angular rate from input +%w.r.t and resolved along ECI-frame axes +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 1/4/2012 by Paul Groves +% +% Inputs: +% tor_i time interval between epochs (s) +% C_b_i body-to-ECI-frame coordinate transformation matrix +% old_C_b_i previous body-to-ECI-frame coordinate transformation matrix +% v_ib_i velocity of body frame w.r.t. ECI frame, resolved along +% ECI-frame axes (m/s) +% old_v_ib_i previous velocity of body frame w.r.t. ECI frame, resolved +% along ECI-frame axes (m/s) +% r_ib_i Cartesian position of body frame w.r.t. ECI frame, resolved +% along ECI-frame axes (m) +% Outputs: +% f_ib_b specific force of body frame w.r.t. ECI frame, resolved +% along body-frame axes, averaged over time interval (m/s^2) +% omega_ib_b angular rate of body frame w.r.t. ECI frame, resolved +% about body-frame axes, averaged over time interval (rad/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +if tor_i > 0 + + % Obtain coordinate transformation matrix from the old attitude to the new + C_old_new = C_b_i' * old_C_b_i; + + % Calculate the approximate angular rate + alpha_ib_b(1,1) = 0.5 * (C_old_new(2,3) - C_old_new(3,2)); + alpha_ib_b(2,1) = 0.5 * (C_old_new(3,1) - C_old_new(1,3)); + alpha_ib_b(3,1) = 0.5 * (C_old_new(1,2) - C_old_new(2,1)); + + % Calculate and apply the scaling factor + temp = acos(0.5 * (C_old_new(1,1) + C_old_new(2,2) + C_old_new(3,3)... + - 1.0)); + if temp>2e-5 %scaling is 1 if temp is less than this + alpha_ib_b = alpha_ib_b * temp/sin(temp); + end %if temp + + % Calculate the angular rate + omega_ib_b = alpha_ib_b / tor_i; + + % Calculate the specific force resolved about ECI-frame axes + % From (5.18) and (5.20), + f_ib_i = ((v_ib_i - old_v_ib_i) / tor_i) - Gravitation_ECI(r_ib_i); + + % Calculate the average body-to-ECI-frame coordinate transformation + % matrix over the update interval using (5.84) + mag_alpha = sqrt(alpha_ib_b' * alpha_ib_b); + Alpha_ib_b = Skew_symmetric(alpha_ib_b); + if mag_alpha>1.E-8 + ave_C_b_i = old_C_b_i * (eye(3) + (1 - cos(mag_alpha)) /mag_alpha^2 ... + * Alpha_ib_b + (1 - sin(mag_alpha) / mag_alpha) / mag_alpha^2 ... + * Alpha_ib_b * Alpha_ib_b); + else + ave_C_b_i = old_C_b_i; + end %if mag_alpha + + % Transform specific force to body-frame resolving axes using (5.81) + f_ib_b = inv(ave_C_b_i) * f_ib_i; + +else + % If time interval is zero, set angular rate and specific force to zero + omega_ib_b = [0;0;0]; + f_ib_b = [0;0;0]; +end %if tor_i +% Ends \ No newline at end of file diff --git a/Kinematics_NED.m b/Kinematics_NED.m new file mode 100644 index 0000000..06597bd --- /dev/null +++ b/Kinematics_NED.m @@ -0,0 +1,101 @@ +function [f_ib_b,omega_ib_b] = Kinematics_NED(tor_i,C_b_n,old_C_b_n,... + v_eb_n,old_v_eb_n,L_b,h_b,old_L_b,old_h_b) +%Kinematics_NED - calculates specific force and angular rate from input +%w.r.t and resolved along north, east, and down +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 1/4/2012 by Paul Groves +% +% Inputs: +% tor_i time interval between epochs (s) +% C_b_n body-to-NED coordinate transformation matrix +% old_C_b_n previous body-to-NED coordinate transformation matrix +% v_eb_n velocity of body frame w.r.t. ECEF frame, resolved along +% north, east, and down (m/s) +% old_v_eb_n previous velocity of body frame w.r.t. ECEF frame, resolved +% along north, east, and down (m/s) +% L_b latitude (rad) +% h_b height (m) +% old_L_b previous latitude (rad) +% old_h_b previous height (m) +% Outputs: +% f_ib_b specific force of body frame w.r.t. ECEF frame, resolved +% along body-frame axes, averaged over time interval (m/s^2) +% omega_ib_b angular rate of body frame w.r.t. ECEF frame, resolved +% about body-frame axes, averaged over time interval (rad/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Parameters +omega_ie = 7.292115E-5; % Earth rotation rate (rad/s) + +% Begins + +if tor_i > 0 + + % From (2.123) , determine the angular rate of the ECEF frame + % w.r.t the ECI frame, resolved about NED + omega_ie_n = omega_ie * [cos(old_L_b); 0; - sin(old_L_b)]; + + % From (5.44), determine the angular rate of the NED frame + % w.r.t the ECEF frame, resolved about NED + [old_R_N,old_R_E] = Radii_of_curvature(old_L_b); + [R_N,R_E] = Radii_of_curvature(L_b); + old_omega_en_n = [old_v_eb_n(2) / (old_R_E + old_h_b);... + -old_v_eb_n(1) / (old_R_N + old_h_b);... + -old_v_eb_n(2) * tan(old_L_b) / (old_R_E + old_h_b)]; + omega_en_n = [v_eb_n(2) / (R_E + h_b);... + -v_eb_n(1) / (R_N + h_b);... + -v_eb_n(2) * tan(L_b) / (R_E + h_b)]; + + % Obtain coordinate transformation matrix from the old attitude (w.r.t. + % an inertial frame) to the new using (5.77) + C_old_new = C_b_n' * (eye(3) - Skew_symmetric(omega_ie_n + 0.5 *... + omega_en_n + 0.5 * old_omega_en_n) * tor_i) * old_C_b_n; + + % Calculate the approximate angular rate w.r.t. an inertial frame + alpha_ib_b(1,1) = 0.5 * (C_old_new(2,3) - C_old_new(3,2)); + alpha_ib_b(2,1) = 0.5 * (C_old_new(3,1) - C_old_new(1,3)); + alpha_ib_b(3,1) = 0.5 * (C_old_new(1,2) - C_old_new(2,1)); + + % Calculate and apply the scaling factor + temp = acos(0.5 * (C_old_new(1,1) + C_old_new(2,2) + C_old_new(3,3)... + - 1.0)); + if temp>2e-5 %scaling is 1 if temp is less than this + alpha_ib_b = alpha_ib_b * temp/sin(temp); + end %if temp + + % Calculate the angular rate + omega_ib_b = alpha_ib_b / tor_i; + + % Calculate the specific force resolved about ECEF-frame axes + % From (5.54), + f_ib_n = ((v_eb_n - old_v_eb_n) / tor_i) - Gravity_NED(old_L_b,old_h_b)... + + Skew_symmetric(old_omega_en_n + 2 * omega_ie_n) * old_v_eb_n; + + % Calculate the average body-to-NED coordinate transformation + % matrix over the update interval using (5.84) and (5.86) + mag_alpha = sqrt(alpha_ib_b' * alpha_ib_b); + Alpha_ib_b = Skew_symmetric(alpha_ib_b); + if mag_alpha>1.E-8 + ave_C_b_n = old_C_b_n * (eye(3) + (1 - cos(mag_alpha)) /mag_alpha^2 ... + * Alpha_ib_b + (1 - sin(mag_alpha) / mag_alpha) / mag_alpha^2 ... + * Alpha_ib_b * Alpha_ib_b) -... + 0.5 * Skew_symmetric(old_omega_en_n + omega_ie_n) * old_C_b_n; + else + ave_C_b_n = old_C_b_n -... + 0.5 * Skew_symmetric(old_omega_en_n + omega_ie_n) * old_C_b_n; + end %if mag_alpha + + % Transform specific force to body-frame resolving axes using (5.81) + f_ib_b = inv(ave_C_b_n) * f_ib_n; + +else + % If time interval is zero, set angular rate and specific force to zero + omega_ib_b = [0;0;0]; + f_ib_b = [0;0;0]; +end %if tor_i +% Ends \ No newline at end of file diff --git a/LC_KF_Epoch.m b/LC_KF_Epoch.m new file mode 100644 index 0000000..e14e2c4 --- /dev/null +++ b/LC_KF_Epoch.m @@ -0,0 +1,128 @@ +function [est_C_b_e_new,est_v_eb_e_new,est_r_eb_e_new,est_IMU_bias_new,... + P_matrix_new] = LC_KF_Epoch(GNSS_r_eb_e,GNSS_v_eb_e,tor_s,... + est_C_b_e_old,est_v_eb_e_old,est_r_eb_e_old,est_IMU_bias_old,... + P_matrix_old,meas_f_ib_b,est_L_b_old,LC_KF_config) +%LC_KF_Epoch - Implements one cycle of the loosely coupled INS/GNSS +% Kalman filter plus closed-loop correction of all inertial states +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 12/4/2012 by Paul Groves +% +% Inputs: +% GNSS_r_eb_e GNSS estimated ECEF user position (m) +% GNSS_v_eb_e GNSS estimated ECEF user velocity (m/s) +% tor_s propagation interval (s) +% est_C_b_e_old prior estimated body to ECEF coordinate +% transformation matrix +% est_v_eb_e_old prior estimated ECEF user velocity (m/s) +% est_r_eb_e_old prior estimated ECEF user position (m) +% est_IMU_bias_old prior estimated IMU biases (body axes) +% P_matrix_old previous Kalman filter error covariance matrix +% meas_f_ib_b measured specific force +% est_L_b_old previous latitude solution +% LC_KF_config +% .gyro_noise_PSD Gyro noise PSD (rad^2/s) +% .accel_noise_PSD Accelerometer noise PSD (m^2 s^-3) +% .accel_bias_PSD Accelerometer bias random walk PSD (m^2 s^-5) +% .gyro_bias_PSD Gyro bias random walk PSD (rad^2 s^-3) +% .pos_meas_SD Position measurement noise SD per axis (m) +% .vel_meas_SD Velocity measurement noise SD per axis (m/s) +% +% Outputs: +% est_C_b_e_new updated estimated body to ECEF coordinate +% transformation matrix +% est_v_eb_e_new updated estimated ECEF user velocity (m/s) +% est_r_eb_e_new updated estimated ECEF user position (m) +% est_IMU_bias_new updated estimated IMU biases +% Rows 1-3 estimated accelerometer biases (m/s^2) +% Rows 4-6 estimated gyro biases (rad/s) +% P_matrix_new updated Kalman filter error covariance matrix + + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants (sone of these could be changed to inputs at a later date) +c = 299792458; % Speed of light in m/s +omega_ie = 7.292115E-5; % Earth rotation rate in rad/s +R_0 = 6378137; %WGS84 Equatorial radius in meters +e = 0.0818191908425; %WGS84 eccentricity + +% Begins + +% Skew symmetric matrix of Earth rate +Omega_ie = Skew_symmetric([0,0,omega_ie]); + +% SYSTEM PROPAGATION PHASE + +% 1. Determine transition matrix using (14.50) (first-order approx) +Phi_matrix = eye(15); +Phi_matrix(1:3,1:3) = Phi_matrix(1:3,1:3) - Omega_ie * tor_s; +Phi_matrix(1:3,13:15) = est_C_b_e_old * tor_s; +Phi_matrix(4:6,1:3) = -tor_s * Skew_symmetric(est_C_b_e_old * meas_f_ib_b); +Phi_matrix(4:6,4:6) = Phi_matrix(4:6,4:6) - 2 * Omega_ie * tor_s; +geocentric_radius = R_0 / sqrt(1 - (e * sin(est_L_b_old))^2) *... + sqrt(cos(est_L_b_old)^2 + (1 - e^2)^2 * sin(est_L_b_old)^2); % from (2.137) +Phi_matrix(4:6,7:9) = -tor_s * 2 * Gravity_ECEF(est_r_eb_e_old) /... + geocentric_radius * est_r_eb_e_old' / sqrt (est_r_eb_e_old' *... + est_r_eb_e_old); +Phi_matrix(4:6,10:12) = est_C_b_e_old * tor_s; +Phi_matrix(7:9,4:6) = eye(3) * tor_s; + +% 2. Determine approximate system noise covariance matrix using (14.82) +Q_prime_matrix = zeros(15); +Q_prime_matrix(1:3,1:3) = eye(3) * LC_KF_config.gyro_noise_PSD * tor_s; +Q_prime_matrix(4:6,4:6) = eye(3) * LC_KF_config.accel_noise_PSD * tor_s; +Q_prime_matrix(10:12,10:12) = eye(3) * LC_KF_config.accel_bias_PSD * tor_s; +Q_prime_matrix(13:15,13:15) = eye(3) * LC_KF_config.gyro_bias_PSD * tor_s; + +% 3. Propagate state estimates using (3.14) noting that all states are zero +% due to closed-loop correction. +x_est_propagated(1:15,1) = 0; + +% 4. Propagate state estimation error covariance matrix using (3.46) +P_matrix_propagated = Phi_matrix * (P_matrix_old + 0.5 * Q_prime_matrix) *... + Phi_matrix' + 0.5 * Q_prime_matrix; + +% MEASUREMENT UPDATE PHASE + +% 5. Set-up measurement matrix using (14.115) +H_matrix = zeros(6,15); +H_matrix(1:3,7:9) = -eye(3); +H_matrix(4:6,4:6) = -eye(3); + +% 6. Set-up measurement noise covariance matrix assuming all components of +% GNSS position and velocity are independent and have equal variance. +R_matrix(1:3,1:3) = eye(3) * LC_KF_config.pos_meas_SD^2; +R_matrix(1:3,4:6) = zeros(3); +R_matrix(4:6,1:3) = zeros(3); +R_matrix(4:6,4:6) = eye(3) * LC_KF_config.vel_meas_SD^2; + +% 7. Calculate Kalman gain using (3.21) +K_matrix = P_matrix_propagated * H_matrix' * inv(H_matrix *... + P_matrix_propagated * H_matrix' + R_matrix); + +% 8. Formulate measurement innovations using (14.102), noting that zero +% lever arm is assumed here +delta_z(1:3,1) = GNSS_r_eb_e -est_r_eb_e_old; +delta_z(4:6,1) = GNSS_v_eb_e -est_v_eb_e_old; + +% 9. Update state estimates using (3.24) +x_est_new = x_est_propagated + K_matrix * delta_z; + +% 10. Update state estimation error covariance matrix using (3.25) +P_matrix_new = (eye(15) - K_matrix * H_matrix) * P_matrix_propagated; + +% CLOSED-LOOP CORRECTION + +% Correct attitude, velocity, and position using (14.7-9) +est_C_b_e_new = (eye(3) - Skew_symmetric(x_est_new(1:3))) * est_C_b_e_old; +est_v_eb_e_new = est_v_eb_e_old - x_est_new(4:6); +est_r_eb_e_new = est_r_eb_e_old - x_est_new(7:9); + +% Update IMU bias estimates +est_IMU_bias_new = est_IMU_bias_old + x_est_new(10:15); + +% Ends \ No newline at end of file diff --git a/License.txt b/License.txt new file mode 100644 index 0000000..ca3c71b --- /dev/null +++ b/License.txt @@ -0,0 +1,24 @@ +This software is distributed under a Modified BSD License as follows: +* +* Redistribution and use in source and binary forms, with or without +* modification, are permitted provided that the following conditions are met: +* * Redistributions of source code must retain the above copyright +* notice, this list of conditions and the following disclaimer. +* * Redistributions in binary form must reproduce the above copyright +* notice, this list of conditions and the following disclaimer in the +* documentation and/or other materials provided with the distribution. +* * Neither the authors' names nor the +* names of its contributors may be used to endorse or promote products +* derived from this software without specific prior written permission. +* +* THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``AS IS'' AND ANY +* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED +* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE +* DISCLAIMED. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY +* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES +* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND +* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +* diff --git a/Loosely_coupled_INS_GNSS.m b/Loosely_coupled_INS_GNSS.m new file mode 100644 index 0000000..b48dcd1 --- /dev/null +++ b/Loosely_coupled_INS_GNSS.m @@ -0,0 +1,338 @@ +function [out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Loosely_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors,... + IMU_errors,GNSS_config,LC_KF_config) +%Loosely_coupled_INS_GNSS - Simulates inertial navigation using ECEF +% navigation equations and kinematic model, GNSS using a least-squares +% positioning algorithm, and loosely-coupled INS/GNSS integration. +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 12/4/2012 by Paul Groves +% +% Inputs: +% in_profile True motion profile array +% no_epochs Number of epochs of profile data +% initialization_errors +% .delta_r_eb_n position error resolved along NED (m) +% .delta_v_eb_n velocity error resolved along NED (m/s) +% .delta_eul_nb_n attitude error as NED Euler angles (rad) +% IMU_errors +% .delta_r_eb_n position error resolved along NED (m) +% .b_a Accelerometer biases (m/s^2) +% .b_g Gyro biases (rad/s) +% .M_a Accelerometer scale factor and cross coupling errors +% .M_g Gyro scale factor and cross coupling errors +% .G_g Gyro g-dependent biases (rad-sec/m) +% .accel_noise_root_PSD Accelerometer noise root PSD (m s^-1.5) +% .gyro_noise_root_PSD Gyro noise root PSD (rad s^-0.5) +% .accel_quant_level Accelerometer quantization level (m/s^2) +% .gyro_quant_level Gyro quantization level (rad/s) +% GNSS_config +% .epoch_interval Interval between GNSS epochs (s) +% .init_est_r_ea_e Initial estimated position (m; ECEF) +% .no_sat Number of satellites in constellation +% .r_os Orbital radius of satellites (m) +% .inclination Inclination angle of satellites (deg) +% .const_delta_lambda Longitude offset of constellation (deg) +% .const_delta_t Timing offset of constellation (s) +% .mask_angle Mask angle (deg) +% .SIS_err_SD Signal in space error SD (m) +% .zenith_iono_err_SD Zenith ionosphere error SD (m) +% .zenith_trop_err_SD Zenith troposphere error SD (m) +% .code_track_err_SD Code tracking error SD (m) +% .rate_track_err_SD Range rate tracking error SD (m/s) +% .rx_clock_offset Receiver clock offset at time=0 (m) +% .rx_clock_drift Receiver clock drift at time=0 (m/s) +% LC_KF_config +% .init_att_unc Initial attitude uncertainty per axis (rad) +% .init_vel_unc Initial velocity uncertainty per axis (m/s) +% .init_pos_unc Initial position uncertainty per axis (m) +% .init_b_a_unc Initial accel. bias uncertainty (m/s^2) +% .init_b_g_unc Initial gyro. bias uncertainty (rad/s) +% .gyro_noise_PSD Gyro noise PSD (rad^2/s) +% .accel_noise_PSD Accelerometer noise PSD (m^2 s^-3) +% .accel_bias_PSD Accelerometer bias random walk PSD (m^2 s^-5) +% .gyro_bias_PSD Gyro bias random walk PSD (rad^2 s^-3) +% .pos_meas_SD Position measurement noise SD per axis (m) +% .vel_meas_SD Velocity measurement noise SD per axis (m/s) +% +% Outputs: +% out_profile Navigation solution as a motion profile array +% out_errors Navigation solution error array +% out_IMU_bias_est Kalman filter IMU bias estimate array +% out_clock GNSS Receiver clock estimate array +% out_KF_SD Output Kalman filter state uncertainties +% +% Format of motion profiles: +% Column 1: time (sec) +% Column 2: latitude (rad) +% Column 3: longitude (rad) +% Column 4: height (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll angle of body w.r.t NED (rad) +% Column 9: pitch angle of body w.r.t NED (rad) +% Column 10: yaw angle of body w.r.t NED (rad) +% +% Format of error array: +% Column 1: time (sec) +% Column 2: north position error (m) +% Column 3: east position error (m) +% Column 4: down position error (m) +% Column 5: north velocity error (m/s) +% Column 6: east velocity error (m/s) +% Column 7: down velocity (error m/s) +% Column 8: attitude error about north (rad) +% Column 9: attitude error about east (rad) +% Column 10: attitude error about down = heading error (rad) +% +% Format of output IMU biases array: +% Column 1: time (sec) +% Column 2: estimated X accelerometer bias (m/s^2) +% Column 3: estimated Y accelerometer bias (m/s^2) +% Column 4: estimated Z accelerometer bias (m/s^2) +% Column 5: estimated X gyro bias (rad/s) +% Column 6: estimated Y gyro bias (rad/s) +% Column 7: estimated Z gyro bias (rad/s) +% +% Format of receiver clock array: +% Column 1: time (sec) +% Column 2: estimated clock offset (m) +% Column 3: estimated clock drift (m/s) +% +% Format of KF state uncertainties array: +% Column 1: time (sec) +% Column 2: X attitude error uncertainty (rad) +% Column 3: Y attitude error uncertainty (rad) +% Column 4: Z attitude error uncertainty (rad) +% Column 5: X velocity error uncertainty (m/s) +% Column 6: Y velocity error uncertainty (m/s) +% Column 7: Z velocity error uncertainty (m/s) +% Column 8: X position error uncertainty (m) +% Column 9: Y position error uncertainty (m) +% Column 10: Z position error uncertainty (m) +% Column 11: X accelerometer bias uncertainty (m/s^2) +% Column 12: Y accelerometer bias uncertainty (m/s^2) +% Column 13: Z accelerometer bias uncertainty (m/s^2) +% Column 14: X gyro bias uncertainty (rad/s) +% Column 15: Y gyro bias uncertainty (rad/s) +% Column 16: Z gyro bias uncertainty (rad/s) +% Column 17: clock offset uncertainty (m) +% Column 18: clock drift uncertainty (m/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Initialize true navigation solution +old_time = in_profile(1,1); +true_L_b = in_profile(1,2); +true_lambda_b = in_profile(1,3); +true_h_b = in_profile(1,4); +true_v_eb_n = in_profile(1,5:7)'; +true_eul_nb = in_profile(1,8:10)'; +true_C_b_n = Euler_to_CTM(true_eul_nb)'; +[old_true_r_eb_e,old_true_v_eb_e,old_true_C_b_e] =... + NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + +% Determine satellite positions and velocities +[sat_r_es_e,sat_v_es_e] = Satellite_positions_and_velocities(old_time,... + GNSS_config); + +% Initialize the GNSS biases. Note that these are assumed constant throughout +% the simulation and are based on the initial elevation angles. Therefore, +% this function is unsuited to simulations longer than about 30 min. +GNSS_biases = Initialize_GNSS_biases(sat_r_es_e,old_true_r_eb_e,true_L_b,... + true_lambda_b,GNSS_config); + +% Generate GNSS measurements +[GNSS_measurements,no_GNSS_meas] = Generate_GNSS_measurements(old_time,... + sat_r_es_e,sat_v_es_e,old_true_r_eb_e,true_L_b,true_lambda_b,... + old_true_v_eb_e,GNSS_biases,GNSS_config); + +% Determine Least-squares GNSS position solution and use to initialize INS +[GNSS_r_eb_e,GNSS_v_eb_e,est_clock] = GNSS_LS_position_velocity(... + GNSS_measurements,no_GNSS_meas,GNSS_config.init_est_r_ea_e,[0;0;0]); +old_est_r_eb_e = GNSS_r_eb_e; +old_est_v_eb_e = GNSS_v_eb_e; +[old_est_L_b,old_est_lambda_b,old_est_h_b,old_est_v_eb_n] =... + pv_ECEF_to_NED(old_est_r_eb_e,old_est_v_eb_e); +est_L_b = old_est_L_b; + +% Initialize estimated attitude solution +old_est_C_b_n = Initialize_NED_attitude(true_C_b_n,initialization_errors); +[temp1,temp2,old_est_C_b_e] = NED_to_ECEF(old_est_L_b,... + old_est_lambda_b,old_est_h_b,old_est_v_eb_n,old_est_C_b_n); + +% Initialize output profile record and errors record +out_profile = zeros(no_epochs,10); +out_errors = zeros(no_epochs,10); + +% Generate output profile record +out_profile(1,1) = old_time; +out_profile(1,2) = old_est_L_b; +out_profile(1,3) = old_est_lambda_b; +out_profile(1,4) = old_est_h_b; +out_profile(1,5:7) = old_est_v_eb_n'; +out_profile(1,8:10) = CTM_to_Euler(old_est_C_b_n')'; + +% Determine errors and generate output record +[delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + old_est_L_b,old_est_lambda_b,old_est_h_b,old_est_v_eb_n,old_est_C_b_n,... + true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); +out_errors(1,1) = old_time; +out_errors(1,2:4) = delta_r_eb_n'; +out_errors(1,5:7) = delta_v_eb_n'; +out_errors(1,8:10) = delta_eul_nb_n'; + +% Initialize Kalman filter P matrix and IMU bias states +P_matrix = Initialize_LC_P_matrix(LC_KF_config); +est_IMU_bias = zeros(6,1); + +% Initialize IMU quantization residuals +quant_residuals = [0;0;0;0;0;0]; + +% Generate IMU bias and clock output records +out_IMU_bias_est(1,1) = old_time; +out_IMU_bias_est(1,2:7) = est_IMU_bias'; +out_clock(1,1) = old_time; +out_clock(1,2:3) = est_clock; + +% Generate KF uncertainty record +out_KF_SD(1,1) = old_time; +for i =1:15 + out_KF_SD(1,i+1) = sqrt(P_matrix(i,i)); +end % for i + +% Initialize GNSS model timing +time_last_GNSS = old_time; +GNSS_epoch = 1; + +% Progress bar +dots = '....................'; +bars = '||||||||||||||||||||'; +rewind = '\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b'; +fprintf(strcat('Processing: ',dots)); +progress_mark = 0; +progress_epoch = 0; + +% Main loop +for epoch = 2:no_epochs + + % Update progress bar + if (epoch - progress_epoch) > (no_epochs/20) + progress_mark = progress_mark + 1; + progress_epoch = epoch; + fprintf(strcat(rewind,bars(1:progress_mark),... + dots(1:(20 - progress_mark)))); + end % if epoch + + % Input data from motion profile + time = in_profile(epoch,1); + true_L_b = in_profile(epoch,2); + true_lambda_b = in_profile(epoch,3); + true_h_b = in_profile(epoch,4); + true_v_eb_n = in_profile(epoch,5:7)'; + true_eul_nb = in_profile(epoch,8:10)'; + true_C_b_n = Euler_to_CTM(true_eul_nb)'; + [true_r_eb_e,true_v_eb_e,true_C_b_e] =... + NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + + % Time interval + tor_i = time - old_time; + + % Calculate specific force and angular rate + [true_f_ib_b,true_omega_ib_b] = Kinematics_ECEF(tor_i,true_C_b_e,... + old_true_C_b_e,true_v_eb_e,old_true_v_eb_e,old_true_r_eb_e); + + % Simulate IMU errors + [meas_f_ib_b,meas_omega_ib_b,quant_residuals] = IMU_model(tor_i,... + true_f_ib_b,true_omega_ib_b,IMU_errors,quant_residuals); + + % Correct IMU errors + meas_f_ib_b = meas_f_ib_b - est_IMU_bias(1:3); + meas_omega_ib_b = meas_omega_ib_b - est_IMU_bias(4:6); + + % Update estimated navigation solution + [est_r_eb_e,est_v_eb_e,est_C_b_e] = Nav_equations_ECEF(tor_i,... + old_est_r_eb_e,old_est_v_eb_e,old_est_C_b_e,meas_f_ib_b,... + meas_omega_ib_b); + + % Determine whether to update GNSS simulation and run Kalman filter + if (time - time_last_GNSS) >= GNSS_config.epoch_interval + GNSS_epoch = GNSS_epoch + 1; + tor_s = time - time_last_GNSS; % KF time interval + time_last_GNSS = time; + + % Determine satellite positions and velocities + [sat_r_es_e,sat_v_es_e] = Satellite_positions_and_velocities(time,... + GNSS_config); + + % Generate GNSS measurements + [GNSS_measurements,no_GNSS_meas] = Generate_GNSS_measurements(... + time,sat_r_es_e,sat_v_es_e,true_r_eb_e,true_L_b,true_lambda_b,... + true_v_eb_e,GNSS_biases,GNSS_config); + + % Determine GNSS position solution + [GNSS_r_eb_e,GNSS_v_eb_e,est_clock] = GNSS_LS_position_velocity(... + GNSS_measurements,no_GNSS_meas,GNSS_r_eb_e,GNSS_v_eb_e); + + % Run Integration Kalman filter + [est_C_b_e,est_v_eb_e,est_r_eb_e,est_IMU_bias,P_matrix] =... + LC_KF_Epoch(GNSS_r_eb_e,GNSS_v_eb_e,tor_s,est_C_b_e,... + est_v_eb_e,est_r_eb_e,est_IMU_bias,P_matrix,meas_f_ib_b,... + est_L_b,LC_KF_config); + + % Generate IMU bias and clock output records + out_IMU_bias_est(GNSS_epoch,1) = time; + out_IMU_bias_est(GNSS_epoch,2:7) = est_IMU_bias'; + out_clock(GNSS_epoch,1) = time; + out_clock(GNSS_epoch,2:3) = est_clock; + + % Generate KF uncertainty output record + out_KF_SD(GNSS_epoch,1) = time; + for i =1:15 + out_KF_SD(GNSS_epoch,i+1) = sqrt(P_matrix(i,i)); + end % for i + + end % if time + + % Convert navigation solution to NED + [est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n] =... + ECEF_to_NED(est_r_eb_e,est_v_eb_e,est_C_b_e); + + % Generate output profile record + out_profile(epoch,1) = time; + out_profile(epoch,2) = est_L_b; + out_profile(epoch,3) = est_lambda_b; + out_profile(epoch,4) = est_h_b; + out_profile(epoch,5:7) = est_v_eb_n'; + out_profile(epoch,8:10) = CTM_to_Euler(est_C_b_n')'; + + % Determine errors and generate output record + [delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n,true_L_b,... + true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + out_errors(epoch,1) = time; + out_errors(epoch,2:4) = delta_r_eb_n'; + out_errors(epoch,5:7) = delta_v_eb_n'; + out_errors(epoch,8:10) = delta_eul_nb_n'; + + % Reset old values + old_time = time; + old_true_r_eb_e = true_r_eb_e; + old_true_v_eb_e = true_v_eb_e; + old_true_C_b_e = true_C_b_e; + old_est_r_eb_e = est_r_eb_e; + old_est_v_eb_e = est_v_eb_e; + old_est_C_b_e = est_C_b_e; + +end %epoch + +% Complete progress bar +fprintf(strcat(rewind,bars,'\n')); + +% Ends \ No newline at end of file diff --git a/NED_to_ECEF.m b/NED_to_ECEF.m new file mode 100644 index 0000000..b8e1eaf --- /dev/null +++ b/NED_to_ECEF.m @@ -0,0 +1,57 @@ +function [r_eb_e,v_eb_e,C_b_e] = NED_to_ECEF(L_b,lambda_b,h_b,v_eb_n,C_b_n) +%NED_to_ECEF - Converts curvilinear to Cartesian position, velocity +%resolving axes from NED to ECEF and attitude from NED- to ECEF-referenced +%当地导航坐标系转换到地心地固坐标系 +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 2/4/2012 by Paul Groves +% +% Inputs: +% L_b latitude (rad) +% lambda_b longitude (rad) +% h_b height (m) +% v_eb_n velocity of body frame w.r.t. ECEF frame, resolved along +% north, east, and down (m/s) +% C_b_n body-to-NED coordinate transformation matrix +% +% Outputs: +% r_eb_e Cartesian position of body frame w.r.t. ECEF frame, resolved +% along ECEF-frame axes (m) +% v_eb_e velocity of body frame w.r.t. ECEF frame, resolved along +% ECEF-frame axes (m/s) +% C_b_e body-to-ECEF-frame coordinate transformation matrix + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Parameters +R_0 = 6378137; %WGS84 Equatorial radius in meters +e = 0.0818191908425; %WGS84 eccentricity + +% Begins + +% Calculate transverse radius of curvature using (2.105) +R_E = R_0 / sqrt(1 - (e * sin(L_b))^2); + +% Convert position using (2.112) +cos_lat = cos(L_b); +sin_lat = sin(L_b); +cos_long = cos(lambda_b); +sin_long = sin(lambda_b); +r_eb_e = [(R_E + h_b) * cos_lat * cos_long;... + (R_E + h_b) * cos_lat * sin_long;... + ((1 - e^2) * R_E + h_b) * sin_lat]; + +% Calculate ECEF to NED coordinate transformation matrix using (2.150) +C_e_n = [-sin_lat * cos_long, -sin_lat * sin_long, cos_lat;... + -sin_long, cos_long, 0;... + -cos_lat * cos_long, -cos_lat * sin_long, -sin_lat]; + +% Transform velocity using (2.73) +v_eb_e = C_e_n' * v_eb_n; + +% Transform attitude using (2.15) +C_b_e = C_e_n' * C_b_n; + +% Ends \ No newline at end of file diff --git a/Nav_equations_ECEF.m b/Nav_equations_ECEF.m new file mode 100644 index 0000000..97b1282 --- /dev/null +++ b/Nav_equations_ECEF.m @@ -0,0 +1,87 @@ +function [r_eb_e,v_eb_e,C_b_e] = Nav_equations_ECEF(tor_i,old_r_eb_e,... + old_v_eb_e,old_C_b_e,f_ib_b,omega_ib_b) +%Nav_equations_ECEF - Runs precision ECEF-frame inertial navigation +%equations +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 1/4/2012 by Paul Groves +% +% Inputs: +% tor_i time interval between epochs (s) +% old_r_eb_e previous Cartesian position of body frame w.r.t. ECEF +% frame, resolved along ECEF-frame axes (m) +% old_C_b_e previous body-to-ECEF-frame coordinate transformation matrix +% old_v_eb_e previous velocity of body frame w.r.t. ECEF frame, resolved +% along ECEF-frame axes (m/s) +% f_ib_b specific force of body frame w.r.t. ECEF frame, resolved +% along body-frame axes, averaged over time interval (m/s^2) +% omega_ib_b angular rate of body frame w.r.t. ECEF frame, resolved +% about body-frame axes, averaged over time interval (rad/s) +% Outputs: +% r_eb_e Cartesian position of body frame w.r.t. ECEF frame, resolved +% along ECEF-frame axes (m) +% v_eb_e velocity of body frame w.r.t. ECEF frame, resolved along +% ECEF-frame axes (m/s) +% C_b_e body-to-ECEF-frame coordinate transformation matrix + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% parameters +omega_ie = 7.292115E-5; % Earth rotation rate (rad/s) + +% Begins + +% ATTITUDE UPDATE +% From (2.145) determine the Earth rotation over the update interval +% C_Earth = C_e_i' * old_C_e_i +alpha_ie = omega_ie * tor_i; +C_Earth = [cos(alpha_ie), sin(alpha_ie), 0;... + -sin(alpha_ie), cos(alpha_ie), 0;... + 0, 0, 1]; + +% Calculate attitude increment, magnitude, and skew-symmetric matrix +alpha_ib_b = omega_ib_b * tor_i; +mag_alpha = sqrt(alpha_ib_b' * alpha_ib_b); +Alpha_ib_b = Skew_symmetric(alpha_ib_b); + +% Obtain coordinate transformation matrix from the new attitude w.r.t. an +% inertial frame to the old using Rodrigues' formula, (5.73) +if mag_alpha>1.E-8 + C_new_old = eye(3) + sin(mag_alpha) / mag_alpha * Alpha_ib_b +... + (1 - cos(mag_alpha)) / mag_alpha^2 * Alpha_ib_b * Alpha_ib_b; +else + C_new_old = eye(3) + Alpha_ib_b; +end %if mag_alpha + +% Update attitude using (5.75) +C_b_e = C_Earth * old_C_b_e * C_new_old; + +% SPECIFIC FORCE FRAME TRANSFORMATION +% Calculate the average body-to-ECEF-frame coordinate transformation +% matrix over the update interval using (5.84) and (5.85) +if mag_alpha>1.E-8 + ave_C_b_e = old_C_b_e * (eye(3) + (1 - cos(mag_alpha)) / mag_alpha^2 ... + * Alpha_ib_b + (1 - sin(mag_alpha) / mag_alpha) / mag_alpha^2 ... + * Alpha_ib_b * Alpha_ib_b) - 0.5 * Skew_symmetric([0;0;alpha_ie])... + * old_C_b_e; +else + ave_C_b_e = old_C_b_e - 0.5 * Skew_symmetric([0;0;alpha_ie]) *... + old_C_b_e; +end %if mag_alpha + +% Transform specific force to ECEF-frame resolving axes using (5.85) +f_ib_e = ave_C_b_e * f_ib_b; + +% UPDATE VELOCITY +% From (5.36), +v_eb_e = old_v_eb_e + tor_i * (f_ib_e + Gravity_ECEF(old_r_eb_e) -... + 2 * Skew_symmetric([0;0;omega_ie]) * old_v_eb_e); + +% UPDATE CARTESIAN POSITION +% From (5.38), +r_eb_e = old_r_eb_e + (v_eb_e + old_v_eb_e) * 0.5 * tor_i; + +% Ends \ No newline at end of file diff --git a/Nav_equations_ECI.m b/Nav_equations_ECI.m new file mode 100644 index 0000000..493fe07 --- /dev/null +++ b/Nav_equations_ECI.m @@ -0,0 +1,74 @@ +function [r_ib_i,v_ib_i,C_b_i] = Nav_equations_ECI(tor_i,old_r_ib_i,... + old_v_ib_i,old_C_b_i,f_ib_b,omega_ib_b) +%Nav_equations_ECI - Runs precision ECI-frame inertial navigation +%equations +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 1/4/2012 by Paul Groves +% +% Inputs: +% tor_i time interval between epochs (s) +% old_r_ib_i previous Cartesian position of body frame w.r.t. ECI +% frame, resolved along ECI-frame axes (m) +% old_C_b_i previous body-to-ECI-frame coordinate transformation matrix +% old_v_ib_i previous velocity of body frame w.r.t. ECI frame, resolved +% along ECI-frame axes (m/s) +% f_ib_b specific force of body frame w.r.t. ECI frame, resolved +% along body-frame axes, averaged over time interval (m/s^2) +% omega_ib_b angular rate of body frame w.r.t. ECI frame, resolved +% about body-frame axes, averaged over time interval (rad/s) +% Outputs: +% r_ib_i Cartesian position of body frame w.r.t. ECI frame, resolved +% along ECI-frame axes (m) +% v_ib_i velocity of body frame w.r.t. ECI frame, resolved along +% ECI-frame axes (m/s) +% C_b_i body-to-ECI-frame coordinate transformation matrix + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% ATTITUDE UPDATE +% Calculate attitude increment, magnitude, and skew-symmetric matrix +alpha_ib_b = omega_ib_b * tor_i; +mag_alpha = sqrt(alpha_ib_b' * alpha_ib_b); +Alpha_ib_b = Skew_symmetric(alpha_ib_b); + +% Obtain coordinate transformation matrix from the new attitude to the old +% using Rodrigues' formula, (5.73) +if mag_alpha>1.E-8 + C_new_old = eye(3) + sin(mag_alpha) / mag_alpha * Alpha_ib_b +... + (1 - cos(mag_alpha)) / mag_alpha^2 * Alpha_ib_b * Alpha_ib_b; +else + C_new_old = eye(3) + Alpha_ib_b; +end %if mag_alpha + +% Update attitude +C_b_i = old_C_b_i * C_new_old; + +% SPECIFIC FORCE FRAME TRANSFORMATION +% Calculate the average body-to-ECI-frame coordinate transformation +% matrix over the update interval using (5.84) +if mag_alpha>1.E-8 + ave_C_b_i = old_C_b_i * (eye(3) + (1 - cos(mag_alpha)) / mag_alpha^2 ... + * Alpha_ib_b + (1 - sin(mag_alpha) / mag_alpha) / mag_alpha^2 ... + * Alpha_ib_b * Alpha_ib_b); +else + ave_C_b_i = old_C_b_i; +end %if mag_alpha + +% Transform specific force to ECI-frame resolving axes using (5.81) +f_ib_i = ave_C_b_i * f_ib_b; + +% UPDATE VELOCITY +% From (5.18) and (5.20), +v_ib_i = old_v_ib_i + tor_i * (f_ib_i + Gravitation_ECI(old_r_ib_i)); + +% UPDATE CARTESIAN POSITION +% From (5.23), +r_ib_i = old_r_ib_i + (v_ib_i + old_v_ib_i) * 0.5 * tor_i; + +% Ends \ No newline at end of file diff --git a/Nav_equations_NED.m b/Nav_equations_NED.m new file mode 100644 index 0000000..123ab7a --- /dev/null +++ b/Nav_equations_NED.m @@ -0,0 +1,113 @@ +function [L_b,lambda_b,h_b,v_eb_n,C_b_n] = Nav_equations_NED(tor_i,... + old_L_b,old_lambda_b,old_h_b,old_v_eb_n,old_C_b_n,f_ib_b,omega_ib_b) +%Nav_equations_NED - Runs precision local-navigation-frame inertial +%navigation equations (Note: only the attitude update and specific force +%frame transformation phases are precise.) +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 1/4/2012 by Paul Groves +% +% Inputs: +% tor_i time interval between epochs (s) +% old_L_b previous latitude (rad) +% old_lambda_b previous longitude (rad) +% old_h_b previous height (m) +% old_C_b_n previous body-to-NED coordinate transformation matrix +% old_v_eb_n previous velocity of body frame w.r.t. ECEF frame, resolved +% along north, east, and down (m/s) +% f_ib_b specific force of body frame w.r.t. ECEF frame, resolved +% along body-frame axes, averaged over time interval (m/s^2) +% omega_ib_b angular rate of body frame w.r.t. ECEF frame, resolved +% about body-frame axes, averaged over time interval (rad/s) +% Outputs: +% L_b latitude (rad) +% lambda_b longitude (rad) +% h_b height (m) +% v_eb_n velocity of body frame w.r.t. ECEF frame, resolved along +% north, east, and down (m/s) +% C_b_n body-to-NED coordinate transformation matrix + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% parameters +omega_ie = 7.292115E-5; % Earth rotation rate (rad/s) + +% Begins + +% PRELIMINARIES +% Calculate attitude increment, magnitude, and skew-symmetric matrix +alpha_ib_b = omega_ib_b * tor_i; +mag_alpha = sqrt(alpha_ib_b' * alpha_ib_b); +Alpha_ib_b = Skew_symmetric(alpha_ib_b); + +% From (2.123) , determine the angular rate of the ECEF frame +% w.r.t the ECI frame, resolved about NED +omega_ie_n = omega_ie * [cos(old_L_b); 0; - sin(old_L_b)]; + +% From (5.44), determine the angular rate of the NED frame +% w.r.t the ECEF frame, resolved about NED +[old_R_N,old_R_E] = Radii_of_curvature(old_L_b); +old_omega_en_n = [old_v_eb_n(2) / (old_R_E + old_h_b);... + -old_v_eb_n(1) / (old_R_N + old_h_b);... + -old_v_eb_n(2) * tan(old_L_b) / (old_R_E + old_h_b)]; + +% SPECIFIC FORCE FRAME TRANSFORMATION +% Calculate the average body-to-ECEF-frame coordinate transformation +% matrix over the update interval using (5.84) and (5.86) +if mag_alpha>1.E-8 + ave_C_b_n = old_C_b_n * (eye(3) + (1 - cos(mag_alpha)) / mag_alpha^2 ... + * Alpha_ib_b + (1 - sin(mag_alpha) / mag_alpha) / mag_alpha^2 ... + * Alpha_ib_b * Alpha_ib_b) -... + 0.5 * Skew_symmetric(old_omega_en_n + omega_ie_n) * old_C_b_n; +else + ave_C_b_n = old_C_b_n -... + 0.5 * Skew_symmetric(old_omega_en_n + omega_ie_n) * old_C_b_n; +end %if mag_alpha + +% Transform specific force to ECEF-frame resolving axes using (5.86) +f_ib_n = ave_C_b_n * f_ib_b; + +% UPDATE VELOCITY +% From (5.54), +v_eb_n = old_v_eb_n + tor_i * (f_ib_n + Gravity_NED(old_L_b,old_h_b) -... + Skew_symmetric(old_omega_en_n + 2 * omega_ie_n) * old_v_eb_n); + +% UPDATE CURVILINEAR POSITION +% Update height using (5.56) +h_b = old_h_b - 0.5 * tor_i * (old_v_eb_n(3) + v_eb_n(3)); + +% Update latitude using (5.56) +L_b = old_L_b + 0.5 * tor_i * (old_v_eb_n(1) / (old_R_N + old_h_b) +... + v_eb_n(1) / (old_R_N + h_b)); + +% Calculate meridian and transverse radii of curvature +[R_N,R_E]= Radii_of_curvature(L_b); + +% Update longitude using (5.56) +lambda_b = old_lambda_b + 0.5 * tor_i * (old_v_eb_n(2) / ((old_R_E +... + old_h_b) * cos(old_L_b)) + v_eb_n(2) / ((R_E + h_b) * cos(L_b))); + +% ATTITUDE UPDATE +% From (5.44), determine the angular rate of the NED frame +% w.r.t the ECEF frame, resolved about NED +omega_en_n = [v_eb_n(2) / (R_E + h_b);... + -v_eb_n(1) / (R_N + h_b);... + -v_eb_n(2) * tan(L_b) / (R_E + h_b)]; + +% Obtain coordinate transformation matrix from the new attitude w.r.t. an +% inertial frame to the old using Rodrigues' formula, (5.73) +if mag_alpha>1.E-8 + C_new_old = eye(3) + sin(mag_alpha) / mag_alpha * Alpha_ib_b +... + (1 - cos(mag_alpha)) / mag_alpha^2 * Alpha_ib_b * Alpha_ib_b; +else + C_new_old = eye(3) + Alpha_ib_b; +end %if mag_alpha + +% Update attitude using (5.77) +C_b_n = (eye(3) - Skew_symmetric(omega_ie_n + 0.5 * omega_en_n + 0.5 *... + old_omega_en_n) * tor_i) * old_C_b_n * C_new_old; + +% Ends \ No newline at end of file diff --git a/Plot_errors.m b/Plot_errors.m new file mode 100644 index 0000000..783187c --- /dev/null +++ b/Plot_errors.m @@ -0,0 +1,91 @@ +function Plot_errors(errors) +%Plots navigation solution errors +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 3/4/2012 by Paul Groves +% +% Input: +% errors Array of error data to plot +% Format is +% Column 1: time (sec) +% Column 2: north position error (m) +% Column 3: east position error (m) +% Column 4: down position error (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll component of NED attitude error (deg) +% Column 9: pitch component of NED attitude error (deg) +% Column 10: yaw component of NED attitude error (deg) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins +fig = figure; +set(fig,'units','normalized'); +set(fig,'OuterPosition',[0.5,0.4,0.45,0.6]); + +subplot(3,3,1); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.9,0.45,0]); +plot(errors(:,1),errors(:,2),'LineWidth',1.5); +title('North position error, m'); +set(gca,'OuterPosition',[0.01,0.68,0.32,0.31]); +subplot(3,3,2); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0,0.9,0.45]); +plot(errors(:,1),errors(:,3),'LineWidth',1.5); +title('East position error, m'); +set(gca,'OuterPosition',[0.34,0.68,0.32,0.31]); +subplot(3,3,3); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.45,0,0.9]); +plot(errors(:,1),errors(:,4),'LineWidth',1.5); +title('Down position error, m'); +set(gca,'OuterPosition',[0.67,0.68,0.32,0.31]); + +subplot(3,3,4); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.9,0,0.45]); +plot(errors(:,1),errors(:,5),'LineWidth',1.5); +title('North velocity error, m/s'); +set(gca,'OuterPosition',[0.01,0.36,0.32,0.31]); +subplot(3,3,5); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.45,0.9,0]); +plot(errors(:,1),errors(:,6),'LineWidth',1.5); +title('East velocity error, m/s'); +set(gca,'OuterPosition',[0.34,0.36,0.32,0.31]); +subplot(3,3,6); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0,0.45,0.9]); +plot(errors(:,1),errors(:,7),'LineWidth',1.5); +title('Down velocity error, m/s'); +set(gca,'OuterPosition',[0.67,0.36,0.32,0.31]); + +subplot(3,3,7); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0,0.7,0.7]); +plot(errors(:,1),radtodeg(errors(:,8)),'LineWidth',1.5); +xlabel('Time, s'); +title('Attitude error about North, deg'); +set(gca,'OuterPosition',[0.01,0,0.32,0.35]); +subplot(3,3,8); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.7,0,0.7]); +plot(errors(:,1),radtodeg(errors(:,9)),'LineWidth',1.5); +xlabel('Time, s'); +title('Attitude error about East, deg'); +set(gca,'OuterPosition',[0.34,0,0.32,0.35]); +subplot(3,3,9); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.7,0.7,0]); +plot(errors(:,1),radtodeg(errors(:,10)),'LineWidth',1.5); +xlabel('Time, s'); +title('Heading error, deg'); +set(gca,'OuterPosition',[0.67,0,0.32,0.35]); + +% Ends \ No newline at end of file diff --git a/Plot_profile.m b/Plot_profile.m new file mode 100644 index 0000000..e6ced96 --- /dev/null +++ b/Plot_profile.m @@ -0,0 +1,94 @@ +function Plot_profile(profile) +%Plots a motion profile +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 3/4/2012 by Paul Groves +% +% Input: +% profile Array of motion profile data to plot +% Format is +% Column 1: time (sec) +% Column 2: latitude (deg) +% Column 3: longitude (deg) +% Column 4: height (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll angle of body w.r.t NED (deg) +% Column 9: pitch angle of body w.r.t NED (deg) +% Column 10: yaw angle of body w.r.t NED (deg) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins +fig = figure; +set(fig,'units','normalized'); +set(fig,'OuterPosition',[0.05,0.4,0.45,0.6]); + +[R_N,R_E] = Radii_of_curvature(profile(1,2)); +subplot(3,3,1); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.9,0.45,0]); +plot(profile(:,1),((profile(:,2) - profile(1,2)) * (R_N + profile(1,4))),... + 'LineWidth',1.5); +title('North displacement, m'); +set(gca,'OuterPosition',[0.01,0.68,0.32,0.31]); +subplot(3,3,2); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0,0.9,0.45]); +plot(profile(:,1),((profile(:,3) - profile(1,3)) * (R_N + profile(1,4)) *... + cos(profile(1,2))),'LineWidth',1.5); +title('East displacement, m'); +set(gca,'OuterPosition',[0.34,0.68,0.32,0.31]); +subplot(3,3,3); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.45,0,0.9]); +plot(profile(:,1),(profile(1,4) - profile(:,4)),'LineWidth',1.5); +title('Down displacement, m'); +set(gca,'OuterPosition',[0.67,0.68,0.32,0.31]); + +subplot(3,3,4); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.9,0,0.45]); +plot(profile(:,1),profile(:,5),'LineWidth',1.5); +title('North velocity, m/s'); +set(gca,'OuterPosition',[0.01,0.36,0.32,0.31]); +subplot(3,3,5); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.45,0.9,0]); +plot(profile(:,1),profile(:,6),'LineWidth',1.5); +title('East velocity, m/s'); +set(gca,'OuterPosition',[0.34,0.36,0.32,0.31]); +subplot(3,3,6); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0,0.45,0.9]); +plot(profile(:,1),profile(:,7),'LineWidth',1.5); +title('Down velocity, m/s'); +set(gca,'OuterPosition',[0.67,0.36,0.32,0.31]); + +subplot(3,3,7); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0,0.7,0.7]); +plot(profile(:,1),radtodeg(profile(:,8)),'LineWidth',1.5); +xlabel('Time, s'); +title('Bank, deg'); +set(gca,'OuterPosition',[0.01,0,0.32,0.35]); +subplot(3,3,8); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.7,0,0.7]); +plot(profile(:,1),radtodeg(profile(:,9)),'LineWidth',1.5); +xlabel('Time, s'); +title('Elevation, deg'); +set(gca,'OuterPosition',[0.34,0,0.32,0.35]); +subplot(3,3,9); +set(gca,'NextPlot','replacechildren'); +set(gca,'ColorOrder',[0.7,0.7,0]); +plot(profile(:,1),radtodeg(profile(:,10)),'LineWidth',1.5); +xlabel('Time, s'); +title('Heading, deg'); +set(gca,'OuterPosition',[0.67,0,0.32,0.35]); + +% Ends \ No newline at end of file diff --git a/Profile_0.csv b/Profile_0.csv new file mode 100644 index 0000000..5aad976 --- /dev/null +++ b/Profile_0.csv @@ -0,0 +1,6001 @@ +0,51,0,10,0,0,0,0,0,0 +0.01,51,0,10,0,0,0,0,0,0 +0.02,51,0,10,0,0,0,0,0,0 +0.03,51,0,10,0,0,0,0,0,0 +0.04,51,0,10,0,0,0,0,0,0 +0.05,51,0,10,0,0,0,0,0,0 +0.06,51,0,10,0,0,0,0,0,0 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b/Radii_of_curvature.m @@ -0,0 +1,33 @@ +function [R_N,R_E]= Radii_of_curvature(L) +%Radii_of_curvature - Calculates the meridian and transverse radii of +%curvature +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 31/3/2012 by Paul Groves +% +% Inputs: +% L geodetic latitude (rad) +% +% Outputs: +% R_N meridian radius of curvature (m) +% R_E transverse radius of curvature (m) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Parameters +R_0 = 6378137; %WGS84 Equatorial radius in meters +e = 0.0818191908425; %WGS84 eccentricity + +% Calculate meridian radius of curvature using (2.105) +temp = 1 - (e * sin(L))^2; +R_N = R_0 * (1 - e^2) / temp^1.5; + +% Calculate transverse radius of curvature using (2.105) +R_E = R_0 / sqrt(temp); + +% Ends \ No newline at end of file diff --git a/Read_profile.m b/Read_profile.m new file mode 100644 index 0000000..db1d9fa --- /dev/null +++ b/Read_profile.m @@ -0,0 +1,53 @@ +function [in_profile,no_epochs,ok]= Read_profile(filename) +%Read_profile - inputs a motion profile in the following .csv format +% Column 1: time (sec) +% Column 2: latitude (deg)纬度 +% Column 3: longitude (deg)经度 +% Column 4: height (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll angle of body w.r.t NED (deg)横滚角 +% Column 9: pitch angle of body w.r.t NED (deg)俯仰角 +% Column 10: yaw angle of body w.r.t NED (deg)航偏角 +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 31/3/2012 by Paul Groves +% +% Inputs: +% filename Name of file to write +% +% Outputs: +% in_profile Array of data from the file +% no_epochs Number of epochs of data in the file +% ok Indicates file has the expected number of columns +% 表明文件的列数和预期的一致 + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Parameters +deg_to_rad = 0.01745329252; + +% Read in the profile in .csv format +in_profile = csvread(filename); + +% Determine size of file +[no_epochs,no_columns] = size(in_profile); + +% Check number of columns is correct (otherwise return)检验列数是否正确 +if no_columns~=10 + disp('Input file has the wrong number of columns') + ok = false; +else + ok = true; + % Convert degrees to radians 把角度转换为弧度 + in_profile(:,2:3) = deg_to_rad * in_profile(:,2:3); + in_profile(:,8:10) = deg_to_rad * in_profile(:,8:10); +end %if + +% Ends \ No newline at end of file diff --git a/Satellite_positions_and_velocities.m b/Satellite_positions_and_velocities.m new file mode 100644 index 0000000..99019f7 --- /dev/null +++ b/Satellite_positions_and_velocities.m @@ -0,0 +1,75 @@ +function [sat_r_es_e,sat_v_es_e] = Satellite_positions_and_velocities(time,... + GNSS_config) +%Satellite_positions_and_velocities - returns ECEF Cartesian positions and +%ECEF velocities of all satellites in the constellation. Simple circular +%orbits with regularly distributed satellites are modeled. +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 11/4/2012 by Paul Groves +% +% Inputs: +% time Current simulation time(s) +% GNSS_config +% .no_sat Number of satellites in constellation +% .r_os Orbital radius of satellites (m) +% .inclination Inclination angle of satellites (deg) +% .const_delta_lambda Longitude offset of constellation (deg) +% .const_delta_t Timing offset of constellation (s) +% Outputs: +% sat_r_es_e (no_sat x 3) ECEF satellite position +% sat_v_es_e (no_sat x 3) ECEF satellite velocity +% + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants (sone of these could be changed to inputs at a later date) +mu = 3.986004418E14; %WGS84 Earth gravitational constant (m^3 s^-2) +omega_ie = 7.292115E-5; % Earth rotation rate in rad/s + +% Begins + +% Convert inclination angle to degrees +inclination = degtorad(GNSS_config.inclination); + +% Determine orbital angular rate using (8.8) +omega_is = sqrt(mu / GNSS_config.r_os^3); + +% Determine constellation time +const_time = time + GNSS_config.const_delta_t; + +% Loop satellites +for j = 1:GNSS_config.no_sat + + % (Corrected) argument of latitude + u_os_o = 2*pi*(j-1)/GNSS_config.no_sat + omega_is*const_time; + + % Satellite position in the orbital frame from (8.14) + r_os_o = GNSS_config.r_os*[cos(u_os_o);sin(u_os_o);0]; + + % Longitude of the ascending node from (8.16) + Omega = (pi*mod(j,6)/3 + degtorad(GNSS_config.const_delta_lambda)) -... + omega_ie*const_time; + + % ECEF Satellite Position from (8.19) + sat_r_es_e(j,1:3) = [r_os_o(1)*cos(Omega) - r_os_o(2)*... + cos(inclination)*sin(Omega);... + r_os_o(1)*sin(Omega) + r_os_o(2)*cos(inclination)*cos(Omega);... + r_os_o(2)*sin(inclination)]'; + + % Satellite velocity in the orbital frame from (8.25), noting that with + % a circular orbit r_os_o is constant and the time derivative of u_os_o + % is omega_is. + v_os_o = GNSS_config.r_os*omega_is*[-sin(u_os_o);cos(u_os_o);0]; + + % ECEF Satellite velocity from (8.26) + sat_v_es_e(j,1:3) = [v_os_o(1)*cos(Omega) - v_os_o(2)*... + cos(inclination)*sin(Omega) + omega_ie*sat_r_es_e(j,2);... + (v_os_o(1)*sin(Omega) + v_os_o(2)*cos(inclination)*cos(Omega) -... + omega_ie*sat_r_es_e(j,1)); v_os_o(2)*sin(inclination)]'; + +end % for j + +% Ends \ No newline at end of file diff --git a/Skew_symmetric.m b/Skew_symmetric.m new file mode 100644 index 0000000..81e2c3f --- /dev/null +++ b/Skew_symmetric.m @@ -0,0 +1,23 @@ +function A = Skew_symmetric(a) +%Skew_symmetric - Calculates skew-symmetric matrix +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 1/4/2012 by Paul Groves +% +% Inputs: +% a 3-element vector +% Outputs: +% A 3x3matrix + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +A = [ 0, -a(3), a(2);... + a(3), 0, -a(1);... + -a(2), a(1), 0]; + +% Ends \ No newline at end of file diff --git a/Smooth_profile_velocity.m b/Smooth_profile_velocity.m new file mode 100644 index 0000000..22398fc --- /dev/null +++ b/Smooth_profile_velocity.m @@ -0,0 +1,70 @@ +function Smooth_profile_velocity(in_filename,out_filename) +%Smooth_profile_velocity - Adjusts the velocity in a motion profile file to +% remove jitter resulting from numerical rounding in the position input to +% Adjust_profile_velocity +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 2/4/2012 by Paul Groves +% +% Inputs +% in_filename Name of inpit file, e.g. 'In_profile.csv' +% out_filename Name of inpit file, e.g. 'Out_profile.csv' + +% Begins + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Parameters +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; + + +% Input truth motion profile from .csv format file +[in_profile,no_epochs,ok] = Read_profile(in_filename); + +% End script if there is a problem with the file +if ~ok + return; +end %if + +% First epoch +out_profile(1,:) = in_profile(1,:); + +% Main loop +for epoch = 2:(no_epochs-1) + + % Input data from profile + time = in_profile(epoch,1); + L_b = in_profile(epoch,2); + lambda_b = in_profile(epoch,3); + h_b = in_profile(epoch,4); + v_eb_n_current = in_profile(epoch,5:7)'; + eul_nb = in_profile(epoch,8:10)'; + v_eb_n_prev = in_profile(epoch - 1,5:7)'; + v_eb_n_next = in_profile(epoch + 1,5:7)'; + + % Smooth velocity + v_eb_n = 0.5 * v_eb_n_current + 0.25 * v_eb_n_prev + 0.25 * v_eb_n_next; + + % Generate output profile record + out_profile(epoch,1) = time; + out_profile(epoch,2) = L_b; + out_profile(epoch,3) = lambda_b; + out_profile(epoch,4) = h_b; + out_profile(epoch,5:7) = v_eb_n'; + out_profile(epoch,8:10) = eul_nb'; + + +end %epoch + +% Last epoch +out_profile(no_epochs,:) = in_profile(no_epochs,:); + + +% Write output profile +Write_profile(out_filename,out_profile); + +% Ends \ No newline at end of file diff --git a/TC_KF_Epoch.m b/TC_KF_Epoch.m new file mode 100644 index 0000000..ca72903 --- /dev/null +++ b/TC_KF_Epoch.m @@ -0,0 +1,184 @@ +function [est_C_b_e_new,est_v_eb_e_new,est_r_eb_e_new,est_IMU_bias_new,... + est_clock_new,P_matrix_new] = TC_KF_Epoch(GNSS_measurements,... + no_meas,tor_s,est_C_b_e_old,est_v_eb_e_old,est_r_eb_e_old,... + est_IMU_bias_old,est_clock_old,P_matrix_old,meas_f_ib_b,... + est_L_b_old,TC_KF_config) +%TC_KF_Epoch - Implements one cycle of the tightly coupled INS/GNSS +% extended Kalman filter plus closed-loop correction of all inertial states +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 12/4/2012 by Paul Groves +% +% Inputs: +% GNSS_measurements GNSS measurement data: +% Column 1 Pseudo-range measurements (m) +% Column 2 Pseudo-range rate measurements (m/s) +% Columns 3-5 Satellite ECEF position (m) +% Columns 6-8 Satellite ECEF velocity (m/s) +% no_meas Number of satellites for which measurements are +% supplied +% tor_s propagation interval (s) +% est_C_b_e_old prior estimated body to ECEF coordinate +% transformation matrix +% est_v_eb_e_old prior estimated ECEF user velocity (m/s) +% est_r_eb_e_old prior estimated ECEF user position (m) +% est_IMU_bias_old prior estimated IMU biases (body axes) +% est_clock_old prior Kalman filter state estimates +% P_matrix_old previous Kalman filter error covariance matrix +% meas_f_ib_b measured specific force +% est_L_b_old previous latitude solution +% TC_KF_config +% .gyro_noise_PSD Gyro noise PSD (rad^2/s) +% .accel_noise_PSD Accelerometer noise PSD (m^2 s^-3) +% .accel_bias_PSD Accelerometer bias random walk PSD (m^2 s^-5) +% .gyro_bias_PSD Gyro bias random walk PSD (rad^2 s^-3) +% .clock_freq_PSD Receiver clock frequency-drift PSD (m^2/s^3) +% .clock_phase_PSD Receiver clock phase-drift PSD (m^2/s) +% .pseudo_range_SD Pseudo-range measurement noise SD (m) +% .range_rate_SD Pseudo-range rate measurement noise SD (m/s) +% +% Outputs: +% est_C_b_e_new updated estimated body to ECEF coordinate +% transformation matrix +% est_v_eb_e_new updated estimated ECEF user velocity (m/s) +% est_r_eb_e_new updated estimated ECEF user position (m) +% est_IMU_bias_new updated estimated IMU biases +% Rows 1-3 estimated accelerometer biases (m/s^2) +% Rows 4-6 estimated gyro biases (rad/s) +% est_clock_new updated Kalman filter state estimates +% Row 1 estimated receiver clock offset (m) +% Row 2 estimated receiver clock drift (m/s) +% P_matrix_new updated Kalman filter error covariance matrix + + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Constants (sone of these could be changed to inputs at a later date) +c = 299792458; % Speed of light in m/s +omega_ie = 7.292115E-5; % Earth rotation rate in rad/s +R_0 = 6378137; %WGS84 Equatorial radius in meters +e = 0.0818191908425; %WGS84 eccentricity + +% Begins + +% Skew symmetric matrix of Earth rate +Omega_ie = Skew_symmetric([0,0,omega_ie]); + +% SYSTEM PROPAGATION PHASE + +% 1. Determine transition matrix using (14.50) (first-order approx) +Phi_matrix = eye(17); +Phi_matrix(1:3,1:3) = Phi_matrix(1:3,1:3) - Omega_ie * tor_s; +Phi_matrix(1:3,13:15) = est_C_b_e_old * tor_s; +Phi_matrix(4:6,1:3) = -tor_s * Skew_symmetric(est_C_b_e_old * meas_f_ib_b); +Phi_matrix(4:6,4:6) = Phi_matrix(4:6,4:6) - 2 * Omega_ie * tor_s; +geocentric_radius = R_0 / sqrt(1 - (e * sin(est_L_b_old))^2) *... + sqrt(cos(est_L_b_old)^2 + (1 - e^2)^2 * sin(est_L_b_old)^2); % from (2.137) +Phi_matrix(4:6,7:9) = -tor_s * 2 * Gravity_ECEF(est_r_eb_e_old) /... + geocentric_radius * est_r_eb_e_old' / sqrt (est_r_eb_e_old' *... + est_r_eb_e_old); +Phi_matrix(4:6,10:12) = est_C_b_e_old * tor_s; +Phi_matrix(7:9,4:6) = eye(3) * tor_s; +Phi_matrix(16,17) = tor_s; + +% 2. Determine approximate system noise covariance matrix using (14.82) +Q_prime_matrix = zeros(17); +Q_prime_matrix(1:3,1:3) = eye(3) * TC_KF_config.gyro_noise_PSD * tor_s; +Q_prime_matrix(4:6,4:6) = eye(3) * TC_KF_config.accel_noise_PSD * tor_s; +Q_prime_matrix(10:12,10:12) = eye(3) * TC_KF_config.accel_bias_PSD * tor_s; +Q_prime_matrix(13:15,13:15) = eye(3) * TC_KF_config.gyro_bias_PSD * tor_s; +Q_prime_matrix(16,16) = TC_KF_config.clock_phase_PSD * tor_s; +Q_prime_matrix(17,17) = TC_KF_config.clock_freq_PSD * tor_s; + +% 3. Propagate state estimates using (3.14) noting that only the clock +% states are non-zero due to closed-loop correction. +x_est_propagated(1:15,1) = 0; +x_est_propagated(16,1) = est_clock_old(1) + est_clock_old(2) * tor_s; +x_est_propagated(17,1) = est_clock_old(2); + +% 4. Propagate state estimation error covariance matrix using (3.46) +P_matrix_propagated = Phi_matrix * (P_matrix_old + 0.5 * Q_prime_matrix) *... + Phi_matrix' + 0.5 * Q_prime_matrix; + +% MEASUREMENT UPDATE PHASE + +u_as_e_T = zeros(no_meas,3); +pred_meas = zeros(no_meas,2); + +% Loop measurements +for j = 1:no_meas + + % Predict approx range + delta_r = GNSS_measurements(j,3:5)' - est_r_eb_e_old; + approx_range = sqrt(delta_r' * delta_r); + + % Calculate frame rotation during signal transit time using (8.36) + C_e_I = [1, omega_ie * approx_range / c, 0;... + -omega_ie * approx_range / c, 1, 0;... + 0, 0, 1]; + + % Predict pseudo-range using (9.165) + delta_r = C_e_I * GNSS_measurements(j,3:5)' - est_r_eb_e_old; + range = sqrt(delta_r' * delta_r); + pred_meas(j,1) = range + x_est_propagated(16); + + % Predict line of sight + u_as_e_T(j,1:3) = delta_r' / range; + + % Predict pseudo-range rate using (9.165) + range_rate = u_as_e_T(j,1:3) * (C_e_I * (GNSS_measurements(j,6:8)' +... + Omega_ie * GNSS_measurements(j,3:5)') - (est_v_eb_e_old +... + Omega_ie * est_r_eb_e_old)); + pred_meas(j,2) = range_rate + x_est_propagated(17); + +end % for j + +% 5. Set-up measurement matrix using (14.126) +H_matrix = zeros((2 * no_meas),17); +H_matrix(1:no_meas,7:9) = u_as_e_T(1:no_meas,1:3); +H_matrix(1:no_meas,16) = ones(no_meas,1); +H_matrix((no_meas + 1):(2 * no_meas),4:6) = u_as_e_T(1:no_meas,1:3); +H_matrix((no_meas + 1):(2 * no_meas),17) = ones(no_meas,1); + +% 6. Set-up measurement noise covariance matrix assuming all measurements +% are independent and have equal variance for a given measurement type. +R_matrix(1:no_meas,1:no_meas) = eye(no_meas) *... + TC_KF_config.pseudo_range_SD^2; +R_matrix(1:no_meas,(no_meas + 1):(2 * no_meas)) =... + zeros(no_meas); +R_matrix((no_meas + 1):(2 * no_meas),1:no_meas) =... + zeros(no_meas); +R_matrix((no_meas + 1):(2 * no_meas),(no_meas + 1):(2 * no_meas)) =... + eye(no_meas) * TC_KF_config.range_rate_SD^2; + +% 7. Calculate Kalman gain using (3.21) +K_matrix = P_matrix_propagated * H_matrix' * inv(H_matrix *... + P_matrix_propagated * H_matrix' + R_matrix); + +% 8. Formulate measurement innovations using (14.119) +delta_z(1:no_meas,1) = GNSS_measurements(1:no_meas,1) -... + pred_meas(1:no_meas,1); +delta_z((no_meas + 1):(2 * no_meas),1) = GNSS_measurements(1:no_meas,2) -... + pred_meas(1:no_meas,2); + +% 9. Update state estimates using (3.24) +x_est_new = x_est_propagated + K_matrix * delta_z; + +% 10. Update state estimation error covariance matrix using (3.25) +P_matrix_new = (eye(17) - K_matrix * H_matrix) * P_matrix_propagated; + +% CLOSED-LOOP CORRECTION + +% Correct attitude, velocity, and position using (14.7-9) +est_C_b_e_new = (eye(3) - Skew_symmetric(x_est_new(1:3))) * est_C_b_e_old; +est_v_eb_e_new = est_v_eb_e_old - x_est_new(4:6); +est_r_eb_e_new = est_r_eb_e_old - x_est_new(7:9); + +% Update IMU bias and GNSS receiver clock estimates +est_IMU_bias_new = est_IMU_bias_old + x_est_new(10:15); +est_clock_new = x_est_new(16:17)'; + +% Ends \ No newline at end of file diff --git a/Tightly_coupled_INS_GNSS.m b/Tightly_coupled_INS_GNSS.m new file mode 100644 index 0000000..160a733 --- /dev/null +++ b/Tightly_coupled_INS_GNSS.m @@ -0,0 +1,336 @@ +function [out_profile,out_errors,out_IMU_bias_est,out_clock,out_KF_SD] =... + Tightly_coupled_INS_GNSS(in_profile,no_epochs,initialization_errors,... + IMU_errors,GNSS_config,TC_KF_config) +%Tightly_coupled_INS_GNSS - Simulates inertial navigation using ECEF +% navigation equations and kinematic model, GNSS and tightly coupled +% INS/GNSS integration. +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 12/4/2012 by Paul Groves +% +% Inputs: +% in_profile True motion profile array +% no_epochs Number of epochs of profile data +% initialization_errors +% .delta_r_eb_n position error resolved along NED (m) +% .delta_v_eb_n velocity error resolved along NED (m/s) +% .delta_eul_nb_n attitude error as NED Euler angles (rad) +% IMU_errors +% .delta_r_eb_n position error resolved along NED (m) +% .b_a Accelerometer biases (m/s^2) +% .b_g Gyro biases (rad/s) +% .M_a Accelerometer scale factor and cross coupling errors +% .M_g Gyro scale factor and cross coupling errors +% .G_g Gyro g-dependent biases (rad-sec/m) +% .accel_noise_root_PSD Accelerometer noise root PSD (m s^-1.5) +% .gyro_noise_root_PSD Gyro noise root PSD (rad s^-0.5) +% .accel_quant_level Accelerometer quantization level (m/s^2) +% .gyro_quant_level Gyro quantization level (rad/s) +% GNSS_config +% .epoch_interval Interval between GNSS epochs (s) +% .init_est_r_ea_e Initial estimated position (m; ECEF) +% .no_sat Number of satellites in constellation +% .r_os Orbital radius of satellites (m) +% .inclination Inclination angle of satellites (deg) +% .const_delta_lambda Longitude offset of constellation (deg) +% .const_delta_t Timing offset of constellation (s) +% .mask_angle Mask angle (deg) +% .SIS_err_SD Signal in space error SD (m) +% .zenith_iono_err_SD Zenith ionosphere error SD (m) +% .zenith_trop_err_SD Zenith troposphere error SD (m) +% .code_track_err_SD Code tracking error SD (m) +% .rate_track_err_SD Range rate tracking error SD (m/s) +% .rx_clock_offset Receiver clock offset at time=0 (m) +% .rx_clock_drift Receiver clock drift at time=0 (m/s) +% TC_KF_config +% .init_att_unc Initial attitude uncertainty per axis (rad) +% .init_vel_unc Initial velocity uncertainty per axis (m/s) +% .init_pos_unc Initial position uncertainty per axis (m) +% .init_b_a_unc Initial accel. bias uncertainty (m/s^2) +% .init_b_g_unc Initial gyro. bias uncertainty (rad/s) +% .init_clock_offset_unc Initial clock offset uncertainty per axis (m) +% .init_clock_drift_unc Initial clock drift uncertainty per axis (m/s) +% .gyro_noise_PSD Gyro noise PSD (rad^2/s) +% .accel_noise_PSD Accelerometer noise PSD (m^2 s^-3) +% .accel_bias_PSD Accelerometer bias random walk PSD (m^2 s^-5) +% .gyro_bias_PSD Gyro bias random walk PSD (rad^2 s^-3) +% .clock_freq_PSD Receiver clock frequency-drift PSD (m^2/s^3) +% .clock_phase_PSD Receiver clock phase-drift PSD (m^2/s) +% .pseudo_range_SD Pseudo-range measurement noise SD (m) +% .range_rate_SD Pseudo-range rate measurement noise SD (m/s) +% +% Outputs: +% out_profile Navigation solution as a motion profile array +% out_errors Navigation solution error array +% out_IMU_bias_est Kalman filter IMU bias estimate array +% out_clock GNSS Receiver clock estimate array +% out_KF_SD Output Kalman filter state uncertainties +% +% Format of motion profiles: +% Column 1: time (sec) +% Column 2: latitude (rad) +% Column 3: longitude (rad) +% Column 4: height (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll angle of body w.r.t NED (rad) +% Column 9: pitch angle of body w.r.t NED (rad) +% Column 10: yaw angle of body w.r.t NED (rad) +% +% Format of error array: +% Column 1: time (sec) +% Column 2: north position error (m) +% Column 3: east position error (m) +% Column 4: down position error (m) +% Column 5: north velocity error (m/s) +% Column 6: east velocity error (m/s) +% Column 7: down velocity (error m/s) +% Column 8: attitude error about north (rad) +% Column 9: attitude error about east (rad) +% Column 10: attitude error about down = heading error (rad) +% +% Format of output IMU biases array: +% Column 1: time (sec) +% Column 2: estimated X accelerometer bias (m/s^2) +% Column 3: estimated Y accelerometer bias (m/s^2) +% Column 4: estimated Z accelerometer bias (m/s^2) +% Column 5: estimated X gyro bias (rad/s) +% Column 6: estimated Y gyro bias (rad/s) +% Column 7: estimated Z gyro bias (rad/s) +% +% Format of receiver clock array: +% Column 1: time (sec) +% Column 2: estimated clock offset (m) +% Column 3: estimated clock drift (m/s) +% +% Format of KF state uncertainties array: +% Column 1: time (sec) +% Column 2: X attitude error uncertainty (rad) +% Column 3: Y attitude error uncertainty (rad) +% Column 4: Z attitude error uncertainty (rad) +% Column 5: X velocity error uncertainty (m/s) +% Column 6: Y velocity error uncertainty (m/s) +% Column 7: Z velocity error uncertainty (m/s) +% Column 8: X position error uncertainty (m) +% Column 9: Y position error uncertainty (m) +% Column 10: Z position error uncertainty (m) +% Column 11: X accelerometer bias uncertainty (m/s^2) +% Column 12: Y accelerometer bias uncertainty (m/s^2) +% Column 13: Z accelerometer bias uncertainty (m/s^2) +% Column 14: X gyro bias uncertainty (rad/s) +% Column 15: Y gyro bias uncertainty (rad/s) +% Column 16: Z gyro bias uncertainty (rad/s) +% Column 17: clock offset uncertainty (m) +% Column 18: clock drift uncertainty (m/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Initialize true navigation solution +old_time = in_profile(1,1); +true_L_b = in_profile(1,2); +true_lambda_b = in_profile(1,3); +true_h_b = in_profile(1,4); +true_v_eb_n = in_profile(1,5:7)'; +true_eul_nb = in_profile(1,8:10)'; +true_C_b_n = Euler_to_CTM(true_eul_nb)'; +[old_true_r_eb_e,old_true_v_eb_e,old_true_C_b_e] =... + NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + +% Determine satellite positions and velocities +[sat_r_es_e,sat_v_es_e] = Satellite_positions_and_velocities(old_time,... + GNSS_config); + +% Initialize the GNSS biases. Note that these are assumed constant throughout +% the simulation and are based on the initial elevation angles. Therefore, +% this function is unsuited to simulations longer than about 30 min. +GNSS_biases = Initialize_GNSS_biases(sat_r_es_e,old_true_r_eb_e,true_L_b,... + true_lambda_b,GNSS_config); + +% Generate GNSS measurements +[GNSS_measurements,no_GNSS_meas] = Generate_GNSS_measurements(old_time,... + sat_r_es_e,sat_v_es_e,old_true_r_eb_e,true_L_b,true_lambda_b,... + old_true_v_eb_e,GNSS_biases,GNSS_config); + +% Determine Least-squares GNSS position solution +[old_est_r_eb_e,old_est_v_eb_e,est_clock] = GNSS_LS_position_velocity(... + GNSS_measurements,no_GNSS_meas,GNSS_config.init_est_r_ea_e,[0;0;0]); +[old_est_L_b,old_est_lambda_b,old_est_h_b,old_est_v_eb_n] =... + pv_ECEF_to_NED(old_est_r_eb_e,old_est_v_eb_e); +est_L_b = old_est_L_b; + +% Initialize estimated attitude solution +old_est_C_b_n = Initialize_NED_attitude(true_C_b_n,initialization_errors); +[temp1,temp2,old_est_C_b_e] = NED_to_ECEF(old_est_L_b,... + old_est_lambda_b,old_est_h_b,old_est_v_eb_n,old_est_C_b_n); + +% Initialize output profile record and errors record +out_profile = zeros(no_epochs,10); +out_errors = zeros(no_epochs,10); + +% Generate output profile record +out_profile(1,1) = old_time; +out_profile(1,2) = old_est_L_b; +out_profile(1,3) = old_est_lambda_b; +out_profile(1,4) = old_est_h_b; +out_profile(1,5:7) = old_est_v_eb_n'; +out_profile(1,8:10) = CTM_to_Euler(old_est_C_b_n')'; + +% Determine errors and generate output record +[delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + old_est_L_b,old_est_lambda_b,old_est_h_b,old_est_v_eb_n,old_est_C_b_n,... + true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); +out_errors(1,1) = old_time; +out_errors(1,2:4) = delta_r_eb_n'; +out_errors(1,5:7) = delta_v_eb_n'; +out_errors(1,8:10) = delta_eul_nb_n'; + +% Initialize Kalman filter P matrix and IMU bias states +P_matrix = Initialize_TC_P_matrix(TC_KF_config); +est_IMU_bias = zeros(6,1); + +% Initialize IMU quantization residuals +quant_residuals = [0;0;0;0;0;0]; + +% Generate IMU bias and clock output records +out_IMU_bias_est(1,1) = old_time; +out_IMU_bias_est(1,2:7) = est_IMU_bias'; +out_clock(1,1) = old_time; +out_clock(1,2:3) = est_clock; + +% Generate KF uncertainty record +out_KF_SD(1,1) = old_time; +for i =1:17 + out_KF_SD(1,i+1) = sqrt(P_matrix(i,i)); +end % for i + +% Initialize GNSS model timing +time_last_GNSS = old_time; +GNSS_epoch = 1; + +% Progress bar +dots = '....................'; +bars = '||||||||||||||||||||'; +rewind = '\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b'; +fprintf(strcat('Processing: ',dots)); +progress_mark = 0; +progress_epoch = 0; + +% Main loop +for epoch = 2:no_epochs + + % Update progress bar + if (epoch - progress_epoch) > (no_epochs/20) + progress_mark = progress_mark + 1; + progress_epoch = epoch; + fprintf(strcat(rewind,bars(1:progress_mark),... + dots(1:(20 - progress_mark)))); + end % if epoch + + % Input data from motion profile + time = in_profile(epoch,1); + true_L_b = in_profile(epoch,2); + true_lambda_b = in_profile(epoch,3); + true_h_b = in_profile(epoch,4); + true_v_eb_n = in_profile(epoch,5:7)'; + true_eul_nb = in_profile(epoch,8:10)'; + true_C_b_n = Euler_to_CTM(true_eul_nb)'; + [true_r_eb_e,true_v_eb_e,true_C_b_e] =... + NED_to_ECEF(true_L_b,true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + + % Time interval + tor_i = time - old_time; + + % Calculate specific force and angular rate + [true_f_ib_b,true_omega_ib_b] = Kinematics_ECEF(tor_i,true_C_b_e,... + old_true_C_b_e,true_v_eb_e,old_true_v_eb_e,old_true_r_eb_e); + + % Simulate IMU errors + [meas_f_ib_b,meas_omega_ib_b,quant_residuals] = IMU_model(tor_i,... + true_f_ib_b,true_omega_ib_b,IMU_errors,quant_residuals); + + % Correct IMU errors + meas_f_ib_b = meas_f_ib_b - est_IMU_bias(1:3); + meas_omega_ib_b = meas_omega_ib_b - est_IMU_bias(4:6); + + % Update estimated navigation solution + [est_r_eb_e,est_v_eb_e,est_C_b_e] = Nav_equations_ECEF(tor_i,... + old_est_r_eb_e,old_est_v_eb_e,old_est_C_b_e,meas_f_ib_b,... + meas_omega_ib_b); + + % Determine whether to update GNSS simulation and run Kalman filter + if (time - time_last_GNSS) >= GNSS_config.epoch_interval + GNSS_epoch = GNSS_epoch + 1; + tor_s = time - time_last_GNSS; % KF time interval + time_last_GNSS = time; + + % Determine satellite positions and velocities + [sat_r_es_e,sat_v_es_e] = Satellite_positions_and_velocities(time,... + GNSS_config); + + % Generate GNSS measurements + [GNSS_measurements,no_GNSS_meas] = Generate_GNSS_measurements(... + time,sat_r_es_e,sat_v_es_e,true_r_eb_e,true_L_b,true_lambda_b,... + true_v_eb_e,GNSS_biases,GNSS_config); + + % Run Integration Kalman filter + [est_C_b_e,est_v_eb_e,est_r_eb_e,est_IMU_bias,est_clock,P_matrix] =... + TC_KF_Epoch(GNSS_measurements,no_GNSS_meas,tor_s,est_C_b_e,... + est_v_eb_e,est_r_eb_e,est_IMU_bias,est_clock,P_matrix,... + meas_f_ib_b,est_L_b,TC_KF_config); + + % Generate IMU bias and clock output records + out_IMU_bias_est(GNSS_epoch,1) = time; + out_IMU_bias_est(GNSS_epoch,2:7) = est_IMU_bias'; + out_clock(GNSS_epoch,1) = time; + out_clock(GNSS_epoch,2:3) = est_clock; + + % Generate KF uncertainty output record + out_KF_SD(GNSS_epoch,1) = time; + for i =1:17 + out_KF_SD(GNSS_epoch,i+1) = sqrt(P_matrix(i,i)); + end % for i + + end % if time + + % Convert navigation solution to NED + [est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n] =... + ECEF_to_NED(est_r_eb_e,est_v_eb_e,est_C_b_e); + + % Generate output profile record + out_profile(epoch,1) = time; + out_profile(epoch,2) = est_L_b; + out_profile(epoch,3) = est_lambda_b; + out_profile(epoch,4) = est_h_b; + out_profile(epoch,5:7) = est_v_eb_n'; + out_profile(epoch,8:10) = CTM_to_Euler(est_C_b_n')'; + + % Determine errors and generate output record + [delta_r_eb_n,delta_v_eb_n,delta_eul_nb_n] = Calculate_errors_NED(... + est_L_b,est_lambda_b,est_h_b,est_v_eb_n,est_C_b_n,true_L_b,... + true_lambda_b,true_h_b,true_v_eb_n,true_C_b_n); + out_errors(epoch,1) = time; + out_errors(epoch,2:4) = delta_r_eb_n'; + out_errors(epoch,5:7) = delta_v_eb_n'; + out_errors(epoch,8:10) = delta_eul_nb_n'; + + % Reset old values + old_time = time; + old_true_r_eb_e = true_r_eb_e; + old_true_v_eb_e = true_v_eb_e; + old_true_C_b_e = true_C_b_e; + old_est_r_eb_e = est_r_eb_e; + old_est_v_eb_e = est_v_eb_e; + old_est_C_b_e = est_C_b_e; + +end %epoch + +% Complete progress bar +fprintf(strcat(rewind,bars,'\n')); + +% Ends \ No newline at end of file diff --git a/Update_curvilinear_position.m b/Update_curvilinear_position.m new file mode 100644 index 0000000..afd7955 --- /dev/null +++ b/Update_curvilinear_position.m @@ -0,0 +1,47 @@ +function [L_b,lambda_b,h_b]= Update_curvilinear_position(tor_i,old_L_b,... + old_lambda_b,old_h_b,old_v_eb_n,v_eb_n) +%Update_curvilinear_position - Updates latitude, longitude, and height by +%integrating the velocity +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 31/3/2012 by Paul Groves +% +% Inputs: +% tor_i time interval between epochs (s) +% old_L_b previous latitude (rad) +% old_lambda_b previous longitude (rad) +% old_h_b previous height (m) +% old_v_eb_n previous velocity of body w.r.t earth, resolved about +% north, east, and down (m/s) +% v_eb_n current velocity of body w.r.t earth, resolved about +% north, east, and down (m/s)% +% Outputs: +% L_b current latitude (rad) +% lambda_b current longitude (rad) +% h_b current height (m) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Calculate meridian and transverse radii of curvature +[old_R_N,old_R_E]= Radii_of_curvature(old_L_b); + +% Update height using (5.56) +h_b = old_h_b - 0.5 * tor_i * (old_v_eb_n(3) + v_eb_n(3)); + +% Update latitude using (5.56) +L_b = old_L_b + 0.5 * tor_i * (old_v_eb_n(1) / (old_R_N + old_h_b) +... + v_eb_n(1) / (old_R_N + h_b)); + +% Calculate meridian and transverse radii of curvature +[R_N,R_E]= Radii_of_curvature(L_b); + +% Update longitude using (5.56) +lambda_b = old_lambda_b + 0.5 * tor_i * (old_v_eb_n(2) / ((old_R_E +... + old_h_b) * cos(old_L_b)) + v_eb_n(2) / ((R_E + h_b) * cos(L_b))); + +% Ends \ No newline at end of file diff --git a/Velocity_from_curvilinear.m b/Velocity_from_curvilinear.m new file mode 100644 index 0000000..5cf0d79 --- /dev/null +++ b/Velocity_from_curvilinear.m @@ -0,0 +1,46 @@ +function v_eb_n = Velocity_from_curvilinear(tor_i,old_L_b,... + old_lambda_b,old_h_b,old_v_eb_n,L_b,lambda_b,h_b) +%Velocity_from_curvilinear - updates velocity by differentiating +%latitude, longitude, and height +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 31/3/2012 by Paul Groves +% +% Inputs: +% tor_i time interval between epochs (s) +% old_L_b previous latitude (rad) +% old_lambda_b previous longitude (rad) +% old_h_b previous height (m) +% old_v_eb_n previous velocity of body w.r.t earth, resolved about +% north, east, and down (m/s) +% L_b current latitude (rad) +% lambda_b current longitude (rad) +% h_b current height (m) +% Outputs: +% v_eb_n current velocity of body w.r.t earth, resolved about +% north, east, and down (m/s)% + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Calculate meridian and transverse radii of curvature +[old_R_N,old_R_E]= Radii_of_curvature(old_L_b); +[R_N,R_E]= Radii_of_curvature(L_b); + +% Differentiate latitude, longitude, and height +lat_rate = (L_b - old_L_b) / tor_i; +long_rate = (lambda_b - old_lambda_b) / tor_i; +ht_rate = (h_b - old_h_b) / tor_i; + +% Derive the current velocity using (5.56) +v_eb_n(1,1) = (old_R_N + h_b) * (2 * lat_rate - old_v_eb_n(1) / (old_R_N +... + old_h_b)); +v_eb_n(2,1) = ((R_E + h_b) * cos(L_b)) * (2 * long_rate - old_v_eb_n(2) /... + ((old_R_E + old_h_b) * cos(old_L_b))); +v_eb_n(3,1) = -2 * ht_rate - old_v_eb_n(3); + +% Ends \ No newline at end of file diff --git a/Write_errors.m b/Write_errors.m new file mode 100644 index 0000000..75f82ec --- /dev/null +++ b/Write_errors.m @@ -0,0 +1,38 @@ +function Write_errors(filename,out_errors) +%Write_errors - outputs the errors in the following .csv format +% Column 1: time (sec) +% Column 2: north position error (m) +% Column 3: east position error (m) +% Column 4: down position error (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll component of NED attitude error (deg) +% Column 9: pitch component of NED attitude error (deg) +% Column 10: yaw component of NED attitude error (deg) +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 31/3/2012 by Paul Groves +% +% Inputs: +% filename Name of file to write +% out_errors Array of data to write + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Parameters +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; + +% Convert attitude errors from radians to degrees +out_errors(:,8:10) = rad_to_deg * out_errors(:,8:10); + +% Write output profile +dlmwrite(filename,out_errors,'newline','pc','precision',12); + +% Ends \ No newline at end of file diff --git a/Write_profile.m b/Write_profile.m new file mode 100644 index 0000000..709b324 --- /dev/null +++ b/Write_profile.m @@ -0,0 +1,39 @@ +function Write_profile(filename,out_profile) +%Write_profile - outputs a motion profile in the following .csv format +% Column 1: time (sec) +% Column 2: latitude (deg) +% Column 3: longitude (deg) +% Column 4: height (m) +% Column 5: north velocity (m/s) +% Column 6: east velocity (m/s) +% Column 7: down velocity (m/s) +% Column 8: roll angle of body w.r.t NED (deg) +% Column 9: pitch angle of body w.r.t NED (deg) +% Column 10: yaw angle of body w.r.t NED (deg) +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 31/3/2012 by Paul Groves +% +% Inputs: +% filename Name of file to write +% out_profile Array of data to write + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Begins + +% Parameters +deg_to_rad = 0.01745329252; +rad_to_deg = 1/deg_to_rad; + +% Convert output profile from radians to degrees +out_profile(:,2:3) = rad_to_deg * out_profile(:,2:3); +out_profile(:,8:10) = rad_to_deg * out_profile(:,8:10); + +% Write output profile +dlmwrite(filename,out_profile,'newline','pc','precision',12); + +% Ends \ No newline at end of file diff --git a/pv_ECEF_to_NED.m b/pv_ECEF_to_NED.m new file mode 100644 index 0000000..30f8697 --- /dev/null +++ b/pv_ECEF_to_NED.m @@ -0,0 +1,80 @@ +function [L_b,lambda_b,h_b,v_eb_n] = pv_ECEF_to_NED(r_eb_e,v_eb_e) +%pv_ECEF_to_NED - Converts Cartesian to curvilinear position and velocity +%resolving axes from ECEF to NED +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 11/4/2012 by Paul Groves +% +% Inputs: +% r_eb_e Cartesian position of body frame w.r.t. ECEF frame, resolved +% along ECEF-frame axes (m) +% v_eb_e velocity of body frame w.r.t. ECEF frame, resolved along +% ECEF-frame axes (m/s) +% +% Outputs: +% L_b latitude (rad) +% lambda_b longitude (rad) +% h_b height (m) +% v_eb_n velocity of body frame w.r.t. ECEF frame, resolved along +% north, east, and down (m/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Parameters +R_0 = 6378137; %WGS84 Equatorial radius in meters +e = 0.0818191908425; %WGS84 eccentricity + +% Begins + +% Convert position using Borkowski closed-form exact solution +% From (2.113) +lambda_b = atan2(r_eb_e(2),r_eb_e(1)); + +% From (C.29) and (C.30) +k1 = sqrt(1 - e^2) * abs (r_eb_e(3)); +k2 = e^2 * R_0; +beta = sqrt(r_eb_e(1)^2 + r_eb_e(2)^2); +E = (k1 - k2) / beta; +F = (k1 + k2) / beta; + +% From (C.31) +P = 4/3 * (E*F + 1); + +% From (C.32) +Q = 2 * (E^2 - F^2); + +% From (C.33) +D = P^3 + Q^2; + +% From (C.34) +V = (sqrt(D) - Q)^(1/3) - (sqrt(D) + Q)^(1/3); + +% From (C.35) +G = 0.5 * (sqrt(E^2 + V) + E); + +% From (C.36) +T = sqrt(G^2 + (F - V * G) / (2 * G - E)) - G; + +% From (C.37) +L_b = sign(r_eb_e(3)) * atan((1 - T^2) / (2 * T * sqrt (1 - e^2))); + +% From (C.38) +h_b = (beta - R_0 * T) * cos(L_b) +... + (r_eb_e(3) - sign(r_eb_e(3)) * R_0 * sqrt(1 - e^2)) * sin (L_b); + +% Calculate ECEF to NED coordinate transformation matrix using (2.150) +cos_lat = cos(L_b); +sin_lat = sin(L_b); +cos_long = cos(lambda_b); +sin_long = sin(lambda_b); +C_e_n = [-sin_lat * cos_long, -sin_lat * sin_long, cos_lat;... + -sin_long, cos_long, 0;... + -cos_lat * cos_long, -cos_lat * sin_long, -sin_lat]; + +% Transform velocity using (2.73) +v_eb_n = C_e_n * v_eb_e; + +% Ends \ No newline at end of file diff --git a/pv_NED_to_ECEF.m b/pv_NED_to_ECEF.m new file mode 100644 index 0000000..6577b70 --- /dev/null +++ b/pv_NED_to_ECEF.m @@ -0,0 +1,52 @@ +function [r_eb_e,v_eb_e] = pv_NED_to_ECEF(L_b,lambda_b,h_b,v_eb_n) +%pv_NED_to_ECEF - Converts curvilinear to Cartesian position and velocity +%resolving axes from NED to ECEF +% +% Software for use with "Principles of GNSS, Inertial, and Multisensor +% Integrated Navigation Systems," Second Edition. +% +% This function created 11/4/2012 by Paul Groves +% +% Inputs: +% L_b latitude (rad) +% lambda_b longitude (rad) +% h_b height (m) +% v_eb_n velocity of body frame w.r.t. ECEF frame, resolved along +% north, east, and down (m/s) +% +% Outputs: +% r_eb_e Cartesian position of body frame w.r.t. ECEF frame, resolved +% along ECEF-frame axes (m) +% v_eb_e velocity of body frame w.r.t. ECEF frame, resolved along +% ECEF-frame axes (m/s) + +% Copyright 2012, Paul Groves +% License: BSD; see license.txt for details + +% Parameters +R_0 = 6378137; %WGS84 Equatorial radius in meters +e = 0.0818191908425; %WGS84 eccentricity + +% Begins + +% Calculate transverse radius of curvature using (2.105) +R_E = R_0 / sqrt(1 - (e * sin(L_b))^2); + +% Convert position using (2.112) +cos_lat = cos(L_b); +sin_lat = sin(L_b); +cos_long = cos(lambda_b); +sin_long = sin(lambda_b); +r_eb_e = [(R_E + h_b) * cos_lat * cos_long;... + (R_E + h_b) * cos_lat * sin_long;... + ((1 - e^2) * R_E + h_b) * sin_lat]; + +% Calculate ECEF to NED coordinate transformation matrix using (2.150) +C_e_n = [-sin_lat * cos_long, -sin_lat * sin_long, cos_lat;... + -sin_long, cos_long, 0;... + -cos_lat * cos_long, -cos_lat * sin_long, -sin_lat]; + +% Transform velocity using (2.73) +v_eb_e = C_e_n' * v_eb_n; + +% Ends \ No newline at end of file