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Example.m
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% This program generates the localization result of a source in MPR with
% TDOA measurements by the algebraic closed-form solutions (2WLS and GTRS)
%
% The figures generated from this code correspond to
% Figs. 2-3 (Accuracy_vs_Range=1), or
% Figs. 4-7 (Accuracy_vs_Range=0)
% in the reference paper.
%
% Reference: Y. Sun, K. C. Ho, and Q. Wan, "Solution and analysis of TDOA
% localization of a near or distant source in closed-form," IEEE Trans.
% Signal Process., vol. 67, no. 2, pp. 320-335, Jan. 2019.
%
% Yimao Sun, K. C. Ho 02-28-2019
%
% Copyright (C) 2019
% Computational Intelligence Signal Processing Laboratory
% University of Missouri
% Columbia, MO 65211, USA.
%
clear all;
%close all; clc;
warning off;
clor = [0, 114, 189;217, 83, 25;237, 177, 32;126, 47, 142;119, 172, 48;77, 190, 238;162, 20, 47]/256;
rng('default');
% *****************************************************************
Accuracy_vs_Range=1; % 1 for Figs. 2-3, 0 for Figs. 4-7
Case3D=1; % 1 if 3D, 0 if 2D
% *****************************************************************
% ----- simulation setting -----
% sensor position
senPos = [
0 0 0
0.4664 -0.8712 0.6294
1.2402 -0.0798 0.8116
0.4437 0.6323 -0.7460
0.5798 -0.2362 0.8268
1.0502 -0.5172 0.2647
-0.8156 1.0448 -0.8049]' * 1e3;
if (~Case3D)
senPos=senPos(1:2,:);
end;
% target direction
theta = 22.13*pi/180;
phi = 14.41*pi/180;
[N,M] = size(senPos);
if (N==2) phi=0; end;
if (Accuracy_vs_Range)
sigmaSquareDB = 0; % 10log(m^2)
range = [5,10,(20:20:460)]*1e3; % m
NumEnsembles = 2000;
else
sigmaSquareDB = -40:10:50; % 10log(m^2)
range = 15*1e3; % m
NumEnsembles = 1000;
end;
K = length(sigmaSquareDB); % number of noise levels
R = length(range); % number of ranges
if (N==3)
srcLoc=13e3*[cos(theta)*cos(phi); sin(theta)*cos(phi); sin(phi)]';
figure(100); plot3(senPos(1,:),senPos(2,:),senPos(3,:),'o','markersize',8,'linewidth',1);
hold on;xlabel('x (km)','fontsize',12);ylabel('y (km)','fontsize',12);;zlabel('z (km)','fontsize',12);
plot3(srcLoc(1), srcLoc(2), srcLoc(3), 'x','markersize',8,'linewidth',1);grid on;hold off;
title('Localization Geometry, Sensors(circle), Source(cross)');
else
srcLoc=13e3*[cos(theta); sin(theta)]';
figure(100); plot(senPos(1,:),senPos(2,:),'o','markersize',8,'linewidth',1);
hold on;xlabel('x (km)','fontsize',12);ylabel('y (km)','fontsize',12);
plot(srcLoc(1), srcLoc(2), 'x','markersize',8,'linewidth',1);grid on;hold off;
title('Localization Geometry, Sensors(circle), Source(cross)');
end;
% ----- Monte-Carlo Simulation -----
[eTh1,eTh2,eTh3,eTh4,eTh5,eTh6, ePh1,ePh2,ePh3,ePh4,ePh5,ePh6, eg1,eg2,eg3,eg4,eg5,eg6, ...
ep1,ep2,ep3,ep4,ep5,ep6, er1,er2,er3,er4,er5,er6, uTh1,uTh2,uTh3,uTh4,uTh5,uTh6, ...
uPh1,uPh2,uPh3,uPh4,uPh5,uPh6, ug1,ug2,ug3,ug4,ug5,ug6] = deal(zeros(K,NumEnsembles));
aveNse = 0;
for l=1:NumEnsembles
aveNse = aveNse + randn(M,1);
end
aveNse = aveNse/NumEnsembles/sqrt(2);
PP = aveNse(2:end) - aveNse(1);
disp('Simulation is running ...');
for ir = 1:R, % loop through ranges
disp(['Range: ',num2str(range(ir)/1000),'km, ',num2str(ir),'/',num2str(R),' ...']);
% -- Generate Data --
% source location
if (N==3)
srcLoc = range(ir) * [cos(theta)*cos(phi); sin(theta)*cos(phi); sin(phi)];
else
srcLoc = range(ir) * [cos(theta); sin(theta)];
end;
% true range
r = sqrt(sum((repmat(srcLoc,1,M)-senPos).^2,1))';
% true TDOAs
rd = r(2:end) - r(1);
for k = 1:K, % loop through noise powers
disp(['Noise power (10log(\sigma^2): ',num2str(sigmaSquareDB(k)),', ',num2str(k),'/',num2str(K),' ...']);
Q = 10^(sigmaSquareDB(k)/10) * (ones(M-1, M-1)+eye(M-1))/2;
% Calculate CRLB
CRB = TDOALocCRLB_MPR( senPos, srcLoc, Q );
if (N==3)
CRLB_a(k,ir) = CRB(1,1)+CRB(2,2); % angle CRLB
CRLB_g(k,ir) = CRB(3,3); % g CRLB
else
CRLB_a(k,ir) = CRB(1,1); % angle CRLB
CRLB_g(k,ir) = CRB(2,2); % g CRLB
end;
if (N==3)
E = [-srcLoc(2), -cos(theta)*srcLoc(3), -r(1)*srcLoc(1);
srcLoc(1), -sin(theta)*srcLoc(3), -r(1)*srcLoc(2);
0, r(1)*cos(phi), -r(1)*srcLoc(3)];
else
E = [ -srcLoc(2), -r(1)*srcLoc(1);
srcLoc(1), -r(1)*srcLoc(2)];
end;
CRBp = E*CRB*E';
CRLB_p(k,ir) = trace(CRBp); % Cartesian position CRLB
CRLB_r(k,ir) = srcLoc'*CRBp*srcLoc/(r(1)^2); % source range CRLB
% Theoretical covariance
Var1 = Cov_SUM_MPR( senPos, srcLoc, Q );
var_T1(k,ir) = Var1(1);
var_P1(k,ir) = Var1(2);
var_g1(k,ir) = Var1(3);
Var2 = Cov_GTRS_MPR( senPos, srcLoc, Q );
var_T2(k,ir) = Var2(1);
var_P2(k,ir) = Var2(2);
var_g2(k,ir) = Var2(3);
% Theoretical bias
Bias1 = Bias_SUM_MPR( senPos, srcLoc, Q );
Bias_a1(k,ir) = norm(Bias1(1:end-1));
Bias_g1(k,ir) = abs(Bias1(end));
Bias_xy1(k,ir) = norm(E*Bias1,2);
Bias_Th1(k,ir) = abs(Bias1(1));
Bias2 = Bias_GTRS_MPR( senPos, srcLoc, Q );
Bias_a2(k,ir) = norm(Bias2(1:end-1));
Bias_g2(k,ir) = abs(Bias2(end));
Bias_xy2(k,ir) = norm(E*Bias2,2);
% -- Obtaining source location estimate in MPR --
nsePwr = 10^(sigmaSquareDB(k)/10);
rng('default');
[bia_p1,bia_p2,bia_p3,bia_p4,bia_p5,bia_p6] = deal(zeros(N,NumEnsembles));
for i = 1:NumEnsembles,
% measured TDOAs
tmp=randn(M,1);
rdNse = sqrt(nsePwr) * ((tmp(2:M)-tmp(1))/sqrt(2)-PP);
rd_m = rd + rdNse;
%% SUM-MPR Method
if (N==3)
[Th, Ph, g, pos] = TDOA_SUM_MPR( senPos, rd_m, Q );
else
[Th, g, pos] = TDOA_SUM_MPR( senPos, rd_m, Q );
Ph=0;
end;
ep1(k,i) = sum(abs(pos-srcLoc).^2);
eTh1(k,i) = abs(theta - Th)^2;
ePh1(k,i) = abs(phi - Ph)^2;
eg1(k,i) = (1/r(1) - g)^2;
bia_p1(:,i) = pos-srcLoc;
er1(k,i) = (r(1) - 1/g)^2;
uTh1(k,i) = Th;
uPh1(k,i) = Ph;
ug1(k,i) = g;
%% GTRS-MPR Method
if (N==3)
[Th, Ph, g, pos] = TDOA_GTRS_MPR( senPos, rd_m, Q );
else
[Th, g, pos] = TDOA_GTRS_MPR( senPos, rd_m, Q );
Ph=0;
end;
ep6(k,i) = sum((pos-srcLoc).^2);
eTh6(k,i) = (theta - Th)^2;
ePh6(k,i) = (phi - Ph)^2;
eg6(k,i) = (1/r(1) - g)^2;
bia_p6(:,i) = pos-srcLoc;
er6(k,i) = (r(1) - 1/g)^2;
uTh6(k,i) = Th;
uPh6(k,i) = Ph;
ug6(k,i) = g;
% % Chan-Ho Method, TSP 1994 (need to download TDOALoc)
% pos_ch = TDOALoc(senPos,rd_m,Q);
% ep2(k,i) = sum((pos_ch-srcLoc).^2);
% Th = atan2(pos_ch(2),pos_ch(1));
% if (N==3)
% Ph = atan2(pos_ch(3),norm(pos_ch(1:2),'fro'));
% else
% Ph = 0;
% end;
% g = 1/norm(pos_ch-senPos(:,1),'fro');
% eTh2(k,i) = (theta-Th).^2;
% ePh2(k,i) = (phi-Ph).^2;
% eg2(k,i) = (1/r(1) - g).^2;
% bia_p2(:,i) = pos_ch-srcLoc;
% er2(k,i) = (r(1) - 1/g)^2;
% uTh2(k,i) = Th;
% uPh2(k,i) = Ph;
% ug2(k,i) = g;
%
% % MLE-MPR (need to download TDOA_CVXMPR_3D, TDOA_MLEMPR_3D)
% upCVX = TDOA_CVXMPR_3D(senPos,rd_m,Q); % CVX-MPR solution
% upMPR = TDOA_MLEMPR_3D(senPos,rd_m,Q,upCVX); % MLE-MPR solution
% if (N==3)
% pos_MPR = [cos(upMPR(1))*cos(upMPR(2));sin(upMPR(1))*cos(upMPR(2));sin(upMPR(2))]/upMPR(3);
% else
% pos_MPR = [cos(upMPR(1));sin(upMPR(1))]/upMPR(2);
% upMPR=[upMPR(1);0;upMPR(2)];
% end;
% ep5(k,i) = sum((pos_MPR-srcLoc).^2);
% eg5(k,i) = (1/r(1) - upMPR(end)).^2;
% bia_p5(:,i) = pos_MPR-srcLoc;
% er5(k,i) = (r(1) - 1/upMPR(end))^2;
% eTh5(k,i) = (theta-upMPR(1)).^2;
% ePh5(k,i) = (phi-upMPR(2)).^2;
% uTh5(k,i) = upMPR(1);
% uPh5(k,i) = upMPR(2);
% ug5(k,i) = upMPR(3);
end
avBia_p1(k,ir) = norm(mean(bia_p1,2),2);
avBia_p2(k,ir) = norm(mean(bia_p2,2),2);
avBia_p5(k,ir) = norm(mean(bia_p5,2),2);
avBia_p6(k,ir) = norm(mean(bia_p6,2),2);
end
% -- calculate MSE --
% MSE of angle
mse_a1(:,ir) = mean(eTh1+ePh1,2);
mse_a2(:,ir) = mean(eTh2+ePh2,2);
mse_a5(:,ir) = mean(eTh5+ePh5,2);
mse_a6(:,ir) = mean(eTh6+ePh6,2);
% MSE of g
mse_g1(:,ir) = mean(eg1,2);
mse_g2(:,ir) = mean(eg2,2);
mse_g5(:,ir) = mean(eg5,2);
mse_g6(:,ir) = mean(eg6,2);
% MSE of position
mse_p1(:,ir) = mean(ep1,2);
mse_p2(:,ir) = mean(ep2,2);
mse_p5(:,ir) = mean(ep5,2);
mse_p6(:,ir) = mean(ep6,2);
% MSE of r
mse_r1(:,ir) = mean(er1,2);
mse_r2(:,ir) = mean(er2,2);
mse_r5(:,ir) = mean(er5,2);
mse_r6(:,ir) = mean(er6,2);
% Bias of angle
avBia_a1(:,ir) = sqrt((mean(abs(uTh1),2)-theta).^2+(mean(abs(uPh1),2)-phi).^2);%mean(sqrt(eTh1+ePh1),2);
avBia_a2(:,ir) = sqrt((mean(abs(uTh2),2)-theta).^2+(mean(abs(uPh2),2)-phi).^2);
avBia_a5(:,ir) = sqrt((mean(abs(uTh5),2)-theta).^2+(mean(abs(uPh5),2)-phi).^2);
avBia_a6(:,ir) = sqrt((mean(abs(uTh6),2)-theta).^2+(mean(abs(uPh6),2)-phi).^2);
% Bias of g
avBia_g1(:,ir) = abs(mean(ug1,2)-1/r(1));
avBia_g2(:,ir) = abs(mean(ug2,2)-1/r(1));
avBia_g5(:,ir) = abs(mean(ug5,2)-1/r(1));
avBia_g6(:,ir) = abs(mean(ug6,2)-1/r(1));
end
% ----- plot results -----
clear eTh1 eTh2 eTh3 eTh4 eTh5 eTh6 ePh1 ePh2 ePh3 ePh4 ePh5 ePh6 eg1 eg2 eg3 eg4 eg5 eg6 ...
ep1 ep2 ep3 ep4 ep5 ep6 bia_p1 bia_p2 bia_p3 bia_p4 bia_p5 bia_p6 er1 er2 er3 er4 er5 er6 ...
uTh1 uTh2 uTh3 uTh4 uTh5 uTh6 uPh1 uPh2 uPh3 uPh4 uPh5 uPh6 ug1 ug2 ug3 ug4 ug5 ug6;
if length(sigmaSquareDB) ~= 1
indR = 1;
% MSE of angle estimate
figure;
plot(sigmaSquareDB, 10*log10(mse_a1(:,indR)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');hold on;grid on;
plot(sigmaSquareDB, 10*log10(mse_a6(:,indR)), 'v', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
% plot(sigmaSquareDB, 10*log10(mse_a2(:,indR)), '*', 'LineWidth', 1.5, 'DisplayName', 'CFS');
% plot(sigmaSquareDB, 10*log10(mse_a5(:,indR)), 'x', 'LineWidth', 1.5, 'DisplayName', 'MLE-MPR');
plot(sigmaSquareDB, 10*log10(CRLB_a(:,indR)), '--', 'LineWidth', 1.5, 'DisplayName', 'CRLB');
xlabel('10log(\sigma_n^2)', 'FontSize', 13);
ylabel('10log(MSE(\theta,\phi)(rad^2))', 'FontSize', 13);
lgd11 = legend('Show');
set(lgd11, 'FontSize',11, 'Location', 'Northwest');
ylim([-110 20]);
% MSE of g estimate
figure;
plot(sigmaSquareDB, 10*log10(mse_g1(:,indR)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');hold on;grid on;
plot(sigmaSquareDB, 10*log10(mse_g6(:,indR)), 'v', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
% plot(sigmaSquareDB, 10*log10(mse_g2(:,indR)), '*', 'LineWidth', 1.5, 'DisplayName', 'CFS');
% plot(sigmaSquareDB, 10*log10(mse_g5(:,indR)), 'x', 'LineWidth', 1.5, 'DisplayName', 'MLE-MPR');
plot(sigmaSquareDB, 10*log10(CRLB_g(:,indR)), '--', 'LineWidth', 1.5, 'DisplayName', 'CRLB');
xlabel('10log(\sigma_n^2)', 'FontSize', 13);
ylabel('10log(MSE(g)(1/m^2))', 'FontSize', 13);
lgd2 = legend('Show');
set(lgd2, 'FontSize',11, 'Location', 'Northwest');
ylim([-170 -10]);set(gca,'YTick',-170:20:-10);
% MSE of position estimate in Cartesian
figure;
plot(sigmaSquareDB, 10*log10(mse_p1(:,indR)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');hold on;grid on;
plot(sigmaSquareDB, 10*log10(mse_p6(:,indR)), 'v', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
% plot(sigmaSquareDB, 10*log10(mse_p2(:,indR)), '*', 'LineWidth', 1.5, 'DisplayName', 'CFS');
% plot(sigmaSquareDB, 10*log10(mse_p5(:,indR)), 'x', 'LineWidth', 1.5, 'DisplayName', 'MLE-MPR');
plot(sigmaSquareDB, 10*log10(CRLB_p(:,indR)), '--', 'LineWidth', 1.5, 'DisplayName', 'CRLB');
xlabel('10log(\sigma_n^2)', 'FontSize', 13);
ylabel('10log(MSE(u)(m^2))', 'FontSize', 13);
lgd3 = legend('Show');
set(lgd3, 'FontSize',11, 'Location', 'Northwest');
% MSE of r estimate
figure;
plot(sigmaSquareDB, 10*log10(mse_r1(:,indR)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');hold on;grid on;
plot(sigmaSquareDB, 10*log10(mse_r6(:,indR)), 'v', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
% plot(sigmaSquareDB, 10*log10(mse_r2(:,indR)), '*', 'LineWidth', 1.5, 'DisplayName', 'CFS');
% plot(sigmaSquareDB, 10*log10(mse_r5(:,indR)), 'x', 'LineWidth', 1.5, 'DisplayName', 'MLE-MPR');
plot(sigmaSquareDB, 10*log10(CRLB_r(:,indR)), '--', 'LineWidth', 1.5, 'DisplayName', 'CRLB');%hold on;grid on;
xlabel('10log(\sigma_n^2)', 'FontSize', 13);
ylabel('10log(MSE(r)(m^{2}))', 'FontSize', 13);
h1 = legend('Show');
set(h1, 'FontSize',11, 'Location', 'Northwest');
% Bias of angle estimate
figure;
plot(sigmaSquareDB, 20*log10(avBia_a1(:,indR)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');hold on;grid on;
plot(sigmaSquareDB, 20*log10(avBia_a6(:,indR)), 'v', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
% plot(sigmaSquareDB, 20*log10(avBia_a2(:,indR)), '*', 'LineWidth', 1.5, 'DisplayName', 'CFS');
% plot(sigmaSquareDB, 20*log10(avBia_a5(:,indR)), 'x', 'LineWidth', 1.5, 'DisplayName', 'MLE-MPR');
plot(sigmaSquareDB, 20*log10(Bias_a1(:,indR)), '-', 'LineWidth', 1.5, 'DisplayName', 'Thy-SUM','Color',clor(1,:));
plot(sigmaSquareDB, 20*log10(Bias_a2(:,indR)), '--', 'LineWidth', 1.5, 'DisplayName', 'Thy-GTRS','Color',clor(2,:));
xlabel('10log(\sigma_n^2)', 'FontSize', 13);
ylabel('20log(Bias(\theta,\phi)(rad))', 'FontSize', 13);
h3 = legend('Show');
set(h3, 'FontSize',11, 'Location', 'Northwest');
xlim([min(sigmaSquareDB),max(sigmaSquareDB)]); ylim([-220 10]);
% Bias of g estimate
figure;
plot(sigmaSquareDB, 20*log10(avBia_g1(:,indR)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');hold on;grid on;
plot(sigmaSquareDB, 20*log10(avBia_g6(:,indR)), 'v', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
% plot(sigmaSquareDB, 20*log10(avBia_g2(:,indR)), '*', 'LineWidth', 1.5, 'DisplayName', 'CFS');
% plot(sigmaSquareDB, 20*log10(avBia_g5(:,indR)), 'x', 'LineWidth', 1.5, 'DisplayName', 'MLE-MPR');
plot(sigmaSquareDB, 20*log10(Bias_g1(:,indR)), '-', 'LineWidth', 1.5, 'DisplayName', 'Thy-SUM','Color',clor(1,:));
plot(sigmaSquareDB, 20*log10(Bias_g2(:,indR)), '--', 'LineWidth', 1.5, 'DisplayName', 'Thy-GTRS','Color',clor(2,:));
xlabel('10log(\sigma_n^2)', 'FontSize', 13);
ylabel('20log(Bias(g)(m^{-1}))', 'FontSize', 13);
h3 = legend('Show');
set(h3, 'FontSize',11, 'Location', 'Northwest');
xlim([min(sigmaSquareDB),max(sigmaSquareDB)]);ylim([-270 0]);
% Bias of position estimate in Cartesian
figure;
plot(sigmaSquareDB, 20*log10(avBia_p1(:,indR)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');hold on;grid on;
plot(sigmaSquareDB, 20*log10(avBia_p1(:,indR)), 'v', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
% plot(sigmaSquareDB, 20*log10(avBia_p2(:,indR)), '*', 'LineWidth', 1.5, 'DisplayName', 'CFS');
% plot(sigmaSquareDB, 20*log10(avBia_p5(:,indR)), 'x', 'LineWidth', 1.5, 'DisplayName', 'MLE-MPR');
plot(sigmaSquareDB, 20*log10(Bias_xy1(:,indR)), '-', 'LineWidth', 1.5, 'DisplayName', 'Thy-SUM','Color',clor(1,:));
plot(sigmaSquareDB, 20*log10(Bias_xy2(:,indR)), '--', 'LineWidth', 1.5, 'DisplayName', 'Thy-GTRS','Color',clor(2,:));
xlabel('10log(\sigma_n^2)', 'FontSize', 13);
ylabel('20log(Bias(u)(m))', 'FontSize', 13);
h3 = legend('Show');
set(h3, 'FontSize',11, 'Location', 'Southeast');
xlim([min(sigmaSquareDB),max(sigmaSquareDB)]);ylim([-100,120]);
end
if length(range) ~= 1
% Plot Figure (sigma^2 = 0dB)
indS = 1; %find(sigmaSquareDB==0);
% MSE of estimated angle
figure;
plot(range/1e3, 10*log10(mse_a1(indS,:)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');hold on;grid on;
plot(range/1e3, 10*log10(mse_a1(indS,:)), 'v', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
% plot(range/1e3, 10*log10(mse_a2(indS,:)), '*', 'LineWidth', 1.5, 'DisplayName', 'CFS');
% plot(range/1e3, 10*log10(mse_a5(indS,:)), 'x', 'LineWidth', 1.5, 'DisplayName', 'MLE-MPR');
plot(range/1e3, 10*log10(CRLB_a(indS,:)), '--', 'LineWidth', 1.5, 'DisplayName', 'CRLB');
ylim([-70 0]);
xlabel('Range(km)', 'FontSize', 13);
ylabel('10log(MSE(\theta,\phi)(rad^2))', 'FontSize', 13);
lgd11 = legend('Show');
set(lgd11, 'FontSize',11, 'Location', 'Northwest');
xlim([min(range),max(range)]/1e3);%ylim([-64.5,-63]);
% MSE of g estimate
figure;
plot(range/1e3, 10*log10(mse_g1(indS,:)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');hold on;grid on;
plot(range/1e3, 10*log10(mse_g6(indS,:)), 'v', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR')
% plot(range/1e3, 10*log10(mse_g2(indS,:)), '*', 'LineWidth', 1.5, 'DisplayName', 'CFS');
% plot(range/1e3, 10*log10(mse_g5(indS,:)), 'x', 'LineWidth', 1.5, 'DisplayName', 'MLE-MPR');
plot(range/1e3, 10*log10(CRLB_g(indS,:)), '--', 'LineWidth', 1.5, 'DisplayName', 'CRLB');
ylim([-140 -40]);
xlabel('Range(km)', 'FontSize', 13);
ylabel('10log(MSE(g)(1/m^2))', 'FontSize', 13);
lgd13 = legend('Show');
set(lgd13, 'FontSize',11, 'Location', 'Northwest');
xlim([min(range),max(range)]/1e3);%ylim([-120,-118]);
% Bias of angle estimate
figure;
plot(range/1e3, 20*log10(avBia_a1(indS,:)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');hold on;grid on;
plot(range/1e3, 20*log10(avBia_a6(indS,:)), 'v', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
% plot(range/1e3, 20*log10(avBia_a2(indS,:)), '*', 'LineWidth', 1.5, 'DisplayName', 'CFS');
% plot(range/1e3, 20*log10(avBia_a5(indS,:)), 'x', 'LineWidth', 1.5, 'DisplayName', 'MLE-MPR');
plot(range/1e3, 20*log10(Bias_a1(indS,:)), '-', 'LineWidth', 1.5, 'DisplayName', 'Thy-SUM','Color',clor(1,:));
plot(range/1e3, 20*log10(Bias_a2(indS,:)), '--', 'LineWidth', 1.5, 'DisplayName', 'Thy-GTRS','Color',clor(2,:));
ylim([-140 -20]);
xlabel('Range(km)', 'FontSize', 13);
ylabel('20log(Bias(\theta,\phi)(rad))', 'FontSize', 13);
h3 = legend('Show');
set(h3, 'FontSize',11, 'Location', 'Southeast');
xlim([min(range/1e3),max(range/1e3)]);
% Bias of g estimate
figure;
plot(range/1e3, 20*log10(avBia_g1(indS,:)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');hold on;grid on;
plot(range/1e3, 20*log10(avBia_g6(indS,:)), 'v', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
% plot(range/1e3, 20*log10(avBia_g2(indS,:)), '*', 'LineWidth', 1.5, 'DisplayName', 'CFS');
% plot(range/1e3, 20*log10(avBia_g5(indS,:)), 'x', 'LineWidth', 1.5, 'DisplayName', 'MLE-MPR');
plot(range/1e3, 20*log10(Bias_g1(indS,:)), '-', 'LineWidth', 1.5, 'DisplayName', 'Thy-SUM','Color',clor(1,:));
plot(range/1e3, 20*log10(Bias_g2(indS,:)), '--', 'LineWidth', 1.5, 'DisplayName', 'Thy-GTRS','Color',clor(2,:));
ylim([-200 -40]);
xlabel('Range(km)', 'FontSize', 13);
ylabel('20log(Bias(g)(m^{-1}))', 'FontSize', 13);
h3 = legend('Show');
set(h3, 'FontSize',11, 'Location', 'Southeast');
xlim([min(range/1e3),max(range/1e3)]);%ylim([-270 0]);
end