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Fig10.m
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% Generation of Figs. 10 in the paper
% Y. Sun, K. C. Ho, G. Wang. J. Chen, Y. Yang, L. Chen, and Q. Wan,
% "Computationally attractive and location robust estimator for IoT device positioning,"
% IEEE Internet Things J., Nov. 2021.
%
% Yimao Sun and K. C. Ho 04-08-2022
%
% Copyright (C) 2022
% Computational Intelligence Signal Processing Laboratory
% University of Missouri
% Columbia, MO 65211, USA.
%
clear all;
% close all;
% clc
rng('default');
% 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');
senPos = [
% minimum number of sensors
10.23 38.38 16.29
46.64 -87.12 62.94
124.02 -7.98 81.16
105.02 -51.72 26.47
-81.56 104.48 -80.49
]';
thetaN = (-180:10:180)*pi/180;
phiN = [-89,-85:5:85,89]*pi/180;
[N,M] = size(senPos);
% setting
sigma_sqr = -10; % 10log(m^2)
range = 500; % m
% range = 10000;
mon = 5000;
R = length(phiN);
K = length(thetaN);
% Monte-Carlo Simulation
aveNse = 0;
for l=1:mon
aveNse = aveNse + randn(M,1);
end
aveNse = aveNse/mon/sqrt(2);
PP = aveNse(2:end) - aveNse(1);
disp('Simulation is running ...');
senPosTmp = senPos;
for t = 1:R
phi = phiN(t);
for k = 1:K
disp(['phi: ',num2str(phiN(t)*180/pi),'(deg), ',num2str(t),'/',num2str(R),'; ','theta: ',num2str(thetaN(k)*180/pi),'(deg), ',num2str(k),'/',num2str(K),' ...']);
theta = thetaN(k);
phiTmp = phi;
souLoc = range * [cos(theta)*cos(phi); sin(theta)*cos(phi); sin(phi)] + senPos(:,1);
souLocTmp = souLoc;
r = sqrt(sum((souLoc-senPos).^2,1))';
rd = r(2:end) - r(1);
rTmp = r;
Q = 10^(sigma_sqr/10) * (ones(M-1, M-1)+eye(M-1))/2;
% calculate CRLB
CRB = ConsCRLB( senPos, souLoc, Q );
CRLB_a(k,t) = CRB(1,1)+CRB(2,2);
CRLB_g(k,t) = CRB(3,3);
% Position and DOA estimate
nsePwr = 10^(sigma_sqr/10);
% SCO-MPR Method
rng('default');
for i = 1:mon
% measured TDOAs
tmp=randn(M,1);
rdNse = sqrt(nsePwr) * ((tmp(2:M)-tmp(1))/sqrt(2)-PP);
rd_m = rd + rdNse;
% SCO
[mprSol,~] = TDOA_SCO_MPR( senPos, rd_m, Q );
Th1 = mprSol(1);Ph1 = mprSol(2);g1 = mprSol(3);
if abs(theta - Th1) > pi
eTh1(k,i) = (2*pi-abs(theta-Th1))^2;
else
eTh1(k,i) = (theta - Th1)^2;
end
ePh1(k,i) = (phi - Ph1)^2;
eg1(k,i) = (1/r(1) - g1)^2;
uTh1(k,i) = Th1;
uPh1(k,i) = Ph1;
ug1(k,i) = g1;
%% SUM-MPR Method
[Th2, Ph2, g2, ~] = TDOA_SUM_MPR( senPos, rd_m, Q );
if abs(theta - Th2) > pi
eTh2(k,i) = (2*pi-abs(theta-Th2))^2;
else
eTh2(k,i) = (theta - Th2)^2;
end
ePh2(k,i) = abs(phi - Ph2)^2;
eg2(k,i) = (1/r(1) - g2)^2;
uTh2(k,i) = Th2;
uPh2(k,i) = Ph2;
ug2(k,i) = g2;
%% GTRS-MPR Method
[Th3, Ph3, g3, ~] = TDOA_GTRS_MPR( senPos, rd_m, Q );
if abs(theta - Th3) > pi
eTh3(k,i) = (2*pi-abs(theta-Th3))^2;
else
eTh3(k,i) = (theta - Th3)^2;
end
ePh3(k,i) = (phi - Ph3)^2;
eg3(k,i) = (1/r(1) - g3)^2;
uTh3(k,i) = Th3;
uPh3(k,i) = Ph3;
ug3(k,i) = g3;
end
end
% calculate MSE
% MSE of angle
mse_a1(:,t) = mean(eTh1+ePh1,2);
mse_a2(:,t) = mean(eTh2+ePh2,2);
mse_a3(:,t) = mean(eTh3+ePh3,2);
% MSE of g
mse_g1(:,t) = mean(eg1,2);
mse_g2(:,t) = mean(eg2,2);
mse_g3(:,t) = mean(eg3,2);
end
figure;
subplot(2,1,1);
plot(thetaN*180/pi, 10*log10(mean(mse_a1./CRLB_a,2)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SCO-MPR'); hold on; grid on;
plot(thetaN*180/pi, 10*log10(mean(mse_a2./CRLB_a,2)), 'v', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');
plot(thetaN*180/pi, 10*log10(mean(mse_a3./CRLB_a,2)), 's', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
xlabel('\theta^o (deg)', 'FontSize', 13);ylabel('$\bar{R}_a(\theta^o)$','Interpreter','Latex', 'FontSize', 13);
xlim([min(thetaN),max(thetaN)]*180/pi);set(gca,'XTick',-180:60:180);
ylim([-0.5,3]);
lgd = legend('show');
set(lgd,'FontSize',11, 'Location', 'Northeast');
subplot(2,1,2);
plot(thetaN*180/pi, 10*log10(mean(mse_g1./CRLB_g,2)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SCO-MPR'); hold on; grid on;
plot(thetaN*180/pi, 10*log10(mean(mse_g2./CRLB_g,2)), 'v', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');
plot(thetaN*180/pi, 10*log10(mean(mse_g3./CRLB_g,2)), 's', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
xlabel('\theta^o (deg)', 'FontSize', 13);ylabel('$\bar{R}_g(\theta^o)$','Interpreter','Latex', 'FontSize', 13);
xlim([min(thetaN),max(thetaN)]*180/pi);set(gca,'XTick',-180:60:180);
ylim([-0.5,3]);
lgd = legend('show');
set(lgd,'FontSize',11, 'Location', 'Northeast');
figure;
subplot(2,1,1);
plot(phiN*180/pi, 10*log10(mean(mse_a1./CRLB_a,1)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SCO-MPR'); hold on; grid on;
plot(phiN*180/pi, 10*log10(mean(mse_a2./CRLB_a,1)), 'v', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');
plot(phiN*180/pi, 10*log10(mean(mse_a3./CRLB_a,1)), 's', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
xlabel('\phi^o (deg)', 'FontSize', 13);ylabel('$\bar{R}_a(\phi^o)$','Interpreter','Latex', 'FontSize', 13);
xlim([-90,90]);set(gca,'XTick',-90:30:90);
ylim([-0.5,3]);
lgd = legend('show');
set(lgd,'FontSize',11, 'Location', 'Northeast');
subplot(2,1,2);
plot(phiN*180/pi, 10*log10(mean(mse_g1./CRLB_g,1)), 'o', 'LineWidth', 1.5, 'DisplayName', 'SCO-MPR'); hold on; grid on;
plot(phiN*180/pi, 10*log10(mean(mse_g2./CRLB_g,1)), 'v', 'LineWidth', 1.5, 'DisplayName', 'SUM-MPR');
plot(phiN*180/pi, 10*log10(mean(mse_g3./CRLB_g,1)), 's', 'LineWidth', 1.5, 'DisplayName', 'GTRS-MPR');
xlabel('\phi^o (deg)', 'FontSize', 13);ylabel('$\bar{R}_g(\phi^o)$','Interpreter','Latex', 'FontSize', 13);
xlim([-90,90]);set(gca,'XTick',-90:30:90);
ylim([-0.5,3]);
lgd = legend('show');
set(lgd,'FontSize',11, 'Location', 'Northeast');