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Example_Figs.m
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Example_Figs.m
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% This program gives an example of how to call the routines for AOA
% localization in MPR using the EV and BR methods that can reproduce the
% simulation figures in the paper
% Y. Sun, K. C. Ho, and Q. Wan, "Eigenspace solution for AOA localization
% in modified polar representation," IEEE Trans. Signal Process.,
% vol. 68, pp. 2256-2271, 2020.
%
% Yimao Sun, K. C. Ho 03-28-2021
%
% Copyright (C) 2020
% Computational Intelligence Signal Processing Laboratory
% University of Missouri
% Columbia, MO 65211, USA
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all;
%clc;
warning off
% =========================================
% im = 1: performance vs noise power (Figs. 3-6)
% im = 2: perforamnce vs sensor position errors (Figs. 7-10)
% im = 3: performance vs source range (Figs. 11-14)
% =========================================
im = 1;
% -- settings --
senPosTrue = [ % sensor positions
0 0 0
-13.1 22.3 -32.4
34.6 44.4 15.5
30.5 -29.4 18.4
9.9 29.2 -8.4
-7.4 48.0 -3.5
4.5 -0.9 21.7
-47.2 -7.3 29.1
]';
thetaSrc = 22.13*pi/180; % source azimuth
phiSrc = 15.41*pi/180; % source elevation
[N,M] = size(senPosTrue);
models = ['nse';'err';'rag'];
model = models(im,:);
switch model
case 'nse'
% ******* vs. noise power config, Fig. 3-6 *******
nsePwr = -70:10:20; % 10log(rad^2)
srcRange = 200; % m
errLvl = -20;
case 'err'
% ******* vs. sensor position error level config, Fig. 7-10 *******
nsePwr = -50; % 10log(rad^2)
srcRange = 200; % m
errLvl = -60:10:40;
case 'rag'
% ******* vs. range config, Fig. 11-14 *******
nsePwr = -20; % 10log(rad^2)
srcRange = [20,50:50:800]; % m
errLvl = -20;
end
T = 1000; % number of ensemble runs
% AOA measurements noise
rng('Default');
nseTmp = zeros(2*M,T);
for m = 1:T
nseTmp(:,m) = randn(2*M,1);
end
nseTmp = nseTmp - mean(nseTmp,2);
% sensor position errors
errTmp = zeros(M*N,1);
for m = 1:T
errTmp(:,m) = randn(M*N,1);
end
errTmp = errTmp - mean(errTmp,2);
Ra=eye(2*M);
aErr = [1,80,80,50,5,3,20,10];
Rs = kron(eye(N),diag(aErr(1:M)));
rng(1);
for ii = 1:2
a1 = rand(3*M,1);
a2 = rand(M,1);
Rt = diag(roundn(a2/mean(a2),-2));
a3 = rand(M,1);
Rp = diag(roundn(a3/mean(a3),-2));
Ra = blkdiag(Rt,Rp);
end
totalTime = zeros(1,2);
% -- perform processing --
% over source range
for ir = 1:length(srcRange)
gSrc = 1/srcRange(ir);
u0 = [cos(thetaSrc)*cos(phiSrc); sin(thetaSrc)*cos(phiSrc); sin(phiSrc)];
srcLoc = srcRange(ir)*u0;
% true AOA measurements
thetaTrue = atan2(srcLoc(2)-senPosTrue(2,:),srcLoc(1)-senPosTrue(1,:))';
phiTrue = atan2(srcLoc(3)-senPosTrue(3,:),sqrt(sum((srcLoc(1:2)-senPosTrue(1:2,:)).^2,1)))';
% over noise power
for in = 1:length(nsePwr)
Qa = 10^(nsePwr(in)/10)*Ra;
% over sensor position error level
for is = 1:length(errLvl)
disp(['source range: ',num2str(srcRange(ir)),'m, 20log10(\sigma_a(rad)): ', num2str(nsePwr(in)),', 20log10(\sigma_s(m)): ',num2str(errLvl(is)),' ...']);
Qs = 10^(errLvl(is)/10)*Rs;
% CRLB
CRB_MPR = AOA3DLocMPR_CCRLB( srcLoc,senPosTrue,Qa,Qs );
crlb_t(ir,in,is) = CRB_MPR(1,1);
crlb_p(ir,in,is) = CRB_MPR(2,2);
crlb_g(ir,in,is) = CRB_MPR(3,3);
% Theoretical covariance matrices
Cov_EV = AOA3DLocMPR_CovEV( srcLoc, senPosTrue, Qa, Qs );
Cov_BR = AOA3DLocMPR_CovBR( srcLoc, senPosTrue, Qa, Qs );
covEV_t(ir,in,is) = Cov_EV(1,1);
covEV_p(ir,in,is) = Cov_EV(2,2);
covEV_g(ir,in,is) = Cov_EV(3,3);
covBR_t(ir,in,is) = Cov_BR(1,1);
covBR_p(ir,in,is) = Cov_BR(2,2);
covBR_g(ir,in,is) = Cov_BR(3,3);
[pos11,pos12,pos13,pos14,pos15,pos16] = deal(zeros(N,T));
% over Monte-Carlo runs
for m = 1:T
angNse = sqrtm(Qa)*nseTmp(:,m);
theta = thetaTrue + angNse(1:M);
phi = phiTrue + angNse((1:M)+M);
senErr = reshape(chol(Qs)'*errTmp(:,m),N,M);
senPos = senPosTrue + senErr;
% EV solution
tic;
mprSol1 = AOA3DLocMPR_EV( theta, phi, senPos, Qa, Qs );
th(1,m) = mprSol1(1);
ph(1,m) = mprSol1(2);
g(1,m) = mprSol1(3);
totalTime(1) = totalTime(1) + toc;
% BR solution
tic;
mprSol2 = AOA3DLocMPR_BR( theta, phi, senPos, Qa, Qs );
th(2,m) = mprSol2(1);
ph(2,m) = mprSol2(2);
g(2,m) = mprSol2(3);
totalTime(2) = totalTime(2) + toc;
end
% performance statistics
algNum = size(g,1);
for ia = 1:algNum
mse_t(ir,in,is,ia) = mean((thetaSrc-th(ia,:)).^2);
mse_p(ir,in,is,ia) = mean((phiSrc-ph(ia,:)).^2);
mse_g(ir,in,is,ia) = mean((gSrc-g(ia,:)).^2);
bias_t(ir,in,is,ia) = abs(mean(th(ia,:)) - thetaSrc);
bias_p(ir,in,is,ia) = abs(mean(ph(ia,:)) - phiSrc);
bias_g(ir,in,is,ia) = (mean(g(ia,:)) - gSrc);
end
end
end
end
% -- plot results --
symbs = ['o','^'];
name = {'EV-MPR','BR-MPR'};
switch model
case 'nse'
xlabtext = '10log(\sigma_a^2(rad^2))';
xdata = nsePwr;
yl_mse = [-70, 20;
-100,-10];
yl_bias = [-120,10;
-160,0];
case 'err'
xlabtext = '10log(\sigma_s^2(m^2))';
xdata = errLvl;
yl_mse = [-65, 20;
-95,-30];
yl_bias = [-130,10;
-170,-40];
case 'rag'
xlabtext = 'Range(m)';
xdata = srcRange;
yl_mse = [-35, 5;
-65,-25];
yl_bias = [-100,0;
-120,0];
end
% MSE
figure(1); clf;
for ia = 1:algNum
plot(xdata,10*log10(reshape(mse_t(:,:,:,ia)+mse_p(:,:,:,ia),[],1)),symbs(ia),'linewidth',1.5,'DisplayName',name{ia});hold on;grid on;
end
plot(xdata,10*log10(reshape(crlb_t(:,:,:)+crlb_p(:,:,:),[],1)),'-','linewidth',1.5,'DisplayName','CRLB');
% plot(xdata,10*log10(reshape(covEV_t(:,:,:)+covEV_p(:,:,:),[],1)),'-','linewidth',1.5,'DisplayName','covEV');
% plot(xdata,10*log10(reshape(covBR_t(:,:,:)+covBR_p(:,:,:),[],1)),'-','linewidth',1.5,'DisplayName','covBR');
xlabel(xlabtext,'FontSize',13);ylabel('10log(MSE(\theta,\phi)(rad^2))','FontSize',13);
leg1 = legend('show','Location','Northwest');
set(leg1,'FontSize',11);
ylim(yl_mse(1,:));
figure(2); clf;
for ia = 1:algNum
plot(xdata,10*log10(reshape(mse_g(:,:,:,ia),[],1)),symbs(ia),'linewidth',1.5,'DisplayName',name{ia});hold on;grid on;
end
plot(xdata,10*log10(reshape(crlb_g(:,:,:),[],1)),'-','linewidth',1.5,'DisplayName','CRLB');
% plot(xdata,10*log10(reshape(covEV_g(:,:,:),[],1)),'-','linewidth',1.5,'DisplayName','covEV');
% plot(xdata,10*log10(reshape(covBR_g(:,:,:),[],1)),'-','linewidth',1.5,'DisplayName','covBR');
xlabel(xlabtext,'FontSize',13);ylabel('10log(MSE(g)(1/m^2))','FontSize',13);
leg1 = legend('show','Location','Northwest');
set(leg1,'FontSize',11);
ylim(yl_mse(2,:));
% bias
figure(3); clf;
for ia = 1:algNum
plot(xdata,20*log10(reshape(sqrt(bias_t(:,:,:,ia).^2+bias_p(:,:,:,ia).^2),[],1)),symbs(ia),'linewidth',1.5,'DisplayName',name{ia});hold on;grid on;
end
xlabel(xlabtext,'FontSize',13);ylabel('20log(Bias(\theta,\phi)(rad))','FontSize',13);
leg1 = legend('show','Location','Northwest');
set(leg1,'FontSize',11);
ylim(yl_bias(1,:));
figure(4); clf;
for ia = 1:algNum
plot(xdata,20*log10(reshape(bias_g(:,:,:,ia),[],1)),symbs(ia),'linewidth',1.5,'DisplayName',name{ia});hold on;grid on;
end
xlabel(xlabtext,'FontSize',13);ylabel('20log(Bias(g)(1/m))','FontSize',13);
leg1 = legend('show','Location','Northwest');
set(leg1,'FontSize',11);
ylim(yl_bias(2,:));
clear mse_t mse_p mse_g bias_t bias_p bias_g crlb_t crlb_p crlb_g;