% 功能：基于chan算法的TDOA三維定位

function [zp] = Chan_3(Noise,MS)

%基站數目

BSN = 7;

%基站位置,每一列為一個基站位置

BS = [0, 2*sqrt(3), -2*sqrt(3), sqrt(3), -sqrt(3), -sqrt(3), sqrt(3);

0, 0, 0, 3, 3, -3, -3;

0, 0, 0, 0, 2, 2, 0];

%無噪聲情況下BS到MS的距離

for i = 1:BSN

R0(i) = sqrt((BS(1,i) - MS(1))^2 + (BS(2,i) - MS(2))^2 + (BS(3,i) - MS(3))^2);

end

%噪聲方差

c = 3*10^5;

%有噪聲情況下BSi到MS的距離與BS1到MS的距離差，實際由TDOA*c求得

for i = 1:BSN-1

R(i) = R0(i+1) - R0(1) +c*Noise(i,1);

end

%% 第一次WLS

%k = x^2+y^2+z^2

for i =1:BSN

k(i) = BS(1,i)^2 + BS(2,i)^2 + BS(3,i)^2;

end

% h

for i = 1:BSN-1

h(i) = 0.5*(R(i)^2 - k(i+1) + k(1));

end

% Ga

for i = 1:BSN-1

Ga(i,1) = -BS(1,i+1);

Ga(i,2) = -BS(2,i+1);

Ga(i,3) = -BS(3,i+1);

Ga(i,4) = -R(i);

end

%Q為TDOA系統的協方差矩陣

Q = cov(R);

%za,距離較遠時

za1 = pinv(Ga'*pinv(Q)*Ga)*Ga'*pinv(Q)*h';

%% 第二次WLS

%h2

X1 = BS(1,1);

Y1 = BS(2,1);

Z1 = BS(3,1);

h2 = [

(za1(1,1) - X1)^2;

(za1(2,1) - Y1)^2;

(za1(3,1) - Z1)^2;

za1(4,1)^2

];

%Ga2

Ga2 = [1,0,0;0,1,0;0,0,1;1,1,1];

%B2

B2 = [

za1(1,1)-X1,0,0,0;

0,za1(2,1)-Y1,0,0;

0,0,za1(3,1)-Z1,0;

0,0,0,za1(4,1)

];

%za2

za2 = pinv( Ga2' * pinv(B2) * Ga' * pinv(Q) * Ga * pinv(B2) * Ga2) * (Ga2' * pinv(B2) * Ga' * pinv(Q) * Ga * pinv(B2)) * h2;

%zp

zp(1,1) = abs(za2(1,1))^0.5+X1;

zp(2,1) = abs(za2(2,1))^0.5+Y1;

zp(3,1) = abs(za2(3,1))^0.5+Z1;

end

% 功能：基于chan算法的TDOA三維定位的MSE曲線

clear;

clc;

account_test =1000;

Counter_Size=account_test;

Zp_mean1=zeros(2,6);

Zp_mse1=zeros(1,6);

M=7;

k=1;

c = 3*10^5; % 單位km

MS = [1,2.5,1];

for Noise_db = -16:2:-6 % 信道所受到的噪聲干擾

Sigma = 10^(Noise_db./10)/c;

for m = 1:1:Counter_Size%%%%%%%%%%%%%%%%%%%%cishu

for i = 1:1:M-1

Noise(i, 1) = gngauss(Sigma);

end

[ zp ] = Chan_3(Noise,MS);

Zp(:,m) = zp;

end

Zp_all(:,1) = 0;

Zp_mse_all = 0;

for i = 1:1:Counter_Size

Zp_all = Zp_all + Zp( :, i);

Zp_mse_all = Zp_mse_all + (Zp(1,i) - MS(1,1))^2 + (Zp(2,i) - MS(1,2))^2 + (Zp(3,i) - MS(1,3))^2;

end

Zp_mean= Zp_all / Counter_Size ; % 計算chan所得的均值

Zp_mean1(1:1:3,k) =Zp_mean;

Zp_mse = Zp_mse_all / Counter_Size ; % 計算chan所得的均方誤差MSE

Zp_mse1(1,k)=Zp_mse;

k=k+1;

end

Zp_mean1

Zp_mse1

plot(-16:2:-6,Zp_mse1,'bo--')

xlabel('10lg(cσ)/dB')

ylabel('均方誤差MSE/km')

legend('Chan算法')

測試結果

總結

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