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highspeedlogic算法仿真-TDOA的matlab仿真

clc;
clear;
close all;
warning off;


%设置信噪比的大小
SNR= [10,20,30,40,50,60,70,80];
%多径延迟
Mpd= [0];
%基站之间的时间同步误差
Timesyn= [0];
%基站数目
N= 3;
%定义光速
c= 3*10^8;
%距离指数
LL= 15000;
%信号长度
SL= 8;
P1x= 0;
P1y= 0;
%产生一个距离
P2x= sqrt(2)*LL + LL;
P2y= 0;
P3x= 0;
%产生一个距离
P3y= sqrt(3)*LL + LL;
BS = [[P1x,P1y]; [P2x,P2y]; [P3x,P3y]];

figure;
plot(P1x,P1y,'b^','Markersize',8);
hold on;
plot(P2x,P2y,'b^','Markersize',8);
hold on;
plot(P3x,P3y,'b^','Markersize',8);
hold on;
text(P1x+800,P1y+800,'BS1');
text(P2x+800,P2y+800,'BS2');
text(P3x+800,P3y+800,'BS3');
xlabel('X axis');
ylabel('Y axis');
axis([-3*LL/20,3*LL,-3*LL/20,3*LL]);
grid on;
%这里随机生成移动物体的位置坐标
P0x = 2*LL/3;
P0y = 3*LL/4;
plot(P0x,P0y,'ro','Markersize',6); hold off;
text(P0x+800,P0y+800,'M');
title('基站位置');


%定义发送信号，这里发送信号根据要求使用AM发送信号
fc= 1000; %载波频率
tau= 10^(-7); %时间间隔
T= 1/fc/2; %频率周期
t= -T*SL+tau:tau:T*SL; %信号的长度，这里使用8个周期进行
No= length(t); %信号的长度
A= 1; %发送信号的幅度
s= A*cos(2*pi*fc*t);


%通过计算理论距离，来模拟出到三个基站的通过延迟后的实际信号
%计算理论距离
R0 = zeros(1,N);
for i = 1:N
R0(i) = sqrt((P0x-BS(i,1))^2 + (P0y-BS(i,2))^2);
end
%通过理论距离计算三个理论延迟大小
tDelay = zeros(1,N); %定义延迟
r= zeros(N,No); %定义时延
for i = 1:N
tDelay(i) = R0(i)/c;
%计算得到实际的延迟后的信号
r(i,:)= A*cos(2*pi*fc*(t-tDelay(i)));
end


rng(1); %use matlab2013b else maybe error
%信道模拟
for j = 1:length(SNR)
%加入噪声
r2(1,:) = awgn(r(1,:),SNR(j));
r2(2,:) = awgn(r(2,:),SNR(j));
r2(3,:) = awgn(r(3,:),SNR(j));

%加入多径
for jj = 1:N
signals= r2(jj,:);
if Mpd == 0
signals2 = signals;
else
signals2 = signals + 0.65*[zeros(1,Mpd),signals(1:end-Mpd)];
end
r3(jj,:) = signals2;
end
%计算延迟相关运算
Peak= zeros(N,1); %定义相关峰的值
delay_theory = zeros(N,1); %通过广义相关运算得到的延迟估计值
for kk = 1:1:LL/10
tau_theory = tau*kk;
temp= r3(1,(No/2-kk+1):(No-kk))*tau;
for i =2:N
data= https://www.it610.com/article/(sum(r3(i,No/2+1:No).*temp))^2;
if Peak(i) < data
Peak(i) = data;
delay_theory(i) = tau_theory;
end
end
end

%通过TDOA方法，根据理论估计延迟得到实际的坐标点位置
R_theory = zeros(1,N);
Kj= zeros(1,N);
for i = 2:N
R_theory(i) = delay_theory(i)*c;
Kj(i)= BS(i,1)^2 + BS(i,2)^2;
end

H_tdoa = BS(2:N,:);
C_tdoa = -1*R_theory(2:N)';
D_tdoa = 0.5*(Kj(2:N)-R_theory(2:N).^2)';
K_tdoa = inv(H_tdoa'*H_tdoa) *(H_tdoa')*C_tdoa;
Q_tdoa = inv(H_tdoa'*H_tdoa) *(H_tdoa')*D_tdoa;
%计算得到abc三个参数
as= sum(K_tdoa.^2) -1;
bs= sum(K_tdoa.*Q_tdoa);
cs= sum(Q_tdoa.^2);
R1= (-bs - sqrt(bs^2-as*cs))/as;
xyChan = K_tdoa.*R1 + Q_tdoa;
%计算估计得到的XY坐标点
X_theory(j) = xyChan(1);
Y_theory(j) = xyChan(2);
【highspeedlogic算法仿真-TDOA的matlab仿真】%计算估计误差值
Err(j) = 100*sqrt((X_theory(j)-P0x)^2+(Y_theory(j)-P0y)^2)/((X_theory(j)+Y_theory(j))/2);

clear xyChan R1 cs bs as Q_tdoa K_tdoa D_tdoa C_tdoa H_tdoa Kj R_theory delay_theory Peak tau_theory temp
end

figure;
plot(SNR,Err,'b-*');
grid on;
title('误差曲线 % ');
xlabel('SNR');
ylabel('Err');
axis([10,80,0,5]);

%显示理论估计值
figure;
plot(P1x,P1y,'b^','Markersize',8); hold on;
plot(P2x,P2y,'b^','Markersize',8); hold on;
plot(P3x,P3y,'b^','Markersize',8); hold on;
axis([-3*LL/20,3*LL,-3*LL/20,3*LL]);
grid on;
xlabel('X axis');
ylabel('Y axis');
text(P1x+800,P1y+800,'BS1');
text(P2x+800,P2y+800,'BS2');
text(P3x+800,P3y+800,'BS3');
plot(P0x,P0y,'bo','Markersize',8);
hold on;
text(P0x-800,P0y-800,'M');

SEL = 1;

plot(X_theory(SEL),Y_theory(SEL),'rs','Markersize',8); hold on;
text(X_theory(SEL)+800,Y_theory(SEL)+800,'estimation');

R1 = sqrt((X_theory(SEL)-P1x)^2+(Y_theory(SEL)-P1y)^2);
R2 = sqrt((X_theory(SEL)-P2x)^2+(Y_theory(SEL)-P2y)^2);
R3 = sqrt((X_theory(SEL)-P3x)^2+(Y_theory(SEL)-P3y)^2);

alpha=0.01*pi:pi/100:0.55*pi;
x1= P1x+R1*cos(alpha);
y1= P1y+R1*sin(alpha);
hold on;
plot(x1,y1,'k-');

alpha=0.5*pi:pi/100:1.0*pi;
x2= P2x+R2*cos(alpha);
y2= P2y+R2*sin(alpha);
hold on;
plot(x2,y2,'k-');

alpha=1.1*pi:pi/100:1.95*pi;
x3= P3x+R3*cos(alpha);
y3= P3y+R3*sin(alpha);
hold on;
plot(x3,y3,'k-');

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