扩展卡尔曼滤波算法的matlab程序--技能提升篇

clear all

v=150; %%目标速度

v_sensor=0;%%传感器速度

t=1; %%扫描周期

xradarpositon=0; %%传感器坐标yradarpositon=0; %%

ppred=zeros(4,4);

Pzz=zeros(2,2);

Pxx=zeros(4,2);

xpred=zeros(4,1);

ypred=zeros(2,1);

sumx=0;

sumy=0;

sumxukf=0;

sumyukf=0;

sumxekf=0;

sumyekf=0; %%%统计的初值

L=4;

alpha=1;

kalpha=0;

belta=2;

ramda=3-L;

azimutherror=0.015; %%方位均方误差rangeerror=100; %%距离均方误差processnoise=1; %%过程噪声均方差

tao=[t^3/3 t^2/2 0 0;

t^2/2 t 0 0;

0 0 t^3/3 t^2/2;

0 0 t^2/2 t]; %% the input matrix of process G=[t^2/2 0

t 0

0 t^2/2

0 t ];

a=35*pi/180;

a_v=5/100;

a_sensor=45*pi/180;

x(1)=8000; %%初始位置

y(1)=12000;

for i=1:200

x(i+1)=x(i)+v*cos(a)*t;

y(i+1)=y(i)+v*sin(a)*t;

end

for i=1:200

xradarpositon=0;

yradarpositon=0;

Zmeasure(1,i)=atan((y(i)-yradarpositon)/(x(i)-xradarpositon))+random('Normal',0,azimutherror,1,1); Zmeasure(2,i)=sqrt((y(i)-yradarpositon)^2+(x(i)-xradarpositon)^2)+random('Normal',0,rangeerror,1,1);

xx(i)=Zmeasure(2,i)*cos(Zmeasure(1,i));%%观测值

yy(i)=Zmeasure(2,i)*sin(Zmeasure(1,i));

measureerror=[azimutherror^2 0;0 rangeerror^2];

processerror=tao*processnoise;

vNoise = size(processerror,1);

wNoise = size(measureerror,1);

A=[1 t 0 0;

0 1 0 0;

0 0 1 t;

0 0 0 1];

Anoise=size(A,1);

for j=1:2*L+1

Wm(j)=1/(2*(L+ramda));

Wc(j)=1/(2*(L+ramda));

end

Wm(1)=ramda/(L+ramda);

Wc(1)=ramda/(L+ramda);%+1-alpha^2+belta; %%%权值

if i==1

xerror=rangeerror^2*cos(Zmeasure(1,i))^2+Zmeasure(2,i)^2*azimutherror^2*sin(Zmeasure(1,i))^2; yerror=rangeerror^2*sin(Zmeasure(1,i))^2+Zmeasure(2,i)^2*azimutherror^2*cos(Zmeasure(1,i))^2; xyerror=(rangeerror^2-Zmeasure(2,i)^2*azimutherror^2)*sin(Zmeasure(1,i))*cos(Zmeasure(1,i));

P=[xerror xerror/t xyerror xyerror/t;

xerror/t 2*xerror/(t^2) xyerror/t 2*xyerror/(t^2);

xyerror xyerror/t yerror yerror/t;

xyerror/t 2*xyerror/(t^2) yerror/t 2*yerror/(t^2)];

xestimate=[Zmeasure(2,i)*cos(Zmeasure(1,i)) 0 Zmeasure(2,i)*sin(Zmeasure(1,i)) 0 ]'; end

cho=(chol(P*(L+ramda)))';%

for j=1:L

xgamaP1(:,j)=xestimate+cho(:,j);

xgamaP2(:,j)=xestimate-cho(:,j);

end

Xsigma=[xestimate xgamaP1 xgamaP2];

F=A;

Xsigmapre=F*Xsigma;

xpred=zeros(Anoise,1);

for j=1:2*L+1

xpred=xpred+Wm(j)*Xsigmapre(:,j);

end

Noise1=Anoise;

ppred=zeros(Noise1,Noise1);

for j=1:2*L+1

ppred=ppred+Wc(j)*(Xsigmapre(:,j)-xpred)*(Xsigmapre(:,j)-xpred)';

end

ppred=ppred+processerror;

chor=(chol((L+ramda)*ppred))';

for j=1:L

XaugsigmaP1(:,j)=xpred+chor(:,j);

XaugsigmaP2(:,j)=xpred-chor(:,j);

end

Xaugsigma=[xpred XaugsigmaP1 XaugsigmaP2 ];

for j=1:2*L+1

Ysigmapre(1,j)=atan(Xaugsigma(3,j)/Xaugsigma(1,j)) ;

Ysigmapre(2,j)=sqrt((Xaugsigma(1,j))^2+(Xaugsigma(3,j))^2);

end

ypred=zeros(2,1);

for j=1:2*L+1

ypred=ypred+Wm(j)*Ysigmapre(:,j);

end

Pzz=zeros(2,2);

for j=1:2*L+1

Pzz=Pzz+Wc(j)*(Ysigmapre(:,j)-ypred)*(Ysigmapre(:,j)-ypred)';

end

Pzz=Pzz+measureerror;