c9l1.m

这是zarchan书的fundamentals of kalman filter的matlab原程序.对学习卡尔曼滤波非常有帮助

TS=1.;
ORDER=4;
PHIS=0.;
SIGTH=.01;
SIGR=100.;
VT=3000.;
GAMDEG=45.;
G=32.2;
XT=0.;
YT=0.;
XTD=VT*cos(GAMDEG/57.3);
YTD=VT*sin(GAMDEG/57.3);
XR=100000.;
YR=0.;
T=0.;
S=0.;
H=.001;
PHI=[1 TS 0 0;0 1 0 0;0 0 1 TS;0 0 0 1];
P=[1000.^2 0 0 0;0 100.^2 0 0;0 0 1000.^2 0;0 0 0 100.^2];
IDNP=eye(ORDER);
Q=zeros(ORDER,ORDER);
TS2=TS*TS;
TS3=TS2*TS;
Q(1,1)=PHIS*TS3/3.;
Q(1,2)=PHIS*TS2/2.;
Q(2,1)=Q(1,2);
Q(2,2)=PHIS*TS;
Q(3,3)=Q(1,1);
Q(3,4)=Q(1,2);
Q(4,3)=Q(3,4);
Q(4,4)=Q(2,2);
PHIT=PHI';
RMAT=[SIGTH^2 0;0 SIGR^2];
XTH=XT+1000.;
XTDH=XTD-100.;
YTH=YT-1000.;
YTDH=YTD+100.;
count=0;
while YT>=0.
	XTOLD=XT;
	XTDOLD=XTD;
	YTOLD=YT;
	YTDOLD=YTD;
	XTDD=0.;
 	YTDD=-G;
 	XT=XT+H*XTD;
 	XTD=XTD+H*XTDD;
	YT=YT+H*YTD;
	YTD=YTD+H*YTDD;
	T=T+H;
	XTDD=0.;
 	YTDD=-G;
 	XT=.5*(XTOLD+XT+H*XTD);
 	XTD=.5*(XTDOLD+XTD+H*XTDD);
	YT=.5*(YTOLD+YT+H*YTD);
	YTD=.5*(YTDOLD+YTD+H*YTDD);
	S=S+H;
	if S>=(TS-.00001)
		S=0.;
		XTB=XTH+TS*XTDH;
		XTDB=XTDH;
		YTB=YTH+TS*YTDH-.5*G*TS*TS;
		YTDB=YTDH-G*TS;
		RTB=sqrt((XTB-XR)^2+(YTB-YR)^2);
		HMAT(1,1)=-(YTB-YR)/RTB^2;
		HMAT(1,2)=0.;
		HMAT(1,3)=(XTB-XR)/RTB^2;
		HMAT(1,4)=0.;
		HMAT(2,1)=(XTB-XR)/RTB;
		HMAT(2,2)=0.;
		HMAT(2,3)=(YTB-YR)/RTB;
		HMAT(2,4)=0.;
		HT=HMAT';
		PHIP=PHI*P;
		PHIPPHIT=PHIP*PHIT;
		M=PHIPPHIT+Q;
		HM=HMAT*M;
		HMHT=HM*HT;
		HMHTR=HMHT+RMAT;
		HMHTRINV=inv(HMHTR);
		MHT=M*HT;
		K=MHT*HMHTRINV;
		KH=K*HMAT;
		IKH=IDNP-KH;
		P=IKH*M;
		THETNOISE=SIGTH*randn;
		RTNOISE=SIGR*randn;
		THET=atan2((YT-YR),(XT-XR));
		RT=sqrt((XT-XR)^2+(YT-YR)^2);
		THETMEAS=THET+THETNOISE;
		RTMEAS=RT+RTNOISE;
		THETB=atan2((YTB-YR),(XTB-XR));
		RTB=sqrt((XTB-XR)^2+(YTB-YR)^2);
		RES1=THETMEAS-THETB;
		RES2=RTMEAS-RTB;
		XTH=XTB+K(1,1)*RES1+K(1,2)*RES2;
		XTDH=XTDB+K(2,1)*RES1+K(2,2)*RES2;
		YTH=YTB+K(3,1)*RES1+K(3,2)*RES2;
		YTDH=YTDB+K(4,1)*RES1+K(4,2)*RES2;
		ERRX=XT-XTH;
		SP11=sqrt(P(1,1));
		ERRXD=XTD-XTDH;
		SP22=sqrt(P(2,2));
		ERRY=YT-YTH;
		SP33=sqrt(P(3,3));
		ERRYD=YTD-YTDH;
		SP44=sqrt(P(4,4));
		SP11P=-SP11;
		SP22P=-SP22;
		SP33P=-SP33;
		SP44P=-SP44;
		count=count+1;
		ArrayT(count)=T;
		ArrayXT(count)=XT;
		ArrayXTH(count)=XTH;
		ArrayYT(count)=YT;
		ArrayYTH(count)=YTH;
		ArrayXTD(count)=XTD;
		ArrayXTDH(count)=XTDH;
		ArrayYTD(count)=YTD;
		ArrayYTDH(count)=YTDH;
		ArrayERRX(count)=ERRX;
		ArraySP11(count)=SP11;
		ArraySP11P(count)=SP11P;
		ArrayERRXD(count)=ERRXD;
		ArraySP22(count)=SP22;
		ArraySP22P(count)=SP22P;
		ArrayERRY(count)=ERRY;
		ArraySP33(count)=SP33;
		ArraySP33P(count)=SP33P;
		ArrayERRYD(count)=ERRYD;
		ArraySP44(count)=SP44;
		ArraySP44P(count)=SP44P;
	end
end
figure
plot(ArrayT,ArrayERRX,ArrayT,ArraySP11,ArrayT,ArraySP11P),grid
xlabel('Time (Sec)')
ylabel('Error in Estimate of Downrange (Ft)')
axis([0 140 -170 170])
figure
plot(ArrayT,ArrayERRXD,ArrayT,ArraySP22,ArrayT,ArraySP22P),grid
xlabel('Time (Sec)')
ylabel('Error in Estimate of Downrange Velocity (Ft/Sec)')
axis([0 140 -20 20])
figure
plot(ArrayT,ArrayERRY,ArrayT,ArraySP33,ArrayT,ArraySP33P),grid
xlabel('Time (Sec)')
ylabel('Error in Estimate of Altitude (Ft)')
axis([0 140 -700 700])
figure
plot(ArrayT,ArrayERRYD,ArrayT,ArraySP44,ArrayT,ArraySP44P),grid
xlabel('Time (Sec)')
ylabel('Error in Estimate of Altitude Velocity (Ft/Sec)')
axis([0 140 -20 20])
clc
output=[ArrayT',ArrayXT',ArrayXTH',ArrayXTD',ArrayXTDH',ArrayYT',ArrayYTH',...
ArrayYTD',ArrayYTDH'];
save datfil.txt output  -ascii
output=[ArrayT',ArrayERRX',ArraySP11',ArraySP11P',ArrayERRXD',ArraySP22',...
ArraySP22P',ArrayERRY',ArraySP33',ArraySP33P',ArrayERRYD',ArraySP44',ArraySP44P'];
save covfil.txt output  -ascii
disp 'simulation finished'