%
%?Example?5.8
%
close?all;
clear?all;
clf;
disp（‘Covariance?analysis?of?radar?tracking?problem‘）;
disp（‘given?as?Example?5.8?in‘）;
disp（‘M.?S.?Grewal?and?A.?P.?Andrews‘）;
disp（‘Kalman?Filtering:?Theory?and?Practice?Using?MATLAB‘）;
disp（‘4th?Edition?Wiley?2014.‘）;
disp（‘?‘）;
disp（‘Plots?histories?of?six?mean?squared?state‘）;
disp（‘uncertainties?and?six?magnitudes?of?Kalman?gains‘）;
disp（‘for?intersample?intervals?of?5?10?and?15?seconds.‘）;
disp（‘?‘）;
disp（‘Six?state?variables:‘）;
disp（‘??1.?Range?to?object?being?tracked.‘）;
disp（‘??2.?Range?rate?of?object?being?tracked.‘）;
disp（‘??3.?object?range?maneuvering?noise?（pseudo?state）.‘）;
disp（‘??4.?Bearing?to?object?being?tracked.‘）;
disp（‘??5.?Bearing?rate?of?object?being?tracked.‘）;
disp（‘??6.?object?bearing?maneuvering?noise?（pseudo?state）.‘）;
disp（‘Pseudo?states?are?used?for?modeling?correlated?noise.‘）;
%
sigma1sq?=?（103/3）^2;
sigma2sq?=?1.3E-8;
sigmarsq?=?（1000）^2;
sigmatsq?=?（.017）^2;
rho??????=?0.5;
%
%?State?Transition?matrix?（the?part?not?depending?on?T）
%
Phi??????=?eye（6）;
Phi（23）?=?1;
Phi（56）?=?1;
Phi（33）?=?rho;
Phi（66）?=?rho;
Q????????=?zeros（6）;
Q（33）???=?sigma1sq;
Q（66）???=?sigma2sq;
R????????=?zeros（2）;
R（11）???=?sigmarsq;
R（22）???=?sigmatsq;
H????????=?zeros（26）;
H（11）???=?1;
H（24）???=?1;
%
%?arrays?for?saving?data?to?be?plotted
%
t????????=?zeros（332）;?%?time?（for?3?plots）
rcov?????=?zeros（332）;?%?Range?covariance
rrcov????=?zeros（332）;?%?Range?Rate?covariance
bcov?????=?zeros（332）;?%?Bearing?covariance
brcov????=?zeros（332）;?%?Bearing?Rate?covariance
rrncov???=?zeros（332）;?%?Range?Rate?Noise?covariance
brncov???=?zeros（332）;?%?Bearing?Rate?Noise?covariance
rkg??????=?zeros（332）;?%?Range?Kalman?gain
rrkg?????=?zeros（332）;?%?Range?Rate?Kalman?gain
bkg??????=?zeros（332）;?%?Bearing?Kalman?gain
brkg?????=?zeros（332）;?%?Bearing?Rate?Kalman?gain
rrnkg????=?zeros（332）;?%?Range?Rate?Noise?Kalman?gain
brnkg????=?zeros（332）;?%?Bearing?Rate?Noise?Kalman?gain
N=0;
???for?T?=?5:5:15
???N=N+1;
???disp（[‘Simulating?tracking?at?‘num2str（T）‘?second?intervals.‘]）;
???Phi（12）?=?T;
???Phi（45）?=?T;
???P????????=?zeros（6）;
???P（11）???=?sigmarsq;
???P（12）???=?sigmarsq/T;
???P（21）???=?P（12）;
???P（22）???=?2*sigmarsq/T^2?+?sigma1sq;
???P（33）???=?sigma1sq;
???P（44）???=?sigmatsq;
???P（45）???=?sigmatsq/T;
???P（54）???=?P（45）;
???P（55）???=?2*sigmatsq/T^2?+?sigma2sq;
???P（66）???=?sigma2sq;
??????for?cycle=0:15
%
%?Save?a?priori?values
%
??????prior??????=?2*cycle+1;
??????t（Nprior）?=?T*cycle;
??????K??????????=?P*H‘/（H*P*H‘+R）;
??????rcov（Nprior）???=?P（11）;?%?Range?covariance
??????rrcov（Nprior）??=?P（22）;?%?Range?Rate?covariance
??????bcov（Nprior）???=?P（44）;?%?Bearing?covariance
??????brcov（Nprior）??=?P（55）;?%?Bearing?Rate?covariance
??????rrncov（Nprior）?=?P（33）;?%?Range?Rate?Noise?covariance
??????brncov（Nprior）?=?P（66）;?%?Bearing?Rate?Noise?covariance
??????rkg