srfaur
srfaur — square-root algorithm
Calling sequence
[p,s,t,l,rt,tt]=srfaur(h,f,g,r0,n,p,s,t,l)
Parameters
| h, f, g | : convenient matrices of the state-space model. |
| r0 | : E(yk*yk'). |
| n | : number of iterations. |
| p | : estimate of the solution after n iterations. |
| s, t, l | : intermediate matrices for successive iterations; |
| rt, tt | : gain matrices of the filter model after n iterations. |
| p, s, t, l | : may be given as input if more than one recursion is desired (evaluation of intermediate values of p). |
Description
square-root algorithm for the algebraic Riccati equation.
Examples
//GENERATE SIGNAL
x=%pi/10:%pi/10:102.4*%pi;
rand('seed',0);rand('normal');
y=[1;1]*sin(x)+[sin(2*x);sin(1.9*x)]+rand(2,1024);
//COMPUTE CORRELATIONS
c=[];for j=1:2,for k=1:2,c=[c;corr(y(k,:),y(j,:),64)];end;end
c=matrix(c,2,128);
//FINDING H,F,G with 6 states
hk=hank(20,20,c);
[H,F,G]=phc(hk,2,6);
//SOLVING RICCATI EQN
r0=c(1:2,1:2);
[P,s,t,l,Rt,Tt]=srfaur(H,F,G,r0,200);
//Make covariance matrix exactly symetric
Rt=(Rt+Rt')/2
See also
phc, faurre, lindquist
