srfaur

Scilab Function
Last update : 12/01/2004

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` ,