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Aide Scilab >> Traitement du Signal > filters > srfaur

# srfaur

square-root algorithm

### Calling Sequence

`[p,s,t,l,rt,tt]=srfaur(h,f,g,r0,n,p,s,t,l)`

### Arguments

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 symmetric
Rt=(Rt+Rt')/2```