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Scilab help >> Signal Processing > filters > lindquist

# lindquist

Lindquist's algorithm

### Calling Sequence

`[P,R,T]=lindquist(n,H,F,G,R0)`

### Arguments

n

number of iterations.

H, F, G

estimated triple from the covariance sequence of `y`.

R0

E(yk*yk')

P

solution of the Riccati equation after n iterations.

R, T

gain matrices of the filter.

### Description

computes iteratively the minimal solution of the algebraic Riccati equation and gives the matrices `R` and `T` of the filter model, by the Lindquist's algorithm.

### Example

```//Generate signal
x=%pi/10:%pi/10:102.4*%pi;
y=[1; 1] * sin(x) + [sin(2*x); sin(1.9*x)] + rand(2,1024,"normal");

//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);

//Find H,F,G with 6 states
hk=hank(20,20,c);
[H,F,G]=phc(hk,2,6);

//Solve Riccati equation
R0=c(1:2,1:2);
[P,R,T]=lindquist(100,H,F,G,R0);```

• srfaur — square-root algorithm
• faurre — filter computation by simple Faurre algorithm
• phc — Markovian representation