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Aide de Scilab >> Traitement du Signal > filters > faurre

# faurre

filter computation by simple Faurre algorithm

### Calling Sequence

`[P,R,T]=faurre(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 matrix of the filter.

### Description

This function computes iteratively the minimal solution of the algebraic Riccati equation and gives the matrices `R` and `T` of the filter model. The algorithm tries to compute the solution P as the growing limit of a sequence of matrices Pn such that

```-1
Pn+1=F*Pn*F'+(G-F*Pn*h')*(R0-H*Pn*H')  *(G'-H*Pn*F')
-1
P0=G*R0 *G'```

Note that this method may not converge,especially when F has poles near the unit circle. Use preferably the srfaur function.

• srfaur — square-root algorithm
• lindquist — Lindquist's algorithm
• phc — Markovian representation