faurre

Scilab Function
Last update : April 1993

faurre - filter computation by simple Faurre algorithm

### Calling Sequence

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

### Parameters

- `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.

### See Also

`srfaur`, `lindquist`, `phc`,

### Author

G. Le V.