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faurre

filter computation by simple Faurre algorithm

Syntax

[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.

See also

  • srfaur — square-root algorithm
  • lindquist — Lindquist's algorithm
  • phc — Markovian representation
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Last updated:
Mon Nov 07 14:58:53 CET 2022