faurre

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