// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) INRIA - 1989 - G. Le Vey
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution.  The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt

function [P,R,T]=faurre(n,H,F,G,R0)
    //[P,R,T]=faurre(n,H,F,G,R0)
    //macro which computes iteratively the minimal solution of the algebraic
    //Riccati equation and gives the matrices Rt and Tt of the filter model.
    //   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.
    //!

    //initialization
    Pn=G*inv(R0)*G'
    //recursion
    for k=1:n,
        A=(G-F*Pn*H');
        Pn=F*Pn*F'+A/(R0-H*Pn*H')*A',
    end;
    P=Pn
    //gain matrices of the filter.
    R=R0-H*P*H';
    T=(G-F*P*H')/R;
endfunction