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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) INRIA - 1988 - C. Bunks
//
// 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-en.txt
function [x1,p1]=srkf(y,x0,p0,f,h,q,r)
//square root kalman filter algorithm
//Input to the macro is:
// f,h :current system matrices
// q,r :covariance matrices of dynamics
// :and observation noise
// x0,p0 :state estimate and error variance
// :at t=0 based on data up to t=-1
// y :current observation
//
//Output from the macro is:
// x1,p1 :updated estimate and error covariance
// :at t=1 based on data up to t=0
//!
n=max(size(x0));
p=max(size(y));
j=[chol(r)',0*r];
g=[0*q,chol(q)'];
mat=[h*p0,j;f*p0,g];
[q,tmat]=qr(mat')';
p1=tmat(p+1:p+n,p+1:p+n);
k=tmat(p+1:p+n,1:p);
re=tmat(1:p,1:p);
epsilon=y-h*x0;
x1=f*x0+k*(re**(-1))*epsilon;
endfunction
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