function [M,P,K,MU,S,LH] = ckf_update(M,P,Y,h,R,h_param)
% CKF_UPDATE - Cubature Kalman filter update step
%
% Syntax:
% [M,P,K,MU,S,LH] = CKF_UPDATE(M,P,Y,h,R,param)
%
% In:
% M - Mean state estimate after prediction step
% P - State covariance after prediction step
% Y - Measurement vector.
% h - Measurement model function as a matrix H defining
% linear function h(x) = H*x, inline function,
% function handle or name of function in
% form h(x,param)
% R - Measurement covariance.
% h_param - Parameters of h.
%
% Out:
% M - Updated state mean
% P - Updated state covariance
% K - Computed Kalman gain
% MU - Predictive mean of Y
% S - Predictive covariance Y
% LH - Predictive probability (likelihood) of measurement.
%
% Description:
% Perform additive form spherical-radial cubature Kalman filter (CKF)
% measurement update step. Assumes additive measurement noise.
%
% Function h should be such that it can be given
% DxN matrix of N sigma Dx1 points and it returns
% the corresponding measurements for each sigma
% point. This function should also make sure that
% the returned sigma points are compatible such that
% there are no 2pi jumps in angles etc.
%
% Example:
% h = inline('atan2(x(2,:)-s(2),x(1,:)-s(1))','x','s');
% [M2,P2] = ckf_update(M1,P1,Y,h,R,S);
%
% See also:
% CKF_PREDICT, CRTS_SMOOTH, CKF_TRANSFORM, SPHERICALRADIAL
%
% References:
% Arasaratnam and Haykin (2009). Cubature Kalman Filters.
% IEEE Transactions on Automatic Control, vol. 54, no. 5, pp.1254-1269
% Copyright (c) 2010 Arno Solin
%
% This software is distributed under the GNU General Public
% Licence (version 2 or later); please refer to the file
% Licence.txt, included with the software, for details.
%%
%
% Check that all arguments are there
%
if nargin < 5
error('Too few arguments');
end
%
% Do transform and make the update
%
if nargin < 6
[MU,S,C,X] = ckf_transform(M,P,h);
else
[MU,S,C,X] = ckf_transform(M,P,h,h_param);
end
S = S + R;
K = C / S;
M = M + K * (Y - MU);
P = P - K * S * K';
if nargout > 5
LH = gauss_pdf(Y,MU,S);
end