function [M,P] = ckf_predict(M,P,f,Q,f_param)
% CKF_PREDICT - Cubature Kalman filter prediction step
%
% Syntax:
%   [M,P] = CKF_PREDICT(M,P,[f,Q,f_param])
%
% In:
%   M - Nx1 mean state estimate of previous step
%   P - NxN state covariance of previous step
%   f - Dynamic model function as a matrix A defining
%       linear function f(x) = A*x, inline function,
%       function handle or name of function in
%       form f(x,param)                   (optional, default eye())
%   Q - Process noise of discrete model   (optional, default zero)
%   f_param - Parameters of f               (optional, default empty)
%
% Out:
%   M - Updated state mean
%   P - Updated state covariance
%
% Description:
%   Perform additive form spherical-radial cubature Kalman filter (CKF)
%   prediction step.
%
%   Function f(.) should be such that it can be given a
%   DxN matrix of N sigma Dx1 points and it returns 
%   the corresponding predictions for each sigma
%   point. 
%
% See also:
%   CKF_UPDATE, 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 which arguments are there
  %
  if nargin < 2
    error('Too few arguments');
  end
  if nargin < 3
    f = [];
  end
  if nargin < 4
    Q = [];
  end

  %
  % Apply defaults
  %
  if isempty(f)
    f = eye(size(M,1));
  end
  if isempty(Q)
    Q = zeros(size(M,1));
  end
  
  %
  % Do transform and add process noise
  %
  if nargin < 5
    [M,P] = ckf_transform(M,P,f);      
  else
    [M,P] = ckf_transform(M,P,f,f_param);
  end
  P = P + Q;