%ETF_SMOOTH1  Smoother based on two extended Kalman filters%% Syntax:%   [M,P] = ETF_SMOOTH1(M,P,Y,A,Q,ia,W,aparam,H,R,h,V,hparam,same_p_a,same_p_h)%% In:%   M - NxK matrix of K mean estimates from Kalman filter%   P - NxNxK matrix of K state covariances from Kalman Filter%   Y - Measurement vector%   A - Derivative of a() with respect to state as%       matrix, inline function, function handle or%       name of function in form A(x,param)       (optional, default eye())%   Q - Process noise of discrete model           (optional, default zero)%  ia - Inverse prediction function as vector,%       inline function, function handle or name%       of function in form ia(x,param)           (optional, default inv(A(x))*X)%   W - Derivative of a() with respect to noise q%       as matrix, inline function, function handle%       or name of function in form W(x,param)    (optional, default identity)%   aparam - Parameters of a. Parameters should be a single cell array, vector or a matrix%           containing the same parameters for each step or if different parameters%           are used on each step they must be a cell array of the format%           { param_1, param_2, ...}, where param_x contains the parameters for%           step x as a cell array, a vector or a matrix.   (optional, default empty)%   H  - Derivative of h() with respect to state as matrix,%        inline function, function handle or name%        of function in form H(x,param)%   R  - Measurement noise covariance.%   h  - Mean prediction (measurement model) as vector,%        inline function, function handle or name%        of function in form h(x,param).  (optional, default H(x)*X)%   V  - Derivative of h() with respect to noise as matrix,%        inline function, function handle or name%        of function in form V(x,param).  (optional, default identity)%   hparam - Parameters of h. See the description of aparam for the format of%             parameters.                  (optional, default aparam)%   same_p_a - If 1 uses the same parameters %              on every time step for a    (optional, default 1) %   same_p_h - If 1 uses the same parameters %              on every time step for h    (optional, default 1) %% Out:%   M - Smoothed state mean sequence%   P - Smoothed state covariance sequence%   % Description:%   Two filter nonlinear smoother algorithm. Calculate "smoothed"%   sequence from given extended Kalman filter output sequence%   by conditioning all steps to all measurements.%% Example:%   [...]%% See also:%   ERTS_SMOOTH1, EKF_PREDICT1, EKF_UPDATE1, EKF_PREDICT2, EKF_UPDATE2% History:%   02.08.2007 JH Changed the name to etf_smooth1%   04.05.2007 JH Added the possibility to pass different parameters for a and h%                 for each step.%   2006       SS Initial version.           %% Copyright (C) 2006 Simo S鋜kk