erts_smooth1.m

documentation for optimal filtering toolbox for mathematical software package Matlab. The methods i

%ERTS_SMOOTH1  Extended Rauch-Tung-Striebel smoother
%
% Syntax:
%   [M,P,D] = ERTS_SMOOTH1(M,P,A,Q,[a,W,param,same_p])
%
% In:
%   M - NxK matrix of K mean estimates from Unscented Kalman filter
%   P - NxNxK matrix of K state covariances from Unscented Kalman Filter
%   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)
%   a - Mean prediction E[a(x[k-1],q=0)] as vector,
%       inline function, function handle or name
%       of function in form a(x,param)                        (optional, default 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)
%   param - 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)
%   same_p - 1 if the same parameters should be
%            used on every time step                          (optional, default 1)
%                                   
%                         
%
% Out:
%   K - Smoothed state mean sequence
%   P - Smoothed state covariance sequence
%   D - Smoother gain sequence
%   
% Description:
%   Extended Rauch-Tung-Striebel smoother algorithm. Calculate
%   "smoothed" sequence from given Kalman filter output sequence by
%   conditioning all steps to all measurements.
%
% Example:
%
% See also:
%   EKF_PREDICT1, EKF_UPDATE1

% History:
%   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