urts_smooth2.m

kalman滤波

%URTS_SMOOTH2  Augmented form Unscented Rauch-Tung-Striebel smoother
%
% Syntax:
%   [M,P,S] = URTS_SMOOTH2(M,P,a,Q,[param,alpha,beta,kappa,mat,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 - Dynamic model function as inline function,
%       function handle or name of function in
%       form a([x;w],param)
%   Q - Non-singular covariance of process noise w
%   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)
%   alpha - Transformation parameter      (optional)
%   beta  - Transformation parameter      (optional)
%   kappa - Transformation parameter      (optional)
%   mat   - If 1 uses matrix form         (optional, default 0)
%   same_p - If 1 uses the same parameters 
%            on every time step      (optional, default 1)   
%
% Out:
%   K - Smoothed state mean sequence
%   P - Smoothed state covariance sequence
%   D - Smoother gain sequence
%   
% Description:
%   Unscented Rauch-Tung-Striebel smoother algorithm. Calculate
%   "smoothed" sequence from given Kalman filter output sequence by
%   conditioning all steps to all measurements.
%
% Example:
%   [...]
%
% See also:
%   URTS_SMOOTH1, UKF_PREDICT2, UKF_UPDATE2

% Copyright (C) 2006 Simo S鋜kk