etf_smooth1.m

用EKF/UKF的Matlab仿真程序包

%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