%URTS_SMOOTH1  Additive form Unscented Rauch-Tung-Striebel smoother%% Syntax:%   [M,P,D] = URTS_SMOOTH1(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 a matrix A defining%       linear function a(x) = A*x, inline function,%       function handle or name of function in%       form a(x,param)                   (optional, default eye())%   Q - NxN process noise covariance matrix or NxNxK matrix%       of K state process noise covariance matrices for each step.%   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:%   M - 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:%   m = m0;%   P = P0;%   MM = zeros(size(m,1),size(Y,2));%   PP = zeros(size(m,1),size(m,1),size(Y,2));%   for k=1:size(Y,2)%     [m,P] = ukf_predict1(m,P,a,Q);%     [m,P] = ukf_update1(m,P,Y(:,k),h,R);%     MM(:,k) = m;%     PP(:,:,k) = P;%   end%   [SM,SP] = urts_smooth(MM,PP,a,Q);%% See also:%   URTS_SMOOTH2, UKF_PREDICT1, UKF_UPDATE1, UKF_PREDICT2, UKF_UPDATE2,%   UKF_PREDICT3, UKF_UPDATE3, UT_TRANSFORM, UT_WEIGHTS, UT_MWEIGHTS,%   UT_SIGMAS% Copyright (C) 2006 Simo S鋜kk