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rts_smooth

PURPOSE ^

RTS_SMOOTH Rauch-Tung-Striebel smoother

SYNOPSIS ^

function [M,P,D] = rts_smooth(M,P,A,Q)

DESCRIPTION ^

RTS_SMOOTH  Rauch-Tung-Striebel smoother

 Syntax:
   [M,P,S] = RTS_SMOOTH(M,P,A,Q)

 In:
   M - NxK matrix of K mean estimates from Kalman filter
   P - NxNxK matrix of K state covariances from Kalman Filter
   A - NxN state transition matrix or NxNxK matrix of K state
       transition matrices for each step.
   Q - NxN process noise covariance matrix or NxNxK matrix
       of K state process noise covariance matrices for each step.

 Out:
   M - Smoothed state mean sequence
   P - Smoothed state covariance sequence
   D - Smoother gain sequence
   
 Description:
   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] = kf_predict(m,P,A,Q);
     [m,P] = kf_update(m,P,Y(:,k),H,R);
     MM(:,k) = m;
     PP(:,:,k) = P;
   end
   [SM,SP] = rts_smooth(MM,PP,A,Q);

 See also:
   KF_PREDICT, KF_UPDATE

CROSS-REFERENCE INFORMATION ^

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