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etf_smooth1

PURPOSE ^

ETF_SMOOTH1 Smoother based on two extended Kalman filters

SYNOPSIS ^

function [M,P] = etf_smooth1(M,P,Y,A,Q,ia,W,aparam,H,R,h,V,hparam,same_p_a,same_p_h)

DESCRIPTION ^

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

CROSS-REFERENCE INFORMATION ^

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