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ekf_update2

PURPOSE ^

EKF_UPDATE2 2nd order Extended Kalman Filter update step

SYNOPSIS ^

function [M,P,K,IM,S,LH] = ekf_update2(M,P,y,H,H_xx,R,h,V,param)

DESCRIPTION ^

EKF_UPDATE2  2nd order Extended Kalman Filter update step

 Syntax:
   [M,P,K,MU,S,LH] = EKF_UPDATE2(M,P,Y,H,H_xx,R,[h,V,param])

 In:
   M  - Nx1 mean state estimate after prediction step
   P  - NxN state covariance after prediction step
   Y  - Dx1 measurement vector.
   H  - Derivative of h() with respect to state as matrix,
        inline function, function handle or name
        of function in form H(x,param)
   H_xx - DxNxN Hessian of h() with respect to state as matrix,
          inline function, function handle or name of function
          in form H_xx(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)
   param - Parameters of h                              (optional, default empty)

 Out:
   M  - Updated state mean
   P  - Updated state covariance
   K  - Computed Kalman gain
   MU - Predictive mean of Y
   S  - Predictive covariance Y
   LH - Predictive probability (likelihood) of measurement.
   
 Description:
   Extended Kalman Filter measurement update step.
   EKF model is

     y[k] = h(x[k],r),   r ~ N(0,R)

 See also:
   EKF_PREDICT1, EKF_UPDATE1, EKF_PREDICT2, DER_CHECK, LTI_DISC,
   KF_UPDATE, KF_PREDICT

CROSS-REFERENCE INFORMATION ^

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