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ckf_update

PURPOSE ^

CKF_UPDATE - Cubature Kalman filter update step

SYNOPSIS ^

function [M,P,K,MU,S,LH] = ckf_update(M,P,Y,h,R,h_param)

DESCRIPTION ^

 CKF_UPDATE - Cubature Kalman filter update step

 Syntax:
   [M,P,K,MU,S,LH] = CKF_UPDATE(M,P,Y,h,R,param)

 In:
   M  - Mean state estimate after prediction step
   P  - State covariance after prediction step
   Y  - Measurement vector.
   h  - Measurement model function as a matrix H defining
        linear function h(x) = H*x, inline function,
        function handle or name of function in
        form h(x,param)
   R  - Measurement covariance.
   h_param - Parameters of h.

 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:
   Perform additive form spherical-radial cubature Kalman filter (CKF)
   measurement update step. Assumes additive measurement noise.

   Function h should be such that it can be given
   DxN matrix of N sigma Dx1 points and it returns 
   the corresponding measurements for each sigma
   point. This function should also make sure that
   the returned sigma points are compatible such that
   there are no 2pi jumps in angles etc.

 Example:
   h = inline('atan2(x(2,:)-s(2),x(1,:)-s(1))','x','s');
   [M2,P2] = ckf_update(M1,P1,Y,h,R,S);

 See also:
   CKF_PREDICT, CRTS_SMOOTH, CKF_TRANSFORM, SPHERICALRADIAL

 References:
   Arasaratnam and Haykin (2009). Cubature Kalman Filters.
    IEEE Transactions on Automatic Control, vol. 54, no. 5, pp.1254-1269

CROSS-REFERENCE INFORMATION ^

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