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ukf_update1

PURPOSE ^

UKF_UPDATE1 - Additive form Unscented Kalman Filter update step

SYNOPSIS ^

function [M,P,K,MU,S,LH] = ukf_update1(M,P,Y,h,R,h_param,alpha,beta,kappa,mat)

DESCRIPTION ^

UKF_UPDATE1 -  Additive form Unscented Kalman Filter update step

 Syntax:
   [M,P,K,MU,S,LH] = UKF_UPDATE1(M,P,Y,h,R,param,alpha,beta,kappa,mat)

 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               (optional, default empty)
   alpha - Transformation parameter      (optional)
   beta  - Transformation parameter      (optional)
   kappa - Transformation parameter      (optional)
   mat   - If 1 uses matrix form         (optional, default 0)

 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 Discrete Unscented Kalman Filter (UKF)
   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] = ukf_update(M1,P1,Y,h,R,S);

 See also:
   UKF_PREDICT1, UKF_PREDICT2, UKF_UPDATE2, UKF_PREDICT3, UKF_UPDATE3,
   UT_TRANSFORM, UT_WEIGHTS, UT_MWEIGHTS, UT_SIGMAS

 History:
   08.02.2008 JH Fixed a typo in the syntax description.
   04.05.2007 JH Made corrections to the description.
   02.05.2007 JH Fixed a bug in likelihood calculation and added
              a "See also"-section.
   2002-2006  SS Initial version


 References:
   [1] Wan, Merwe: The Unscented Kalman Filter

CROSS-REFERENCE INFORMATION ^

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