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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);

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
2002-2006  SS Initial version

References:
 Wan, Merwe: The Unscented Kalman Filter```

## CROSS-REFERENCE INFORMATION This function calls:
This function is called by:
• uimm_smooth UIMM_SMOOTH UKF based Fixed-interval IMM smoother using two IMM-UKF filters.
• uimm_update IMM_UPDATE UKF based Interacting Multiple Model (IMM) Filter update step
• utf_smooth1 UTF_SMOOTH1 Smoother based on two unscented Kalman filters

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