Title :
Analysis of Kalman Filter Approximations for Nonlinear Measurements
Author :
Morelande, Mark R. ; Garcia-Fernandez, Angel F.
Author_Institution :
Melbourne Syst. Lab., Univ. of Melbourne, Parkville, VIC, Australia
Abstract :
A theoretical analysis is presented of the correction step of the Kalman filter (KF) and its various approximations for the case of a nonlinear measurement equation with additive Gaussian noise. The KF is based on a Gaussian approximation to the joint density of the state and the measurement. The analysis metric is the Kullback-Leibler divergence of this approximation from the true joint density. The purpose of the analysis is to provide a quantitative tool for understanding and assessing the performance of the KF and its variants in nonlinear scenarios. This is illustrated using a numerical example.
Keywords :
AWGN; Kalman filters; approximation theory; filtering theory; Gaussian approximation; Kalman filter approximation analysis; Kullback-Leibler divergence; additive Gaussian noise; nonlinear measurement equation; true joint density; Approximation methods; Covariance matrices; Density measurement; Equations; Joints; Kalman filters; Noise measurement; Bayesian filtering; Kalman filtering; Kullback-Leibler divergence; nonlinear measurement;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2013.2279367
