Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 61, Issue 22, Pages 5477-5484Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2013.2279367
Keywords
Bayesian filtering; Kalman filtering; nonlinear measurement; Kullback-Leibler divergence
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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.
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