Asymptotic Optimality of the Maximum-Likelihood Kalman Filter for Bayesian Tracking With Multiple Nonlinear Sensors

Bayesian tracking is a general technique for state estimation of nonlinear dynamic systems, but it suffers from the drawback of computational complexity. This paper is concerned with a class of Wiener systems with multiple nonlinear sensors. Such a system consists of a linear dynamic system followed...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2015-09, Vol.63 (17), p.4502-4515
Main Authors: Marelli, Damian, Minyue Fu, Ninness, Brett
Format: Article
Language:English
Subjects:
Approximation methods
Bayes methods
Bayesian tracking
distributed estimation
Kalman filters
Mathematical model
maximum likelihood
Maximum likelihood estimation
sensor networks
Sensors
Signal processing algorithms
Wiener systems
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Summary:Bayesian tracking is a general technique for state estimation of nonlinear dynamic systems, but it suffers from the drawback of computational complexity. This paper is concerned with a class of Wiener systems with multiple nonlinear sensors. Such a system consists of a linear dynamic system followed by a set of static nonlinear measurements. We study a maximum-likelihood Kalman filtering (MLKF) technique which involves maximum-likelihood estimation of the nonlinear measurements followed by classical Kalman filtering. This technique permits a distributed implementation of the Bayesian tracker and guarantees the boundedness of the estimation error. The focus of this paper is to study the extent to which the MLKF technique approximates the theoretically optimal Bayesian tracker. We provide conditions to guarantee that this approximation becomes asymptotically exact as the number of sensors becomes large. Two case studies are analyzed in detail.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2015.2440220