Asymptotic Optimality of the Maximum-likelihood Filter for Bayesian Tracking in Sensor Networks

DAMIÁN MARELLI; MINYUE FU

Ciudad del Cabo

Congreso; IFAC World Congress; 2014

International Federation of Automatic Control

A recently proposed Bayesian tracking procedure for sensor networks approximatesthe update equation, which involves non-linear measurements, with a simple equation usingthe maximum likelihood (ML) estimate of the unknown state. This approach permits anumerically efficient implementation of the tracking procedure, and is suitable for a distributedimplementation. In this paper we study the extent to which this approach approximates thetheoretical Bayesian solution. We provide conditions to guarantee that the approximationbecomes asymptotically exact, as the number of nodes becomes large. This result is relevantin applications where each sensor obtains a measurement with limited information about thestate, but a large number of sensors is available. We apply our result to a case study, and presentnumerical simulations, showing that the approximation error becomes negligible for a relativelysmall number of nodes.