Distributed Target Tracking Using Maximum Likelihood Kalman Filter with Non-Linear Measurements

Abstract

We propose a distributed method for tracking a target with linear dynamics and non-linear measurements acquired by a number of sensors. The proposed method is based on a Bayesian tracking technique called maximum likelihood Kalman filter (MLKF), which is known to be asymptotically optimal, in the mean squared sense, as the number of sensors becomes large. This method requires, at each time step, the solution of a maximum likelihood (ML) estimation problem as well as the Hessian matrix of the likelihood function at the optimal. In order to obtain a distributed method, we compute the ML estimate using a recently proposed fully distributed optimization method, which yields the required Hessian matrix as a byproduct of the optimization procedure. We call the algorithm so obtained the distributed MLKF (DMLKF). Numerical simulation results show that DMLKF largely outperforms other available distributed tracking methods, in terms of tracking accuracy, and that it asymptotically approximates the optimal Bayesian tracking solution, as the number of sensors and inter-node information fusion iterations increase.