Multitarget tracking via restless bandit marginal productivity indices and Kalman filter in discrete time

Abstract

This paper designs, evaluates, and tests a tractable priority-index policy for scheduling target updates in a discrete-time multitarget tracking model, which aims to be close to optimal relative to a discounted or average performance objective accounting for tracking-error variance and measurement costs. The policy is to be used by M phased-array radars who coordinate to track the positions of N targets moving according to independent scalar Gauss-Markov linear dynamics, which allows use of the Kalman filter for track estimation. The paper exploits the natural problem formulation as a multiarmed restless bandit problem (MARBP) with real-state projects subject to deterministic dynamics by deploying Whittle's (1988) index policy for the MARBP. The challenging issues of indexability (existence of the index) and index evaluation are resolved by applying a method recently introduced by the first author for the analysis of real-state restless bandits. Preliminary computational results are reported demonstrating the tractability of index evaluation and comparing the MP index policy against myopic policies advocated in previous work.