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

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.