Resource-Constrained Adaptive Search and Tracking for Sparse Dynamic Targets

This paper considers the problem of resource-constrained and noise-limited localization and estimation of dynamic targets that are sparsely distributed over a large area. We generalize an existing framework [Bashan et al, 2008] for adaptive allocation of sensing resources to the dynamic case, accounting for timevarying target behavior such as transitions to neighboring cells and varying amplitudes over a potentially long time horizon. The proposed adaptive sensing policy is driven by minimization of a surrogate function for mean squared error within locations containing targets. We provide theoretical upper bounds on the performance of adaptive sensing policies by analyzing solutions with oracle knowledge of target locations, gaining insight into the effect of target motion and amplitude variation as well as sparsity. Exact minimization of the multi-stage objective function is infeasible, but myopic optimization yields a closed-form solution. We propose a simple non-myopic extension, the Dynamic Adaptive Resource Allocation Policy (D-ARAP), that allocates a fraction of resources for exploring all locations rather than solely exploiting the current belief state. Our numerical studies indicate that D-ARAP has the following advantages: (a) it is more robust than the myopic policy to noise, missing data, and model mismatch; (b) it performs comparably to well-known approximate dynamic programming solutions but Gregory Newstadt and Alfred Hero are with the Dept. of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, E-mail: ({newstage},{hero}@umich.edu). Dennis Wei is with the IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA, E-mail: [email protected]. The research in this paper was partially supported by Air Force Office of Scientific Research award FA9550-06-1-0324, by Air Force Research Laboratory award FA8650-07-D-1221-TO1, and by Army Research Office MURI grant number W911NF11-1-0391. This work was presented in part at IEEE CAMSAP 2013 and Asilomar Conference on Signals, Systems and Computers 2011. 2 at significantly lower computational complexity; and (c) it improves greatly upon non-adaptive uniform resource allocation in terms of estimation error and probability of detection.