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This paper considers the problem of resource-constrained and noise-limitedlocalization and estimation of dynamic targets that are sparsely distributedover a large area. We generalize an existing framework [Bashan et al, 2008] foradaptive allocation of sensing resources to the dynamic case, accounting fortime-varying target behavior such as transitions to neighboring cells andvarying amplitudes over a potentially long time horizon. The proposed adaptivesensing policy is driven by minimization of a modified version of thepreviously introduced ARAP objective function, which is a surrogate functionfor mean squared error within locations containing targets. We providetheoretical upper bounds on the performance of adaptive sensing policies byanalyzing solutions with oracle knowledge of target locations, gaining insightinto the effect of target motion and amplitude variation as well as sparsity.Exact minimization of the multi-stage objective function is infeasible, butmyopic optimization yields a closed-form solution. We propose a simplenon-myopic extension, the Dynamic Adaptive Resource Allocation Policy (D-ARAP),that allocates a fraction of resources for exploring all locations rather thansolely exploiting the current belief state. Our numerical studies indicate thatD-ARAP has the following advantages: (a) it is more robust than the myopicpolicy to noise, missing data, and model mismatch; (b) it performs comparablyto well-known approximate dynamic programming solutions but at significantlylower computational complexity; and (c) it improves greatly upon non-adaptiveuniform resource allocation in terms of estimation error and probability ofdetection.

Resource-Constrained Adaptive Search and Tracking for Sparse Dynamic Targets