Adaptive search for dynamic targets under resource constraints

Abstract

Previous work on resource constrained adaptive search for sparse static targets has produced two-stage allocation policies with desirable properties. For example, for large asymptotic SNR, such policies converge to the true region of interest (ROI) and attain optimal energy allocations relative to exhaustive search. This work investigates the problem of extending previous allocation policies to T >> 2 stages, with particular emphasis on cases where the SNR for any particular stage is considerably less than the asymptotic SNR. Furthermore, a new formulation is given that can account for non-static targets, including a dynamic transition model for target location and a population model to account for targets that leave or enter the scene. Under this formulation, a dynamic adaptive resource allocation policy (D-ARAP) is proposed that performs well and has low computational cost. It is shown that this policy provides significant gains over an exhaustive search policy in both static and dynamic target cases with near optimal performance as T → ∞. Moreover, D-ARAP is shown to be more robust than a greedy (myopic) policy when there are outliers or when targets may be obscured for periods of time. I. MOTIVATIONIn recent years, there has been significant interest in learning the sparse support of a signal β by intelligently choosing the measurement matrix X given noisy measurements of the form y = Xβ + nGiven conditions on X, compressive sensing and sparse approximation methods have shown that one can recover the sparse vector β with probability 1 by using many fewer measurements than the size of β. When the user has the additional degree of freedom to choose X adaptively as measurements are acquired, it has been shown that one can perform significantly better compared to static polices. Benefits include near-optimal gains in estimation error and related cost functions [1], provable convergence to the true support of β [1] often at rates significantly faster than nonadaptive policies [2] and reliably with significantly smaller

Adaptive search for sparse dynamic targets

“…Finally, D-ARAP has increased robustness to noise and model mismatch as compared to myopic policies. The current paper improves upon our preliminary work [7] on a similar problem by further developing the optimization methods, comparing to goldstandard methods in POMDP approximation, and extending the performance analysis.…”

“…In this paper, we provide a Bayesian formulation akin to [1] and [7], namely the Dynamic Adaptive Resource Allocation Policy (D-ARAP). This approach can simultaneously account for multiple targets as well as continuous allocation of sensing resources.…”