Constrained Adaptive Sensing

Suppose that we wish to estimate a vector x∈Cn from a small number of noisy linear measurements of the form y=Ax+z, where z represents measurement noise. When the vector x is sparse, meaning that it has only s nonzeros with s≪n, one can obtain a significantly more accurate estimate of x by adaptively selecting the rows of A based on the previous measurements provided that the signal-to-noise ratio (SNR) is sufficiently large. In this paper we consider the case where we wish to realize the potential of adaptivity but where the rows of A are subject to physical constraints. In particular, we examine the case where the rows of A are constrained to belong to a finite set of allowable measurement vectors. We demonstrate both the limitations and advantages of adaptive sensing in this constrained setting. We prove that for certain measurement ensembles, the benefits offered by adaptive designs fall far short of the improvements that are possible in the unconstrained adaptive setting. On the other hand, we also provide both theoretical and empirical evidence that in some scenarios adaptivity does still result in substantial improvements even in the constrained setting. To illustrate these potential gains, we propose practical algorithms for constrained adaptive sensing by exploiting connections to the theory of optimal experimental design and show that these algorithms exhibit promising performance in some representative applications

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 time-varying 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 modified version of the previously introduced ARAP objective function, which is 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 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.Comment: 49 pages, 1 table, 11 figure

Resource Constrained Adaptive Sensing.

RESOURCE CONSTRAINED ADAPTIVE SENSING by Raghuram Rangarajan Chair: Alfred O. Hero III Many signal processing methods in applications such as radar imaging, communication systems, and wireless sensor networks can be presented in an adaptive sensing context. The goal in adaptive sensing is to control the acquisition of data measurements through adaptive design of the input parameters, e.g., waveforms, energies, projections, and sensors for optimizing performance. This dissertation develops new methods for resource constrained adaptive sensing in the context of parameter estimation and detection, sensor management, and target tracking. We begin by investigating the advantages of adaptive waveform amplitude design for estimating parameters of an unknown channel/medium under average energy constraints. We present a statistical framework for sequential design (e.g., design of waveforms in adaptive sensing) of experiments that improves parameter estimation (e.g., scatter coefficients for radar imaging, channel coefficients for channel estimation) performance in terms of reduction in mean-squared error (MSE). We derive optimal adaptive energy allocation strategies that achieve an MSE improvement of more than 5dB over non adaptive methods. As a natural extension to the problem of estimation, we derive optimal energy allocation strategies for binary hypotheses testing under the frequentist and Bayesian frameworks which yield at least 2dB improvement in performance. We then shift our focus towards spatial design of waveforms by considering the problem of optimal waveform selection from a large waveform library for a state estimation problem. Since the optimal solution to this subset selection problem is combinatorially complex, we propose a convex relaxation to the problem and provide a low complexity suboptimal solution that achieves near optimal performance. Finally, we address the problem of sensor and target localization in wireless sensor networks. We develop a novel sparsity penalized multidimensional scaling algorithm for blind target tracking, i.e., a sensor network which can simultaneously track targets and obtain sensor location estimates.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57621/2/rangaraj_1.pd