Constrained Robust Submodular Sensor Selection with Application to Multistatic Sonar Arrays

Abstract

We develop a framework to select a subset of sensors from a field in which the sensors have an ingrained independence structure. Given an arbitrary independence pattern, we construct a graph that denotes pairwise independence between sensors, which means those sensors may operate simultaneously. The set of all fully-connected subgraphs (cliques) of this independence graph forms the independent sets of matroids over which we maximize the average and minimum of a set of submodular objective functions. The average case is submodular, so it can be approximated. The minimum case is both non-submodular and inapproximable. We propose a novel algorithm called MatSat that exploits submodularity and, as a result, returns a near-optimal solution with approximation guarantees on a relaxed problem that are within a small factor of the average case scenario. We apply this framework to ping sequence optimization for active multistatic sonar arrays by maximizing sensor coverage for both average and minimum case scenarios and derive lower bounds for minimum probability of detection for a fractional number of targets. In these ping sequence optimization simulations, MatSat exceeds the fractional lower bounds and reaches near-optimal performance, and submodular function optimization vastly outperforms traditional approaches and nearly achieves optimal performance.