Constrained robust submodular sensor selection with applications to multistatic sonar arrays

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 a matroid over which we maximize the minimum of a set of submodular objective functions. We propose a novel algorithm called MatSat that exploits submodularity and, as a result, returns a near-optimal solution with approximation guarantees 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 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.