Stein Coverage: A Variational Inference Approach to Distribution-Matching Multisensor Deployment

This letter addresses a spatial coverage optimization problem where multiple heterogeneous sensors are deployed in a convex environment with a known area priority function. Each sensor's coverage is defined by an anisotropic spatial distribution. We introduce the Stein Coverage algorithm, a distribution-matching coverage approach that aims to place sensors at positions and orientations that result in a collective coverage distribution that is as close as possible to the event distribution. To select the most important representative points from the coverage event distribution, Stein Coverage utilizes the Stein Variational Gradient Descent (SVGD), a deterministic sampling method from the variational inference literature. An innovation in our work is the introduction of a repulsive force between the samples in the SVGD algorithm to spread the samples and avoid footprint overlap for the deployed sensors. After pinpointing the points of interest for deployment, Stein Coverage solves the multisensor assignment problem using a bipartite optimal matching process. Simulations demonstrate the advantages of the Stein Coverage method compared to conventional Voronoi partitioning multisensor deployment methods.