Convex Clustering for Multistatic Active Sensing via Optimal Mass Transport

In multistatic active sensing, such as active sonar, exploiting the spatial diversity provided by the use of several transmitting and receiving units can lead to increased resolution and target localization performance. For multi-target scenarios, the success of the task depends on correctly identifying the subsets of measurements associated with each target, a problem of combinatorial nature. In this paper, we propose to address this problem using a convex relaxation. In particular, we propose a method inspired by the concept of optimal mass transport capable of jointly performing the measurement clustering and target localization. We show that this method may be interpreted as maximum likelihood estimation on a grid, allowing for local post-processing achieving statistical efficiency. The behavior of the proposed method is illustrated using simulated 2D examples.