Distributed Gaussian Mixture PHD Filtering Under Communication Constraints

The Gaussian mixture probability hypothesis density (GM-PHD) filter is an almost exact closed-form approximation to the Bayes-optimal multi-target tracking algorithm. Due to its optimality guarantees and ease of implementation, it has been studied extensively in the literature. However, the challenges involved in implementing the GM-PHD filter efficiently in a distributed (multi-sensor) setting have received little attention. The existing solutions for distributed PHD filtering either have a high computational and communication cost, making them infeasible for wireless sensor networks with limited communication bandwidths, and/or are unable to guarantee the asymptotic convergence of the algorithm to an optimal solution. In this paper, we develop a distributed GM-PHD filtering recursion that uses a probabilistic communication rule to limit the communication bandwidth of the algorithm, while ensuring asymptotic convergence of the algorithm. The proposed algorithm uses weighted average consensus of Gaussian mixtures (GMs) to lower (and asymptotically minimise) the Cauchy–Schwarz divergences between the sensors' local estimates. In addition, the proposed probabilistic communication rule is able to avoid the issue of false positives, which has previously been noted to impact the filtering performance of distributed multi-target tracking. Through numerical simulations, it is demonstrated that our proposed method is an effective solution for distributed multi-target tracking in resource-constrained sensor networks.