  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 resource-constrained
applications, or are unable to guarantee the asymptotic convergence of the
distributed PHD 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 optimality of the algorithm. We derive the convergence properties of
this recursion, which uses weighted average consensus of Gaussian mixtures
(GMs) to lower (and asymptotically minimize) the Cauchy-Schwarz divergence
between the sensors' local estimates. In addition, the proposed method 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.
