Yi‐Chieh Sun

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.

The Gaussian mixture probability density (GM‐PHD) filter has become a popular approach to solve the multiple‐target tracking (MTT) problem because it can effectively and efficiently estimate the number of targets and target states that change over time from noisy measurements. In the GM‐PHD filter, the target detection and survival probabilities, and the birth rate are assumed to be constant, irrespective of the target state. However, in some applications, for example, when the target follows the planned trajectory, the detection, survival and birth of the target depend on its state. Besides, when the target reaches a waypoint along the planned trajectory, it will take a manoeuvre to go to the next waypoint, but the GM‐PHD filter does not accommodate manoeuvring targets that switch between several motion models. To address this, we propose a multiple‐model GM‐PHD filter with state‐dependent probabilities, which can explicitly consider the mode transition probabilities, the probabilities of detection and survival, and the birth rate as a function of the target state. The performance of the proposed algorithm is demonstrated by illustrative MTT scenarios which include target manoeuvres during occlusion.