Arithmetic Average Based Multi-sensor TPHD Filter for Distributed Multi-target Tracking

Compared with the probability hypothesis density (PHD) filter for sets of targets, the trajectory probability hypothesis density (TPHD) filter can estimate the sets of trajectories in a principle way and has better target tracking performance. This paper aims at extending the TPHD filter to distributed multi-target tracking (MTT) for the multi-sensor system. However, in the trajectory set based distributed fusion implementation, the trajectory state difference phenomenon makes the clustering and merging techniques unfeasible in trajectory state space. To address this problem, this paper studies the space decomposition of the TPHD and proposes a distributed MTT method based on the TPHD filter with the weighted arithmetic average (WAA) fusion rule. First, we prove the rationality of the space decomposition in the posterior density of the TPHD filter. Then, based on the proposed property, we derive the WAA fusion formulation of the TPHD filter by minimizing the weighted sum of Kullback-Leibler divergences (KLD) from local posterior densities, and develop the analytical Gaussian mixture (GM) implementation with the L-scan approximation. Numerical results demonstrate the efficacy of the proposed fusion method.