Extended target trajectory Poisson multi-Bernoulli mixture filters with unknown detection probability

Abstract

In most multi-extended target tracking scenarios, the target detection probability is usually unknown and time-varying, which leads to biased estimation of the state and cardinality of extended targets in online filtering. In addressing the challenge, this paper presents the unknown detection probability extended target trajectory Poisson multi-Bernoulli mixture (U-TPMBM) filter. Compared to the existing extended target Poisson multi-Bernoulli Mixture (PMBM) filter, the U-TPMBM is firstly based on sets of trajectories, which allows for direct output of target trajectory and can lead to improved trajectory estimation performance. Besides, the U-TPMBM filter integrates the unknown detection probability with the target trajectory state and thus obtains the augmented state space. By recursively estimating the augmented states via multi-target filtering approaches, it successfully realizes online and joint estimates of the unknown detection probability and the target trajectory. Finally, the U-TPMBM filter is implemented by the Beta-Gamma Gaussian Inverse Wishart (BGGIW) mixture method, especially the BGGIW-TPMBM filter. The Beta distribution is utilized to propagate densities of the unknown detection probability and the GGIW distribution to propagate densities of the target trajectory. Based on the BGGIW distribution, the trackers's recursive and closed solutions are derived in detail. The simulation experiments demonstrate that the BGGIW-TPMBM proposed in this paper can achieve robust tracking performance, even when dealing with unknown detection probabilities.