The Poisson Multi-Bernoulli Mixture (PMBM) density is a conjugate multi-target density for the standard point target model with Poisson point process birth. This means that both the filtering and predicted densities for the set of targets are PMBM. In this paper, we first show that the PMBM density is also conjugate for sets of trajectories with the standard point target measurement model. Second, based on this theoretical foundation, we develop two trajectory PMBM filters that provide recursions to calculate the posterior density for the set of all trajectories that have ever been present in the surveillance area, and the posterior density of the set of trajectories present at the current time step in the surveillance area. These two filters therefore provide complete probabilistic information on the considered trajectories enabling optimal trajectory estimation. Third, we establish that the density of the set of trajectories in any time window, given the measurements in a possibly different time window, is also a PMBM. Finally, the trajectory PMBM filters are evaluated via simulations, and are shown to yield state-of-the-art performance compared to other multi-target tracking algorithms based on random finite sets and multiple hypothesis tracking.
Poisson multi-Bernoulli mixture filter for trajectory measurements
Department of Electrical Engineering and Electronics, University of Liverpool（利兹大学电子工程与电子系）；IPTC, ETSI de Telecomunicación, Universidad Politécnica de Madrid（马德里理工大学电信工程系）
Set-Type Belief Propagation with Applications to Poisson Multi-Bernoulli SLAM
Chungnam National University（忠南大学）；University of Liverpool（利物浦大学）；Universidad Antonio de Nebrija（安东尼奥·德·内布里哈大学）；Chalmers University of Technology（查尔姆斯理工大学）；Linköping University（林雪平大学）
本文提出适用于元素数量未知 RFS 序列因子图的集合型 BP 规则，并将其用于 PMB-SLAM，推导多种新滤波器且性能优于向量型 BP-SLAM。
