Poisson Multi-Bernoulli Mixture Conjugate Prior for Multiple Extended Target Filtering

Abstract

This paper presents a Poisson multi-Bernoulli mixture (PMBM) conjugate prior for multiple extended object filtering. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture describes the distribution of the targets that have been detected. The prediction and update equations are presented for the standard transition density and measurement likelihood. Both the prediction and the update preserve the PMBM form of the density, and in this sense the PMBM density is a conjugate prior. However, the unknown data associations lead to an intractably large number of terms in the PMBM density, and approximations are necessary for tractability. A gamma Gaussian inverse Wishart implementation is presented, along with methods to handle the data association problem. A simulation study shows that the extended target PMBM filter performs well in comparison to the extended target δ-GLMB and LMB filters. An experiment with Lidar data illustrates the benefit of tracking both detected and undetected targets.

Poisson Multi-Bernoulli Mixture Trackers: Continuity Through Random Finite Sets of Trajectories

“…As in [6], [21]- [24], we hypothesise that the set of trajectories density is a multi-target conjugate prior of the PMBM form, and we will show that the PMBM form is preserved through prediction and update. In tracking with standard models, the PPP represents trajectories that are hypothesised to exist, but have never been detected, e.g., because they have been occluded or have been located in an area where the sensor(s) have low detection probability.…”

LIDAR Extended Object Tracking of a Maritime Vessel Using an Ellipsoidal Contour Model

“…One of the advantages with the Gaussian mixture modelling of the LIDAR measurements is that it enables the use of EKF, which is a well-known tracking method. More recent RFS approaches using the Poisson multi-Bernoulli mixture (PMBM) filter are given in Granström et al [2017a] and Granström et al [2017b]. Together with the most recent approach in Granström et al [2018], these contributions represent the state-of-theart methods in multi-target extended object tracking.…”

Extended Target Marginal Distribution Poisson Multi-Bernoulli Mixture Filter

“…To solve the point MTT problem, in the early stage, many RFS-based filters have been proposed, such as the Probability Hypothesis Density (PHD) filter [ 24 , 25 , 26 ], the Cardinalized Probability Hypothesis Density (CPHD) filter [ 27 , 28 , 29 , 30 ] and a series of multi-Bernoulli (MB) filters [ 31 , 32 , 33 , 34 ]. In recent years, scholars have proposed many RFS-based filters to solve the extended MTT problem, such as PHD for extended target tracking (ETT-PHD) [ 9 , 35 , 36 , 37 ], ETT-CPHD [ 38 , 39 , 40 ], gamma-Gaussian-inverse Wishart-Poisson multi-Bernoulli mixture (GGIW-PMBM) [ 40 , 41 ], GGIW implementation of the Labelled Multi-Bernoulli (GGIW-LMB) [ 42 , 43 ], and so on [ 22 , 44 ].…”

“…This strategy can greatly reduce the target missed detection rate and improve tracking accuracy. In reference [ 40 ], it has been shown that the point target tracking filter based on PMBM conjugate prior outperforms the filter based on the GLMB conjugate prior in terms of tracking accuracy and computing time; thus, in this paper we used the PMBM conjugate prior.…”

“…The existence of a single target can be modeled by a Bernoulli RFS [ 14 , 31 , 32 , 33 , 34 , 40 , 41 , 42 ]. The cardinality of a Bernoulli RFS can either be 1 (with probability ) or empty (with probability ), and the Bernoulli density distribution of can be defined as …”