[Paper Review] Extended target Poisson multi-Bernoulli mixture trackers based on sets of trajectories

Yuxuan Xia, Karl Granström+3 more|arXiv (Cornell University)|Nov 19, 2019

Target Tracking and Data Fusion in Sensor Networks30 references4 citations

TL;DR

This paper proposes two extended target tracking filters based on Poisson multi-Bernoulli mixture (PMBM) distributions over sets of trajectories, enabling explicit track continuity and closed-form prediction/update recursions. The method achieves superior performance over the labeled GLMB filter in both accuracy and computational efficiency, with negligible track switching and a 33x speedup in processing time.

ABSTRACT

The Poisson multi-Bernoulli mixture (PMBM) is a multi-target distribution for which the prediction and update are closed. By applying the random finite set (RFS) framework to multi-target tracking with sets of trajectories as the variable of interest, the PMBM trackers can efficiently estimate the set of target trajectories. This paper derives two trajectory RFS filters for extended target tracking, called extended target PMBM trackers. Compared to the extended target PMBM filter based on sets on targets, explicit track continuity between time steps is provided in the extended target PMBM trackers.

Motivation & Objective

• To address the lack of explicit track continuity in standard PMBM filters for extended target tracking.
• To extend the PMBM framework from sets of targets to sets of trajectories, ensuring consistent trajectory estimation across time steps.
• To derive closed-form prediction and update equations for extended target PMBM filters operating on trajectory RFSs.
• To compare the proposed tracker’s performance against the labeled GLMB filter in terms of accuracy, track continuity, and computational cost.
• To demonstrate that PMBM-based trajectory filtering offers a more efficient parameterization than GLMB for extended target tracking.

Proposed method

• Formulates multi-target tracking as a random finite set (RFS) of trajectories, where each trajectory represents a complete path of a target over time.
• Applies the PMBM conjugate prior to the trajectory RFS, combining a Poisson RFS for undetected targets and a multi-Bernoulli mixture for detected targets.
• Derives closed-form prediction and update equations for the PMBM density over trajectory sets, using the Gamma-Gaussian inverse-Wishart (GGIW) model for extended target extent and kinematics.
• Implements trajectory extraction by selecting the highest-weight MB component and retaining trajectories with existence probability > 0.5.
• Uses the Gaussian Wasserstein Distance (GWD) as a base metric, integrated into a trajectory metric with location/extent error cutoff and track switch cost for performance evaluation.
• Employs Monte Carlo simulations with 100 runs to evaluate tracking performance, including error metrics and processing time.

Experimental results

Research questions

• RQ1 Can the PMBM filter be extended to operate on sets of trajectories for extended target tracking while maintaining closed-form recursions?
• RQ2 Does trajectory-based PMBM filtering provide better track continuity than labeled GLMB filters in challenging scenarios?
• RQ3 How does the computational complexity of the trajectory PMBM tracker compare to the labeled GLMB filter in extended target tracking?
• RQ4 To what extent does the PMBM tracker reduce track switching errors compared to the GLMB filter?
• RQ5 Is the trajectory PMBM tracker more efficient in terms of filtering performance and processing time than existing methods for extended targets?

Key findings

• The extended target PMBM tracker outperforms the δ-GLMB filter in trajectory estimation error, with significantly lower total error and false detection error.
• The tracker exhibits negligible track switch error, indicating stable and consistent trajectory estimation across time steps.
• Processing time for the PMBM tracker was 45 seconds per sequence, compared to 1502 seconds for the GLMB filter, representing a 33x speedup.
• The PMBM tracker maintains explicit track continuity by directly modeling trajectories, avoiding the label-switching issues common in labeled filters.
• The GGIW-PMBM formulation enables efficient parameterization with fewer global hypotheses than δ-GLMB, contributing to improved performance and lower computational cost.
• The simulation results confirm that the PMBM-based trajectory filter is both more accurate and computationally efficient than the state-of-the-art δ-GLMB filter for extended target tracking.