[Paper Review] Poisson Multi-Bernoulli Approximations for Multiple Extended Object Filtering

Yuxuan Xia, Karl Granström+4 more|arXiv (Cornell University)|Jan 4, 2018

Target Tracking and Data Fusion in Sensor Networks71 references4 citations

TL;DR

This paper proposes two computationally efficient Poisson multi-Bernoulli (PMB) filters for multiple extended object tracking by introducing a novel local hypothesis representation where each measurement generates a new Bernoulli component. Using track-oriented and variational multi-Bernoulli approximations, the PMB filters achieve near-PMBM performance with significantly reduced complexity, especially in high-coalescence scenarios where variational methods outperform track-oriented approaches.

ABSTRACT

The Poisson multi-Bernoulli mixture (PMBM) is a multi-object conjugate prior for the closed-form Bayes random finite sets filter. The extended object PMBM filter provides a closed-form solution for multiple extended object filtering with standard models. This paper considers computationally lighter alternatives to the extended object PMBM filter by propagating a Poisson multi-Bernoulli (PMB) density through the filtering recursion. A new local hypothesis representation is presented where each measurement creates a new Bernoulli component. This facilitates the developments of methods for efficiently approximating the PMBM posterior density after the update step as a PMB. Based on the new hypothesis representation, two approximation methods are presented: one is based on the track-oriented multi-Bernoulli (MB) approximation, and the other is based on the variational MB approximation via Kullback-Leibler divergence minimisation. The performance of the proposed PMB filters with gamma Gaussian inverse-Wishart implementations are evaluated in a simulation study.

Motivation & Objective

• To reduce the computational complexity of the extended object Poisson multi-Bernoulli mixture (PMBM) filter while preserving estimation accuracy.
• To address the challenges of determining the number of Bernoulli components, selecting which hypotheses to merge, and merging them effectively in extended object filtering.
• To develop a more efficient local hypothesis representation where each measurement generates a new Bernoulli component, reducing the number of components compared to traditional subset-based representations.
• To evaluate two PMB approximation methods—track-oriented and variational—on extended object filtering with gamma-Gaussian inverse-Wishart (GGIW) models.
• To demonstrate that the proposed PMB filters offer a favorable trade-off between accuracy and computational efficiency, particularly in dense and coalescing scenarios.

Proposed method

• Introduce a new local hypothesis representation where each measurement creates a distinct Bernoulli component, drastically reducing the number of components compared to subset-based representations.
• Develop the track-oriented PMB (TO-PMB) filter using a nearest-neighbor-like assignment to merge hypotheses, minimizing computational cost in the prediction and update steps.
• Propose the variational PMB (V-PMB) filter that minimizes the Kullback–Leibler divergence between the true PMBM posterior and the approximated PMB density to improve accuracy.
• Implement both filters using the gamma-Gaussian inverse-Wishart (GGIW) family for extended object states, enabling closed-form propagation of kinematic and extent parameters.
• Apply the PMB filters recursively through prediction and update steps, maintaining a PMB density throughout the filtering process.
• Use the GGIW family to model object states and birth processes, enabling conjugate filtering and efficient computation of posterior moments.

Experimental results

Research questions

• RQ1 Can a PMB approximation of the extended object PMBM filter be constructed with significantly reduced computational complexity while maintaining high estimation accuracy?
• RQ2 How does a measurement-based local hypothesis representation compare to subset-based representations in terms of component count and filtering performance?
• RQ3 Does the variational PMB approximation, based on KL divergence minimization, outperform the track-oriented MB approximation in scenarios with high data association uncertainty or object coalescence?
• RQ4 How do the proposed PMB filters perform relative to the full PMBM filter and other state-of-the-art filters (e.g., MBM, LMB) in terms of GOSPA error and computational time?
• RQ5 What is the impact of birth model choice (Poisson vs. MB) on the performance and efficiency of PMB-based extended object filters?

Key findings

• The PMBM filter achieves the best overall estimation performance across all scenarios, serving as the performance benchmark.
• The V-PMB-LP filter, based on variational approximation, achieves estimation performance closest to the PMBM filter and significantly outperforms the TO-PMB-M filter, especially in high-coalescence scenarios.
• The TO-PMB-C variant, which creates more Bernoulli components, shows slightly better accuracy than TO-PMB-M but incurs higher computational cost due to increased component count.
• All PMB filters with a Poisson birth model outperform their counterparts with a multi-Bernoulli (MB) birth model in both estimation accuracy and computational efficiency.
• The V-PMB-LP filter exhibits the lowest data association uncertainty, as it maintains fewer Bernoulli components, reducing ambiguity in measurement-to-object association.
• The mean cycle time for the V-PMB-LP filter is significantly lower than that of the PMBM filter, demonstrating a strong computational advantage with minimal performance loss.