[Paper Review] Multisensor Multiobject Tracking with Improved Sampling Efficiency

Wenyu Zhang, Florian Meyer|arXiv (Cornell University)|Dec 30, 2022

Target Tracking and Data Fusion in Sensor Networks4 citations

TL;DR

This paper proposes a particle flow-based sum-product algorithm (SPA-PF) for multisensor multiobject tracking (MOT) in high-dimensional state spaces with nonlinear, low-dimensional measurements. By leveraging particle flow to efficiently propagate particles toward high-likelihood regions, the method avoids particle degeneracy and achieves superior tracking accuracy and runtime efficiency compared to state-of-the-art methods in a 3D passive acoustic monitoring scenario using time-difference-of-arrival (TDOA) measurements.

ABSTRACT

Passive monitoring of acoustic or radio sources has important applications in modern convenience, public safety, and surveillance. A key task in passive monitoring is multiobject tracking (MOT). This paper presents a Bayesian method for multisensor MOT for challenging tracking problems where the object states are high-dimensional, and the measurements follow a nonlinear model. Our method is developed in the framework of factor graphs and the sum-product algorithm (SPA) and implemented using random samples or "particles". The multimodal probability density functions (pdfs) provided by the SPA are effectively represented by a Gaussian mixture model (GMM). To perform the operations of the SPA with improved sample efficiency, we make use of Particle flow (PFL). Here, particles are migrated towards regions of high likelihood based on the solution of a partial differential equation. This makes it possible to obtain good object detection and tracking performance even in challenging multisensor MOT scenarios with single sensor measurements that have a lower dimension than the object positions. We perform a numerical evaluation in a passive acoustic monitoring scenario where multiple sources are tracked in 3-D from 1-D time-difference-of-arrival (TDOA) measurements provided by pairs of hydrophones. Our numerical results demonstrate favorable detection and estimation accuracy compared to state-of-the-art reference techniques.

Motivation & Objective

• To address the challenge of particle degeneracy in high-dimensional, nonlinear multiobject tracking (MOT) with multisensor systems.
• To improve sampling efficiency in Bayesian MOT when object states are high-dimensional and measurements are low-dimensional, such as in TDOA-based acoustic tracking.
• To develop a scalable, graph-based Bayesian framework that maintains accuracy while reducing computational overhead compared to traditional particle filtering and unscented filtering approaches.
• To enable robust tracking of multiple objects in complex scenarios with unknown object counts and measurement-origin uncertainty (MOU).
• To demonstrate the effectiveness of particle flow in maintaining posterior approximation quality during initial object appearance, where beliefs are uninformative and multimodal.

Proposed method

• The method employs a factor graph representation of the MOT problem, with random variables and factors encoding statistical dependencies and measurement models.
• The sum-product algorithm (SPA) is used to compute approximate posterior marginals, with beliefs represented as Gaussian Mixture Models (GMMs) for multimodal distributions.
• Particle flow (PFL) is applied to perform SPA message updates in high-dimensional spaces, replacing standard importance sampling to avoid particle degeneracy.
• PFL uses a homotopy function and a partial differential equation (PDE) to compute particle velocities, enabling systematic migration of particles toward high-likelihood regions of the posterior distribution.
• The approach uses the localized exact Daum and Huang (LEDH) filter variant, which computes PFL equations independently for each particle, improving accuracy at the cost of increased computation.
• The framework is evaluated in a 3D passive acoustic monitoring scenario using time-difference-of-arrival (TDOA) measurements from hydrophone pairs, simulating realistic multisensor MOT conditions.

Experimental results

Research questions

• RQ1 Can particle flow-based message updates in the sum-product algorithm effectively mitigate particle degeneracy in high-dimensional, nonlinear multiobject tracking?
• RQ2 How does the proposed SPA-PF method compare in accuracy and runtime to state-of-the-art MOT techniques such as SPA-UT and SPA-PM in challenging acoustic tracking scenarios?
• RQ3 Does the use of particle flow improve tracking performance during the initial time steps after a new object appears, when posterior beliefs are highly uninformative and multimodal?
• RQ4 To what extent does the method maintain accuracy when measurements are low-dimensional relative to the object state (e.g., 1D TDOA for 3D object states)?
• RQ5 Can the proposed method achieve favorable performance with lower memory requirements than unscented transform-based approaches?

Key findings

• The SPA-PF and SPA-PF-H methods achieve the lowest MOSPA (Multiple Object Tracking Precision) values in 15 out of 18 parameter configurations, with SPA-PF-H consistently outperforming SPA-PF.
• In the scenario with the least informative measurements (σv = 2×10⁻⁶ s), SPA-PM performs best due to reduced particle degeneracy, but SPA-PF-H still achieves the second-best MOSPA and lowest runtime.
• For σv = 5×10⁻⁷ s, where particle degeneracy is most severe, SPA-PF-H achieves a MOSPA of 2.40, significantly lower than SPA-PM (18.60) and SPA-UT-2 (4.28), demonstrating superior robustness.
• The proposed method maintains competitive runtime, with SPA-PF-H averaging 13.19–21.26 seconds per time step, comparable to SPA-UT-1 and SPA-UT-2, while achieving better accuracy.
• The main performance bottleneck occurs at the initial time step after object appearance, where beliefs are multimodal and uninformative, requiring more effective sampling strategies.
• The results confirm that particle flow-based sampling is highly effective in high-dimensional, nonlinear MOT, especially in early tracking stages and with low-dimensional measurements.