Multisensor Multiobject Tracking with Improved Sampling Efficiency

TL;DR

This work tackles multisensor multiobject tracking with high-dimensional, nonlinear state spaces by integrating factor-graph based SPA with invertible particle flow and Gaussian mixture representations. The method enhances sampling efficiency and handles measurement-origin uncertainty through parallel PFs across GMM components and association hypotheses, yielding asymptotically optimal posterior representations. It demonstrates superior tracking accuracy and computational efficiency in challenging 3-D passive source scenarios and real underwater acoustic data, outperforming traditional bootstrap and unscented PF baselines. The approach offers a scalable, real-time capable framework for passive surveillance and underwater monitoring, with potential for GPU acceleration and broader applications.

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.

Figures (7)

• Figure 1: Particle degeneracy in a tracking scenario with 3-D object state, $\bm{x} = [x_1 \space\space x_2 \space\space x_3]^{\mathrm{T}}\space\space$, and a single 1-D tdoa measurement $z_1$. A single time step in considered. The 1-D tdoa measurement is generated by the sensor shown as gray circle. Assuming no measurement noise, the 1-D tdoa measurement describes potential 3-D object locations on the hyperboloid shown in red. The object, shown in black, is located on the hyperboloid. Note that any other location on the hyperboloid will lead to the same measurement in the case without noise. (a): The prior pdf, $f(\bm{x})$, is Gaussian, with the mean depicted as a big blue dot. 2000 particles, shown as small light blue dots, are drawn from the prior distribution. On the right, the prior and posterior pdf for the case with measurement noise are shown in three separate 2-D plots. Each of these plots is obtained by depicting the prior and posterior pdf along the three axes of the coordinate system. (b): After importance sampling, as performed by the conventional "bootstrap" particle filter, only a single particle has a nonzero weight. This single particle does not accurately represent the posterior pdf $p(\bm{x}|z_1)$ for future processing, e.g., of a measurement, $z_2$, provided by a second sensor.
• Figure 2: Example of pf in the tracking scenario with 3-D object state and a single 1-D tdoa measurement discussed in Fig. \ref{['fig:particleDegeneracy']}. (a): 2000 particles represent the prior pdf at the onset of the flow, i.e., at pseudo time $\lambda=0$, are depicted. (b): An intermediate flow state corresponding to $\lambda=2 \times 10^{-9}$ is shown. The tracks of 8 selected particles are indicated as red dashed line with arrows. (c): At pseudo time $\lambda=1$, particle migration is completed and the resulting particles represent the hyperboloid-shaped posterior pdf. (d): The histogram of the flowed particles together with 1-D prior and posterior pdf is drawn. The representation of the posterior pdf provided by the particles after the flow is much more accurate than the single "degenerated" particle resulting from conventional particle filtering discussed in Fig. \ref{['fig:particleDegeneracy']}. Due to approximations performed in pf, there can be a small mismatch of particles after the flow and the true posterior pdf. Such a mismatch can also be seen in (d) by comparing the posterior pdf with the histogram of particles at $\lambda \space=\space 1$. Invertible pf can eliminate such mismatch and provide an asymptotical optimal representation of the posterior pdf by making it possible to compute particle weights for importance sampling.
• Figure 3: OSPA performance for high uncertainty of prior with $\sigma_{\bm{ \mathsfbr{w} }} = 1$ m/s$^2$. Other parameters are set as $\mu_{\mathrm{fp}}=5$, $\sigma_{\bm{ \mathsfbr{v} }}=10^{-6}\!$ s, $p_{\text{d}}=0.9$.
• Figure 4: OSPA performance for informative measurement model with $\sigma_{\bm{ \mathsfbr{v} }}=5\!\times\!10^{-7}\!$ s. Other parameters are set as $\mu_{\mathrm{fp}}=5$, $\sigma_{\bm{ \mathsfbr{w} }}=0.1$ m/s$^2$, $p_{\text{d}}=0.9$.
• Figure 5: OSPA performance of SPA-PM and SPA-PF-H for different number number of kernels, $N_k$.