Variational Bayesian Inference for Multiple Extended Targets or Unresolved Group Targets Tracking

TL;DR

This work tackles tracking multiple extended or unresolvable group targets in clutter with unknown measurement rates and ambiguous data origins. It introduces an RMM-based Gamma-GIW joint-state model and employs Variational Bayesian Inference to approximate the intractable posterior, enabling simultaneous estimation of target kinematics, extent, and measurement rate. To make the approach practical, two lightweight schemes are proposed: gating+clustering to prune joint association events and a marginal association probability method to avoid full enumeration. Empirical results on simulated and real data show that the proposed RM-VB framework delivers higher accuracy and robustness than several JPDA and RFS-based benchmarks, particularly in cluttered environments. The method offers scalable integration with existing VB-based estimators and provides principled uncertainty quantification for extended-target tracking tasks.

Abstract

In this work, we propose a method for tracking multiple extended targets or unresolvable group targets in a clutter environment. Firstly, based on the Random Matrix Model (RMM), the joint state of the target is modeled as the Gamma Gaussian Inverse Wishart (GGIW) distribution. Considering the uncertainty of measurement origin caused by the clutters, we adopt the idea of probabilistic data association and describe the joint association event as an unknown parameter in the joint prior distribution. Then the Variational Bayesian Inference (VBI) is employed to approximately solve the non-analytical posterior distribution. Furthermore, to ensure the practicability of the proposed method, we further provide two potential lightweight schemes to reduce its computational complexity. One of them is based on clustering, which effectively prunes the joint association events. The other is a simplification of the variational posterior through marginal association probabilities. Finally, the effectiveness of the proposed method is demonstrated by simulation and real data experiments, and we show that the proposed method outperforms current state-of-the-art methods in terms of accuracy and adaptability.

Figures (15)

• Figure 1: An example of a valid joint association event.
• Figure 2: Ground truth of two targets in the simulation scenario. (The circle shows the extended shape of the targets. We use the green dashed line to mark the trajectory of Tar. 1, and the red dashed line to mark the trajectory of Tar. 2. The points on the trajectory specify the position of the targets' center)
• Figure 3: An example MC run of the simulation scenario.
• Figure 4: Simulation results of GWD. (We use different colors to distinguish methods and different markers to distinguish targets. The marker of Tar. 1 is '$\bullet$', and the marker of Tar. 2 is '$\blacktriangle$')
• Figure 5: Simulation results of ${\rm RMSE}_{\mathrm{Pos}}$. (The upper subfigure corresponds to Tar. 1, while the lower subfigure corresponds to Tar. 2)

Theorems & Definitions (5)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5