Influence Diagrams for Robust Multi-Target Tracking

TL;DR

This work investigates the limitations of Kalman-filter–based JPDAF for multi-target tracking in colored-noise environments and under ill-conditioned covariance updates. It introduces ID-JPDAF, an influence-diagram–based extension that reformulates the Kalman prediction and update using Gaussian influence diagrams, enabling node removal and arc reversals to avoid covariance inversions. The approach yields enhanced numerical stability and robustness to model mismatch, demonstrated by substantial RMSE reductions (often 30–70%) for moderate-to-high noise correlation, while preserving JPDAF data association performance. The results suggest influence-diagram inference as a promising direction for robust radar-based multi-target tracking and motivate future work on nonlinear dynamics, adaptive tuning, and scalability.

Abstract

Multi-Target Tracking (MTT) is foundational for radar, defense, and autonomous systems, where tracking accuracy directly affects decision-making and safety. For linear systems with Gaussian process and measurement noise, the Kalman filter remains the gold standard for state estimation. However, its performance can degrade in real-world scenarios where measurement noise is temporally correlated. This violates the white-noise assumptions that Kalman filters have. Various approaches include state augmentation of the Kalman filter, but this approach is susceptible to failure due to ill-conditioned problem formulations. This work investigates the limitations of classical Kalman filtering in colored noise environments and presents an influence diagram-based approach to the Joint Probabilistic Data Association Filter (JPDAF). Simulation results on benchmark scenarios demonstrate that the Influence Diagram JPDAF (ID-JPDAF) achieves lower root mean square error (RMSE) than classical methods. These findings highlight the potential of influence diagram models for advancing multi-target tracking performance in radar and related applications.

Figures (6)

• Figure 1: JPDAF Pipeline
• Figure 2: Gaussian influence diagram for discrete-time filtering. Each of these nodes is assumed to be normally distributed, taking the form $x \sim \mathcal{N}(\mu,\, \Sigma)$. The blue nodes are deterministic, and the pink nodes are stochastic
• Figure 3: This figure plots the value of RMSE with the aforementioned simulation setup, where the blue line represents ID-JPDAF and the red line represents JPDAF
• Figure 4: RMSE with the filter mismatch where true values are underestimated.
• Figure 5: RMSE with the filter mismatch where true values are overestimated.