Von Mises–Based Uncertainty Quantification for Closely Spaced Automotive Radar Targets

Automotive radar systems typically output point estimates for target range, velocity, and angle, which lack intrinsic uncertainty measures. This lack of calibrated uncertainty complicates downstream data association and sensor fusion, particularly for closely spaced or extended targets in dense traffic. The authors investigate whether explicitly modeling angular uncertainty using circular statistics can improve the robustness and integration of direction-of-arrival (DOA) estimation.

The researchers propose a probabilistic neural network that models DOA using a von Mises (VM) distribution, which is naturally suited for angular data. They employ a Product-of-Experts (PoE) formulation to handle multi-target hypotheses and use an ensemble of these models to approximate Bayesian Model Averaging. This approach is compared against an Evidential Deep Learning (EDL) baseline, which uses a Normal-Inverse-Gamma formulation to produce a Student-t predictive distribution in Euclidean space. Both models are evaluated on synthetic radar data representing closely spaced targets, using risk-coverage and ROC/AUROC metrics to assess performance under in-distribution and out-of-distribution (OOD) conditions.

The von Mises ensemble (ENS) achieves lower uncertainty under nominal conditions and demonstrates superior geometric consistency compared to the EDL baseline. While EDL provides smoother uncertainty variation and slightly better ranking consistency for OOD detection, the ENS framework's output—parameterized by mean direction and concentration—allows for direct, closed-form probabilistic integration into association modules. This makes the ENS approach particularly well-suited for unified detection-tracking pipelines where angular geometry is critical.

In autonomous driving, sensor fusion and tracking rely heavily on the reliability of individual measurements. By providing a physically interpretable measure of angular uncertainty that respects the circular nature of radar data, the proposed method reduces the burden on downstream association algorithms. This work highlights a fundamental trade-off in uncertainty-aware perception: the ENS framework prioritizes geometric consistency for seamless integration, whereas the EDL framework offers statistical generality and computational efficiency for resource-constrained edge devices.