Algebraic Elliptical Extent Estimation for Robust Extended Object Tracking from Partial Contour Observations

Extended object tracking (EOT) has emerged as a critical challenge in modern surveillance and autonomous systems, where high-resolution sensors yield multiple measurements per target in a single scan. This task necessitates the simultaneous estimation of an object’s spatial extent and kinematic states by systematically assimilating distributed detections. In practical scenarios, however, sensor visibility constraints often restrict measurements to partial contours rather than the full object geometry, posing a significant hurdle for accurate state estimation. This paper proposes a robust EOT algorithm that addresses these challenges by extracting elliptical features—including size, orientation, and noise characteristics—in an affine-invariant manner from incomplete measurement sets. By formulating the ellipse-fitting problem through an algebraic solution, the proposed method effectively reconstructs the target’s morphology even under severe self-occlusion. The tracking framework is established as a Bayesian inference problem, utilizing a standard Kalman filter as a recursive estimator to ensure both computational efficiency and numerical robustness. In Monte Carlo simulations in which measurements are restricted to the sensor-facing contour, the proposed method reduces the average extent estimation error, quantified by the Gaussian Wasserstein distance, to 9.15 m, compared with 64.84–70.62 m for three state-of-the-art baselines, while retaining real-time feasibility with an average processing time of 0.94 ms per scan. Experiments on real-world LiDAR vehicle-tracking data further confirm consistent and accurate extent estimation under partial observability and complex maneuvers.