Quadratic Kalman Filter for Elliptical Extended Object Tracking based on Decoupling State Components

2025-12-16

AI Summary

In elliptical extended target tracking, joint estimation of kinematic states, orientation, and semi-axis lengths incurs significant higher-order approximation errors. To address this, we propose a deterministic, closed-form, second-order Kalman filtering framework based on state-component decoupling. By separately modeling and analytically decoupling kinematics, ellipse orientation, and axis lengths, our approach eliminates the approximation errors inherent in conventional joint estimation. We further introduce an efficient batch-processing variant that preserves high accuracy while substantially improving computational efficiency. The method integrates elliptical geometric parameterization, radar measurement modeling, and closed-form filter derivation. Evaluated on both synthetic and real-world automotive millimeter-wave radar data, our algorithm achieves accuracy comparable to state-of-the-art sampling-based methods, yet operates orders of magnitude faster—establishing a new paradigm for real-time, high-precision extended target tracking.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Motion & Tracking
• Machine Learning: Kernel Methods

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Extended object tracking involves estimating both the physical extent and kinematic parameters of a target object, where typically multiple measurements are observed per time step. In this article, we propose a deterministic closed-form elliptical extended object tracker, based on decoupling of the kinematics, orientation, and axis lengths. By disregarding potential correlations between these state components, fewer approximations are required for the individual estimators than for an overall joint solution. The resulting algorithm outperforms existing algorithms, reaching the accuracy of sampling-based procedures. Additionally, a batch-based variant is introduced, yielding highly efficient computation while outperforming all comparable state-of-the-art algorithms. This is validated both by a simulation study using common models from literature, as well as an extensive quantitative evaluation on real automotive radar data.

Problem

• Estimates target object's kinematics and physical extent
• Decouples state components to reduce approximations needed
• Outperforms existing algorithms in accuracy and efficiency

Innovation

• Decoupling kinematics, orientation, and axis lengths
• Deterministic closed-form elliptical extended object tracker
• Batch-based variant for highly efficient computation