Equivariant Filter for Radar-Inertial Odometry

2026-04-24

AI Summary

This work addresses the sensitivity of conventional Extended Kalman Filter–based Radar-Inertial Odometry (EKF-RIO) to extrinsic calibration between radar and IMU, which often leads to divergence due to linearization errors. For the first time, Equivariant Filtering (EqF) is introduced to this domain, leveraging Lie group symmetries to construct a geometrically coupled model of navigation states and IMU biases. The proposed framework integrates online extrinsic calibration with multi-state constraint updates, significantly enhancing estimation consistency and robustness. Notably, it remains stable and converges reliably even under severe extrinsic misalignment—conditions under which EKF-RIO fails. Experimental validation on two distinct UAV platforms demonstrates state-of-the-art accuracy, establishing the method as a leading solution in radar-inertial odometry.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Multi-modal Vision

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Radar-Inertial Odometry (RIO) based on the Extended Kalman Filter (EKF) relies on accurate extrinsic calibration between the radar and the Inertial Measurement Unit (IMU) and is sensitive to disturbances, as large linearization errors can degrade performance or even cause divergence. To address these limitations, this letter proposes an Equivariant Filter (EqF) for RIO based on a Lie group symmetry that geometrically couples navigation states and IMU biases, extending it to incorporate radar-IMU extrinsic calibration and multi-state constraint updates. This equivariant formulation inherently preserves consistency and enhances robustness, enabling reliable state estimation even under poor or completely wrong initialization of calibration states. Real-world experiments on two different Uncrewed Aerial Vehicles (UAVs) show that the proposed EqF-RIO achieves state-of-the-art accuracy under correct extrinsic calibration and offers improved convergence under large calibration errors, where the conventional EKF-RIO fails. Evaluation code is open-sourced.

Problem

• Radar-Inertial Odometry
• Extrinsic Calibration
• Extended Kalman Filter
• Linearization Error
• State Estimation

Innovation

• Equivariant Filter
• Radar-Inertial Odometry
• Lie group symmetry
• extrinsic calibration
• robust state estimation