Equivariant Filter for Radar-Inertial Odometry

TL;DR

This paper introduces an Equivariant Filter for Radar-Inertial Odometry that leverages Lie group symmetry to improve robustness, consistency, and accuracy, especially under calibration errors, demonstrated through UAV experiments.

Contribution

It extends existing RIO methods by incorporating a Lie group-based equivariant filter that handles calibration and biases more reliably.

Findings

Achieves state-of-the-art accuracy with correct calibration.

Improves convergence under large calibration errors.

Maintains consistency and robustness in state estimation.

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.