Equivariant Filter for Radar-Inertial Odometry

A team of researchers including Giulio Delama and colleagues has introduced an Equivariant Filter (EqF) for Radar-Inertial Odometry (RIO) that addresses key limitations of traditional Extended Kalman Filter (EKF)-based approaches. The EKF-RIO method is notoriously sensitive to poor extrinsic calibration between the radar and inertial measurement unit (IMU), and large linearization errors can degrade performance or cause divergence. The new EqF-RIO formulation uses Lie group symmetry to geometrically couple navigation states and IMU biases, and extends this to incorporate radar-IMU extrinsic calibration and multi-state constraint updates. This approach inherently preserves consistency and enhances robustness, enabling reliable state estimation even under completely wrong initialization of calibration states.

Real-world experiments on two different Uncrewed Aerial Vehicles (UAVs) demonstrate that EqF-RIO achieves state-of-the-art accuracy when extrinsic calibration is correct, and offers improved convergence under large calibration errors, where conventional EKF-RIO fails. The method's ability to handle poor initialization is particularly valuable for practical deployments where precise calibration is difficult or impossible. The evaluation code has been open-sourced, allowing the robotics community to build upon this work. This advancement could significantly improve the reliability of radar-inertial navigation systems in autonomous drones and other robotic platforms operating in challenging environments.