Equivariant Filter for Radar-Inertial Odometry

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.

Radar-Inertial Odometry For Computationally Constrained Aerial Navigation

Recently, the progress in the radar sensing technology consisting in the miniaturization of the packages and increase in measuring precision has drawn the interest of the robotics research community. Indeed, a crucial task enabling autonomy in robotics is to precisely determine the pose of the robot in space. To fulfill this task sensor fusion algorithms are often used, in which data from one or several exteroceptive sensors like, for example, LiDAR, camera, laser ranging sensor or GNSS are fused together with the Inertial Measurement Unit (IMU) measurements to obtain an estimate of the navigation states of the robot. Nonetheless, owing to their particular sensing principles, some exteroceptive sensors are often incapacitated in extreme environmental conditions, like extreme illumination or presence of fine particles in the environment like smoke or fog. Radars are largely immune to aforementioned factors thanks to the characteristics of electromagnetic waves they use. In this thesis, we present Radar-Inertial Odometry (RIO) algorithms to fuse the information from IMU and radar in order to estimate the navigation states of a (Uncrewed Aerial Vehicle) UAV capable of running on a portable resource-constrained embedded computer in real-time and making use of inexpensive, consumer-grade sensors. We present novel RIO approaches relying on the multi-state tightly-coupled Extended Kalman Filter (EKF) and Factor Graphs (FG) fusing instantaneous velocities of and distances to 3D points delivered by a lightweight, low-cost, off-the-shelf Frequency Modulated Continuous Wave (FMCW) radar with IMU readings. We also show a novel way to exploit advances in deep learning to retrieve 3D point correspondences in sparse and noisy radar point clouds.