Radar-Inertial Odometry with Online Spatio-Temporal Calibration via Continuous-Time IMU Modeling

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.

Visual-Inertial Odometry (VIO) is a staple for reliable state estimation on constrained and lightweight platforms due to its versatility and demonstrated performance. However, pertinent challenges regarding robust operation in dark, low-texture, obscured environments complicate the use of such methods. Alternatively, Frequency Modulated Continuous Wave (FMCW) radars, and by extension Radar-Inertial Odometry (RIO), offer robustness to these visual challenges, albeit at the cost of reduced information density and worse long-term accuracy. To address these limitations, this work combines the two in a tightly coupled manner, enabling the resulting method to operate robustly regardless of environmental conditions or trajectory dynamics. The proposed method fuses image features, radar Doppler measurements, and Inertial Measurement Unit (IMU) measurements within an Iterated Extended Kalman Filter (IEKF) in real-time, with radar range data augmenting the visual feature depth initialization. The method is evaluated through flight experiments conducted in both indoor and outdoor environments, as well as through challenges to both exteroceptive modalities (such as darkness, fog, or fast flight), thoroughly demonstrating its robustness. The implementation of the proposed method is available at: https://github.com/ntnu-arl/radvio.

Millimeter-wave radar enables robust perception in visually degraded environments, yet radar-inertial estimation remains prone to drift: body-frame velocity measurements do not constrain heading and position, and the gyroscope bias, which governs heading drift, is poorly observable over the short horizons of sliding-window estimators. We propose a hierarchical radar-inertial factor graph that separates estimation into a fixed-lag navigation graph, which fuses IMU preintegration, radar velocities, ZUPT, and ground-plane constraints into smooth, low-latency odometry, and a keyframe mapping graph, which combines this odometry with submap registration and loop closures. Loop closures additionally calibrate the IMU: the part of a loop residual explained by a bias error is estimated through preintegration Jacobians chained over the loop interval and enters the navigation graph as a prior on the bias alone. Since this calibration is irreversible, it uses only loop closures accepted by the mapping graph and a cycle-consistency test. Extensive evaluations demonstrate high accuracy and drift-reduced estimation at real-time speeds.