H-RINS: Hierarchical Tightly-coupled Radar-Inertial State Estimation via Smoothing and Mapping

Radar odometry is crucial for robust localization in challenging environments; however, the sparsity of reliable returns and distinctive noise characteristics impede its performance. This paper introduces geometrically-constrained radar-inertial odometry and mapping that jointly consolidates point and pose uncertainty. We employ the continuous trajectory model to estimate the pose uncertainty at any arbitrary timestamp by propagating uncertainties of the control points. These pose uncertainties are continuously integrated with heteroscedastic measurement uncertainty during point projection, thereby enabling dynamic evaluation of observation confidence and adaptive down-weighting of uninformative radar points. By leveraging quantified uncertainties in radar mapping, we construct a high-fidelity map that improves odometry accuracy under imprecise radar measurements. Moreover, we reveal the effectiveness of explicit geometrical constraints in radar-inertial odometry when incorporated with the proposed uncertainty-aware mapping framework. Extensive experiments on diverse real-world datasets demonstrate the superiority of our method, yielding substantial performance improvements in both accuracy and efficiency compared to existing baselines. We release our open-source implementation at https://github.com/wooseongY/GeoRIO.

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.

4D radar is increasingly attractive for robotic mapping because it provides range, azimuth, elevation, and Doppler measurements while remaining robust in adverse visibility conditions. Although recent radar and radar--inertial odometry methods have achieved promising online state estimation performance, offline global map refinement for 4D radar remains underexplored. This paper presents RAMBA, a radar bundle-adjustment framework for globally consistent 4D radar mapping. Given initial poses and radar frames from a radar--inertial odometry front-end, RAMBA jointly refines radar frame states using covariance-weighted geometric residuals, IMU preintegration factors, and radar ego-velocity constraints. The geometric residuals extend pairwise GICP to a multi-frame optimization by forming voxel-based correspondences across selected frames and weighting each residual with point covariances. To improve robustness against drift and revisits, RAMBA enforces temporal consistency during correspondence formation while explicitly supporting loop-closure constraints. Experiments on the ColoRadar and SNAIL Radar datasets show that RAMBA improves map consistency and usually enhances trajectory accuracy over radar--inertial odometry and pose-graph optimization baselines.