Radar-Inertial Odometry

Compact extraplanetary rovers and micro aerial vehicles require robust state estimation frameworks designed to operate under strict computational constraints in unforgiving environments. Typical solutions involving vision- or LiDAR-based sensing are computationally expensive and vulnerable to environments with perceptual degradation, making them poorly suited for resource-constrained platforms and austere conditions. Alternatively, Frequency Modulated Continuous Wave (FMCW) radar offers both robustness and computational efficiency by directly providing velocity measurements coupled with inherent resilience to perceptual degradation. These factors enable robust estimation, thereby reducing reliance on human operators for supervision to ensure platform safety in challenging environments. In this manuscript, we propose an embedded radar-inertial estimator tailored for low-compute platforms. All sensor drivers, data processing, and aided inertial navigation are performed on a single-core microcontroller, demonstrating its computational efficiency. Flight experiments show translational APE of $0.51-0.82\,\mathrm{m}$ and RPE of $<$3,% against motion capture, alongside closed-loop flight through an unmodified PX4 stack. The firmware and printed circuit board design are openly available on GitHub at ntnu-arl/embedded_rio and ntnu-arl/embedded_rio-pcb respectively.

Existing radar-LiDAR fusion methods rely on fixed residual weights, even though the informativeness of radar Doppler and LiDAR geometry is scan- and direction-dependent, leading to uniform radar weighting that misallocates Doppler information across translational directions. To address this limitation, we propose two degeneracy-aware Doppler reweighting modules within a tightly coupled Radar-IMU-LiDAR odometry framework: per-point radar reweighting and scan-wise radar gain scheduling. Since geometric degeneracy is directional, we first identify weak translational directions from the LiDAR geometry and reweight individual radar Doppler constraints based on their alignment with the weak subspace. We further adjust the overall radar contribution using LiDAR geometric anisotropy such that radar is emphasized when LiDAR observability is poor and suppressed when LiDAR constraints are already reliable. Across 13 evaluated sequences, TRaIL-Odom achieves state-of-the-art overall performance, with clear advantages in geometrically degenerate scenes. In ablation experiments on three degenerate sequences, combining the two adaptive weighting modules reduces RMSE ATE and RTE by 86.0% and 78.5% relative to the fixed-weight baseline. We make our code and an accompanying dataset publicly available at https://github.com/ChiyunNoh/TRaIL-Odom.

Sensing ego-velocity estimation is fundamental to state estimation in visually degraded environments, where camera- and LiDAR-based pipelines can become unreliable. Millimetre-wave radar is well suited to these conditions because it provides direct Doppler velocity sensing and remains robust to poor illumination, textureless scenes, and airborne particulates. However, conventional radar ego-velocity pipelines typically apply constant false alarm rate (CFAR) thresholding to convert dense radar spectra into sparse point clouds, prematurely discarding sub-threshold returns that may still retain useful Doppler motion cues. We present Dense Soft Weighting, an analytic radar front-end that maps every range-Doppler cell to a continuous confidence metric rather than enforcing a binary detection threshold. Ego-velocity is then estimated using a deterministic robust weighted least-squares formulation, while the same weighted measurements provide a closed-form, measurement-derived velocity covariance for integration with a shared inertial back-end. The method requires no platform-specific training data or learning-based uncertainty model, supporting transfer across single-chip radar configurations. Across two public datasets and one self-collected dataset, Dense Soft Weighting reduces mean absolute pose error by 31-45% relative to the strongest CFAR point-cloud baseline under an identical inertial back-end, while running in real time on embedded hardware.

Radar SLAM is attractive for autonomous ground vehicles operating in visually degraded environments, however, scanning radars are noisy, have low scanning rates, and their measurements are challenging to match reliably over long trajectories. This paper presents FD-SLAM, a fast dense radar-inertial SLAM system that extends dense radar-inertial odometry with frequency-domain loop closure and pose graph optimization. The proposed method preserves an image-like structure of scanning radar measurements by using a compact frequency-domain polar descriptor for loop-candidate retrieval and a multi-stage verification pipeline based on temporal filtering, phase-correlation screening, scan-alignment similarity, and geometric consistency checks. Verified loop closures are added as non-sequential constraints in an SE(2) pose graph together with radar-inertial odometry factors. FD-SLAM is evaluated on a publicly available dataset using standard KITTI evaluation metrics. The results show that FD-SLAM improves FD-RIO baseline, achieves competitive performance against current state-of-the-art radar SLAM methods, and provides favorable rotational accuracy across multiple evaluated driving trajectories. Runtime analysis further indicates that the radar-inertial front-end operates above the radar sampling rate on a CPU-only setup, while loop closure detection and graph optimization remain suitable for parallel background execution.

Frequency Modulated Continuous Wave (FMCW) radar is a promising sensor for aided inertial navigation, due to its robustness in environments that challenge traditional alternatives, such as LiDAR and vision. However, its widespread adoption is hindered by complex, noisy measurements, which make reliable estimation difficult. This manuscript addresses these challenges by analyzing the fundamental measurement relations of FMCW radar sensing and developing a reliable estimator. Noise models are derived by applying first principles to the underlying signal processing of a typical radar sensor. These models guide the design of a factor graph-based estimator, utilizing a first-order approximation for the measurement noise propagation. The approach is first examined through simulation, evaluating the significance of different noise sources, the validity of the first-order approximation, and the state-dependent nature of the covariance expressions. Extensive experiments demonstrate the superior robustness and accuracy of the proposed method across diverse field environments and flight profiles, including beyond the radar's standard operating range. Furthermore, the experiments confirm the insights from the simulation regarding the behavior and performance of different estimator configurations relative to their operating conditions. The evaluation data and estimator implementation are made available at https://github.com/ntnu-arl/rig.

Radar offers unique advantages for localization in unstructured environments, including robustness to weather, lighting, and airborne particulates. While most prior work has studied radar odometry in urban, largely planar settings, its performance in off-road environments remains less understood. In this paper, we investigate the potential of radar for off-road odometry estimation and identify key challenges that arise from full $SE(3)$ vehicle motion, terrain-induced ground returns, and sparse or unstable features. To address these issues, we introduce two simple baselines: Radar-KISSICP, which applies motion compensation to generate 3D-aware radar pointclouds, and Radar-IMU, which leverages IMU preintegration to stabilize scan matching. Experiments on the Great Outdoors (GO) dataset demonstrate that these baselines improve trajectory estimation in challenging routes and provide a reference point for future development of radar odometry in off-road robotics.

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.

Rotating FMCW radar odometry methods often assume flat ground conditions. While this assumption is sufficient in many scenarios, including urban environments or flat mining setups, the highly dynamic terrain of subarctic environments poses a challenge to standard feature extraction and state estimation techniques. This paper benchmarks three existing radar odometry methods under demanding conditions, exhibiting up to 13° in pitch and 4° in roll difference between consecutive scans, with absolute pitch and roll reaching 30° and 8°, respectively. Furthermore, we propose a novel radar-inertial odometry method utilizing tilt-proximity submap search and a hard threshold for vertical displacement between scan points and the estimated axis of rotation. Experimental results demonstrate a state-of-the-art performance of our method on an urban baseline and a 0.3% improvement over the second-best comparative method on a 2-kilometer-long dynamic trajectory. Finally, we analyze the performance of the four evaluated methods on a complex radar sequence characterized by high lateral slip and a steep ditch traversal.

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.

Millimeter-wave radar enables robust perception in visually degraded environments, yet radar-inertial estimation remains prone to drift: sparse body-frame velocity measurements weakly constrain absolute orientation, leaving IMU biases poorly observable over the short horizons of sliding-window estimators. We propose a tightly coupled, hierarchical radar-inertial factor graph that decouples estimation into a high-rate resetting graph and a persistent global graph. The resetting graph fuses IMU preintegration, radar velocities, and adaptive ZUPT to produce smooth, low-latency odometry for real-time control. The persistent graph maintains a full state (poses, velocities, and biases) via keyframe-based geometric mapping and loop closures. Fully observable biases and their exact covariances are continuously injected from the persistent graph as priors into the resetting graph, anchoring the high-rate estimator against integration drift. Extensive evaluations demonstrate high accuracy and drift-reduced estimation at faster than real-time speeds. Code and datasets will be released upon paper acceptance.

Deployment of legged robots for navigating challenging terrains (e.g., stairs, slopes, and unstructured environments) has gained increasing preference over wheel-based platforms. In such scenarios, accurate odometry estimation is a preliminary requirement for stable locomotion, localization, and mapping. Traditional proprioceptive approaches, which rely on leg kinematics sensor modalities and inertial sensing, suffer from irrepressible vertical drift caused by frequent contact impacts, foot slippage, and vibrations, particularly affected by inaccurate roll and pitch estimation. Existing methods incorporate exteroceptive sensors such as LiDAR or cameras. Further enhancement has been introduced by leveraging gravity vector estimation to add additional observations on roll and pitch, thereby increasing the accuracy of vertical pose estimation. However, these approaches tend to degrade in feature-sparse or repetitive scenes and are prone to errors from double-integrated IMU acceleration. To address these challenges, we propose GaRLILEO, a novel gravity-aligned continuous-time radar-leg-inertial odometry framework. GaRLILEO decouples velocity from the IMU by building a continuous-time ego-velocity spline from SoC radar Doppler and leg kinematics information, enabling seamless sensor fusion which mitigates odometry distortion. In addition, GaRLILEO can reliably capture accurate gravity vectors leveraging a novel soft S2-constrained gravity factor, improving vertical pose accuracy without relying on LiDAR or cameras. Evaluated on a self-collected real-world dataset with diverse indoor-outdoor trajectories, GaRLILEO demonstrates state-of-the-art accuracy, particularly in vertical odometry estimation on stairs and slopes. We open-source both our dataset and algorithm to foster further research in legged robot odometry and SLAM. https://garlileo.github.io/GaRLILEO