Inertial Odometry

Autonomous nano-UAV navigation requires accurate ego-motion estimation under stringent size, weight, power, and computing (SWaP-C) constraints, where visual sensors and LiDARs exceed payload limits, optical flow degrades in low-texture scenes, and inertial-only state estimation is susceptible to accumulated drift. While multi-zone time-of-flight (ToF) arrays provide a lightweight metric complement, 6-DoF estimation from merely 384 ranges per frame is challenged by invalid returns, anisotropic observability, and temporal computational scaling. We propose TIO-FORMER, a camera-free, optical-flow-free, and mapless range-inertial odometry framework driven by an IMU and an ultra-lightweight (15 g) payload of six orthogonal 8 x 8 ToF arrays. Our frontend pairs consecutive range grids with a bilateral gated difference, while IMU-guided cross-attention dynamically routes directional features conditioned on platform kinematics. A Streaming Causal Transformer couples an uncompressed Local KV cache with compressed Chunk-FIFO memory, maintaining bounded inference cost and memory footprint independent of flight duration. In real-flight evaluations, TIO-FORMER reduces open-loop position error by 54.4% compared to nano-UAV optical flow and by 66.4%-89.1% over learned inertial baselines. We also evaluate performance across multiple environments and robustness under severe sensing degradation. Deployed on an edge RISC-V companion computer, TIO-FORMER achieves a P95 latency of 10.466 ms and peak resident memory of 6.324 MiB (less than 5 percent system RAM), demonstrating that sparse range sensing provides practical geometric anchoring for resource-constrained micro-aerial robots. Code is available at https://github.com/Ly041021/TIO-Former.

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.

Inertial odometry (IO) is critical for aerial robots, where aggressive maneuvers and poor lighting degrade visual sensors. Recent learning-based IO methods improve traditional integration-based approaches by learning motion priors from IMU and platform-specific sensors, then fusing the predictions within an extended Kalman filter. However, learning velocity through regression is difficult, while jointly estimating uncertainty with a separate decoder and negative log-likelihood (NLL) loss further complicates training and can lead to over-confident estimates. We introduce VeloBins, which reformulates velocity regression as classification over discretized velocity bins. We decode both the velocity from the bin distribution's expectation and the uncertainty from its variance, removing the need for a separate uncertainty decoder. We further supervise the uncertainty explicitly using an error-conditioned Gaussian label centered at the ground-truth velocity, with a standard deviation set to the velocity error. We evaluate VeloBins on four aerial datasets, ranging from free-form aggressive flights and a 27 g nano-quadrotor to drone racing at over 21~m/s. VeloBins achieves the lowest average errors on all four datasets, reducing velocity, relative trajectory, and absolute trajectory errors by 3-27%, 8-40%, and 6-53%, respectively, compared with the strongest baseline. Notably, the proposed supervision achieves the lowest NLL and best filter consistency despite never optimizing an NLL loss. The code will be available upon acceptance.

Dense metric depth prediction from cameras and millimeter-wave radar offers a cost-effective sensing solution for autonomous systems. However, radar measurements are inherently sparse and susceptible to clutter, multipath reflections, and projection errors. While aggregating multiple radar frames provides denser metric cues, it also introduces temporal misalignment and dynamic-object interference. Directly propagating such unreliable measurements can therefore corrupt large regions of the predicted depth map. To address this issue, we propose RbFT-Net, an end-to-end rectify-before-fuse framework for multi-frame 4D radar-camera depth completion. Rather than assuming accumulated radar returns to be accurate, RbFT-Net treats them as noisy temporal anchor candidates. An image-conditioned rectification module jointly corrects their image-plane locations and metric depths while estimating pointwise reliability. The rectified anchors are then selectively propagated before high-level multi-modal fusion, suppressing the influence of unreliable measurements. Experiments on ZJU-4DRadarCam and a newly collected 4D radar-camera-LiDAR dataset show that RbFT-Net consistently outperforms the evaluated independent radar-camera methods and remains competitive with plug-in pipelines using auxiliary monocular depth models. Cross-platform evaluation and component analyses further support the effectiveness of the proposed rectification and reliability-aware propagation strategy.

Recent advances in 4D radar enable robust perception in adverse weather; however, the inherent sparsity, noise, and limited positional precision of radar point clouds pose significant challenges for registration-based odometry. In this letter, we propose RaDiVe, a 4D radar odometry framework designed to improve the accuracy and robustness of radar point-cloud registration. We introduce a distance-bounded Normal Distributions Transform (NDT), which improves optimization stability and computational efficiency by restricting the correspondence search to near-distance voxel pairs. To mitigate measurement ambiguity, we propose a velocity-discrepancy point uncertainty model that weights each input 4D radar point according to the discrepancy between its measured Doppler radial velocity and the radial velocity predicted from the estimated ego-velocity. Furthermore, we incorporate Signed Distance Function (SDF)-based surface point extraction via implicit neural mapping to construct a geometrically consistent and noise-filtered local submap. Evaluations across multiple public datasets demonstrate that RaDiVe outperforms existing 4D radar odometry baselines by 44.4% in translational Absolute Trajectory Error (ATE) and 21.3% in rotational ATE on average, while maintaining real-time performance. The source code will be made publicly available to the robotics community: https://github.com/to-be-open-sourced.

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.

The training of learned inertial odometry depends on dense, high-precision position ground truth from motion capture, visual-inertial odometry or SLAM, which is costly and hard to acquire at scale. We propose DINS-IO, which learns inertial odometry directly from raw IMU streams without position labels. Our key insight is that the strapdown INS velocity recursion is a strong, fully differentiable consistency prior: the predicted velocity, rotated into the navigation frame, must agree with the integrated specific force up to an unknown initial velocity and a constant accelerometer bias. We cast this constraint as a sliding-window least-squares problem with a globally shared bias, solve it in closed form, and use the solver residual as a self-supervised loss whose gradient flows back to the network through the analytic solution. To supply this per-sample constraint, we design a high-frequency network that emits dense body-frame velocity at the IMU rate. Since the self-supervised network learns consistent motion but its velocity is not yet metrically calibrated, we calibrate it to true metric velocity from a few labeled trajectories by directly supervising the predicted body-frame velocity and adapting only low-rank (LoRA) patches. On standard benchmarks, DINS-IO pretrained self-supervised and fine-tuned with a small fraction of labels matches or surpasses fully supervised baselines.

Accurate and robust attitude estimation is a key challenge for autonomous vehicles, particularly in GNSS-denied conditions and during highly accelerated flight. In such conditions, Inertial Measurement Units (IMUs) alone are insufficient for reliable tilt estimation due to the ambiguity between gravitational and inertial accelerations. Although auxiliary velocity sensors such as GNSS, Pitot tubes, Doppler radar, or Visual Inertial Odometry are commonly used, they may be unavailable, intermittent, or costly. This paper introduces a barometer-aided attitude estimation architecture that exploits barometric altitude measurements to provide complementary information on the vehicle's vertical motion, thereby enhancing attitude estimation within nonlinear observers on SO(3). The contributions are twofold. First, we design a deterministic Riccati observer cascaded with a complementary filter, ensuring almost-global asymptotic stability (AGAS) under a uniform observability (UO) condition while preserving the geometric structure of the attitude dynamics. Second, we propose a nonlinear observer evolving on SO(3)xR2, which integrates IMU measurements as inputs and barometer and magnetometer measurements as outputs within a unified framework, guaranteeing local exponential stability (LES) under relaxed uniform observability conditions. The proposed approaches are validated using both simulated and real flight data. The results demonstrate that barometer-aided estimation provides a lightweight, reliable, and effective complementary sensing modality for attitude estimation in minimal-sensing configurations, offering a practical alternative when conventional velocity measurements are unavailable or degraded.

In this study, the learning-based inertial odometry problem is investigated using raw IMU measurements obtained from the EuRoC MAV benchmark dataset. Instead of absolute position regression-a formulation that may lead to large constant errors-the models are trained to estimate the incremental displacement (Δp) over a fixed 50 ms sliding window, and the full trajectory is reconstructed through numerical integration. A standard Multi-Layer Perceptron (MLP) is compared with a Kolmogorov-Arnold Network (KAN) equipped with learnable B-spline activations. Although KAN has 6.9 times fewer parameters than MLP (8,444 versus 57,859), it produces a 44% lower error in terms of final cumulative drift on the test trajectory (9.61 m versus 17.23 m). In addition, KAN exhibits more stable behavior in terms of long-term error accumulation, with lower P_50 and P_90 cumulative drift values. These findings indicate that learnable B-spline-based activations have the potential to reduce error accumulation in the inertial odometry problem.

Reliable navigation in underwater environments remains a key challenge in marine robotics. In such scenarios, forward-looking sonars are a natural choice for long-range perception, offering wide coverage even in turbid, low-visibility conditions. However, sonar images are inherently noisy, contain artifacts, and lack rich semantic structure, causing standard computer vision methods for keypoint detection and matching to perform poorly. In this paper, we introduce ISOPoT, an imaging sonar odometry method based on modern point tracking techniques. We propose a sonar odometry pipeline that uses multi-frame point tracks as its primary correspondence representation, augmented with lightweight optimizations to improve robustness. We evaluated the proposed method on the Aracati 2017 dataset, as well as on an internal sonar dataset collected in real-world underwater environments. Our results show that ISOPoT outperforms previous state-of-the-art methods consistently in both sonar-only scenarios and in multi-sensor settings.

An invariant extended Kalman filter (IEKF) is developed for state estimation of serial rigid manipulators with an arbitrary number of links, formulated entirely within the Lie group SE(3). The group-affine property of the kinematic equations makes the linearised error dynamics autonomous, so the Riccati equation governs the true error covariance rather than a local approximation. A physically separated noise model treats gyroscope and accelerometer channels independently: the accelerometer provides translational twist via gravity-compensated integration, yielding a measurement covariance that scales with the sample interval in exact analogy with process noise discretisation; a state-dependent Coriolis noise term captures gyroscope noise propagating through the nonlinear dynamics, vanishing at rest and growing with twist magnitude. The filter is structured as a modular chain of per-link IEKFs in which the predicted covariance of each link depends on its predecessor only through the Adjoint-transformed posterior, giving linear computational cost in link count. Exponential ultimate boundedness in mean square is established via a Lie algebra Lyapunov function, with per-link bounds chained through the Adjoint operator norm to yield a stability certificate that is modular and scalable to arbitrary chain length. Numerical results validate the design.

A precise state estimate is crucial for a tight feedback control that enables agile and near-obstacle flights of UAVs. The state-of-the-art methods fuse slow pose measurements with high-frequency inertial measurements to obtain a precise state estimate. However, the inertial measurements from the IMU onboard the UAV are degraded by vibrations from spinning propellers and the precision of the estimated state suffers. We propose a novel approach based on the preintegration of accelerations obtained from motor speeds. We show that the accelerations obtained in this manner can be used for state propagation on their own to achieve better precision without including the IMU. Further, we propose a factor composed of the preintegrated motor speeds that can be directly employed in factor graph optimization frameworks. We combine our factor with LiDAR measurements into the proposed Motor Angular Speed LiDAR Odometry (MAS-LO) algorithm for precise state estimation, which we open-source. Lastly, we evaluate the estimation precision against a state-of-the-art inertial algorithm LIO-SAM to show 28% improvement in position and 65% in velocity estimation accuracy, 14% lower measurement lag, and high robustness to wrong parameter values.

Thermal infrared (TIR) imaging has been a popular choice for field robotics due to its robust perception capability under low light visual degradation, but it suffers from severe stochastic and fixed-pattern noise that breaks downstream estimation. This noise is intensified indoors due to low thermal contrast and uniform temperature distributions, contributing to the relative lack of indoor TIR deployments. Existing TIR denoising methods exhibit a poor accuracy-efficiency tradeoff, either too slow for online deployment required in robotics or insufficiently robust to severe degradation, while typically being trained on synthetic noise. Addressing these problems, we propose TIDY, a lightweight wavelet-domain denoiser trained on real clean-noisy TIR data. By reformulating TIR denoising in the wavelet domain, TIDY explicitly disentangles noise from structural content, enabling targeted suppression with reduced spatial complexity, significantly improving inference speed over prior methods (~34Hz). TIDY introduces two new metrics, Wavelet Entropy and Wavelet Directional Stripe Index, as complementary loss terms to explicitly suppress stochastic noise and stripe artifacts. Across severe indoor corruption and zero-shot settings, TIDY improves robustness and yields consistent gains in downstream robotics tasks including thermal inertial odometry and monocular depth estimation. Code and dataset is available at: https://github.com/williamrheeth/TIDY

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.

Robust inertial odometry is essential for various carriers when external sensing is unreliable. Learning-based methods reduce integration drift by capturing local motion priors, but these methods often remain tied to a particular carrier, limiting generalization across heterogeneous platforms. We present MosaicIMU, a carrier-conditioned Mixture-of-Experts (MoE) pretraining-and-adaptation framework for generalizable neural inertial odometry. MosaicIMU uses a prototype-based router to compose carrier-specific expert features, decodes local velocity and uncertainty constraints, and integrates them with a history-aware EKF. For unseen domain adaptation, it freezes the pretrained base model and learns a new lightweight expert residual branch. For edge-deployment, it further reuses the router to select informative online samples for efficient incremental updates. Experiments show that MosaicIMU consistently outperforms learning-based baselines, reducing average ATE and RTE-10s by 40% and 34%, respectively. These results highlight that MosaicIMU provides a scalable pretraining-to-deployment paradigm for generalizable and adaptive neural inertial odometry.

Inertial odometry (IO) using only Inertial Measurement Units (IMUs) provides a lightweight solution for human motion tracking in augmented reality (AR) and wearable devices. Recent learning-based IO methods have improved the generalizability of inertial localization through large-scale pretraining on human motion datasets. However, these approaches remain prone to drift and noise because they do not explicitly capture human motion dynamics, especially on daily activity datasets such as Nymeria. In this work, we propose to ground inertial odometry in human kinematics through a learned IMU-inferred pose prior, which promotes physically consistent motion constraints. We integrate this pose prior into existing IO architectures and reduce positional drift by up to 36% on the challenging Nymeria dataset, which is 5x larger than datasets used in prior work. We further improve long-term performance with a sensor-fusion framework that incorporates auxiliary signals from lightweight sensors already available on commercial AR glasses, including magnetometers, barometers, and secondary IMUs. With this fusion strategy, positional drift is reduced by up to 42%, improving robustness and generalization across diverse motion conditions. Together, our results introduce a new paradigm for inertial and lightweight odometry by unifying human motion kinematics with multimodal sensing, setting a new benchmark for accurate and robust camera-less human tracking. Our website is available at https://spice-lab.org/projects/MARIO/.

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.

Due to the difficulty of obtaining ground-truth data for 4D radar scene flow estimation, previous methods typically rely on either self-supervised losses or cross-modal supervision using 3D LiDAR data, 2D images, and odometry. However, self-supervised approaches often yield suboptimal results due to radar's inherently low-fidelity measurements, while existing cross-modal supervised methods introduce complex multi-task architecture and require costly LiDAR sensors to generate pseudo radar scene flow labels from pretrained 3D tracking models. To overcome these limitations, we propose a task-specific iterative framework for weakly supervised radar scene flow learning, using only images and odometry for auxiliary supervision during training. Specially, we establish two novel instance-aware self-supervised losses by exploiting off-the-shelf 2D tracking and segmentation algorithms to obtain tracked instance masks, which are back-projected into 3D space to provide instance-level semantic guidance; for static regions, we integrate vehicle odometry with radar's intrinsic motion cues to construct a rigid static loss. Extensive experiments on the real-world View-of-Delft (VoD) dataset demonstrate that our method not only surpasses state-of-the-art cross-modal supervised approaches that rely on 3D multi-object tracking on dense LiDAR point clouds but also outperforms existing fully supervised scene flow estimation methods. The code is open-sourced at \href{https://github.com/FuJingyun/IterFlow}{https://github.com/FuJingyun/IterFlow}.

Humanoid and legged robots interact with the environment through intermittent contacts, making accurate motion estimation fundamentally dependent on reasoning about contact dynamics. However, standard sensing pipelines-whether based on onboard proprioception with Extended Kalman Filters (EKFs) or external motion capture systems-recover only kinematics, while contact forces, contact timing, and inertial parameters remain unobserved. As a result, purely kinematic reconstructions often violate rigid-body dynamics, particularly during contact-rich motions. To enable accurate motion estimation from onboard kinematics in real-world deployment, we propose PRIME (Physically-consistent Robotic Inertial and Motion Estimation), a Maximum A Posteriori (MAP) formulation that refines measured kinematics and actuator commands into a dynamically consistent trajectory while jointly estimating frictional contact forces and physically consistent inertial parameters. Our approach incorporates differentiable contact dynamics with smoothed complementarity constraints and an Anitescu-style friction model, yielding a smooth optimization problem that remains tractable across versatile contact transitions. We evaluate PRIME on contact-rich locomotion with quadrupedal robots and the Unitree G1 humanoid, demonstrating improved trajectory consistency and accurate inertial parameter identification. Beyond improving state estimation and feedback control with calibrated inertial parameters, PRIME produces force- and contact-annotated motion reconstructions from real robots in deployment, which can be used to provide high-quality data for downstream learning applications, including large-scale behavior modeling and robot foundation models.

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.

Inertial measurement units (IMUs), which provide high-frequency linear acceleration and angular velocity measurements, serve as fundamental sensing modalities in robotic systems. Recent advances in deep neural networks have led to remarkable progress in inertial odometry. However, the heavy reliance on ground truth data during training fundamentally limits scalability and generalization to unseen and diverse environments. We propose KISS-IMU, a novel self-supervised inertial odometry framework that eliminates ground truth dependency by leveraging simple LiDAR-based ICP registration and pose graph optimization as a supervisory signal. Our approach embodies two key principles: keeping the IMU stable through motion-aware balanced training and keeping the IMU strong through uncertainty-driven adaptive weighting during inference. To evaluate performance across diverse motion patterns and scenarios, we conducted comprehensive experiments on various real-world platforms, including quadruped robots. Importantly, we train only the IMU network in a self-supervised manner, with LiDAR serving solely as a lightweight supervisory signal rather than requiring additional learnable processes. This design enables the framework to ensure robustness without relying on joint multi-modal learning or ground truth supervision. The supplementary materials are available at https://sparolab.github.io/research/kiss_imu.

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