Ground-Optimized 4D Radar-Inertial Odometry via Continuous Velocity Integration using Gaussian Process

Ayoung Kim; Hyesu Jang; Wooseong Yang

REVIEW 4 major objections 5 minor 32 references

Ground-Optimized 4D Radar-Inertial Odometry via Continuous Velocity Integration using Gaussian Process

T0 review · 4 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Gaussian-process fusion of radar Doppler with IMU and uncertainty-aware ground filtering yields full 6-DOF radar-inertial odometry from asynchronous data, keeping vertical drift below 1 percent of path length.

desk verdict Solid radar-inertial odometry paper with two genuine extensions that deserves peer review, though the 'assumption-free' claim overreaches and key GP parameters are missing. read the letter →

arxiv 2502.08093 v2 pith:HNC63WBM submitted 2025-02-12 cs.RO

Wooseong Yang , Hyesu Jang , Ayoung Kim This is my paper · ORCID

classification cs.RO

keywords 4Dradarradar-inertialodometryGaussianprocesspreintegrationcontinuous-timemotionestimationgroundsegmentationDopplervelocityasynchronoussensorfusionposegraphoptimization

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that radar-inertial odometry does not need to ignore the different sampling times of radar and IMU. By modeling radar Doppler velocity and IMU angular velocity as continuous functions drawn from a Gaussian process, the relative motion between any two times can be inferred directly from asynchronous measurements, giving full 6-DOF increments without time synchronization. The paper pairs this with a radar-specific ground filter that segments the ground zone by zone using per-point uncertainty, rather than fitting one plane to noisy radar returns. If these claims are right, radar odometry in weather-degraded conditions can achieve reliable trajectories with substantially less vertical drift than discretized radar-inertial baselines. On the public datasets tested, the reported vertical drift is below 1 percent of path length.

What carries the argument

The load-bearing object is a continuous preintegration over SE(3) built from two Gaussian processes. Angular-velocity derivatives are modeled as zero-mean GPs so that rotation can be inferred at any query time from asynchronous gyroscope samples; linear radar velocity components are modeled as GPs with a prior mean so that velocity and translation can be inferred at any time from asynchronous Doppler measurements. Combining the two gives a motion increment $T_{\mathrm{INT}}\in SE(3)$ directly from the raw asynchronous streams. The complementary mechanism is a zone-based ground filter: the point cloud is divided into concentric zones of growing width, and within each zone a plane is fit by minimizing Mahalanobis distances weighted by per-point covariance, with flatness convergence deciding which points are ground and which are below-ground noise.

What would settle it

On a sequence with a deliberately injected constant gyro bias, or with the GP kernel hyperparameters held fixed while the motion profile changes sharply, compute the ATE and vertical drift of the proposed pipeline; a large error increase beyond measurement-noise predictions would falsify the claim of assumption-free asynchronous fusion.

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Extended reading notes

Core claim

The central claim is that a continuous Gaussian-process preintegration of radar velocity with IMU, combined with uncertainty-aware ground filtering, produces accurate 6-DOF radar-inertial odometry directly from asynchronous raw measurements. The paper reports the lowest ATE among tested open-source radar-inertial odometry methods on most sequences of the two public automotive radar datasets used, and shows that the proposed system reaches less than 1 percent vertical drift over path lengths of several kilometers, for example roughly 18 m over 2.5 km on one rural sequence.

Load-bearing premise

The main load-bearing premise is that the IMU gyroscope can be treated as bias-free and that a fixed Gaussian-process prior, with its kernel and hyperparameters, remains accurate across all test sequences; if either fails, the continuous integration and the reported vertical accuracy will degrade.

Editorial extensions

If this is right

Radar and IMU no longer need synchronized sampling for tight fusion; motion increments can be evaluated at arbitrary times from the asynchronous Doppler and gyro streams.
Discretized constant-state propagation, which degrades on sharp turns and high vehicle speeds, can be replaced by a smooth continuous model that is also more robust to measurement noise.
Ground segmentation for radar can be made reliable on slopes and imprecise point distributions by optimizing per-zone plane fits with point covariance instead of global height thresholds.
On public automotive 4D radar datasets, elevation drift can be held under one percent of path length, improving the consistency of maps built in adverse weather.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Inference: the same continuous preintegration recipe could be applied to other asynchronous velocity sensors paired with an IMU, such as wheel encoders or Doppler lidar, because the GP query time decouples integration from measurement times.
Inference: the ground filter's height-refinement step inherits ego-velocity errors, so iterating refinement with the improved continuous velocity estimate is a testable way to push vertical accuracy further in highly dynamic scenes.
Inference: the method's 'assumption-free' claim is about time synchronization only; gyro bias and kernel hyperparameters remain fixed inputs, and adding online bias estimation would make the approach more portable to unseen platforms.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This is a competent systems paper with two real extensions: uncertainty-aware zone-based ground filtering for radar and GP-based continuous preintegration of radar Doppler velocity. The results on public datasets look strong, especially vertical drift (0.72% on RURAL_A2), and the ablations show both modules contribute. The writing is clear and the comparisons are fair, with loop closure removed and public baselines used.

The genuinely new piece is applying Le Gentil and Vidal-Calleja's GP preintegration to radar velocity instead of only IMU. That is a meaningful step over prior radar-inertial methods that discretize or ignore asynchronous timing. The ground filter is also new for radar, using concentric zones plus Mahalanobis distance-based plane fitting to handle slopes better than naive RANSAC or height thresholds. I was impressed by the ablation in Table III: both modules independently improve ATE by large margins on most sequences.

Soft spots: the stress-test concern is real. The GP model in Section III-B is the core novelty, yet the kernel functions, hyperparameters, noise scales, and the prior mean mu_i(t) are never specified. Equation (5) uses raw gyro measurements with no bias term, and Section V admits bias modeling is future work. So the claim of "motion estimation ... without any assumptions" is not supported as stated; there are implicit assumptions about the GP prior and bias-free IMU. This is primarily a reproducibility problem rather than a fatal flaw, but it matters because the empirical results may not generalize to sensors with significant gyro bias or to trajectories where the GP prior is a poor fit. The paper also lacks error bars, does not report thresholds epsilon_d and epsilon_f, and the computational cost table shows GP integration at 615–790 ms, which is only real-time if the parallelism holds as described.

For whom: researchers working on radar-inertial odometry or continuous-time preintegration. I would send this to peer review with a request for parameter values, a toned-down abstract, and ideally error bars. It is a solid engineering contribution, not a breakthrough, but it deserves a serious look.

Referee Report

4 major / 5 minor

Summary. The paper proposes a 4D radar-inertial odometry system, Go-RIO, with two claimed contributions: an uncertainty-aware, zone-based ground filtering method that models radar-specific ground points, and a continuous velocity preintegration scheme that uses Gaussian processes to fuse asynchronous radar Doppler velocity measurements with IMU angular velocity. The system is evaluated on the NTU4DRadLM and MSC-RAD4R public datasets against 4DRadarSLAM, EKF-RIO, BCV, and DeRO, with ATE and RPE tables, elevation-over-path plots, ablation studies for the two modules, and a computation-time table. The headline claims are less than 1% vertical drift on the tested sequences and the lowest ATE on most sequences among the compared open-source methods. Code is promised to be released.

Significance. If the empirical results hold, the paper makes a useful practical contribution: it demonstrates that continuous, asynchronous radar-IMU fusion can improve elevation accuracy on public benchmarks, and the ground filtering module is evaluated with ablations and comparison against RANSAC and Patchwork++. A notable strength is that the evaluation uses public datasets and published baselines, so the central performance claim is not circular. A second strength is the ablation table, which isolates the contributions of filtering and continuous integration. However, the paper's core methodological novelty is under-specified at the exact point where it matters: the GP priors, kernel choices, hyperparameters, and noise scales in Section III-B are not reported, and the abstract/conclusion's phrase "without any assumptions" is contradicted by the acknowledged absence of gyro bias modeling. These issues are fixable within the manuscript's scope, but they currently prevent a reader from reproducing or independently assessing the mechanism behind the reported vertical accuracy.

major comments (4)

[Section III-B, Eqs. (3)-(9)] The continuous GP model is under-specified at the point of novelty. The kernels k_theta_i and k_v_i, their hyperparameters, the noise scales sigma_i, epsilon_i, and Sigma_gp, and especially the prior mean mu_i(t) in Eq. (6) are never defined: mu_i(t) appears both as a function and as a vector in Eq. (7), and its functional form is not given. Because Eqs. (4), (7), and (8) generate the T_INT edge that drives the odometry, the reported ATE and vertical drift cannot be reproduced or checked for sensitivity to these choices. Please specify the kernel family, hyperparameters, and prior mean, state whether they are fixed across all sequences or tuned per sequence, and provide a sensitivity analysis if feasible.
[Eq. (5) and Section V] The claim of "assumption-free" motion estimation is not supported by the model. The gyroscope measurement term in Eq. (5) uses raw angular velocity with no bias term, and Section V explicitly defers gyro bias and accelerometer integration to future work. A non-negligible gyro bias will bias the inferred rotation theta^*(t) and hence the continuous preintegrated T_INT, directly affecting the reported vertical accuracy. Please either add gyro bias estimation, explicitly state the bias-free assumption, or provide a sensitivity test showing what bias magnitude the method tolerates.
[Section IV, Tables I-III] All evaluation numbers are single-run results with no error bars, standard deviations, or number of trials, and no statistical comparison is reported. Some advantages over baselines are small relative to plausible run-to-run variation, for example the nyl ATE of 5.009 m in Table III versus 5.888 m for the filtering-only configuration. Because the central qualitative claim is consistent outperformance across diverse conditions, please report repeated runs or, if the evaluation procedure is deterministic, state that explicitly and describe the exact protocol used.
[Algorithm 1 and Section III-D] The ground segmentation thresholds epsilon_d and epsilon_f, the concentric zone configuration, the sensor height hs, and the keyframe selection threshold are not reported. These parameters are load-bearing for the ground filtering contribution and for the "less than 1% vertical drift" claim, since the abstract attributes the result to "meticulous conditions." Please report the parameter values and, if possible, show how sensitive the ATE and vertical drift are to them.

minor comments (5)

[Eq. (1)] The Mahalanobis distance expression appears dimensionally inconsistent: (n^top + d) should presumably be (p_i^top n + d) or similar, and the relation between the minimization objective and kappa = n^top C n needs clarification.
[Eq. (4)] The notation t is used both as a scalar query time and as a vector of timestamps, and k_theta_i(t,t) is written once as a vector and once as a covariance object; please disambiguate the notation throughout Section III-B.
[Eqs. (7)-(8)] The prior mean mu_i(t) should be defined and typed consistently as a function versus a vector of prior means evaluated at radar timestamps.
[Table III caption] The ablation labels RAW, CONT, FILTER, and FULL are explained only in the text; please state explicitly in the caption that RAW is discrete integration without filtering, CONT is continuous integration without filtering, FILTER is discrete integration with the proposed filter, and FULL contains both modules.
[Abstract] The phrase "meticulous conditions" is unclear in an abstract; consider replacing it with "challenging conditions" or naming the relevant environmental conditions.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The system's central claim rests on standard GP regression, a Doppler rigid-body model, a planar-ground zone model, and a bias-free IMU assumption. No new physical entities are introduced. The main under-specified inputs are GP kernels and hyperparameters, segmentation thresholds, and keyframe parameters.

free parameters (5)

GP kernel hyperparameters for angular velocity and velocity = not reported
Kernels k_theta and k_v are introduced in Eqs (3) and (6), but the kernel family and length scales are never given; continuous preintegration accuracy depends on them.
GP noise variances sigma_i (gyro) and epsilon_i (velocity) = not reported
Used in Eqs (4) and (7) for GP inference; values likely come from sensors or tuning, but are not stated.
Ground segmentation thresholds epsilon_d and epsilon_f = not reported
Algorithm 1 uses these to merge points and stop flatness iteration; no values or sensitivity analysis are given.
Concentric zone configuration = not reported
Zone widths and number of zones from CZM [26] are not specified, though they control how well slopes are handled.
Keyframe selection threshold = not reported
New keyframes are selected when motion increment exceeds a predefined threshold; the value and its effect on accuracy are not reported.

assumptions (5)

standard math Gaussian process regression formulas (Eqs (3)-(8)) correctly model the time derivatives of rotation vector and linear velocity components.
The preintegration factor uses GP interpolation and integration to compute motion increments; the paper invokes these formulas without proof.
domain assumption Radar Doppler velocity obeys the rigid-body projection used in Eq (2) and in the velocity residual of Eq (9), with static scatterers dominating.
Height refinement and velocity preintegration both rely on this model; dynamic objects are handled only by a post-hoc removal step.
domain assumption The IMU gyroscope measurements are unbiased, or bias is small enough to ignore over the integration interval.
No gyro bias state is estimated; the conclusion section lists developing a comprehensive bias model as future work, so the current claim depends on this assumption.
domain assumption Ground can be approximated by locally planar patches inside concentric zones, with pointwise covariance matrices available for radar points.
The uncertainty-aware filter in Algorithm 1 fits planes per zone and removes points below them; non-planar terrain or unreliable covariances would break the filter.
ad hoc to paper The GP prior mean functions mu_i(t) for velocity and the kernel choices are appropriate without per-sequence tuning.
mu_i and kernel hyperparameters are introduced in Eqs (6)-(7) but never specified or justified; the 'assumption-free' claim depends on them being data-independent.

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Cite this review

Pith. "Pith review of Ground-Optimized 4D Radar-Inertial Odometry via Continuous Velocity Integration using Gaussian Process." pith.science (2026). https://pith.science/paper/HNC63WBM

@misc{pith2026250208093,
  author       = {Pith},
  title        = {Pith review of: Ground-Optimized 4D Radar-Inertial Odometry via Continuous Velocity Integration using Gaussian Process},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HNC63WBM}},
  note         = {Machine review of arXiv:2502.08093}
}

read the original abstract

Radar ensures robust sensing capabilities in adverse weather conditions, yet challenges remain due to its high inherent noise level. Existing radar odometry has overcome these challenges with strategies such as filtering spurious points, exploiting Doppler velocity, or integrating with inertial measurements. This paper presents two novel improvements beyond the existing radar-inertial odometry: ground-optimized noise filtering and continuous velocity preintegration. Despite the widespread use of ground planes in LiDAR odometry, imprecise ground point distributions of radar measurements cause naive plane fitting to fail. Unlike plane fitting in LiDAR, we introduce a zone-based uncertainty-aware ground modeling specifically designed for radar. Secondly, we note that radar velocity measurements can be better combined with IMU for a more accurate preintegration in radar-inertial odometry. Existing methods often ignore temporal discrepancies between radar and IMU by simplifying the complexities of asynchronous data streams with discretized propagation models. Tackling this issue, we leverage GP and formulate a continuous preintegration method for tightly integrating 3-DOF linear velocity with IMU, facilitating full 6-DOF motion directly from the raw measurements. Our approach demonstrates remarkable performance (less than 1% vertical drift) in public datasets with meticulous conditions, illustrating substantial improvement in elevation accuracy. The code will be released as open source for the community: https://github.com/wooseongY/Go-RIO.

Figures

Figures reproduced from arXiv: 2502.08093 by the authors.

**Figure 1.** Top: Our uncertainty-aware ground filtering efficiently eliminates the noise (red) from radar. Middle: Mapping result of RURAL A2. Our continuous velocity integration with the Gaussian Process (GP) proficiently handles the sharp turns and roundabouts. Bottom: The proposed method shows the lowest elevation error (18m over 2.5km of path length, only 0.72%). While mitigating inherent noise in radar, estimating 6- degre… view at source ↗

**Figure 2.** The overall pipeline of our algorithm. discrepancies between radar and IMU, yet it encountered zaxis drifts due to high uncertainties on elevation. To address these limitations, Park et al. [20] configured two orthogonal radars to achieve accurate 3D velocity with a velocity factor. Recent works have integrated spatial information in odometry. Michalczyk et al. [21] proposed EKF-based radarinertial odometry with … view at source ↗

**Figure 3.** Comparison between naive plane fitting and our zone-based [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: As the vehicle moves t to t+1, prominent features maintain the structures in radar (yellow, cyan). The higher weight is allocated to correspondences within the consistent cluster (green line). [20], and DeRO [23]. Unfortunately, other ground-aided radar-inertial odomet…

**Figure 5.** Figure 5: (a) The trajectory plots of loop2 in NTU4DRadLM. The proposed method (blue) best aligns with the ground truth (black). (b) Estimated rotation in loop3. In terms of heading (a zoomed view ‘C’ in (b)), both 4DRadarSLAM and ours demonstrate superior performance; however, …

**Figure 6.** Figure 6: (a) Qualitative analysis of the proposed odometry in [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 7.** Figure 7: (a) Qualitative results of each filtering method projected onto the [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

A New Wave in Robotics: Survey on Recent mmWave Radar Applications in Robotics,

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