PaperlayerView exact revision on arXiv

Source-linked AI summary

TRaIL-Odom: Tightly Coupled Continuous Time Radar-IMU-LiDAR Odometry with Adaptive Doppler Weighting

Chiyun Noh, Turcan Tuna, William Talbot, Marco Hutter, Laurent Kneip, Ayoung Kim

arXiv:2609.03561v1cs.RO

TL;DR

Existing radar-LiDAR fusion methods use fixed weights despite scan- and direction-dependent sensing quality. TRaIL-Odom adapts Doppler constraints per point and per scan within a tightly coupled continuous-time Radar-IMU-LiDAR odometry framework, achieving state-of-the-art overall performance and clear gains in degenerate scenes.

  • Problem

    Existing radar-LiDAR fusion methods rely on fixed residual weights although radar Doppler and LiDAR geometry are informative in scan- and direction-dependent ways.

  • Method

    TRaIL-Odom uses continuous-time B-splines and reweights radar Doppler per point toward weak translational directions while scheduling scan-wise radar gain from LiDAR geometry.

  • Results

    TRaIL-Odom achieves state-of-the-art overall performance across 13 sequences, with clear advantages in geometrically degenerate scenes.

  • Takeaways & Limitations

    Adaptive Doppler weighting typically preserves or improves accuracy by reinforcing weakly observable directions without unnecessarily increasing radar influence in well-constrained directions.

Abstract

from arXiv · show

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.

I. INTRODUCTION

TRaIL-Odom addresses scene- and direction-dependent radar informativeness by adapting Doppler weighting within a tightly coupled Radar-IMU-LiDAR odometry framework. It combines per-point reweighting toward weak translational directions with scan-wise gain scheduling based on LiDAR degeneracy.

  • Motivation: Fixed radar residual weights do not account for scene-dependent or directional geometric degradation, motivating adaptive modulation of radar contribution.Geometric degeneracy can weaken only a subset of translational directions, while others remain well constrained by LiDAR.
  • Approach: TRaIL-Odom fuses asynchronous Radar-IMU-LiDAR measurements in a tightly coupled continuous-time B-spline optimization framework.The framework uses a split pose representation with separate position and orientation splines.
  • Approach: Per-point radar reweighting reallocates Doppler information toward weak translational directions identified from LiDAR pointcloud geometry.Radar influence is limited along directions already well constrained by LiDAR.
  • Approach: Scan-wise radar gain scheduling adjusts overall Doppler contribution using LiDAR geometric anisotropy, emphasizing radar under severe degeneracy and limiting it in well-constrained scans.This module complements per-point weights, which shape directional distribution but not overall radar scale.
  • Resources: The work contributes a real-world dataset spanning six sequences across three degenerate scenes, together with extensive ablations and released code.The dataset includes accurate position ground truth.

II. RELATED WORK

Prior radar-LiDAR odometry methods improve robustness by adding Doppler or other complementary modalities, but explicit adaptation to directional geometric degradation remains underexplored. TRaIL-Odom instead modulates radar kinematic information using LiDAR observability at both measurement and scan levels.

  • Radar-LiDAR Odometry: Radar complements weak LiDAR geometry through direct line-of-sight radial-velocity measurements and has been integrated into tightly coupled and filter-based odometry systems.Prior work also explores velocity-aware gravity estimation and dynamic object removal.
  • Research Gap: Existing works are often validated in limited scenarios, while explicit modulation of radar contribution remains underexplored.The paper frames robust generalization around adapting Doppler influence to LiDAR geometric observability.
  • Adaptive Fusion: Adding modalities alone does not guarantee higher accuracy because relative measurement uncertainty changes with scene degradation, making fixed fusion weights vulnerable to over-trusting unreliable measurements.Related methods therefore adapt information-source contributions as conditions change.
  • TRaIL-Odom: TRaIL-Odom directs radar kinematic information toward weak directions and suppresses unnecessary influence in well-constrained scenes through per-measurement and per-scan reweighting.This differs from approaches that switch modules or globally adjust parameters.

III. METHOD

TRaIL-Odom fuses asynchronous IMU, radar, and LiDAR measurements through continuous-time B-spline trajectory modeling and tightly coupled optimization. Its objective adaptively modulates radar Doppler weights to support directions where LiDAR geometry is weak.

  • III. METHOD: TRaIL-Odom uses continuous-time B-splines in a tightly coupled Radar-IMU-LiDAR framework to fuse asynchronous measurements.The pose uses separate position and orientation splines.
  • III. METHOD: Each LiDAR scan is processed by filtering radar points, performing RI initialization, diagnosing translational degeneracy, reweighting Doppler constraints, and jointly estimating pose.This sequence is summarized in the TRaIL-Odom overview.
  • III. METHOD: The sliding-window state includes active position and orientation spline control points plus IMU biases, optimized jointly over IMU, radar, LiDAR, and marginalization residuals.The window spans one LiDAR scan and the associated IMU and radar measurements.
  • III. METHOD: The effective radar Doppler weight is adaptively modulated using a per-point factor and a scan-wise gain to reinforce LiDAR-weak translational directions.Fixed residual weights cannot actively reinforce directions with weak or anisotropic LiDAR constraints.

D. Radar-Inertial (RI) Initialization

RI initialization supplies a velocity-consistent starting point for the joint optimization. Before initialization, radar detections are filtered using predicted ego-motion to suppress outliers.

  • D. Radar-Inertial (RI) Initialization: RI initialization provides a velocity-consistent starting point and remains stable even without LiDAR geometric information.It is used because the nonlinear objective requires reliable initialization for each window.
  • D. Radar-Inertial (RI) Initialization: Radar detections are filtered using the previous optimization window’s predicted ego velocity before RI optimization.The predicted radial component is obtained by projecting the radar-frame ego velocity onto each point’s line of sight.
  • D. Radar-Inertial (RI) Initialization: Detections whose measured radial velocities deviate significantly from the predicted radial components are discarded.The velocity threshold is set to 0.3m/s.
  • D. Radar-Inertial (RI) Initialization: The retained radar inliers form the Doppler residual set and are optimized jointly with IMU residuals for initial pose estimation.The retained measurements support the RI initialization problem.

2) Initial Pose Estimation:

The method diagnoses translational degeneracy from a scan-level LiDAR normal information matrix rather than control-point Hessian conditioning. Small eigenvalues identify weak translational directions.

  • 2) Initial Pose Estimation:: 86.0% RMSE ATE and 78.5% RTE reductions are not supported by the supplied passages for this section.
  • 2) Initial Pose Estimation:: Control-point-space Hessian conditioning can misdiagnose geometric degeneracy because spline basis coupling and knot placement affect LiDAR residuals.The issue arises specifically in continuous-time B-spline LIO.
  • 2) Initial Pose Estimation:: Degeneracy diagnosis is restricted to translation because IMU gyroscopes typically constrain orientation well, while accelerometer integration causes translational drift.Accelerometer errors accumulate through double integration.
  • 2) Initial Pose Estimation:: A scan-level 3 × 3 normal information matrix aggregates unit normals from planar LiDAR features to indicate translational observability.Local neighborhood plane fitting extracts the features directly within the current scan.
  • 2) Initial Pose Estimation:: Eigen-directions with eigenvalues small relative to the dominant eigenvalue form the LiDAR-frame degeneracy subspace.The threshold ratio is τ = 0.2 in the experiments.

F. Degeneracy-Aware Per-Point Radar Reweighting

Per-point radar reweighting aligns Doppler constraints with weak LiDAR translational directions when radar line-of-sight coverage is sufficient. A coverage test disables reweighting when radar cannot adequately excite the weak subspace.

  • F. Degeneracy-Aware Per-Point Radar Reweighting: Radar points whose line-of-sight directions align with the LiDAR-diagnosed degeneracy subspace receive larger Doppler weights than uniformly weighted points.Each Doppler measurement contributes a rank-1 directional constraint.
  • 1) Degeneracy Subspace LOS Coverage Check: Radar line-of-sight coverage is checked before reweighting so Doppler constraints are applied selectively to the diagnosed weak subspace.Projected line-of-sight vectors are stacked to form a sensitivity and coverage representation.
  • 1) Degeneracy Subspace LOS Coverage Check: For a two-dimensional degeneracy subspace, reweighting is enabled only when the coverage matrix satisfies cond(M) < 30.A one-dimensional subspace is accepted by default; otherwise degeneracy-aware reweighting is disabled.
  • F. Degeneracy-Aware Per-Point Radar Reweighting: When coverage is sufficient, a non-negative per-point factor αj is computed for each radar Doppler residual.The factor is defined from the alignment of each radar constraint with the weak subspace.

2) Calculate Per-Point Weight:

The per-point scheme forms a weighted Doppler information matrix and assigns each radar point a weight based on alignment with LiDAR-identified weak translational directions.

  • Each radar point contributes a rank-1 term to the Doppler information matrix, which is shaped by the diagonal per-point weight matrix.
  • Per-point weights are set from each point’s alignment with the LiDAR-diagnosed weak translational subspace.The alignment score is defined using the projection vector z_j.
  • The weights use an exponential function normalized to unit mean, with η controlling distribution sharpness.The number of radar points is q, and η is selected empirically and evaluated in ablation experiments.
  • The resulting reweighting emphasizes points aligned with degenerate directions and reduces influence along directions already constrained by LiDAR.

G. Radar Gain Scheduling

Radar gain scheduling adjusts the overall Doppler contribution per scan using LiDAR geometric anisotropy, increasing radar weight as LiDAR information becomes less isotropic.

  • The global gain γ adjusts the radar Doppler contribution per scan after per-point weights shape its directional distribution.State estimation then solves the tightly coupled nonlinear least-squares problem with the resulting radar weighting.
  • LiDAR plane-normal sphericity approaches one for isotropic geometry and decreases when information concentrates in fewer translational directions.
  • A monotone mapping increases γ as sphericity decreases, giving radar more weight under anisotropic LiDAR geometry.
  • The effective radar Doppler weight is applied when the translation-degeneracy and LOS-coverage checks pass.

IV. EXPERIMENT

Experiments compare TRaIL-Odom with LiDAR-only and radar-LiDAR baselines across datasets containing well-constrained and degenerate sequences. Radar-aided methods succeed consistently on the in-house sequences, while adaptive radar weighting improves or preserves performance across most GaRLILEO sequences.

  • A. Datasets and Evaluation Metric: The in-house evaluation uses the GaRLILEO and Boxi datasets, including sequences with well-constrained, semi-degenerate, and optimization-degenerate geometry.The comparison includes LiDAR-based and radar-LiDAR fusion state-estimation methods.
  • B. In-house Dataset: Radar-aided methods are the only approaches that succeed on all six in-house sequences and deliver consistently low errors.Ours-RLIO achieves the best RTE on five sequences and the lowest ATE on BikeTunnel1/2 and Airfield1.
  • C. GaRLILEO Dataset: On GaRLILEO, radar improves ATE on five of seven sequences and improves RTE on four, with clear gains on BiCorridor and Quad.RTE is unchanged on two sequences and degrades slightly only on Overpass.

D. Degeneracy-Aware Behavior of Adaptive Radar Weighting

On CorriLoop, adaptive weighting responds to changing LiDAR observability: scan-wise gain rises in degenerate corridors, while per-point weights favor radar measurements aligned with weak directions.

  • Visualization: Fig. 5 compares radar-point effective weights and trajectory scan-wise gains across representative CorriLoop corridor segments.The figure marks three radar examples and shows γ over the ground-truth trajectory and time.
  • Adaptive scan-wise gain: Scan-wise gain γ increases in geometrically weak corridor segments but remains near unity in informative regions such as corners.Repeated traversals show similar γ profiles across corresponding corridor regions, suggesting scene-geometry-driven adaptation.
  • Per-point reweighting: Per-point factor α assigns larger effective weights to radar measurements that better support weakly observable directions.Its spatial distribution is non-uniform, reallocating Doppler information according to directional observability.

E. Ablation Study

The ablations show complementary roles for the two modules: γ controls when radar contributes more, while α directs that contribution toward weak directions. Their combination yields the strongest relative RTE improvements and supports real-time operation.

  • Individual modules: γ improves ATE and RTE on all sequences, whereas α improves both metrics more selectively across sequences.This reflects γ's scan-level control of overall radar strength and α's directional redistribution without increasing total strength.
  • Module combination: Combined α & γ further reduces RTE on all evaluated ablation sequences compared with either module alone.The evidence attributes the gain to α directing γ-induced additional curvature toward weak directions.
  • Runtime: The full pipeline remains below 100 ms per LiDAR scan, satisfying the real-time requirement for the 10 Hz setup.Reweighting adds 0.93–2.95 ms, while joint optimization requires about 40–51 ms per scan.
Loading 2609.03561v1…