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arxiv: 2604.12027 · v2 · submitted 2026-04-13 · 💻 cs.RO

3DRO: Lidar-level SE(3) Direct Radar Odometry Using a 2D Imaging Radar and a Gyroscope

Cedric Le Gentil , Daniil Lisus , Timothy D. Barfoot This is my paper

Pith reviewed 2026-05-12 01:45 UTC · model grok-4.3

classification 💻 cs.RO
keywords radar odometrySE(3) estimationgyroscope integrationdirect radar odometryego-motion estimationlidar comparisonautonomous navigation
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The pith

2D imaging radar fused with a 3D gyroscope enables full SE(3) odometry at lidar accuracy levels.

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

The paper extends the existing SE(2) Direct Radar Odometry method to handle three-dimensional motion by combining its planar velocity estimates with integrated gyroscope readings. This produces SE(3) ego-motion estimates while keeping the radar data processing in two dimensions. A sympathetic reader would care because the approach claims to match lidar performance using simpler, cheaper hardware. The claim is supported by results across 643 km of real driving data from the Boreas-RT dataset.

Core claim

This paper presents 3DRO, an extension of the SE(2) Direct Radar Odometry (DRO) framework to perform state estimation in SE(3). While still assuming planarity of the data through DRO's 2D velocity estimates, it integrates 3D gyroscope measurements over SO(3) to estimate SE(3) ego motion. This simple approach provides lidar-level odometry accuracy as demonstrated using 643km of data from the Boreas-RT dataset.

What carries the argument

The central mechanism is the combination of DRO's 2D velocity estimates, which assume planar radar data, with SO(3) integration of 3D gyroscope measurements to lift the output to full SE(3) ego-motion.

If this is right

  • Existing 2D radar hardware can now support full three-dimensional motion tracking without additional 3D sensors.
  • Odometry accuracy comparable to lidar is achievable on long driving sequences totaling hundreds of kilometers.
  • The method keeps the direct radar processing pipeline intact while adding only gyroscope integration for the extra degrees of freedom.
  • State estimation for robotics tasks requiring SE(3) becomes feasible with lower-cost sensor suites.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Replacing lidar with this radar-gyro combination could lower system cost and power draw for autonomous platforms.
  • Performance may hold better than lidar in fog, dust, or rain where optical sensors degrade.
  • Removing the planarity assumption in future extensions could yield general 3D radar odometry without gyroscopes.

Load-bearing premise

The radar returns are assumed to stay effectively planar so that the original 2D velocity estimates remain valid even while 3D motion is being reconstructed.

What would settle it

A dataset sequence containing large vertical displacements or strong non-planar terrain where the reported trajectory error exceeds that of a lidar baseline by more than a few percent would falsify the lidar-level accuracy claim.

Figures

Figures reproduced from arXiv: 2604.12027 by Cedric Le Gentil, Daniil Lisus, Timothy D. Barfoot.

Figure 1
Figure 1. Figure 1: Imaging radars collect data by sweeping radio waves around [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the misalignment between the radar sensing plane [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example of odometry trajectories obtained with 3DRO and the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Per-axis velocity estimates obtained with 3DRO on three different sequences of the Boreas-RT dataset. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Recently, the robotics community has regained interest in radar-based perception and state estimation. A 2D imaging radar provides dense 360deg information about the environment. Despite the radar antenna's cone of emission and reception, the collected data is generally assumed to be limited to the plane orthogonal to the radar's spinning axis. Accordingly, most methods based on 2D imaging radars only perform SE(2) state estimation. This paper presents 3DRO, an extension of the SE(2) Direct Radar Odometry (DRO) framework to perform state estimation in SE(3). While still assuming planarity of the data through DRO's 2D velocity estimates, it integrates 3D gyroscope measurements over SO(3) to estimate SE(3) ego motion. While simple, this approach provides lidar-level odometry accuracy as demonstrated using 643km of data from the Boreas-RT dataset.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents 3DRO, an extension of the SE(2) Direct Radar Odometry (DRO) framework to SE(3) ego-motion estimation. It retains the 2D radar velocity estimates from DRO (which assume planarity of returns) while integrating 3D gyroscope measurements over SO(3) to recover full 6DOF poses. The central claim is that this simple combination achieves lidar-level accuracy, as demonstrated on 643 km of data from the Boreas-RT dataset.

Significance. If the accuracy claims hold under the stated assumptions, the work would be significant for radar-based state estimation in robotics: it enables full SE(3) odometry using inexpensive 2D imaging radars plus a gyroscope, potentially lowering hardware costs relative to lidar while maintaining competitive performance on large-scale outdoor data. The scale of the evaluation (643 km) is a clear strength.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (method description): The lidar-level SE(3) accuracy claim rests on the planarity assumption implicit in the 2D DRO velocity solver, yet no quantitative check (e.g., measured pitch/roll variation, residual error after gyro integration, or sensitivity to terrain slope) is reported for the Boreas-RT sequences. Systematic bias in the 2D velocities would integrate into uncorrectable drift that the gyroscope cannot mitigate.
  2. [Evaluation section] Evaluation section (presumably §5 or §6): The abstract asserts 'lidar-level' performance on 643 km but the provided text contains no explicit error metrics (RMSE, drift rates), direct baseline comparisons to lidar odometry, or ablation on the contribution of the gyro integration versus pure SE(2) DRO. Without these, the central claim cannot be verified.
minor comments (2)
  1. [§3] Notation: The transition from SE(2) velocities to SE(3) poses via SO(3) integration should be accompanied by an explicit equation showing how the 2D velocity vector is lifted into the 3D body frame before integration.
  2. [Figures] Figure clarity: Any trajectory or error plots comparing 3DRO to lidar ground truth should include scale bars or zoomed insets for the 643 km dataset to allow visual assessment of drift.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the opportunity to respond to the referee's comments. We appreciate the positive assessment of the work's significance and the scale of the evaluation. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (method description): The lidar-level SE(3) accuracy claim rests on the planarity assumption implicit in the 2D DRO velocity solver, yet no quantitative check (e.g., measured pitch/roll variation, residual error after gyro integration, or sensitivity to terrain slope) is reported for the Boreas-RT sequences. Systematic bias in the 2D velocities would integrate into uncorrectable drift that the gyroscope cannot mitigate.

    Authors: We agree that a quantitative validation of the planarity assumption would strengthen the manuscript. The Boreas-RT dataset primarily involves driving on flat roads and highways, where the assumption of planar radar returns is reasonable. However, we did not report specific checks such as pitch/roll statistics or sensitivity to slope in the original submission. In the revised version, we will include an analysis of the gyroscope-derived pitch and roll variations over the dataset and discuss potential impacts on velocity estimates. revision: yes

  2. Referee: [Evaluation section] Evaluation section (presumably §5 or §6): The abstract asserts 'lidar-level' performance on 643 km but the provided text contains no explicit error metrics (RMSE, drift rates), direct baseline comparisons to lidar odometry, or ablation on the contribution of the gyro integration versus pure SE(2) DRO. Without these, the central claim cannot be verified.

    Authors: We acknowledge that the central claim requires supporting quantitative evidence for verification. The manuscript does present results on 643 km of data, but to ensure clarity and verifiability, we will revise the evaluation section to explicitly include RMSE and drift rate metrics, direct comparisons with lidar odometry baselines, and an ablation study on the gyroscope integration. We will also update the abstract to reference key performance numbers. revision: yes

Circularity Check

0 steps flagged

No significant circularity; method fuses independent 2D radar velocities with external gyro integration

full rationale

The derivation chain consists of taking the existing SE(2) DRO velocity estimates (which embed the planarity assumption) and integrating separate 3D gyroscope measurements over SO(3) to obtain SE(3) poses. No equation reduces the final SE(3) output to a parameter fitted from the same data, nor does any step redefine a quantity in terms of itself. The planarity assumption is stated explicitly rather than smuggled in via self-citation, and the lidar-level accuracy claim is presented as an empirical result on the Boreas-RT dataset rather than a mathematical necessity. A minor self-citation to the original DRO framework supplies the velocity module but does not bear the load of the SE(3) extension or the accuracy claim.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the planarity assumption inherited from the 2D DRO method and on standard numerical integration of gyroscope angular velocities; no new entities or fitted parameters are mentioned in the abstract.

axioms (2)
  • domain assumption The radar returns lie in a plane orthogonal to the spinning axis and can be treated as planar for velocity estimation.
    Stated explicitly in the abstract as the retained assumption from prior DRO work.
  • domain assumption Gyroscope measurements can be integrated over SO(3) to recover accurate 3D orientation without drift correction from other sensors.
    Implicit in the description of integrating 3D gyroscope measurements.

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Reference graph

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