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NTU VIRAL LiDAR-LiDAR Extrinsic

The first LiDAR-LiDAR calibration in Calibrex. It estimates T_reference_target between the two Ouster OS1-16 units of the NTU VIRAL UAV: one horizontal (/os1_cloud_node1/points) and one mounted on its side (/os1_cloud_node2/points). The dataset's license is CC BY-NC-SA 4.0.

calibrex lidar-lidar ros2 tnp_01_rosbag2 \
  --reference-topic /os1_cloud_node1/points --target-topic /os1_cloud_node2/points \
  --point-time-field t \
  --body-transforms tnp_01/lidar_horz.yaml tnp_01/lidar_vert.yaml \
  --dataset-family ntu_viral --dataset-license "CC BY-NC-SA 4.0" \
  --output tnp_01.yaml

--body-transforms reads the dataset's T_Body2Lidar files (OpenCV YAML). Their composition inv(T_body_horz) T_body_vert serves two purposes: it is the initial value, and it is the reference that the result is compared against after the fit. These are design values (-0.55 m, 90 deg turns), not a measurement.

Method

The two LiDARs see only a small overlap at any instant, and a 16-beam LiDAR turned on its side gives a weak odometry. The method therefore registers target scans to reference maps, instead of matching the two sensors' motions.

  1. The reference LiDAR's odometry places its scans in one frame.
  2. Every 10th target scan (1 Hz) becomes a sample. It must land on the local map built from the 11 reference scans around its time, through P X: P is the reference pose and X = T_reference_target.
  3. All samples are solved jointly for one X, by Gauss-Newton on point-to-plane residuals with Huber weights (calibrex.solvers.lidar_lidar_map_solver).
  4. Evidence, as for the other pairs:
  5. samples are grouped in 10-second blocks, and every third block is held out;
  6. an 8-group block jackknife;
  7. known-bad shifts of 1 deg per rotation axis and 5 cm per translation axis must raise the held-out chi-square by at least 9;
  8. the reference transform is scored on the same held-out blocks.

Rotation std and reference differences are small rotations about the reference LiDAR's axes. This keeps them meaningful for the side-mounted unit, whose Euler angles sit at (90, 0, 180) deg.

Result on tnp_01 (development recording)

Verdict: inconclusive. Five of the six DoFs are estimated; roll's jackknife std of 0.108 deg is just above the 0.1 deg bound.

DoF Estimate Reported std (analytic / jackknife) Difference to design 1 deg / 5 cm held-out control
roll 89.981 deg 0.108 (0.008 / 0.108) deg +0.02 deg Δχ² 3,509
pitch -0.460 deg 0.016 (0.002 / 0.016) deg +0.46 deg Δχ² 95,379
yaw 179.843 deg 0.019 (0.003 / 0.019) deg -0.16 deg Δχ² 111,112
x -0.490 m 7.2 mm +9.8 mm Δχ² 7,176
y -0.024 m 6.8 mm -53.6 mm Δχ² 3,097
z 0.042 m 8.6 mm +47.2 mm Δχ² 13,756
  • Samples. 578 samples: 388 train and 190 held out, with 197,000 and 95,000 correspondences.
  • Residuals. The robust residual sigma is 86 mm, and the held-out median residual is 61 mm. The per-point noise is dominated by the 16-beam scans and the odometry drift over a map window.
  • The design value is rejected. Replacing the estimate with it raises the held-out chi-square by 48,901: the data point about 0.5 deg of pitch and 5 cm in y and z away from it. The design value is rounded, so a real difference of this size is plausible, but no independent measurement exists.
  • The solver hit its 30-iteration cap, with the last updates still moving. The jackknife std covers that.
  • The first 300 s agree. Run alone, they give differences to design within 0.03 deg of these for pitch and yaw, 0.13 deg for roll (the least constrained axis), and 1.6 cm for translation.

Artifact.

What did not work

  • Motion-based hand-eye. A X = X B on the two odometries was tried on the first 300 s.
  • The rotation came within about 1 deg of design, but the translation was unobservable (x off by 0.5 m, std 0.3 m).
  • The per-motion residuals (0.75 deg, 9 cm median) show that the side-mounted 16-beam odometry is too weak for this.
  • Gyro-aided deskewing and larger local maps did not help.
  • The hand-eye solver changes stay. It now starts from the axis-alignment rotation as well as the yaw starts, so arbitrary mountings converge. Its jackknife and reference differences now use small rotations about the parent axes.

Pre-registered audit: refuted

The claim, metrics, and thresholds were committed in ntu_viral_lidar_lidar_preregistration.yaml (commit f5ab3c2), before lidar-lidar ran on any evaluation recording. The evaluation recordings are rtp_01, spms_01, and tnp_02 (1333 samples, 45 held-out blocks); development was tnp_01 only. Scoring runs tools/score_ntu_lidar_lidar.py, and the audit is built by tools/build_ntu_lidar_lidar_audit.py.

Verdict: refuted, 2/4 gates (protocol, result).

Gate Observed Threshold
Rotation error to the design value 0.489 deg ≤ 1.0 deg
Translation error to the design value 0.077 m ≤ 0.10 m
Paired improvement over scan-to-scan on held-out blocks, 95 % CI low −0.0048 ≥ 0
Cross-recording consistency (mean) 1.143 ≤ 1.0
  • Accuracy passes. The pooled extrinsic is 0.49 deg and 7.7 cm from the rounded design value: (pitch, yaw) +0.47 and −0.13 deg, and (y, z) −5.3 and +4.7 cm, consistent with the development recording.
  • The method does not beat concurrent scan-to-scan. The paired 95 % CI low is −0.0048: the two are tied. On tnp_01 they were also indistinguishable.
  • Cross-recording consistency fails. Fitting Calibrex on one recording and on the others' train blocks disagrees by 1.29 (rtp_01), 1.46 (spms_01), and 0.69 (tnp_02), against the 1.0 bound of 0.3 deg / 3 cm. The recordings were taken with the same rig and design values, so this is odometry-driven scatter in the side-mounted 16-beam LiDAR, not a real difference.

The development result is what the pre-registration records: Calibrex's fitted extrinsic differs from the design value by 0.46 deg of rotation and 6.2 cm of translation, but the three scored methods are statistically indistinguishable on tnp_01. The claim was therefore about accuracy against the design value and cross-recording reproducibility, not a margin over a baseline. The concurrent-scan and design baselines are reported for transparency only.

The held-out recordings are now spent. A future claim would need to fix the cross-recording scatter (more samples per recording, the LiDAR clock offset, or a better side-mount odometry) and be pre-registered on new recordings.

Next

  • Use more sequences.
  • Estimate the LiDAR-to-LiDAR clock offset.
  • Improve roll, which the development recording leaves unobservable.

No SOTA claim is made for lidar-lidar.