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KITTI INS-LiDAR Hand-Eye

This page reports Calibrex's native INS-LiDAR trajectory hand-eye calibration on KITTI raw. The evidence artifact is kitti_ins_lidar_2011_09_26.yaml (slac.ins_lidar_hand_eye/v0.1). The run pools drives 0005 and 0009 of 2011-09-26, which share one calibration (597 Velodyne sweeps, 165 motions).

Verdict: inconclusive, a partial calibration. Roll, pitch, and the clock offset are constrained by the data, and held-out blocks detect a known-bad shift of each. Yaw and the three translations are not reliably determined by these two drives, and the artifact says so instead of reporting numbers that look precise.

Results

The reference is KITTI's calib_imu_to_velo.txt, inverted to T_imu_velo. It is used only for this comparison, never in the fit, and it is itself an estimate rather than independent metrology.

DoF Status Estimate Reported std KITTI reference Difference Held-out control
roll estimated -0.974 deg 0.062 deg -0.849 deg -0.124 deg 1 deg detected (Δχ² 17.5)
pitch estimated 0.056 deg 0.072 deg 0.117 deg -0.060 deg 1 deg detected (Δχ² 148.9)
yaw unobservable -0.211 deg 0.514 deg 0.043 deg -0.254 deg 1 deg detected (Δχ² 93.8)
x unobservable 0.871 m 0.637 m 0.811 m 0.060 m 0.1 m not detected
y unobservable -0.243 m 0.408 m -0.307 m 0.064 m 0.1 m not detected
z unobservable 0.576 m 3.600 m 0.803 m -0.227 m 0.1 m not detected
clock offset estimated +4.0 ms 1.9 ms — — 20 ms detected (Δχ² 100.9)
reference scale estimated 1.0001 0.0042 — — —

The reported std is the larger of the analytic std and the block-jackknife spread. For yaw the data do respond to a 1 deg shift, but leaving out a single 5-second block moves the estimate by about 0.5 deg. The estimate depends on one or two turns, so yaw stays unobservable.

The held-out median motion residual is 0.089 deg in rotation and 0.079 m in translation, which matches the training fit (0.090 deg, 0.107 m).

Method

  1. LiDAR odometry from LiDAR alone. A vectorized point-to-plane scan-to-scan registration starts from a constant-velocity guess, scaled across dropped frames. It never uses the INS as a prior, so the LiDAR motions cannot inherit the extrinsic under test.
  2. Joint solve. A(t + dt) X = X B is solved for X = T_ins_lidar, the clock offset dt, and a reference trajectory scale, with Huber IRLS. Translation noise grows with motion length.
  3. Observability. Each DoF is estimated, prior, or unobservable according to its reported std. A declared prior (for example --prior z=0.80:0.02 from a CAD model) can constrain a DoF, and the artifact labels it as prior rather than data.
  4. Held-out evidence.
  5. Every third 5-second block is held out.
  6. The block jackknife runs over the training blocks.
  7. Each DoF is moved by a known-bad amount (1 deg, 0.1 m, or 20 ms).
  8. A pass is refused while any extrinsic DoF is unobservable.

Reproduce with:

calibrex ins-lidar kitti \
  2011_09_26/2011_09_26_drive_0005_sync 2011_09_26/2011_09_26_drive_0009_sync \
  --output kitti_ins_lidar_2011_09_26.yaml

Findings along the way

  • Positional frame pairing is wrong after dropped frames. Drive 0009 lacks Velodyne files 177-180. Its timestamp file keeps a blank line for each missing file, so pairing sweeps with OXTS packets by directory position shifts every later frame. The median Velodyne-OXTS time difference becomes 394 ms, and single-step motion residuals triple. Calibrex pairs frames by file index and interpolates the INS at LiDAR timestamps.
  • Rotation-first hand-eye fails silently on vehicles. Near-planar driving aligns all rotation axes with the vertical. A Park-Martin solve on these drives reported "converged, rank 3" with a yaw error of up to 13 deg, and its holdout closure did not flag it. Solving rotation and translation jointly recovers yaw from the translation equations. Only translation along the vertical axis stays unobservable, which synthetic tests confirm.
  • The OXTS track and the LiDAR disagree on distance. On drive 0005 the Mercator-projected OXTS steps are about 3 % shorter than the LiDAR-measured ones and 2.4 % shorter than OXTS's own velocity integral. On 0009 the mismatch is below 0.4 %. Without the scale nuisance this mismatch is absorbed by the lever arm; on 0005 it shifted the lateral translation by about 0.5 m.
  • Trajectory errors are correlated in time. Lateral and vertical residuals grow roughly linearly with motion length. The analytic covariance is therefore overconfident: on drive 0009 alone it gave yaw ±0.06-0.08 deg while landing 0.38-0.42 deg from the reference. The block jackknife is what keeps the reported uncertainty honest.
  • Absolute timestamps froze the clock offset. At UNIX times near 1.3e9 s, float64 resolves only about 0.2 µs, which is finer than the optimizer's finite-difference step. The solver now works in epoch-relative time; a regression test covers it.

Limitations

  • Velodyne sweeps are registered as rigid snapshots, without motion compensation within a sweep.
  • Drive 0001 has no OXTS timestamps. It is excluded rather than paired by position.
  • Two drives from one day are one rig and one dataset family. A SOTA claim needs at least two dataset families, so the SOTA leaderboard keeps ins-lidar at no_claim.
  • For weakly constrained DoFs, the analytic std varies by up to about 20 % between numerically equivalent runs, because Huber weights can switch for residuals near the threshold. The jackknife and the larger-of rule absorb this variation.