Shared rotations in LiDAR-IMU calibration

Native gyro deskew and joint cubic B-spline fitting reuse rotation terms to reduce the remaining cost of calibrex imu-lidar joint. The implementation uses the ordinary NumPy/SciPy CPU dependencies. Public callbacks, calibration settings, result schemas and evidence policy keep their existing interfaces.

What changes

Gyro deskew previously constructed an orientation and a bias Jacobian matrix for every return, then composed several matrices before applying the result to a point. For a fixed bias, the new internal model projects the cumulative bias sums into three-vectors once. The rotation identity Q Exp(-Q.T ds) = Exp(-ds) Q lets it apply the equivalent rotations directly to points. Each scan reuses its rotated coordinates across deskew rounds, while the translation follows the updated motion estimate. The original matrix callback remains available. Extrapolated times, large biases, non-orthogonal matrices and unusual inputs use that reference path.

The spline fitter computes each referenced adjacent control rotation, its logarithm and inverse right Jacobian once, then gathers those terms for the timestamps in that segment. Residuals and analytic Jacobians share their exponential rotations. Plane residuals evaluate pose only; gyro residuals also evaluate velocity; accelerometer residuals retain acceleration. The plane orientation derivative accumulates adjacent 3-by-3 blocks through the rotation suffix rather than propagating mostly empty 3-by-12 arrays.

These are algebraic changes to the same models. Sampling, feedback passes, iteration caps, LM acceptance, sparse solve, covariance and signed controls retain their existing settings. Temporary shared terms consume memory proportional to the selected returns; there is no persistent trajectory cache. Caller edits to controls are observed on the next evaluation.

Public-data comparison

The comparison starts from the analytic-Jacobian implementation in the preceding benchmark. It reads the same original public GLIM Livox livox.bag: the first 12 seconds of /livox/points with point time t, and /livox/imu with acceleration in g. Four map rounds retain the default sampling and 30-iteration fit caps. The supplied GT trajectory is not used.

Three alternating fresh-process pairs use one BLAS thread and frozen source trees. Whole time includes startup, bag reading, initial calibration, gyro-deskewed odometry, association, all four fits and covariance, noise updates, holdout, signed controls, result saving, hashing and verified imports. The fit time includes covariance. Source preparation is outside the worker.

Scope	Analytic-Jacobian baseline	Shared rotations	Speedup
Complete worker	142.930 s	100.615 s	1.421x
Four fits, including covariance	50.106 s	33.072 s	1.515x

The incremental whole-run gain is modest: 1.421x after the preceding analytic-Jacobian optimization. It does not establish another large end-to-end acceleration. This implementation is a candidate for review.

The complete evidence archive retains every trial, result, full per-round covariance and trajectory, actual module digests, frozen source trees, launcher and tool-only schemas. Raw bag data is an external input. Exploratory profiles had changing background load; their wall-time ratios are excluded from the reported comparison.

Quality and limits

Tests compare direct point rotation with the preserved matrix callback, including nonzero bias, epoch timestamps, input mutation and reference fallback. An odometry integration test checks reuse across deskew rounds, float32 point offsets and ordinary custom callbacks. Prepared spline states match the public evaluator, including repeated timestamps and knots. The orientation Jacobian is independently checked by central differences at small, ordinary and near-pi rotations. Synthetic calibration recovery keeps the existing accuracy and covariance assertions.

Public result comparisons use the fixed tolerances of the preceding benchmark. Decisions must agree exactly; numerical estimates, evidence, full per-round trajectories and covariance must agree within the declared tolerances. Results remain INCONCLUSIVE on this capture. Its estimated map and formal covariance do not provide independent extrinsic truth. This is a regression and performance result for one clip; larger captures and different point densities can have different speedups. Ratios from separate benchmark cohorts should not be multiplied.

Reproduce and audit

python -m tools.benchmark_bspline_lidar_imu \
  --baseline-commit 6df5aa2526b1fb4d5bc8511b7e9a0265d1266abc \
  --bag data/public/glim_versatile/livox.bag \
  --max-seconds 12 --max-rounds 4 --repeats 3 \
  --output outputs/glim-shared-rotations-comparison
python -m tools.audit_bspline_lidar_imu_benchmark \
  docs/assets/lidar_imu_shared_rotations

The output directory must be new and runtime sources must be committed. The CPU-only archive audit checks all file digests, full result models, imported sources and covariance, and recomputes quality and median ratios.