Joint B-spline LiDAR-IMU acceleration

The native joint B-spline fitter uses analytic control-point rotation Jacobians and shares the evaluated trajectory states with the residuals and calibration derivatives. This speeds up calibrex imu-lidar joint and calibrex trajectory recover-lidar-imu-joint --trajectory cubic_bspline on the CPU, with the same public interfaces and result schemas.

The previous fitter reevaluated every local spline 24 times per residual family to differentiate four rotation controls along three axes. The new fitter differentiates the cumulative SO(3) recursion once, using right tangents. Plane returns need only the orientation derivative; gyro factors also need angular velocity, and accelerometer factors need angular acceleration. Bias, gravity, IMU mounting rotation and lever-arm derivatives reuse the base states. The clock-offset column retains central differences and independently selects the segment at each perturbed time, including across knots. Residuals, LM settings, sparse solve, covariance and evidence gates are unchanged.

Public-data comparison

The input is the public AIST GLIM Livox Avia livox.bag, described in the checked stream manifest. The comparison reads its first 12 seconds: /livox/points with per-point t, and /livox/imu with acceleration in g. It uses the native angular-rate initial estimate and gyro-deskewed odometry, then four map rounds with the default sampling, 30 fit iterations per round, gravity prior and interleaved IMU holdout. The supplied GT trajectory is not used by this run.

Both complete source trees are frozen before measuring. Three alternating pairs run in fresh processes with one BLAS thread. Whole time includes startup, bag reading, initial estimates, map construction/association, all fits, marginal covariance, noise updates, holdout, 32 signed controls, saved results, input hashing and verified imports. Fit time is the sum of the four full fits, including their covariance. Neither is a kernel-only measurement. See the complete evidence archive.

Scope	Prior median	Analytic median	Speedup
Complete worker	325.065 s	127.257 s	2.554x
Four fits, including covariance	251.629 s	39.818 s	6.320x

Quality and limits

Independent central differences test every local rotation axis at small, ordinary and near-pi rotations and at the segment boundaries. The assembled plane, gyro and accelerometer Jacobians are checked against perturbations of the actual residuals. Synthetic joint recovery and bag tests retain known truth, holdout and signed-control assertions.

The public comparison fixes physical tolerances before measuring: 0.001 deg rotation, 10 micrometres lever arm, 0.1 microseconds clock offset and 1e-5 whitened holdout RMS. It also checks block estimates, formal std, last-round changes, signed-control chi-square and correlations; all policy, block, control, separability and convergence decisions must agree. Full per-round covariance and trajectory arrays are retained for inspection.

This is a performance and regression result for one 12-second public clip. The plane map is estimated from the same trajectory; its formal covariance holds that map fixed. The final calibration remains INCONCLUSIVE, so the timing result does not establish absolute extrinsic accuracy or a conclusive calibration on this capture. Throughput depends on the number of returns, knots, fit iterations and the cost of the initial odometry.

Reproduce

Place the original public GLIM livox.bag under data/public/glim_versatile/; the raw recording is an external input and is not redistributed in this repository. With the ROS bag reader installed:

python -m tools.benchmark_bspline_lidar_imu \
  --baseline-commit b89e50bbd9e48a05a2acb6010ac46e50ece9220f \
  --bag data/public/glim_versatile/livox.bag \
  --max-seconds 12 --max-rounds 4 --repeats 3 \
  --output outputs/glim-joint-bspline-comparison

The output directory must not exist and runtime sources must be committed. Each worker verifies every imported Calibrex module against its frozen source tree. Failures leave their logs and attempt records intact. The comparison deliberately uses the GLIM topic, point-time and IMU unit conventions above.

Audit the published archive without downloading a bag or installing CUDA:

python -m tools.audit_bspline_lidar_imu_benchmark

The audit validates the complete models and file digests, checks actual source imports, and recomputes quality and all reported median speed ratios.