Camera–IMU rotation and clock-offset experiment

The browser's Camera–IMU tab uses the committed real Hilti 2022 exp21 camera-rate and gyro series. The original provenance records extraction, topics, source hashes and Hilti SLAM Challenge 2022 terms. No rendered angular rates or new recordings are substituted.

Select a plot axis, inject −50 to +50 ms relative to the saved time estimate, and vary −5 to +5 degrees around a selected camera-frame rotation axis. The rate plot compares camera-derived rates with gyro means over the same camera intervals; the next plot shows their selected-axis difference. The lower plot shows the three-axis residual RMSE over the selected 59- or 20-observation window at the selected rotation. Its vertical scale and those of the two other plots stay fixed while either injection changes. Click the sensitivity curve to change time only; Zero rotation changes rotation only, and Reset both returns both injections to zero.

Measured motion windows

Compare the full 59 exported observations with two non-overlapping, contiguous windows of 20 observations each. The producer chooses the pair with the largest difference in camera-derived three-axis angular-rate RMS, breaking ties by the first ascending pair of start indices. Gyro residuals and calibration estimates do not enter this selection. The higher-rate window is exported observations 40–59 (34.15 deg/s RMS); the lower-rate window is observations 15–34 (14.41 deg/s RMS). These identifiers refer to the exported subset.

The two small heatmaps show both windows side by side. Selecting a window keeps the injected time and rotation unchanged and updates the main heatmap, curves, observation count, timestamp range and numerical interval inspection. Colour and curve scales remain shared across windows. Each window uses its fixed intervals throughout the ±50 ms range, without extrapolation.

These are post-hoc development windows. Higher camera-rate RMS measures motion amplitude, potentially including tracking noise; it does not establish richer excitation, observability or accuracy. Equal counts do not make their motions, durations or noise identical. Comparing their residual minima or contour areas is not an independent accuracy ranking or uncertainty estimate.

Rotation × time heatmap

The heatmap evaluates 41 rotation angles (0.25° spacing) and 101 clock shifts (1 ms spacing). Every cell uses the same measured camera intervals within the selected window. The colour scale is shared by all measured windows and X/Y/Z rotation slices. Clicking a cell updates both controls and the interval curves; equivalent keyboard access is available through the two sliders. The plot axis and injected rotation axis are independent.

The white cross marks the selected cell; the cyan square marks the saved estimate. The cyan contour encloses cells within +0.5 deg/s of that slice's minimum. This is a displayed residual contour, not a confidence region, covariance estimate, success gate or proof of observability. Its width can reflect noise and model errors as well as similar parameter combinations. Inspect slice minimum selects the lowest displayed grid value; it does not run a full calibration optimizer or assert the true clock/extrinsic solution.

Only one rotation axis and time vary in each slice. The other two rotation components and IMU-frame gyro bias are not refitted. A narrow region in this two-parameter view does not establish that the complete calibration is uniquely constrained. Other parameter directions, unseen motions and independent data remain untested.

The clock convention is:

t_IMU = t_camera + saved_offset + injected_shift.

Positive injection samples later IMU timestamps for the same camera interval. The saved offset is approximately +1.701 ms. Zero time injection restores that estimate; it does not assert clock truth. Rotation is applied as R_candidate = R_camera_axis(injected_angle) × R_saved using the right-hand rule. The saved rotation supplies the baseline; the saved IMU-frame gyro bias remains fixed. Rotating the already bias-corrected camera-frame mean is equivalent to applying this candidate rotation to the original IMU mean.

Gyro means use the difference of sampled trapezoidal cumulative integrals, linearly interpolated at the two shifted endpoints and divided by interval duration. This matches the existing recorded-comparison metric. Both camera and gyro curves show interval means, not instantaneous measurements. No extrapolation or changing interval subset is permitted over the slider range.

This is a development-window sensitivity experiment, not a new optimization, independent accuracy benchmark or calibration verdict. Camera tracking noise, rotation error, bias and timing can all contribute to residuals. Even the displayed-window minimum would not establish the true recording-wide clock offset. The earlier GIF remains linked as a separate saved rotation/time/bias comparison; it is not presented as actual optimization progress.

Rebuild with PYTHONPATH=src:tools python tools/build_camera_imu_timing_demo.py. The generated asset binds original series, producer and existing metric source to SHA-256. Reference values are computed with the existing Python interval metric at −50, −10, 0, +10 and +50 ms, and checked against the browser implementation. Additional rotation/time references use the original Python metric with the left-multiplied candidate rotation R_camera_axis × R_saved. The fast surface calculation uses rotation-invariant vector energies and cross-moments; tests compare it with direct vector rotation and residual evaluation. All updates run locally after the measured series loads; no animation starts automatically.

Window references also compare the browser against original IMU cumulative integrals and the saved bias/rotation, independently of camera-frame moments.