IMU model

CamCalib solves IMU intrinsics — scale and misalignment for gyroscope and accelerometer, optional g-sensitivity, and biases — rather than assuming a datasheet. Symbols follow Notation & glossary.

Measurement model

$$\boldsymbol{\omega}_m = \mathbf{D}_w\, \boldsymbol{\omega} + \mathbf{T}_g\, \mathbf{a} + \mathbf{b}_g + \mathbf{n}_g$$ $$\mathbf{a}_m = \mathbf{D}_a\, \mathbf{a} + \mathbf{b}_a + \mathbf{n}_a$$

Dw / Da carry scale and misalignment, Tg the g-sensitivity — how linear acceleration leaks into the gyro reading — and b_g / b_a the biases.

Three conventions

cam_imu.yaml

solve:
  imu_intrinsics_model: kalibr    # kalibr | rpng | calyx

The nine entries of each D are not all identifiable — the frame must be pinned to something, and what it is pinned to is the convention:

Model	Pins the frame to	Notes
kalibr	accelerometer triad	Matches Kalibr output
rpng	gyroscope triad	RPNG lineage
calyx	—	Gyro correction as a full 3×3, decomposed post-hoc into rotation × upper-triangular

The convention is not a quality lever

On real data — TUM-VI and MIC, with camera intrinsics pinned or freed — all three recover identical extrinsics and intrinsics. Choose the one that matches whatever you are comparing against; do not expect accuracy from the choice.

The matrices themselves are not numerically comparable across conventions. Before concluding that two calibrations disagree, check they used the same one.

t_ga — the gyro↔accel offset

Many IMU drivers publish gyro and accelerometer on one timestamp even though the two channels are sampled at different rates and instants. t_ga is that internal offset: the combined stamp is taken as the gyro clock, and the accel stored at t is modelled as physically sampled at t − t_ga.

cam_imu.yaml

solve:
  estimate_t_ga: true
  sigma_t_ga: 0.001

It is estimated inside the ACI factor — one extra Jacobian column in the preintegration (∂a/∂t_ga = ȧ from per-step finite differences, coupled into the gyro row through Tg) plus an optional sixth factor key with a staged prior. With the flag off, the five-key factor is untouched.

In simulation, injected offsets of −2, +1, and +5 ms recover with |z| ≤ 1.3 at σ = 0.024 ms, with no td / Dw / Da cross-contamination.

On real data, the T265’s Bosch BMI055 measures t_ga ≈ −6.2 ms, stable to about 0.2 ms across bags — roughly 16σ. That number is a direct measurement of the driver’s accel-interpolation artefact.

t_ga is reported in the result JSON, the calibration YAML, and the text report; apply-calib corrects it by re-interpolating the accel channel at t + t_ga, and roundtrip checks that it collapses toward zero.

Gyro-only auxiliaries

The other answer to an untrustworthy accelerometer — skip it:

cam_imu.yaml

input:
  imus:
    - {}                    # base IMU
    - {gyro_only: true}     # aux

Solves extrinsic rotation, td, Dw, and gyro bias; lever arm, Da, and Tg are pinned. Not permitted on the base IMU, which needs the accelerometer for gravity and metric scale. The calibration self-documents with a gyro_only: true flag per IMU.

On the T265 this makes the td collapse in a correct→recalibrate round-trip (+8.6 → −9.0 ms becomes +0.9 → +0.4 ms) and halves the residual lever drift.

Which to reach for

Both address the same defect. gyro_only avoids the bad accelerometer; estimate_t_ga measures the offset causing it. Prefer estimate_t_ga on the base IMU, where you have no choice but to use the accel — and where the measured value is itself worth having. Prefer gyro_only for an auxiliary whose accelerometer adds nothing you need.

What is actually observable

Scale and misalignment need excitation on every axis. G-sensitivity needs simultaneous rotation and strong linear acceleration, which most hand-held calibration motions do not produce — when Tg returns near its initial value with a wide covariance, it was not observed. See Degeneracy.