Technical Field Note #14 · November 2026

IMU noise and bias of a stereo+IMU egocentric rig, measured from static recordings

Field Note #14 · IMU noise, bias and spectrum from static segments (ODL-EGO S1 capture rig, R8 stereo+IMU)

Visual-inertial pipelines need the IMU noise parameters of the actual unit. The calibration file shipped with our rig carries generic priors and says so. We measured the unit from 5 static segments (22 minutes in total, longest 519 s) found inside the 2026-10-26 calibration recordings, without new capture. Gyro white noise is 0.00014–0.00018 rad/s/√Hz per axis and accelerometer white noise 0.0009–0.0014 m/s²/√Hz, roughly 12× and 22× below the priors. Two practical traps: the gyro z axis has strong high-frequency noise, so a per-sample standard deviation overstates its noise density 2.4×; and the gyro reads -0.32 °/s on z at rest, about 19° of heading per minute if not removed. Random walk could not be identified from records this short.

Published November 2026⏱ 12 min readStatus Preliminary · automated analysisOpen data GitHub · Hugging Face · Kaggle
0.00014–0.00018 rad/s/√HzGyro white noise (Allan fit, 3 axes)prior 0.002; longest static segment (519 s)Verified (automated)
0.0009–0.0014 m/s²/√HzAccelerometer white noise (Allan fit, 3 axes)prior 0.02Verified (automated)
-0.34 to -0.27 °/sGyro z bias at rest5 static segments, same dayVerified (automated)
0.000041–0.000060 rad/sGyro bias instability (Allan minimum)at τ = 7–20 sVerified (automated); short record

Why this matters

Noise parameters decide how much a fusion filter trusts the IMU

VIO and SLAM back-ends weigh the IMU against the cameras using four numbers per sensor: white-noise density and bias random walk for the gyroscope and the accelerometer. Priors that are too large make the IMU nearly useless; priors that are too small make the filter over-trust it and drift.

Our rig's calibration file states its IMU values are priors to be replaced by a dedicated static recording. We had not made one. This note shows that the calibration session already contained enough still time to measure the white-noise part reliably, and where it does not suffice.

Data

5 static segments from four existing recordings

Source: the IMU streams of four recordings made on 2026-10-26 during the ChArUco calibration sessions (Field Notes #11 and #12), when the rig sat still on a desk while targets were moved. No new capture was made.

Static detection: 1 s windows with every gyro axis standard deviation below 0.06 rad/s, runs of at least 60 s, 2 s trimmed at each edge. This gave 5 segments from 59 to 519 s (1348 s in total). The gyro and accelerometer each run at 501.5 Hz; the gyro output step is 0.000533 rad/s (0.0305 °/s), consistent with a ±1000 °/s range.

Method: overlapping Allan deviation per axis; white noise N fitted on the −½ slope between τ = 0.05 and 1 s; bias instability taken as the Allan minimum (reported as the raw minimum, without the 0.664 factor); bias as the segment mean.

White noise

About 12× below the priors, on every axis and segment

On the longest segment (519 s) the gyro white noise is 0.00014, 0.00017 and 0.00018 rad/s/√Hz on x, y and z, and the accelerometer 0.00093, 0.00137 and 0.00093 m/s²/√Hz. Across all 5 segments the gyro values stay within 0.00014–0.00024 and the accelerometer within 0.00085–0.00137.

The priors in the calibration file (0.002 and 0.02) are about 12× and 22× larger. At long averaging times the picture changes: the gyro Allan deviation turns upward after 7–20 s, and at τ ≈ 100 s it is 0.000124–0.000363 rad/s, comparable to the 0.000200 rad/s the priors imply there. So the priors are far too pessimistic for short-term noise but not obviously wrong for slow drift.

Log-log plot of gyroscope Allan deviation for three axes against a dashed prior line
Figure 1. Gyroscope Allan deviation, 519 s static segment, with the white-noise prior from the calibration file.
Log-log plot of accelerometer Allan deviation for three axes against a dashed prior line
Figure 2. Accelerometer Allan deviation, same segment.
Table 1. About 12× below the priors, on every axis and segment
QuantityxyzCalibration-file prior
Gyro white noise N, Allan fit (rad/s/√Hz)0.000140.000170.000180.002
Gyro noise from per-sample std (rad/s/√Hz)0.000240.000140.00043—
Gyro bias instability, Allan minimum (rad/s)0.0000600.0000580.000041—
at averaging time (s)71220—
Gyro Allan deviation at τ ≈ 100 s (rad/s)0.0003630.0002260.0001240.000200 (white + random walk)
Gyro bias at rest (°/s)+0.13-0.07-0.32—
Accel white noise N, Allan fit (m/s²/√Hz)0.000930.001370.000930.02
Accel bias instability, Allan minimum (m/s²)0.000260.000450.00047—

Trap 1

The gyro z axis is not white: do not estimate it from the sample standard deviation

A quick estimate divides the per-sample standard deviation by √(sample rate). For x and y this lands near the Allan value. For z it gives 0.00043 rad/s/√Hz, 2.4× the Allan fit, because the z noise rises toward the Nyquist frequency (lag-1 autocorrelation -0.67). That high-frequency part averages out within a few milliseconds and does not drive drift.

The spectrum also shows narrow peaks near 30, 44, 59 and 215 Hz. Their source (a desk-borne vibration, a fan, or electronics) was not identified; they do not change the Allan fit but are worth checking on a mounted rig.

Gyroscope amplitude spectral density for three axes from 0 to 250 Hz
Figure 3. Gyroscope amplitude spectral density on the static segment (Welch, 4096-sample Hann windows).

Trap 2

A 0.3 °/s gyro bias at rest

At rest the gyro reads +0.05 to +0.32 °/s on x, -0.16 to -0.04 °/s on y and -0.34 to -0.27 °/s on z across the 5 segments. Left uncorrected, the z value alone rotates the heading by about 19° per minute.

The z bias is stable across the day; x varies more. A fusion filter estimates the bias online, but initialising it from the first still second of each recording, rather than from zero, shortens convergence.

  • Keep the rig still for 2–3 s at the start of every recording.
  • Initialise gyro bias from that still window.
  • Do not compare gyro biases across recordings to judge sensor health without accounting for warm-up.
Grouped bar chart of gyroscope bias at rest per axis for five static segments
Figure 4. Mean gyro output at rest per axis for each static segment.
Table 2. A 0.3 °/s gyro bias at rest
Static segmentDuration (s)Gyro bias x / y / z (°/s)Gyro N, median of axesAccel norm (m/s²)
12:42 #0321+0.15 / -0.08 / -0.310.000179.802
12:42 #1276+0.05 / -0.04 / -0.340.000189.802
14:28 #0172+0.32 / -0.16 / -0.270.000199.803
14:32 #0519+0.13 / -0.07 / -0.320.000179.782
15:01 #059+0.14 / -0.07 / -0.330.000179.796

Interpretation

What we will put in the calibration file

Verified: the white-noise densities above, the gyro bias at rest, and the gyro output step. Recommendation for our deliveries: state measured white-noise densities with the usual inflation for unmodelled effects rather than the current 10–20× generic priors, and keep the random-walk terms as priors until a dedicated recording of several hours exists.

Not identified: bias random walk (records ≤519 s cannot separate random walk from warm-up drift), temperature dependence (the raw temperature field's scale is unconfirmed), accelerometer biases (each segment had a different tilt, so bias and gravity direction are not separable; the measured gravity norm was 9.782–9.803 m/s²), and behaviour on a head mount.

SCOPE AND LIMITS

Limitations

What this note does not show, stated up front.

  • Single R8 stereo+IMU unit, desk-mounted, one indoor office, one day (2026-10-26); results are not a population estimate for other units.
  • All measurements are automated. No independent human re-analysis was performed: AI/algorithm-only preliminary analysis.
  • Static segments are 59–519 s long; Allan values beyond about one quarter of the segment length are not reported and random walk is not identified.
  • Static detection uses a gyro threshold; two segments show slow accelerometer changes (likely the desk being touched) and were kept but not used for the headline numbers.
  • IMU part number and configured ranges are as reported by the supplier and the data; the accelerometer range setting was not confirmed. The temperature field was not used.
  • Raw IMU streams are released only after approval; derived tables are included.

FAQ

Questions data buyers ask

Q01What is the gyroscope white-noise density of this rig?
0.00014–0.00018 rad/s/√Hz per axis from an Allan-deviation fit on a 519 s static recording, about 12× below the 0.002 prior in the calibration file.
Q02Can you measure IMU noise without a dedicated static recording?
For white noise, yes, if existing recordings contain a few minutes of the rig standing still. Bias random walk needs hours of continuous static data.
Q03Why does the per-sample standard deviation give a different noise density?
Because the noise is not white. The gyro z axis has extra noise near the Nyquist frequency, so the per-sample estimate is 2.4× the Allan value. Allan deviation separates that from the noise that causes drift.
Q04How large is the gyro bias at rest?
About -0.32 °/s on z, steady across the day, and up to +0.32 °/s on x; enough to rotate heading by roughly 19° per minute if not removed.
Q05Should the calibration-file priors be replaced?
The white-noise terms should be replaced by measured values with modest inflation. The random-walk terms should stay as priors until a multi-hour static recording is made.

OPEN DATA AND CODE

Reproduce and inspect the evidence

Every number in this note can be checked: derived tables, analysis code, figures and a runnable notebook are public.

GitHubAnalysis code and reproduction stepsorigin-data-lab/imu-noise-bias-static-characterization-stereo-imu-rigView repository Hugging FaceDataset card, tables and figuresorigin-data-lab/imu-noise-bias-static-characterization-stereo-imu-rigOpen dataset KaggleData explorer and runnable notebookorigindatalab/odl-static-imu-allanExplore on Kaggle
Run the notebook on Kaggle

Licence: CC BY 4.0 (data and figures) · MIT (code)

Cite this note

Origin Data Lab (2026). Technical Field Note #14: IMU noise and bias of a stereo+IMU egocentric rig, measured from static recordings. https://origindatalab.io/technical-field-notes/imu-noise-bias-static-characterization-stereo-imu-rig.html

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