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Gyroscope sensitivity (also called scale factor) tells you how much the output changes for a given angular rate. Bias is the rate a gyro reports when it is actually stationary, while bias stability describes how that apparent zero changes over time. Noise is the random variation around the underlying signal. These are different error sources and must be measured with different tests.
An Allan deviation plot separates the time scales: short averaging times usually reveal white-rate noise and angle random walk, the curve minimum estimates in-run bias stability, and rising long-time sections expose random-walk or ramp processes. The number is meaningful only with its test temperature, bandwidth, sample rate, duration, vibration state, units and averaging time.
What the three terms mean
Sensitivity (scale factor)
Sensitivity is the gain between true angular rate and the sensor’s reported rate. If a gyro has a sensitivity error, every rate is proportionally too high or too low. A fixed zero-rate offset is a different error and is calibrated separately.
The ADIS16501 datasheet defines nominal sensitivity as “the slope of the line of best fit for the angular rate and acceleration transfer functions” over the full-scale range. In practical terms, a scale-factor calibration applies a multiplier so the measured response matches known rates across the intended range.
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A simple error model is:
reported rate = (scale factor × true rate) + bias + noise
Scale-factor accuracy matters most when the vehicle rotates quickly or when an error must remain proportional over a wide full-scale range. It can also vary with temperature, supply conditions and axis alignment, so a value quoted at one operating point should not be treated as valid everywhere.
Bias
Bias is the output that remains when the true angular rate is zero. A gyro can have excellent short-term noise yet still report a nonzero rate while sitting still. Integrating that false rate into angle creates an error that grows with time.
Bias stability
Bias stability describes how the apparent zero changes during operation. It is a statistical, time-dependent property, not a promise that the zero will remain fixed indefinitely. Analog Devices’ glossary notes that in-run bias stability (IRBS) “is also found as the minimum of the AVAR plot.” The minimum occurs where averaging has reduced short-term noise but longer-term drift has not yet become dominant.
How gyro noise differs from drift
Noise is random variation. Drift is a change in the underlying output or bias over a longer interval. The two are related because averaging suppresses some noise but cannot remove low-frequency processes that move the bias.
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Short-term white-rate noise and angle random walk
At short averaging times, a stationary gyro commonly shows white-rate noise. Averaging neighboring samples reduces this component. When the rate is integrated to angle, the corresponding parameter is angle random walk (ARW). ARW is often reported in degrees per square-root hour (°/√hr), while a rate-noise density may be expressed in degrees per second per square-root hertz (°/s/√Hz). Do not compare those units without converting them and checking the bandwidth and sample-rate assumptions.
Flicker noise and bias instability
At intermediate times, low-frequency or flicker-like processes can flatten the Allan-deviation curve. The lowest point is used as the in-run bias-stability estimate. Because that point is tied to a particular averaging time and test setup, it is not interchangeable with a permanent bias specification.
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At long averaging times, the curve can rise as random-walk or ramp processes accumulate. Temperature changes, vibration, acceleration sensitivity, electronics and mechanical stress can all contribute. A gyro with a lower laboratory bias-stability number may perform worse in a vibrating vehicle if its environmental sensitivities are larger.
How to read an Allan variance or Allan deviation plot
Allan variance is a time-domain method for analyzing a sequence of data, as described by the NXP/Freescale application note Allan Variance: Noise Analysis for Gyroscopes (2015). Allan deviation is the square root of Allan variance and is normally plotted against averaging time on logarithmic axes.
1. Record the gyro while it is stationary
Mount the sensor securely and keep all axes as still as possible. Record a continuous rate stream long enough to cover the longest averaging time of interest. A short record can make the long-time section unreliable and can hide drift processes.
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2. Document the test setup before processing
Write down the sample rate, total duration, temperature, vibration state, output bandwidth, digital filtering, axis orientation, calibration state and output units. If the sensor is inside a temperature-controlled chamber, record the set point and stability. If it is on a bench, note whether nearby machinery or airflow could add motion.
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For a series of cluster times, divide the stationary record into adjacent or overlapping groups, calculate the average rate in each group, and evaluate the difference between neighboring averages. The resulting Allan variance is a function of averaging time. Taking its square root gives Allan deviation.
4. Plot on log-log axes
Put averaging time on the horizontal axis and Allan deviation in the chosen rate or angle-related unit on the vertical axis. The shape is more informative than a single point: falling short-time behavior indicates that averaging is reducing white noise; the minimum is the IRBS estimate; rising long-time behavior indicates random-walk or ramp effects.
5. Extract parameters only from the appropriate region
Use the short-time region to estimate ARW, the minimum to report bias instability, and the long-time rising region to investigate rate random walk or rate ramp. MathWorks’ inertial-sensor workflow uses Allan-variance data to estimate the N, K and B noise parameters corresponding to these processes. Do not fit one line across the entire plot: each process occupies a different time range.
| Plot region | What it usually represents | What to report |
|---|---|---|
| Short averaging times, descending curve | White-rate noise and angle random walk | ARW or noise density, with sample rate and bandwidth |
| Curve minimum | Balance between averaged white noise and low-frequency drift | In-run bias stability and the averaging time at the minimum |
| Long averaging times, ascending curve | Rate random walk, rate ramp or environmental drift | Fitted process, time range and evidence of temperature or vibration influence |
Why test conditions change the number
Every sensitivity, noise or stability figure is conditional. A complete specification states:
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- Sample rate: the rate at which output data were collected.
- Bandwidth and filtering: analog and digital filters alter measured noise.
- Duration: the record must support the averaging times used for the estimate.
- Temperature: include the actual temperature and whether it was controlled.
- Motion and vibration: static, vibration-free data do not represent a moving platform.
- Calibration state: factory calibration, user calibration and raw output are not equivalent.
- Units and axis: identify whether the result is rate, angle, ARW, or noise density and which gyro axis was tested.
- Statistical status: distinguish a typical example from a guaranteed limit.
Without those details, two apparently different gyros may simply have been measured under different filters, temperatures or averaging ranges.
Interpreting a vendor example correctly
InertialSense documentation published in 2026 gives an example for its IMX-6 of 0.10 °/√hr angle random walk and 0.9–0.95 °/hr bias instability. Those figures were reported under static, vibration-free conditions at 25 °C, 1000 Hz and 24-hour duration. They are vendor-specific examples, not universal limits for every IMU or operating environment.
| Reported item | Value | Conditions and qualification |
|---|---|---|
| Angle random walk | 0.10 °/√hr | IMX-6 example; static, vibration-free, 25 °C, 1000 Hz, 24 hours; InertialSense 2026 documentation |
| Bias instability | 0.9–0.95 °/hr | IMX-6 example under the same stated conditions; vendor example, not a universal guarantee |
| Scale-factor accuracy | Not stated in this example | Requires a separate sensitivity or calibration specification |
| Temperature coefficient and vibration sensitivity | Not stated in this example | Must be evaluated separately for an operating platform |
The example illustrates why ARW and bias instability should not be collapsed into one “noise” number. ARW describes short-time averaging behavior; bias instability identifies the best long-time operating region in that specific test.
Comparing gyroscopes for a real application
Build the comparison around the error source that limits your system, rather than choosing the smallest isolated number.
| Comparison axis | Question to ask | Why it matters |
|---|---|---|
| Sensitivity or scale-factor accuracy | How large is the gain error over the required full-scale rate and temperature range? | A proportional error corrupts every nonzero rate and can dominate fast rotation measurements. |
| Short-term noise | Is the figure ARW or noise density, and what bandwidth and sample rate produced it? | Determines how much angle uncertainty accumulates during short maneuvers. |
| Long-term stability | What is the minimum Allan deviation, at what averaging time, and for how long was the sensor observed? | Shows when averaging stops helping and bias drift becomes significant. |
| Environmental sensitivity | What are the temperature coefficient, vibration or acceleration sensitivity and cross-axis effects? | Bench results can fail to predict performance on a vehicle or machine. |
| Test method | Was the record stationary, calibrated and processed with Allan deviation using comparable units? | Ensures that the figures are genuinely like-for-like. |
Calibration and measurement workflow
Separate scale factor from bias
Use known angular-rate references or a calibrated turntable to estimate the slope of measured output versus true rate. Then perform a zero-rate test to estimate the fixed offset. Do not use a zero-rate correction to compensate for a scale-factor error: it fixes the intercept but leaves the slope wrong.
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Use Allan analysis to choose an operating average
After collecting a stationary record, locate the Allan-deviation minimum. That averaging time is the point at which additional averaging no longer improves the estimate because low-frequency drift is taking over. A navigation filter can use this information to choose process-noise values and update rates, but the chosen values must match the application’s temperature and motion conditions.
Repeat at relevant temperatures and vibration levels
A single room-temperature, quiet-bench run characterizes intrinsic behavior under those conditions. Repeat the procedure across the expected temperature range and with representative vibration if the gyro will be mounted on a motor, vehicle or industrial machine. Compare the resulting curves rather than carrying one laboratory number into every environment.
Common interpretation mistakes
- Calling sensitivity “accuracy” without qualification: sensitivity is the gain; bias and noise are separate terms.
- Treating bias stability as a fixed offset: the stability figure describes how the offset wanders over time.
- Reading the minimum without its time coordinate: a bias-stability value is incomplete without the averaging time where it occurs.
- Comparing ARW to noise density directly: they use different units and depend on bandwidth and sampling assumptions.
- Using too little data: long-time Allan-deviation points need a record that is substantially longer than the averaging time being estimated.
- Ignoring filters: changing output bandwidth changes the measured short-term noise.
- Assuming static performance predicts vehicle performance: vibration, acceleration and temperature can dominate the error budget.
- Mixing axes or calibration states: report the tested axis and whether the data were raw, factory-calibrated or user-calibrated.
A concise specification checklist
Before accepting a gyro specification, verify that the document identifies:
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- The sensitivity definition and full-scale range.
- The bias definition and whether the quoted stability is in-run or another metric.
- ARW or noise density with units, bandwidth and sample rate.
- The Allan-deviation minimum and its averaging time.
- Record duration, temperature, vibration state and filtering.
- Whether each figure is typical, measured on one sample, or guaranteed across production.
- Environmental coefficients and cross-axis behavior relevant to the installation.
With those fields present, sensitivity, bias stability and noise become separate, actionable entries in an error budget instead of competing marketing numbers.
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