Budgeting Gyroscope Bias as Accumulated Angle Error

A stationary gyroscope can report a small nonzero angular rate that looks harmless on a live plot. Integrating that rate turns the residual into a growing angle error. Evaluate the required observation time explicitly instead of judging a gyro only by the apparent quietness of its instantaneous readings.

Separate bias from random noise

The Analog Devices discussion of gyroscope drift identifies slowly varying bias and angular random walk as distinct contributors to integrated angle error. They require different models and cannot be represented by one arbitrary constant drift number.

Record initial bias, temperature dependence, repeatability after power cycling, and the noise measure relevant to the integration interval. A single short stationary average estimates the bias during that interval; it does not establish its stability over an entire mission.

Calculate the deterministic contribution

For constant residual rate bias, angle error equals bias multiplied by elapsed time. A hypothetical residual of 0.02 degrees per second accumulates 1.2 degrees in one minute and 12 degrees in ten minutes.

Use this simple calculation to allocate the allowed residual bias from the required angle accuracy and duration. Keep it separate from stochastic noise calculations and errors caused by scale factor, axis alignment, or timing.

Validate the stationary calibration

Confirm that the assembly is actually stationary while estimating bias. Vibration, slow fixture movement, or a user moving the product during startup can contaminate the estimate. Define how the system detects an unsuitable calibration interval.

Repeat after different off times and across the intended thermal transitions. Log sensor temperature and raw rate together. A bias measured immediately after power up may not represent the value after the enclosure and electronics warm.

Check integration and reference updates

Integrate using the correct sample interval and account for missing samples or timestamp discontinuities. A rate sensor with a good bias estimate can still produce an incorrect angle if software assumes the wrong time base.

If another sensor or external observation constrains the estimate, document which axes it observes and when the correction is trustworthy. Do not assume that gravity information alone provides an absolute heading reference about the vertical axis.

Save raw stationary records, calibration conditions, timestamps, temperature, and integrated error over the required duration. Repeat the comparison with calibration enabled and disabled so its contribution is visible. A defensible gyro budget explains how error grows between valid reference updates. A small average rate displayed for a few seconds is not a substitute for demonstrating the required angle accuracy over the application’s actual operating interval.