Gyroscope drift on mobile phones

Question

Lots of posts talk about the gyro drift problem. Some guys say that the gyro reading has drift, however others say the integration has drift.

1. The raw gyro reading

Answer 1

If the gyro reading has "drift", it is called bias and not drift.

The drift is due to the integration and it occurs even if the bias is exactly zero. The drift is because you are accumulating the white noise of the reading by integration.

For drift cancellation, I highly recommend the Direction Cosine Matrix IMU: Theory manuscript, I have implemented sensor fusion for Shimmer 2 devices based on it.

(Edit: The document is from the MatrixPilot project, which has since moved to Github, and can be found in the Downloads section of the wiki there.)

If you insist on the Kalman filter then see https://stackoverflow.com/q/5478881/341970.

By why are you implementing your own sensor fusion algorithm?

Both Android (SensorManager under Sensor.TYPE_ROTATION_VECTOR) and iPhone (Core Motion) offers its own.

Answer 2

In this discussion both Ali and Stefano have raised two fundamental aspects of drifts due to ideal integration.

Basically zero mean white noise is an idealized concept and even for such ideal noise integration offer higher gain over lower frequency component of noise, which introduces a low frequency drift in the integrated signal. By theory the zero mean noise should not cause any drift iff observed over significantly long time but practically ideal integration never works.

On the other hand, even a minor dc-offset in the reading (input signal) can cause a significant drift over a time, if an ideal integration (loss-less summation) is performed on it. It can ramp up a very small dc-offsets in the system, as ideal integration has infinite gain on DC component of an input signal. Therefore for the practical purpose we substitute ideal integration by a low pass filter whose cut-off can be as low as required but can not be zero or too low for practical purpose.

Answer 3

The dear Ali wrote something that is really questionable and imprecise (wrong).

The drift is the integration of the bias. It is the visible "effect" of bias when you integrate. The noise - any kind of stationary noise - that has mean zero, consequently has integral zero (I am not talking of the integral of PSD, but of the additive noise of the signal integrated in time).

The bias changes in time, as a function of voltage and exercise temperature. E.g. if voltage changes (and it changes), bias changes. The bias it is not fixed nor "predictable". That is why you can not eliminate bias using the proposed subtraction of the estimated bias by the signal. Also any estimate has an error. This error cumulates in time. If the error is lower, the effects of cumulation (the drifting) become visible in a longer interval, but it still exists.

Theory says that a total elimination of bias it is not possible, at the present days. At the state of the art, no one has still found a way to eliminate the bias - based only gyroscopes and accelerometers magnetometers - that could filter all the bias out.

Android and iPhone have limited implementations of bias elimination algorithms. They are not totally free by bias effects (e.g. in small intervals). For some applications this can cause severe problems and unpredictable results.

Answer 4

Motivated by Ali reply (thanks Ali!), I did some reading and some numerical experiments and decided to post my own reply about the nature of gyro drift.

I've written a simple octave online script plotting white noise and integrated white noise:

The angle plot with reduced offset that is shown in the question seems to resemble a typical random walk. Mathematical random walks has zero mean value, so that cannot be accounted as drift. However, I believe numerical integration of white noise leads to non-zero mean (as can be seen in the histogram plot for random walk below). This, together with linearly increasing variance could be associated to the so-called gyro drift.

There is a great introduction to errors arising from gyroscopes and accelerometers here. In any case, I still have much to learn, so I could be wrong.

Regarding the complimentary filter, there's some discussion here, showing how the gyro drift is reduced by it. The article is very informal, but I found it interesting.