How to gyroscopically measure number of rotations on one axis when there is concurrent random motion on another axis

Question

Can a gyroscopic sensor (comparable to the type that are typically used in smartphones) that is embedded in this black object

that is rotating around the X axis measure the number of rotations around the X axis if the object may or may not also be rotating at the same time in random ways (number of partial or full rotations, speeds, and directions) around the Z axis?

If so, is the Z axis rotation irrelevant, or is there special mathematics involved in filtering out the affects of the Z rotation on the measurement of X axis rotation? Or does another measurement such as acceleration or magnetism need to be used to solve the problem?

Is there any impact in using a 2-axis vs. a 3-axis gyroscopic sensor for this measurement scenario?

Answer 1

I believe the term you are looking for is 'Cross sensitivity'. This term describes the effect that motion in one axis has on the measured motion of other orthogonal axes in accelerometers or gyroscopes

Cross Sensitivity is normally stated by the manufacturer of the sensor and (depending on the quality/type of the sensor) is typically 1-5%. So, for example, a 10 rad/s rotation around the x axis might also give an output of 0.1 rad/s around the y axis and -0.2rad/s around the z axis which will lead to drift in the calculated position/angle of the device Also, the cross-sensitivity may be different between different pairs of axes so there may be 3 values Sxy, Syz, Sxz.

In a perfect sensor the motion around one axis would not affect the others but in a real device there is always some effect.