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Is gyroscope in modern phones/tablets able to detect the phone position even when phone is not moving? I installed Gyroscope Explorer to my Samsung Galaxy S5 and according to this it looks like gyroscope, unlike accelerometer, is able to detect the phone position regardless that phone is still.
Well this all depends on the drift of the gyroscope.
I know that the original Boeing 747 IMU gyros were developed to be good enough that they could track the rotation of the Earth around the sun, and if you averaged out the drift of a few units in a test bench you could start to detect the motion of the solar system around the Milky Way coming out of the noise.
Gyroscopes in phones are actually rate gyros. They only detect rotation, not absolute orientation. Orientation is given by integration aka dead reckoning . I don't know how much the drift is. Normally you combine the gyro information with the accelerometer and magnetic compass to cancel the drift and provide an absolute reference.