On the Relation between the Accelerometer and the Gyroscope Measurements

This paper investigates the use of microelectromechanical systems such as gyroscope and accelerometer. One issue regarding these devices is their calibration. If accelerometer calibration does not imply special problems, gyroscope calibration is more difficult. Thus, one of the methods for gyroscope calibration is based on the relation between accelerometer and gyroscope measurements. We present two such relations. The first one uses the fact that the derivative of the accelerometer measurements is equal with the cross product between the accelerometer measurements itself and the angular rate. The second method computes the accelerometer measurements as a product between the rotation matrix and initial value of the accelerometer measurements. The angles used in the rotation matrix are computed using the integration of gyroscope measurements. We present experimental results that demonstrate the two claims. Data measurements are acquired either from a smartphone or a device that contains inertial sensors and is compatible with Bluetooth low energy. Finally, we conclude about the gyroscope calibration.