Design, geometry evaluation, and calibration of a gyroscope-free inertial measurement unit

This work reports on a gyroscope-free inertial measurement unit (GF-IMU) that only comprises linear accelerometers in order to directly measure the transversal acceleration as well as the angular acceleration and velocity. The accuracy of the calculated body motion depends on the geometrical setup and the variance of the employed accelerometers. Therefore, an analytical evaluation of the sensor placement for the propagation of the sensor variance is provided here. The positions and orientations of the sensors within the body frame have to be known precisely in order to calculate the exact inertial movement of the body. With the calibration scheme presented here it is possible to identify these parameters completely even without any previous knowledge. Furthermore, the variance of the parameters can be determined, which can be used to evaluate the performance of the calibration. Using only acceleration sensors it is not possible to determine the direction of a rotation. To overcome this drawback, an Unscented Kalman filter (UKF) is applied to merge the information of the angular acceleration and the angular rate and thus robustly estimate the sign of the angular velocity. Measurements on a 3D-rotation table were carried out to exemplarily demonstrate the accuracy improvements after the calibration. Thereby, the RMS error of the angular rate was reduced by a factor of 2.8.