Calibration of the accelerometer triad of an inertial measurement unit, maximum likelihood estimation and Cramér-Rao bound

In this paper, a simple method to calibrate the accelerometer cluster of an inertial measurement unit (IMU) is proposed. The method does not rely on using a mechanical calibration platform that rotates the IMU into different precisely controlled orientations. Although the IMU is rotated into different orientations, these orientations do not need to be known. Assuming that the IMU is stationary at each orientation, the norm of the input is considered equal to the gravity acceleration. As the orientations of the IMU are unknown, the calibration of the accelerometer cluster is stated as a blind system identification problem where only the norm of the input to the system is known. Under the assumption that the sensor noises have a white Gaussian distribution the system identification problem is solved using the maximum likelihood estimation method. The accuracy of the proposed calibration method is compared with the Cramér-Rao bound for the considered calibration problem.