A distributed set of accelerometers based on the minimum number of 12 accelerometers allows for computation of the magnitude of angular rate without using the integration operation. However, it is not easy to extract the magnitude of angular rate in the presence of the accelerometer noises, and even worse, it is difficult to determine the direction of a rotation because the angular rate is present in its quadratic form within the inertial measurement system equations. In this paper, an extended Kalman filter scheme to correctly estimate both the direction and magnitude of the angular rate through fusion of the angular acceleration and quadratic form of the angular rate is proposed. We also provide observability analysis for the general distributed accelerometers-based inertial measurement unit, and show that the angular rate can be correctly estimated by general nonlinear state estimators such as an extended Kalman filter, except under certain extreme conditions.
Keywords: Kalman filter; distributed accelerometers; inertial measurement unit; observability.