Influence of Warpage on the State Estimation of a MEMS-Based Gyro-Free Inertial Measurement Unit

In this paper, we investigate the influence of warpage on the state estimation of the gyro-free IMU. A configuration-optimized gyro-free IMU is designed for investigation. Four triaxial MEMS accelerometers with specified configuration are used in order to directly determine the magnitude and sign of the angular velocity without integration. An optimized configuration geometry is presented to increase the observability of the body motion since the performance of the gyro-free IMU is affected by the configuration geometry of the distributed accelerometers. An effective unscented Kalman filter (UKF) is applied to estimate the system state. The mechatronic implementation of the distributed accelerometers consists of four triaxial MEMS accelerometers, each mounted on a separate board. The warpage model of the board based on thermal stress is built and developed. The main assumptions of this model are that the material of the board is FR4 which is widely used in Printed Circuit Board (PCB) and accelerometers are all rigid. Temperature is set within operating temperature ranging from -40 degrees C to +85 degrees C. We analyze the board warpage induced by thermal stress at -40 degrees C, room temperature (+25 degrees C) and +85 degrees C. Then the position and sensing direction errors of each accelerometer are obtained from the simulation results respectively. Consequently, the board state is robustly estimated by the applied UKF. The results show that warpage induces errors to state estimation of a gyro-free IMU.