On-chip capacitive sensing and tilting motion estimation of a micro-stage for in situ MEMS gyroscope calibration

In this paper, we introduce a novel on-chip capacitive sensor design and a motion estimation method for measuring multi-axis out-of-plane tilting motion of a micro-stage that is used for in situ calibration of an integrated MEMS gyroscope. On-chip sensing and motion estimation is critical for this application, since precision in measuring high frequency tilting motion of the micro-stage determines how accurately an on-stage MEMS gyroscope can be calibrated in the field with respect to this motion. To obtain decoupled sensing signals from multi-axis out-of-plane tilting motion, a capacitive sensing layout with high off-axis signal rejection capability is introduced. With the proposed design specifications and range of tilting motion, a dual axis capacitive sensor model is developed, and simulation results show that the sensor is able to reject more than 99.90% of the off-axis signal. The sensor also permits detection of perturbations to stage geometry due to ambient temperature variation through the effects of nonlinear behavior on signal timing. To measure tilting motion with the obtained sensing signal, a motion estimator with extended Kalman Filter (EKF) is also developed. With assistance of a laser Doppler vibrometer (LDV), experiments are performed to identify the parameters of the motion estimator and validate its performance. The experimental results demonstrate a 286 ppm error in scale factor calibration of a commercial MEMS gyroscope by the micro-stage with moderate temperature variation.