Accurate Tilt Sensing with Linear Model

We propose a tilt sensing scheme using a physical model with three sensitive axes of microelectromechanical systems (MEMS) accelerometers. Based on the physical model in which the gravitational acceleration is resolved into three components, we propose three numerical models to sense the tilt angle. First, two exact numerical models are presented to measure the gravitational acceleration and its one component along the tilt direction, respectively. The parameters of these two models are specific angles of the physical model, which can be used to assess the configuration of the physical model. Next, the measurement bias model is introduced to reduce the error resulting from the nonlinear relation between the gravitational acceleration and the tilt angle. Third, all the three numerical models are unified into a linear model whose parameters can be efficiently estimated using the least squares method. In the experiments, we evaluate the performance of the proposed scheme by examining the mean, the standard deviation, and the maximum of the errors. The experiment results show that our scheme is able to perform accurate tilt sensing with the average error below 0.1° in the measurement range (0°, 120°).