Tilt estimation of MEMS IMU using a fractional-order Kalman filter

Tilt estimation is essential in many fields such as consumer electronics, robotics and vertical structural monitoring. Tilt can be detected by micro-electromechanical-system(MEMS) inertial measurement unit(IMU), which includes a triaxial accelerometer and gyroscope. However, in dynamic environments, external accelerations and gyroscope drift can result in significant tilt estimation errors. This paper introduces a fractional-order Kalman filter(FKF) for tilt estimation using MEMS IMU. Based on Grünwald-Letnikov fractional calculus, we construct a FKF algorithm for tilt estimation. The gyroscope measurements are used as the control vector in the state equation, while the accelerometer-specific force serves as the measurement vector in the observation equation. Simulation experiment is carried out to verify the proposed FKF algorithm for MEMS IMU tilt estimation. The results indicate that the FKF shows minimal improvement in a static environment. However, under dynamic conditions, the FKF exhibits superior robustness and faster convergence, reducing the root mean square error (RMSE) of tilt estimation by over 3 degrees within 7 seconds.