A Comparative Study of Extended Kalman Filtering and Unscented Kalman Filtering on Lie Group for Stewart Platform State Estimation

For Stewart platform, high-quality kinematic motion signal plays an vital role in assessing flight training fidelity and providing feedback for trajectory following. In addition to relying on numerically solving forward kinematic problem from measurement of six leg displacement sensors to obtain kinematic motion, some researchers began to employ sensor fusion scheme through deploying inertial measurement unit (IMU) on upper moving platform. In this paper, we will construct Extended Kalman Filtering (EKF) and Unscented Kalman Filtering (UKF) on Lie group to address this fusion problem. This fusion problem is slightly different from Simultaneous Localization and Mapping (SLAM) or Visual Inertial Odometry (VIO) in that six linear displacement sensors are tightly coupled with IMU sensors while those sensors in SLAM or VIO problem still provides partial measurement of motion state. Numerical simulation experiment shows that both Lie group-based EKF (EKF-LG) and UKF (UKF-LG) which satisfy group affine property behave better than conventional Kalman filtering in consistency and accuracy.