Extended Kalman Filter for spacecraft pose estimation using dual quaternions

Based on the highly successful Quaternion Multiplicative Extended Kalman Filter (Q-MEKF) for spacecraft attitude estimation using unit quaternions, this paper proposes a Dual Quaternion Multiplicative Extended Kalman Filter (DQ-MEKF) for spacecraft pose (i.e., attitude and position) and linear and angular velocity estimation using unit dual quaternions. By using the concept of error unit dual quaternion, defined analogously to the concept of error unit quaternion in the Q-MEKF, this paper proposes, as far as the authors know, the first multiplicative EKF for pose estimation. Compared to existing literature, the state of the DQ-MEKF only includes six elements of a unit dual quaternion, instead of eight, resulting in obvious computational savings. A version of the DQ-MEKF is presented that takes only discrete-time pose measurements with noise and, hence, is suitable for uncooperative satellite proximity operation scenarios where the chaser satellite has only access to measurements of the relative pose, but requires the relative velocities for control. Finally, the DQ-MEKF is experimentally validated and compared with two alternative EKF formulations on a 5-DOF air-bearing platform.