Unscented Kalman Filter for Spacecraft Pose Estimation Using Twistors

This study presents a new method to solve the pose estimation problem of the combined spacecraft translational and rotational motion using twistors. The twistor representation enables the use of the unscented Kalman filter in the proposed pose estimation method to achieve a higher estimation accuracy than can be achieved with the method using a dual-quaternion-based extended Kalman filter. The unscented Kalman filter is difficult to design using dual quaternions because of the normalization constraint problem. To overcome this problem, the twistor representation in the framework of dual numbers is introduced to describe the spacecraft local pose error, whereas dual quaternions are used to describe the absolute pose. The unscented Kalman filter schemes, each of which uses different measurements, are designed based on the twistor representation. The proposed unscented Kalman filter schemes using twistors are compared with the dual-quaternion-based multiplicative extended Kalman filter through simulations. The results demonstrate the effectiveness of the proposed method and indicate that the twistor-based unscented Kalman filter is superior to the dual-quaternion-based multiplicative extended Kalman filter when both the initial estimation errors are large and the observation model is highly nonlinear.