Extended Kalman Filter for Spacecraft Pose Estimation Using Dual Quaternions

Based on the highly successful quaternion multiplicative extended Kalman filter for spacecraft attitude estimation using unit quaternions, this paper proposes a dual quaternion multiplicative extended Kalman filter 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 quaternion multiplicative extended Kalman filter, this paper proposes, as far as the authors know, the first multiplicative extended Kalman filter for pose estimation. The state estimate of the dual quaternion multiplicative extended Kalman filter can directly be used by recently proposed pose controllers based on dual quaternions, without any additional conversions, thus providing an elegant solution to the output dynamic compensation problem of the full six degree-of-freedom motion of a rigid body. Three formulations of the dual quaternion multiplicative extended Kalman filter are presented. The first takes continuous-time linear and angular velocity measurements with noise and bias and discrete-time pose measurements with noise. The second takes only discrete-time pose measurements with noise and hence is suitable for satellite proximity operation scenarios where the chaser satellite has only access to measurements of the relative pose, but requires the relative linear and angular velocities for control. The third formulation takes continuous-time angular velocity and linear acceleration measurements with noise and bias and discrete-time pose measurements with noise. The proposed dual quaternion multiplicative extended Kalman filter is compared with two alternative extended Kalman filter formulations on a five degree-of-freedom air-bearing platform and through extensive Monte Carlo simulations.