Extended Kalman Filter for Spacecraft Pose Estimation Using Dual Quaternions

Abstract

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-offreedom 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 discretetime 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.

Adaptive pose and inertial parameters estimation of free-floating tumbling space objects using dual vector quaternions

“…Also, the dual quaternion-based representations have the similar form of the traditional ones, which is one of the most appealing feature of the dual quaternionbased method. 14 Brodsky and Shoham 15 describe the dual quaternion-based rigid body kinematics and dynamics modeling in detail. Goddard 16 and Zu et al 17 use the dual quaternion-based kinematics and the EKF to estimate the pose parameters of a target in space.…”

“…Goddard 16 and Zu et al 17 use the dual quaternion-based kinematics and the EKF to estimate the pose parameters of a target in space. Filipe et al 14 utilize the error dual quaternions to model the targets kinematics and then make the pose parameters estimation with the EKF. However, all the researches mentioned above only utilize the dual quaternion-based kinematics to accomplish the pose parameter estimation, and none of them uses the dual quaternion dynamics to estimate the space targets.…”

Relative Navigation in Asteroid Missions Using Dual Quaternion Filtering

“…In [16] the measurement model incorporates velocity and/or acceleration measurements only, which is not adapted to state-of-art sensors that equip nowadays spacecraft for asteroid circumnavigation. Strapdown inertial navigation systems [13] are not yet adapted to asteroid missions as they heavily rely on the asteroid's gravity field knowledge -a dominant source of uncertainty.…”

“…Research shows that it could result in higher accuracy and faster convergence [14,15], while redundancy in the position representation can be efficiently handled via order reduction [16], alike the approach used for multiplicative attitude quaternion EKF [17,18].…”

“…Dual quaternions provide an alternate representation [9][10][11] and have spawned growing attention with applications ranging from image processing to spacecraft navigation [12][13][14][15][16]. Research shows that it could result in higher accuracy and faster convergence [14,15], while redundancy in the position representation can be efficiently handled via order reduction [16], alike the approach used for multiplicative attitude quaternion EKF [17,18].…”