Motion Representation and Inertial Navigation in Clifford Algebras

The quaternion and dual quaternion have been widely used in describing the three-dimensional rigid-body motion. This work starts by introducing their Clifford algebra representations, followed by proposing the Clifford algebra formulation of the trident quaternion, fulfilling the simultaneous representation of attitude, velocity and position. Besides, the exponential/logarithmic map of trident quaternion is developed. Finally, the kinematic model of the trident quaternion is presented, and the left/right-error kinematic models of the inertial navigation system are used to design extended Kalman filters (EKFs). Land vehicle experiments demonstrate that the EKF developed with the Clifford algebra has better performance in odometer-aided in-motion alignment.