A Trident Quaternion Framework for Inertial-Based Navigation Part I: Rigid Motion Representation and Computation

Strapdown inertial navigation research involves the parameterization and computation of the attitude, velocity, and position of a rigid body in a chosen reference frame. The community has long devoted to finding the most concise and efficient representation for the strapdown inertial navigation system (INS). The current work is motivated by simplifying the existing dual quaternion representation of the kinematic model. This article proposes a compact and elegant representation of the body's attitude/velocity/position, with the aid of a devised trident quaternion tool, which is an extension of dual quaternions. And the position is accounted for by adding a second dual part to the dual quaternion. Eventually, the kinematics of the strapdown INS are cohesively unified in one concise differential equation, which bears the same form as the classical attitude quaternion differential equation. In addition, the numerical solution to this trident quaternion-based kinematic equation is dealt with the recently proposed functional iterative integration approach. Numerical results are provided to verify the analysis. The new representation not only provides an elegant kinematic form of inertial navigation, but gives birth to precision inertial navigation algorithm.