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Strapdown inertial navigation research involves the parameterization andcomputation of the attitude, velocity and position of a rigid body in a chosenreference frame. The community has long devoted to finding the most concise andefficient representation for the strapdown inertial navigation system (INS).The current work is motivated by simplifying the existing dual quaternionrepresentation of the kinematic model. This paper proposes a compact andelegant representation of the body's attitude, velocity and position, with theaid of a devised trident quaternion tool in which the position is accounted forby adding a second imaginary part to the dual quaternion. Eventually, thekinematics of strapdown INS are cohesively unified in one concise differentialequation, which bears the same form as the classical attitude quaternionequation. In addition, the computation of this trident quaternion-basedkinematic equation is implemented with the recently proposed functionaliterative integration approach. Numerical results verify the analysis and showthat incorporating the new representation into the functional iterativeintegration scheme achieves high inertial navigation computation accuracy aswell.

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