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

TL;DR

This paper introduces a novel trident quaternion framework that simplifies and unifies the representation and computation of rigid body motion in inertial navigation systems, enhancing accuracy and efficiency.

Contribution

It proposes a compact trident quaternion representation for attitude, velocity, and position, unifying the kinematic equations into a single differential equation and demonstrating improved computational accuracy.

Findings

The new representation simplifies the kinematic model.

The approach achieves high computational accuracy.

Numerical results confirm the effectiveness of the method.

Abstract

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 paper proposes a compact and elegant representation of the body's attitude, velocity and position, with the aid of a devised trident quaternion tool in which the position is accounted for by adding a second imaginary part to the dual quaternion. Eventually, the kinematics of strapdown INS are cohesively unified in one concise differential equation, which bears the same form as the classical attitude quaternion equation. In addition, the computation of this trident quaternion-based kinematic equation is implemented with the recently proposed functional iterative integration approach. Numerical results verify the analysis and show that incorporating the new representation into the functional iterative integration scheme achieves high inertial navigation computation accuracy as well.