  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.
