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This work deals with error models for trident quaternion framework proposedin the companion paper (Part I) and further uses them to investigate theodometer-aided static/in-motion inertial navigation attitude alignment for landvehicles. By linearizing the trident quaternion kinematic equation, the leftand right trident quaternion error models are obtained, which are found to beequivalent to those derived from profound group affine. The two error modelsare used to design their corresponding extended Kalman filters (EKF), namely,the left-quaternion EKF (LQEKF) and the right-quaternion EKF (RQEKF).Simulations and field tests are conducted to evaluate their actualperformances. Owing to the high estimation consistency, the L/RQEKF convergemuch faster in the static alignment than the traditional error model-based EKF,even under arbitrary large heading initialization. For the in-motion alignment,the L/RQEKF possess much larger convergence region than the traditional EKFdoes, although they still require the aid of attitude initialization so as toavoid large initial attitude errors.

A Trident Quaternion Framework for Inertial-based Navigation Part II: Error Models and Application to Initial Alignment