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

This article deals with error models for a trident quaternion framework proposed in the companion paper (Part I) and further uses them to investigate the odometer-aided static/in-motion inertial navigation attitude alignment for land vehicles. By linearizing the trident quaternion kinematic equation, the left- and right-trident-quaternion error models are obtained, which are found to be equivalent to those derived from profound group affine. The two error models are used to design their corresponding extended Kalman filters (EKFs), namely, the left-quaternion EKF (LQEKF) and the right-quaternion EKF (RQEKF). Simulations and field tests are conducted to evaluate their actual performances. Owing to the high estimation consistency, the LQEKF and the RQEKF converge much faster in the static alignment than the traditional error-model-based EKF, even under arbitrary large heading initialization. For the in-motion alignment, the LQEKF and the RQEKF possess much larger convergence region than the traditional EKF does, although they still require the aid of attitude initialization so as to avoid large initial attitude errors.