  This work deals with error models for 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 (EKF), 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 L/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 L/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.
