This work deals with error models for trident quaternion framework proposed in the companion paper "A Trident Quaternion Framework for Inertial-based Navigation Part I: Motion Representation and Computation" and further uses them to investigate the static and in-motion alignment for land vehicles. Specifically, the zero-velocity and odometer velocity measurements are applied in the static and in-motion alignment process, respectively. By linearizing the trident quaternion kinematic equation, the right and left trident quaternion error models are obtained. The resultant models are found to be equivalent to those derived from profound group affine. Then the two models are used to design the 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. For the static alignment, owing to their high consistency, the L/RQEKF converge much faster than the EKF even without any heading information. For the in-motion alignment, however, the two filters still need the assistance of the analytical/optimization-based in-motion alignment methods at the very start to avoid extremely large attitude errors, although they possess much larger convergence region than the traditional EKF does.

中文翻译：

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基于惯性导航的三叉戟四元数框架第二部分：错误模型及其在初始对准中的应用

这项工作处理了伴随文件“基于惯性导航的三叉戟四元数框架第一部分：运动表示和计算”中提出的三叉戟四元数框架的误差模型，并进一步使用它们研究了陆地车辆的静态和运动对准。具体而言，零速度和里程表速度测量分别应用于静态和运动中对齐过程。通过线性化三叉戟四元数运动方程，获得左右三叉戟四元数误差模型。发现所得模型与衍生自深层仿射的模型等效。然后，使用这两个模型来设计相应的扩展卡尔曼滤波器（EKF），即左四元数EKF（LQEKF）和右四元数EKF（RQEKF）。进行模拟和现场测试以评估其实际性能。对于静态对齐，由于其高一致性，即使没有任何航向信息，L / RQEKF的收敛速度也比EKF快得多。对于运动中对齐，尽管这两个滤波器比传统的EKF具有更大的会聚区域，但它们仍然在开始时仍需要基于分析/优化的运动中对齐方法的帮助，以避免出现极大的姿态误差。做。