The task of strapdown inertial navigation system (SINS) initial alignment is to calculate the attitude transformation matrix from body frame to navigation frame. In this paper, such attitude transformation matrix is divided into two parts through introducing the initial inertially fixed navigation frame as inertial frame. The attitude changes of the navigation frame corresponding to the defined inertial frame can be exactly calculated with known velocity and position provided by GNSS. The attitude from body frame to the defined inertial frame is estimated based on the SINS mechanization in inertial frame. The attitude, velocity and position in inertial frame are formulated together as element of the group of double direct spatial isometries.It is proven that the group state model in inertial frame satisfies a particular "group affine" property and the corresponding error model satisfies a "log linear" autonomous differential equation on the Lie algebra. Based on such striking property, the attitude from body frame to the defined inertial frame can be estimated based on the linear error model with even extreme large misalignments. Two different error state vectors are extracted based on right and left matrix multiplications and the detailed linear state space models are derived based on the right and left errors for SINS mechanization in inertial frame. With the derived linear state space models, the explicit initial alignment procedures have been presented. Extensive simulation and field tests indicate that the initial alignment based on the left error model can perform quite well within a wide range of initial attitude errors, although the used filter is still a type of linear Kalman filter. This method is promising in practical products abandoning the traditional coarse alignment stage.

中文翻译：

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基于双直接空间象素群的捷联惯性导航系统初始对准

捷联惯性导航系统（SINS）的初始对准的任务是计算从车身框架到导航框架的姿态转换矩阵。通过引入初始惯性固定导航框架作为惯性框架，将这种姿态变换矩阵分为两部分。可以使用GNSS提供的已知速度和位置来精确计算与定义的惯性框架相对应的导航框架的姿态变化。基于惯性坐标系中的SINS机械化，估算从车身框架到定义的惯性坐标系的姿态。惯性系中的姿态，速度和位置被公式化为双直接空间等距组的元素。证明惯性系中的组状态模型满足特定的“组仿射” 性质和相应的误差模型满足李代数上的“对数线性”自治微分方程。基于这样的打击特性，可以基于线性误差模型估计从车身框架到定义的惯性框架的姿态，甚至具有非常大的失准。基于左右矩阵乘法提取两个不同的误差状态向量，并基于左右误差导出详细的线性状态空间模型，用于惯性系中的SINS机械化。利用导出的线性状态空间模型，已经提出了显式的初始对准程序。大量的模拟和现场测试表明，基于左误差模型的初始对准可以在各种初始姿态误差范围内很好地执行，尽管使用的滤波器仍然是线性卡尔曼滤波器的一种。该方法在放弃传统的粗调准阶段的实际产品中很有希望。