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数十年来,四元数及其解法成功地应用于捷联惯性导航和制导系统中,成为经典的算法。它定义了从导航坐标系到飞行器体坐标系的四元数,然后给出四元数更新方程,再根据实时确定的四元数求出体系到导航坐标系的方向余弦矩阵,以便将测得的体系的视速度增量转换到导航系。从制导和导航角度看,上述方向余弦矩阵是必不可少的,而四元数却是中间变量,因此,本文跨越了四元数及其算法,根据方向余弦矩阵微分方程直接导出方向余弦矩阵的更新递推公式。数学仿真表明该算法的精度与四元数算法接近,但它具有更容易理解、计算量小、编程简单等优点,可以代替四元数方法。
For decades, quaternions and their solutions have been successfully applied to strapdown inertial navigation and guidance systems as classical algorithms. It defines the quaternion from the navigational coordinate system to the vehicle body coordinate system, then gives the quaternion updating equation, and then finds the direction cosine matrix of the system to the navigational coordinate system based on the quaternion determined in real time so that the measured The apparent velocity of the system is converted to the navigation system. From the guidance and navigation point of view, the direction of the cosine matrix is essential, but the quaternion is the intermediate variable, so this article span the quaternion and its algorithm, according to the direction cosine matrix differential equation directly derived from the direction cosine matrix Update recursion formula. Mathematical simulation shows that the accuracy of the algorithm is close to that of the quaternion method, but it has the advantages of easier to understand, less computation and simple programming. It can replace the quaternion method.