捷联惯性导航、制导系统中方向余弦矩阵的递推算法

A New Recursion Formula Used In The Matrix of the Direction Cosine In The Strapdown Inertial Navigation and Guidance System

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。

Quaternion method, which has been successfully applied to the Strapdown Inertial Navigation and Guidance for tens year, is classical. In general, the practical using of the direction cosine matrix relating body frame to navigation frame is essential. However, the quaternion, which is only impermanent variable, can be leaved out. So the paper proposes a new recursion algorithm for the direction cosine matrix without quaternion. Mathematical simulation shows that the algorithm based on the differential equation of the matrix of the direction cosine is comprehensive, simple, and calculating time is shorter.