中国空间科学技术

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四元数微分方程最小参数解法研究

刘瑞华   

  1. 中国民航学院空中交通管理学院 天津300300
  • 发布日期:2003-12-25

The Minimal Parameter Solution for the Quaternion Differential Equation

Liu Ruihua (College of ATM, Civil Aviation University of China, Tianjin 300300)   

  • Published:2003-12-25

摘要： 对一种求解正交矩阵微分方程的三阶最小参数方法进行改造 ,将其用于四元数微分方程求解 ,并对其在捷联惯性导航系统姿态矩阵实时求解中的应用进行了仿真。结果表明 ,其计算精度比经典的三阶Peano Baker数值解法提高 35倍 ,而浮点运算次数则仅为后者的一半 ,对于提高捷联惯性导航系统姿态计算的精度具有重要意义。

关键词: 四元数, 姿态, 微分方程, 捷联式惯性导航

Abstract: A new method of 3 rd order minimal parameter solution for the orthogonal matrix differential equation is modified and used to solve the quaternion differential equation, and the numerical simulation is done in the Strap-down Inertial Navigation System(SINS). The result shows that when the new algorithm is used, the precision of the solved attitude angle is about 3 to 5 times higher than that by using the classical method, but the floating-point operations is only about half of the old one. So it is an important method to improve the precision of SINS.