四元数微分方程最小参数解法研究

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3～5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。

The Minimal Parameter Solution for the Quaternion Differential Equation

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.