一种基于微分代数的任意阶空间目标轨道传播方法及其分析

An Arbitrary Order Orbit Propagation Method of Space Target Based on Differential Algebra

给出了一种基于微分代数的任意阶空间目标轨道传播方法。微分代数方法可以在不改变当前算法计算过程的基础上,给出函数对自变量任意阶导数的精确值。首先,将初始微分代数代入轨道传播方程,然后用获得的高阶导数构造新的高阶微分代数。通过使用新的高阶微分代数迭代前述过程,可求解空间目标状态对时间的任意阶导数。最后,将任意阶导数代入泰勒展开公式,求解空间目标轨道的单步传播。该方法要求轨道传播方程采用的摄动力模型在轨道传播积分区间上是解析的。通过仿真分析验证了所提方法的有效性。

The paper presents a method of space target orbit propagation of arbitrary order based on the differential algebra.The differential-algebraic method can give the exact value of arbitrary order derivative of the function with respect to its independent variable without changing the calculation process of the current algorithm.This method substitutes the initial differential algebra into the orbital propagation equation firstly,and then uses the obtained high-order derivatives to construct a new high-order differential algebra.By iterating the process with the new high-order differential algebra,arbitrary order derivative of the space target state with respect to time can be solved.Finally,we can substitute the derivative of arbitrary order into the Taylor expansion formula to solve the single-step propagation of the space target orbit.The perturbation force model required by this method must be analytic in the integration interval.The article gives a simulation analysis of the method,which verifies the effectiveness of the method.