一种自适应变步长RKF方法及其在卫星轨道预报中的应用  

An adaptive variable step-size RKF method and its application in satellite orbit prediction

作　　者：张志[1] 廖瑛[1] 文援兰[1] 

机构地区：[1]国防科学技术大学航天科学与工程学院,湖南长沙410073

出　　处：《计算机工程与科学》2015年第4期842-846,共5页Computer Engineering & Science

基　　金：航天科技创新基金资助项目(CASC201101)

摘　　要：为提高常规的变步长RKF方法的运算效率,提出了一种基于范数控制的自适应变步长RKF法。该方法给出局部截断误差范数值、误差限与步长的定量函数关系,根据这种函数关系自动调整步长,并对局部误差范数值为0或极小值的情况进行了讨论。卫星轨道动力学系统的描述可以归结为一阶向量常微分方程初值问题的求解,将自适应变步长RKF方法应用在该问题上,实现了考虑地球非球形和日月等三体摄动下的卫星轨道积分。仿真结果表明,该算法能满足高精度的轨道预报要求,提高了计算速度,在轨道预报中具有很好的使用价值。To improve the computing efficiency of the ordinarily used variable stepsize RKF algorithm, an adaptive variable stepsize RKF method based on norm control is presented. The quantitative functional relationship between the local truncation error, tolerance and stepsize is given, and then the stepsizes are automatically adjusted, and the conditions under which the local error norm equals to zero or minimum are discussed. The description of the satellite orbit dynamic system can be attributed to the solution to the initial value problems of first-order vector ordinary differential equations. The proposed method is used to solve this problem to achieve the satellite orbit integral under the consideration of earth non-spherical and a third body perturbation. Simulation results indicate that the proposed method can satisfy the requirements of high precision orbit prediction, improve computing speed, and is worthy of use in the orbit prediction.

关 键 词：RKF法 变步长 范数控制 误差限 

分 类 号：V474[航空宇航科学与技术—飞行器设计]