小步长低阶Collocation方法轨道积分性能研究

介绍了Collocation方法的原理及误差构成，以Collocation方法在逐历元滤波轨道解算中的应用为切入点对小步长低阶Collocation方法轨道积分的性能进行了研究。分别就二体问题及真实GPS星座卫星轨道为对象进行了一系列验算，得到了一些有益结论：就积分方法本身性能而言，Collocation积分方法较传统数值积分法精度要高且稳定性要好；在一定长度的积分步长范围内，将小步长低阶Collocation方法用于滤波轨道解算是可行且有效的。 但在积分步长很小的情形下，从计算效率方面考虑，不推荐使用Collocation方法；利用小步长低阶Collocation方法取代大步长高阶方法能提高效率且可抑制蚀现象引起的积分结果发散。经试验表明：选用积分步长为900s的4阶方法是合适的。

Performance Research of Small Steplength and Low Order Collocation Method in Orbit Determination

Both principle and error constitution of the Collocation method are introduced in this paper. With a view of its application in filter orbit determination, the performance of the small steplength and low order Collocation method is researched. Based on a set of both orbit integration calculations of two body problem and GPS constellation, some meaningful conclusions are obtained that performance of Collocation method is better than that of traditional numerical integration method; it is practical and effective to adopt small steplength and low order Collocation method in filter orbit determination, but when the steplength is much small; instead of large step and high order Collocation method, the small steplength and low order method has higher efficiency and can inhibit integration divergence caused by eclipse. It is most suitable to use the fourth order collocation method of integration steplength of 900s.