低轨卫星轨道拟合及预报方法研究

DISCUSSION ON ORBIT FITTING AND ORBIT FORECASTING OF LOW EARTH ORBIT SATELLITES

以低轨卫星CHAMP为例,采用切比雪夫多项式对其轨道进行拟合与外推,分析不同拟合时间长度和多项式阶数对拟合精度的影响,并讨论短时间预报的可行性。切比雪夫多项式与拉格朗日插值、常规多项式的拟合效果的比较结果表明,切比雪夫多项式明显优于后二者。以m级精度的星载GPS单点定轨结果分析切比雪夫多项式对CHAMP卫星轨道的预报精度,验证了该方法的数值稳定性。切比雪夫多项式可用于低轨卫星实时定轨中短时间的轨道外推。

The orbit fitting and forecasting of CHAMP satellite as an LEO example is discussed. The influence on fitting accuracy in the selection of different fitting time length and different polynomial order by use of Chebyshev polynomial is analyzed, and the feasibility of orbit forecasting in a short time is discussed as well. The fitting results with Chebyshev polynomial, Lagrange polynomial and normal polynomial are compared with each other, it indicates that Chebyshev polynomial is superior to both the others. In addition, the accuracy of forecasting orbit by using Chebyshev polynomial based on the m-level orbit of single point orbiting, and numerical stability of the method is veri- fied. it is proved that the Chebyshev polynomial can be used for real-time forecasting LEO orbit in a short time.