多种插值计算方法在卫星轨道计算中的应用
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摘要
插值方法是获取卫星轨道任意历元卫星坐标的重要手段,对于GNSS导航中的多轨道实时导航计算问题,进行高精度测量时需要对精密星历进行轨道插值。目前应用较为广泛的插值方法包括拉格朗日法、牛顿多项式插值以及线性逐次内维尔插值方法。本文通过研究常见的插值方法,结合具体算例进行精度及时间的对比分析,并对牛顿插值进行改进,得出结论:牛顿插值经加窗处理后卫星位置误差精度可达mm级。它的计算效率大约是拉格朗日插值及内维尔插值方法的10倍。
Interpolation method is an important means for satellite orbit satellite coordinates of any epoch for the computation of multi orbit real-time navigation in GNSS navigation,the high precision measurement need to track the precise ephemeris interpolation. At present,the widely used interpolation methods include Lagrange method,Newton polynomial interpolation and linear successive Neville interpolation method. Through the study of common interpolation method,and comparative analysis with the examples of precision and time,and the Newton interpolation is improved. The following conclusions can be drawn: the accuracy of the satellite position error can reach mm level after the addition of the Newton interpolation method. Its computational efficiency is about 10 times of Lagrange interpolation and Neville interpolation method.
Interpolation method is an important means for satellite orbit satellite coordinates of any epoch for the computation of multi orbit real-time navigation in GNSS navigation,the high precision measurement need to track the precise ephemeris interpolation. At present,the widely used interpolation methods include Lagrange method,Newton polynomial interpolation and linear successive Neville interpolation method. Through the study of common interpolation method,and comparative analysis with the examples of precision and time,and the Newton interpolation is improved. The following conclusions can be drawn: the accuracy of the satellite position error can reach mm level after the addition of the Newton interpolation method. Its computational efficiency is about 10 times of Lagrange interpolation and Neville interpolation method.
引文
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[2]魏二虎,柴华.GPS精密星历插值方法的比较研究[J].全球定位系统,2006,31(5):13-15,20.
[3]王清平,关玉梅,王紫燕,等.GPS卫星轨道三维坐标插值算法比较[J].地球物理学进展,2014,29(2):573-579.
[4]仝海波,沙海,张国柱,等.一种GNSS卫星轨道高精度实时插值方法[J].国防科技大学学报,2012,34(2):59-63.
[5]王波,张书毕,李益斌,等.精密GPS卫星钟差两种插值方法的比较[J].全球定位系统,2007,32(6):33-35.
[6]Mark Schenewerk.A Brief Review of Basic GPS Orbit Interpolation Strategies[J].GPS Solutions,2003,6(4):265-267.
[7]孙华丽,张政治,胡思才.五次样条插值在GPS卫星轨道标准化中的应用[J].大地测量与地球动力学,2012,32(1):76-79.
[2]魏二虎,柴华.GPS精密星历插值方法的比较研究[J].全球定位系统,2006,31(5):13-15,20.
[3]王清平,关玉梅,王紫燕,等.GPS卫星轨道三维坐标插值算法比较[J].地球物理学进展,2014,29(2):573-579.
[4]仝海波,沙海,张国柱,等.一种GNSS卫星轨道高精度实时插值方法[J].国防科技大学学报,2012,34(2):59-63.
[5]王波,张书毕,李益斌,等.精密GPS卫星钟差两种插值方法的比较[J].全球定位系统,2007,32(6):33-35.
[6]Mark Schenewerk.A Brief Review of Basic GPS Orbit Interpolation Strategies[J].GPS Solutions,2003,6(4):265-267.
[7]孙华丽,张政治,胡思才.五次样条插值在GPS卫星轨道标准化中的应用[J].大地测量与地球动力学,2012,32(1):76-79.