GPS卫星精密星历内插方法比较分析

摘要

This paper Based on the GPS satellite ephemeris,using Lagrange polynomial interpolation method and Chebyshev polynomial fitting method to interpolate the instantaneous position of the GPS satellite,The relationship between the interpolation precision and the interpolation order is determined,and the advantages and disadvantages of these two methods are compared and analyzed.The calculation results show that the two methods should not be too high or too low in the selection order of interpolation,the interpolation order of three-dimensional coordinates component in the best interpolation accuracy is not exactly the same,Chebyshev polynomial fitting method is better than the Lagrange polynomial interpolation method.Therefore,it is recommended that the Chebyshev polynomial fitting method is used to select different interpolation orders for the 3D coordinate component,in order to achieve the best interpolation accuracy.%借助GPS卫星精密星历,使用Lagrange多项式插值法和Chebyshev多项式拟合法内插出GPS卫星的瞬时位置,确定了插值精度与插值阶数的关系,并对这两种方法的优缺点进行了对比分析.计算结果表明:内插卫星瞬时坐标时所选取的插值阶数不应过高或过低,三维坐标分量在最佳插值精度时选取的插值阶数并不完全相同,Chebyshev多项式拟合法相比Lagrange多项式插值法的插值效果更好.因此,建议在优先选用Chebyshev多项式拟合法内插卫星瞬时坐标的同时,对三维坐标分量分别选取不同的插值阶数,以达到最优的插值精度.