勒让德多项式拟合IGS精密星历的算法改进

Improvement of legendre polynomial fitting algorithm for IGS precise ephemeris

国际GNSS服务(IGS)精密星历每隔15 min提供一次卫星坐标,为了提高定位精度,往往需要获取任意时刻的卫星位置.对IGS精密星历进行插值和拟合是获得连续历元卫星坐标常用的方法.运用改进的勒让德多项式算法拟合卫星轨道坐标,并与常规算法进行比较,结果表明:常规算法仅在拟合阶数较低时能保持较高的精度.在拟合时段为6 h时,LU分解(LU Decomposition)法与奇异值分解(SVD)法对奇异矩阵求解时均能保持较高的精度,而在拟合时段为12 h时,SVD分解法是对条件数较低的矩阵B进行分解求得多项式系数矩阵C,从而避免了病态矩阵产生的误差,因此仍能保持较高的精度.在高阶拟合时,SVD分解法无论是在精度还是稳定性方面均优于LU分解法和常规算法,优势明显.

The International GNSS Service(IGS) precise ephemeris provides satellite coordinates every 15 minutes.In order to improve the positioning accuracy,it is often necessary to obtain the satellite position at any time.Interpolation and fitting of IGS precise ephemeris is a common method to obtain satellite coordinates of continuous epochs.The improved Legendre polynomial algorithm is used to fit the satellite orbit coordinates,and compared with the conventional algorithm.The results show that the conventional algorithm can maintain high accuracy only when the fitting order is low.When the fitting period is 6 h,LU decomposition method and singular value decomposition(SVD) method can maintain high accuracy in solving singular matrix,while when the fitting period is 12 h,SVD decomposition method decomposes the matrix B with low condition number to obtain polynomial coefficient C,so as to avoid the error caused by ill conditioned matrix,so it can still maintain high accuracy.In high-order fitting,SVD decomposition method is superior to LU decomposition method and conventional algorithm in both accuracy and stability.