Comparison and Analysis of Non-sliding and Sliding Lagrange Interpolation in BDS Precision Ephemeris Interpolation

Interpolating precision ephemeris is a fundamental task in the high-precision processing of satellite positioning data.In this paper, Lagrange polynomial interpolation method is used to analyze the precision of BDS precision ephemeris from three aspects, which are namely the interpolation accuracy of non-sliding Lagrange interpolation method in different interpolation orders, the sliding Lagrange interpolation method in different interpolation orders and the non-sliding and sliding Lagrange interpolation methods in the same interpolation order. Example results show:if the interpolation order is taken as the abscissa with rightward as positive and the interpolation accuracy is taken as the ordinate with upward as positive, the interpolation accuracy and interpolation order of non-sliding Lagrange interpolation show an parabolic curve which opens downward. When the interpolation order of the sliding Lagrange interpolation method takes above 7, the interpolation accuracy is in a stable and high state. The maximum value of interpolation error is about 1.1mm, and the mean square error is about 0.4mm; In the same interpolation order, the accuracy of sliding Lagrange interpolation is higher than that of non-sliding Lagrange interpolation.