滑动式Thiele型连分式插值方法在GPS精密星历中的应用

在动态GPS精密定位中，必须使用高精度的GPS卫星轨道数据，但是IGS组织只提供15min间隔的精密星历，无法满足间隔时间较短的动态定位要求，用多项式逼近效果很差，另外对于不同的星历插值没有高效的方法能确定最佳多项式阶数。因此，利用Thiele型连分式建立有理函数，并在此基础上提出滑动式Thiele型连分式插值的方法，简化了方法又提高了内插精度，并通过算例与Lagrange多项式和Chebyshev多项式进行了分析和比较，结果表明该插值方法可以更加有效地改进插值精度。

Application of the Sliding Thiele-type Continued Fraction Difference Method Used in GPS Precise Ephemeris

In dynamic GPS precise positioning, high precision GPS satellite orbit data are required, whereas IGS organization only provides a precise ephemeris with 15min intervals which fails to fulfill the dynamic positioning requir-ements of short time intervals. In addition, data deficiency occurs around the marginal time 24:00, so polynomial approximation cannot applied with a satisfactory effect acquired. Therefore, this paper uses Thiele-type continued fraction to establish a rational function, and on that basis raises the method of sliding Thiele-type continued fraction interpolation, with which increases both interpolation and extrapolation precisions. This paper also analyzes and compares it with Lagrange and Chebyshev polynomials, which shows this interpolation method can exert a more effective refinement on the interpolation precision.