关键词: GPS, 精密钟差, 分形插值, 垂直比例因子, 分形变差函数

Abstract: It is shown that time series of GPS precise satellite clock bias satisfies the third\|order stationary hypothesis. Based on the hypothesis, multi\|order fractal variation method is presented for calculating fractal dimension of satellite clock bias. Then, the modified fractal interpolation algorithm is proposed by using the vertical scaling factor determined by fractal dimension for precise satellite clock bias. Both new method and algorithm are respectively applied to investigating the fractal feature of satellite clock bias and to comparing the interpolation accuracy of the fractal algorithm, the cubic spline algorithm and the Chebyshev algorithm. Results show that fractal dimension can be used as an invariant indicator quantitatively describing the dynamics characteristic of satellite clock error, the fractal interpolation algorithm is superior to other two algorithms, and meets application requirements of rapid and high sampling rate precise satellite clock bias.

Key words: GPS, Clock bias, Fractal interpolation, Vertical scaling factor, Fractal variation