精密卫星钟差分形插值算法研究

研究发现精密GPS卫星钟差时序满足三阶平稳假设，由此提出了计算卫星钟差分形维的多阶分形变差法，进而提出了基于分形维确定垂直比例因子的精密卫星钟差分形插值算法。将新方法应用于2010年8个节气日的32颗GPS在轨卫星钟差分形维计算，并选取Block IIA、IIR和IIR\|M各2颗卫星进行钟差插值精度比较。结果表明，分形维可作为定量描述卫星钟差动力学特征的不变量指标；分形插值算法优于三次样条和切比雪夫算法，可以满足快速与高采样率精密卫星钟差应用需求。

Fractal Interpolation Method for GPS Precise Satellite Clock Bias

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.