切比雪夫多项式拟合卫星轨道与钟差的精度分析

Accuracy analysis of Chebyshev polynomial to fit satellite orbit and clock error

利用切比雪夫多项式拟合卫星轨道,用经验统计法确定轨道不同弧段数据的满足精度要求的拟合阶数区间,发现非最佳拟合阶数会引入较大的拟合噪声,因此在精密计算时应选择最佳拟合阶数。本文用此多项式拟合卫星钟差,能达到内插钟差同等的精度,而且与拉格朗日滑动内插相比,拟合残差序列分布更好,计算效率更高;提出利用残差自相关进行精度评定的方法,当精度变化微小时相比一般的精度评定方法具有明显优势。

Using Chebyshev polynomial to fit the satellite orbit, counting the range of the fitting order of different orbit data by u- sing the empirical statistic method, and finding that the un-best fitting order can introduce a lager noise, therefore, the best fitting order should be chosen in precise calculation. Using the polynomial to fit the clock error, achieving the same accuracy as the way of Lagrange interpolation, and the fitting residuals has a better distribution and calculating efficient than that of Lagrange siding interpolating. A new method of evaluating accuracy that is residual serial correlation was proposed in this paper, which has obvious advantages than the general method when the accuracy changes a little.