GPS动态变形分析中的傅里叶级数恒星日滤波

Fourier Series Sidereal Filtering in GPS Dynamic Deformation Analysis

针对恒星日滤波中计算GPS卫星轨道运行周期提前时间的问题,提出一种基于傅里叶级数曲线拟合的提前时间估计方法。根据跨度达8 526d的广播星历计算每天中所有可用卫星运行周期相对于前1d的平均提前时间,将此平均提前时间作为采样点,以8阶三角函数形式展开的傅里叶级数进行曲线拟合,将卫星运行周期的提前时间拟合成关于时间的单一变量函数,免去了繁琐的计算步骤。实验结果表明,傅里叶级数恒星日滤波法缩小了监测点N、E、U三个方向坐标残差序列的均方根值,有效消除了GPS动态变形监测分析中的多路径影响,提高了复杂工程环境下动态变形监测中变形信息提取的能力。

High-rate GPS receivers are popular in real-time dynamic monitoring, but the multi-path effect is one of the key obstacles that restricts its development. However, a sidereal filter can elimi- nate this effect and improve positioning accuracy. The sidereal filter requires the preset time of each satellite compared to the day before. In this research, 8 526 days broadcast ephemerides are used to calculate the preset time. The Fourier series of 8 orders trigonometric functions is used to fit the series of the preset time. It shows a simple and effective way to estimate the preset time, instead of a more complex calculation. Using this method, the root mean square values of the residual coordinate se- quences of N, E and U directions are reduced, and the ability of extracting deformation information is improved. This method therefore can be applied in engineering dynamic deformation monitoring.