多面函数GPS水准高程拟合中光滑因子求定方法

Calculation of Smooth Factor in GPS Level/Elevation Fitting by Hardy Function

采用数值模拟方法研究了多面函数GPS水准拟合时光滑因子对拟合精度的影响规律.结果表明:对于正双曲面核函数来说,拟合精度随着光滑因子的增大而提高,但并不是所有的核函数都有这样的规律,倒双曲面核函数的光滑因子存在极大值,超过这个值拟合精度就会降低.为了找到适合所有核函数的光滑因子,通过大量的模拟计算与数理统计分析,首次提出了计算光滑因子的公式,解决了在利用多面函数进行GPS水准拟合时,由于光滑因子不能准确确定致使精度不稳定的问题.

The software GLSPA（GPS level simulation process analysis）was numerically applied to the investigation of the effects of different smooth factors in GPS level/elevation fitting by Hardy function on the fitting precision. The results showed that the fitting precision is improved with increasing smooth factor for forward hyperbolic kernel functions but not for all kernel functions, and there is a maximum of smooth factors for inverse hyperbolic kernel function and the fitting precision lowers if exceeding the maximum. To find out smooth factor that is appropriate to all of relevant kernel functions, lots of analog computation and mathematical statistics were done with the results analyzed to propose first a formula to calculate the smooth factor. The formula is available to solve the problem that the fitting precision is unstable because the smooth factors cannot be determined accurately when fitting the GPS level/elevation by Hardy function.