基于Matlab的GPS高程曲线和曲面拟合研究及应用

Research and Application of GPS Elevation Curve and Surface Fitting Based on Matlab

随着GPS测量技术快速发展,传统的测量技术已经无法满足工程中高程测量的精度要求,如何选取更高精度、更高分辨率的大地水准模型来提高GPS高程水准的精度,以满足一定区域的工程水准测量要求成为研究热点。结合内蒙古酸刺沟矿区实例,对GPS点进行曲面和曲线拟合,分析得出了一些成果。基于Matlab的Ploynomial(多项式)和Gauss(高斯)拟合分别用X、Y对高程异常进行曲线拟合,4次中有3次取得较好的拟合结果,R-square值均大于0.7,整体拟合良好,函数模型次数需根据拟合情况不断调整,且次数不是越高越好;在二次曲面拟合中,通过Matlab编写程序并运行,实现拟合点的建模和检核点的校验,得到的拟合结果满足四等水准的精度。

With the rapid development of GPS measurement technology,traditional measurement techniques are currently unable to meet the accuracy of elevation measurement in engineering.Therefore,how to select a higher precision and higher resolution geodetic leveling model to improve the accuracy of current GPS elevation leveling to meet the engineering leveling measurement of a certain area has become a research hotspot.By combining the example of the Suancigou mining area in Inner Mongolia,some results were obtained through surface and curve ftting of GPS points.In Matlab,Ploynomial and Gauss ftting were used to fit the elevation anomaly E using X and Y,respectively.Three out of four fitting results were obtained,and the R-square values were all greater than O.7,indicating a good overall fit.The number of function model iterations should be continuously adjusted to the appropriate number according to the fitting situation,and the higher the iteration,the better;In quadratic surface ftting,a program is wrtten and run in Matlab to achieve modeling of fitting points and verification of check points,resulting in ftting results that meet fourth-order accuracy.