正则矩阵及平滑参数与GPS水准面拟合精度关系分析

针对GPS高程转换求解高程异常时,由于大地高和正常高所涉及的基准面以及各类椭球参数和全球重力场对局部水准面起伏的影响致使高程异常的解算中存在难以参数化的系统误差,提出将系统误差看作非参数信号,采用补偿最小二乘法来处理。在补偿最小二乘模型中,正则矩阵R和平滑参数α的选取对拟合结果起决定性作用,讨论了正则矩阵R和平滑参数α的选取对拟合结果的影响,在此基础上提出了一种求解平滑参数α的Xu函数法,最后对某GPS测区的高程数据进行了解算,与其他求平滑参数的方法相比,Xu函数法获得了理想的结果。

Research on accuracy of quasi-geoids by fitting methods under different regular matrix and smoothing parameter

In order to solve the problem that the effect of local level surface fluctuation caused by geodetic height,and because of the normal height involving datum and ellipsoid parameter as well as the global gravity field can lead to height anomaly systematic error which is difficult to parametric,this article proposed that model error as nonparametric using penalized least squares to deal with. In penalized least squares model,regular matrix R and smoothing parameter α play a decisive role to fitting results. This article discusses how to choose regular matrix and smoothing parameter to affect the results of fitting. In the research of solving method based on the smoothing parameter,a method of function Xu（α） is presented, and experiment on a GPS leveling measurement data conducted. Compared with solving smoothing parameter of other methods,function Xu（α） can gain quite ideal result.