基于主成分回归的GPS高程曲面拟合  

A new method of GPS elevation interpolation based on principal component regression

作　　者：冯光财[1] 陈正阳[1] 

机构地区：[1]中南大学测绘与国土信息工程系,长沙410083

出　　处：《测绘科学》2007年第1期51-52,共2页Science of Surveying and Mapping

摘　　要：本文阐述了多项式曲面拟合GPS高程中参数数目对法方程条件数和结果的影响,当过度参数化时,观测方程的法方程会病态,传统的最小二乘无法得到可靠的结果,岭估计到目前为止仍然没有一种很好的确定岭参数的方法,主成分估计可以在保持原始数据信息损失最少的前提下,实现数据的降维避免法方程病态,从而得到参数的精确估值。并且把该方法运用于某测区,通过比较不同方法和不同参数数目时的计算结果,得出主成分估计在不同参数时都可以取得比较满意的结果,同时计算结果表明中心化和标准化对于多项式曲面拟合GPS高程的必要性。Firstly,this paper analyzes the number of parameter of polynomial surface fitting models to the influence of normal equation conditions and results.Then,it points out that the normal equation of observation equation will be morbid if over parameterized.Traditional least squares can't get reliable result.Ridge estimation still has not a good method to determine ridge parameter at present.While,principal component estimation can get precise estimation value of parameter.Finally,this method is used at a test area.The result shows that principal component regression can obtain good result in the different number of parameter;and the result is showed that centering and standardization is very important to improve the precision.

关 键 词：主成分分析 岭估计 GPS高程 多项式曲面拟合 

分 类 号：P228[天文地球—大地测量学与测量工程]