• 本期要文(可全文下载) •

DEM构建的多面函数加权抗差算法

1. 山东科技大学测绘科学与工程学院, 青岛 266590
• 收稿日期:2013-11-08 修回日期:2013-12-01 出版日期:2013-12-25 发布日期:2013-12-25
• 作者简介:陈传法（1982-），男，山东沂源人，博士，副教授，研究方向为地学曲面建模。E-mail：chencf@lreis.ac.cn
• 基金资助:

国家自然科学基金项目（41101433、41371367）；山东省优秀中青年科学家科研奖励基金项目（BS2012HZ010）；青岛市科技计划基础研究项目（13-1-4-239-jch）。

A Robust Multiquadratic Method and Its Application to DEM Construction

CHEN Chuanfa, LI Wei, LI Mingfei, DAI Honglei

1. Geomatics College, Shandong University of Science and Technology, Qingdao 266590, China
• Received:2013-11-08 Revised:2013-12-01 Online:2013-12-25 Published:2013-12-25

Abstract:

In order to resist the effect of outliers on DEM construction, a robust multiquadric method (MQ-R) has been developed. MQ-R firstly takes the estimation of the classical MQ as the initial values to compute the residuals of all sampling points, and then a weighted function has been constructed to determine the weights of sampling points based on the above residuals. Finally, a iteratively re-weighted MQ is formed to decrease the effect of outliers on DEM construction. At the same time, the smoothing parameter of MQ and MQ-R is determined based on a k-fold cross-validation. A synthetic surface was employed to comparatively analyze the estimation accuracies of MQ-R and the classcial MQ, where the sampling points are contaminated by three groups of errors with different distributions. These include the standard normal distribution, contaminated normal distribution with the contaminating proportion of 10%, 20% and 30%, and Cauchy distribution. Numerical tests indicate that when sampling errors are from the standard normal distribution, the accuracy of MQ-R is comparative to that of MQ. As the contaminating proportion increases, the accuracy of MQ becomes lower, whereas MQ-R can resist oultiers very well. When sampling errors are from Cauchy distribution, the results of MQ are completely destroyed, but those of MQ-R are still satisfactory. In conclusions, MQ-R with a high efficiency and a high robustness can be used to resist outliers in DEM construction.

Key words: accuracy, DEM, robust, thin plate spline