DEM构建的多面函数加权抗差算法  

A Robust Multiquadratic Method and Its Application to DEM Construction

作　　者：陈传法[1] 李伟[1] 李明飞[1] 戴洪磊[1] 

机构地区：[1]山东科技大学测绘科学与工程学院,青岛266590

出　　处：《地球信息科学学报》2013年第6期840-845,共6页Journal of Geo-information Science

基　　金：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)

摘　　要：为了抑制采样点中粗差对DEM构建精度影响,本文以较高精度的多面函数(MQ)为基函数,发展了一种MQ迭代加权抗差算法(MQ-R)。MQ-R以传统MQ计算结果为初始值,以MQ函数模拟值与对应采样点的差值确定采样点权重,以加权MQ优化初始值,重复迭代直至收敛。以数值模拟曲面为研究对象,本文比较并分析了采样误差服从正态分布、被污染的正态分布,以及Cauchy分布时MQ-R与MQ模拟结果精度。数值分析表明,当采样误差服从正态分布时,MQ-R计算精度和传统MQ相当;随着污染率的提高,MQ计算精度急剧降低,而MQ-R计算结果受粗差影响较小;当采样误差来源于C(0,1)分布时,MQ计算结果完全失真,而MQ-R可在一定程度上抑制粗差影响。总之,相比于传统MQ算法,MQ-R不仅具有较高的计算效率,而且有较高的抗差性。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 re- siduals 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 ef- fect of outliers on DEM construction. At the same time, the smoothing parameter of MQ and MQ-R is deter- mined based on a k-fold cross-validation. A synthetic surface was employed to comparatively analyze the estima- tion accuracies of MQ-R and the classcial MQ, where the sampling points are contaminated by three groups of er- rors with different distributions. These include the standard normal distribution, contaminated normal distribu- tion 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 ro- bustness can be used to resist outliers in DEM construction.

关 键 词：抗差 薄板样条 精度 DEM 

分 类 号：P207[天文地球—测绘科学与技术]