DEM构建的多面函数加权抗差算法
收稿日期: 2013-11-08
修回日期: 2013-12-01
网络出版日期: 2013-12-25
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
Received date: 2013-11-08
Revised date: 2013-12-01
Online published: 2013-12-25
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。
陈传法, 李伟, 李明飞, 戴洪磊 . DEM构建的多面函数加权抗差算法[J]. 地球信息科学学报, 2013 , 15(6) : 840 -845 . DOI: 10.3724/SP.J.1047.2013.00840
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
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