中文摘要：

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。

英文摘要：

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.