DEM是对地球表面地形地貌离散表达，其精度取决于采样数据质量等因素。数据采集中，受仪器噪声等影响，测量数据中不可避免含有粗差，进而严重影响DEM构建精度。抗差估计是在粗差不可避免前提下，选择特定估计方法，使未知量估计尽可能降低粗差影响，得出正常模式下最佳估值。为此，本研究预基于高精度多面函数（MQ）为基函数，发展MQ抗差插值法（MQ-R），实现DEM抗差构建。MQ-R将首先借助空间填充法从采样数据中选择部分数据作为MQ节点，构建超定方程组；然后以高崩溃污染率截尾最小二乘解算该方程组，获取节点权重初值，提高模型抗差性；最后以加权最小二乘优化初值，提高模型计算精度。拟以数学曲面数值试验，设计受不同粗差污染的采样数据，验证和优化MQ-R抗差性；以不同地面覆盖物LIDAR数据为实例，基于MQ-R构建测区DEM，验证模型实用性。本项目研究成果可为空间信息服务等构建高精度DEM提供理论方法和技术支撑。

A digital elevation model (DEM) is the discrete representation of terrain elevation as a function of geographic location. The quality of data source is one of the significant factors affecting the accuracy of DEMs. With the rapid development of GIS and remote-sensing technology, various spatial databases have been developed in recent decades in support of DEM construction. However, due to the malfunction or improper calibration of instruments, mistaken readings and gross recording, sampling points are always subject to errors, and the existence of incorrect values, termed outliers, can seriously affect the accuracy of DEMs constructed by means of an interpolation method. Multiquadric method (MQ) with high interpolation accuracy has been widely used for interpolating spatial data. However, MQ is an exact interpolation method, which is improper to interpolate noisy sampling data. Although the least squares MQ (LSMQ) has the ability to smooth out sampling errors, it is inherently not robust to outliers due to the least squares criterion in estimating the weights of sampling knots. In order to reduce the impact of outliers on the accuracy of DEMs, a robust method of MQ (MQ-R) is to be developed. MQ-R includes two independent procedures, namely, knot selection and the solution of the system of linear equations. Knot selection is first achieved by the space-filling design, where the number of knots is fewer than that of sampling points. Hence, an over-determined system is constructed based on the MQ equation set. Then, the least trimmed squares method is employed to robustly solve the system of MQ linear equations to obtain the initial weights of the knots. Finally, the knot weights are improved by the iteratively re-weighted least squares method. Gaussian synthetic surface, which is subject to a series of errors with different distributions, is employed to compare the performance of MQ-R with that of LSMQ. A real-world example of DEM construction based on LiDAR-derived sampling points is adopted to evaluate the robustness of MQ-R. In conclusion, when sampling data is subject to outliers, MQ-R will be considered as an alternative method for DEM construction.