DEM构建的多面函数抗差插值算法研究

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.

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。

数字地形建模是对地球表面地形地貌的一种数字建模过程，这种建模结果称为数字地面模型。目前，遥感技术以大尺度、高时效和高分辨率等优势已经成为数字地形建模的主要数据源。但受传感器设计理论缺陷、地面纹理不清晰、多路径反射以及遮挡等因素影响，采样数据中不可避免的含有异常值。为了抑制异常值对数字地形建模精度影响，本项目提出了数字地形稳健模拟方法，实现了高质量数字地形建模，为地理国情动态监测、地质灾害预警等领域提供了理论方法和技术支撑。具体研究内容如下：.（1）针对单一尺度下地面种子点难以准确捕捉地形细节信息的问题，构建了多尺度层次点云滤波方法，最大程度上提高了地面种子点数量，显著抑制了低层次错分点对高层次地面参考面构建精度影响，实现了机载LiDAR点云高精度滤波。用国际摄影测量与遥感学会提供的15组基准数据分析表明，该方法滤波精度处于同期最好水平，为数字地形建模提供了高质量数据源。相关研究成果发表三区SCI论文2篇。.（2）发展了数字地形稳健模拟方法，构建了目标函数全局最优求解模型，较好抑制了采样数据中异常值对数字地面建模精度影响，实现了高质量数字地面模型构建，成果被烟台经济开发区用于公路设计。相关研究成果发表SCI论文4篇，其中二区论文3篇，三区论文1篇。相应模型还用于解决支持向量机鲁棒性问题，研究成果发表SCI论文3篇，其中二区论文2篇，三区论文1篇。.（3）针对遥感数据庞大数据量问题，提出了机载LiDAR点云精简方法，实现了地形特征保持的遥感点云数据快速简化，为机载LiDAR点云数据高效管理提供了有效工具。相关研究成果发表SCI论文2篇，其中一区论文1篇，二区论文1篇。.项目组四年共发表期刊论文18篇，其中SCI论文14篇，EI论文2篇；培养毕业研究生3名，在读研究生3名。本项目研究成果实现了遥感点云数据高精度分类，提高了数据管理能力，确保了高质量数字地形稳健模拟。