一种综合考虑采样点水平和高程误差的DEM建模算法

为了降低采样点水平和高程误差对数字高程模型（digital elevation model，DEM）建模精度的影响，受总体最小二乘算法启发，以较高精度的多面函数（multiquadric function，MQ）为基函数，发展了整体最小二乘MQ算法（MQ-T），并分别借助数值实验和实例分析验证模型计算精度。数值实验中，以高斯合成曲面为研究对象，设计了受不同误差分量影响的采样数据，借助MQ-T曲面建模，并将计算结果与传统MQ进行比较。结果表明，当采样点仅受高程误差分量影响时，MQ-T计算结果精度与MQ相当；当采样数据受水平误差分量影响时，MQ-T计算结果中误差小于MQ中误差。实例分析中，以全站仪获取的采样数据为研究对象，借助MQ-T构建测区DEM，并将计算结果与传统插值算法进行比较，如反距离加权（inverse distance weighted，IDW）法、克里金（Kriging）法和澳大利亚国立大学DEM专用插值软件（（Australian National University DEM，ANUDEM）法。精度分析表明，随着采样点密度降低，各种插值算法精度逐步降低；不管采样密度多少，MQ-T计算精度始终高于传统插值算法；对山体阴影图分析表明，MQ-T相比Kriging法有一定峰值削平现象。

A Total Error-Based Interpolation Method for DEM Generation

Motivated by the idea of total least squared method, a total error-based multiquadric method (MQ-T) has been developed to decrease the effect of both horizontal and vertical errors inherent in sample points on surface modeling. Two examples including a numerical test and a real-world example were, respectively, employed to test the robustness of MQ-T to sample errors. The numerical test indicates that when sample points are only subject to vertical errors, MQ-T has a similar performance to MQ. When sample points are subject to horizontal errors, MQ-T is more accurate than MQ. In the real-world example, MQ-T was used to construct DEMs with sample points collected by a total station instrument, and its accuracy was compared with those of classical interpolation methods including inverse distance weighting, ordinary Kriging (Kriging) and ANUDEM. Results indicate that with the decrease of sample density, the interpolation accuracies of all methods become lower. Regardless of sample density, MQ-T is always more accurate than the other methods. Yet, compared with Kriging, MQ-T has a peak-cutting problem.