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- 2018
一种综合考虑采样点水平和高程误差的DEM建模算法
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Abstract:
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
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