DEM误差为逼近论模型的又一力证

DEM误差性质属系统(函数)误差或是偶然误差是一个基本概念问题,是DEM误差理论的关键,也是DEM产品质量保障体系的核心.本文通过对现有的地面DEM各种不同观点的分析,对把地面或其局部视为随机曲面的观点以及以随机误差概括DEM误差的流行观点和方法提出明确异议,引述并理论解读了文献[1]的研究成果,指出了DEM地形描述精度Et极强烈统计相关于V、R事实,表明了Et与V、R具有确定的函数关系,并由数学逼近理论给出的对于Et的裁断误差的V、R函数表达,指出了统计数学和数学逼近在这一问题上的"殊途同归",论证了DEM高程误差具有同样的性质:数学逼近理论和统计数学途径的一致性.

A convincing evidence of approximation model:Error type of DEM

Whether DEM error is system error or random error is the key problem of DEM guarantee system. This paper presents clear viewpoints that differ from usual viewpoints that regard the ground surface as a random surface and the popular method that describes DEM error only with random error.Based on the analysis of literature,it is pointed out that DEM terrain representation error(Et) has strong correlation with DEM profile curvature(V) and DEM resolution(R) on statistics,which indicates that they have function relation.This paper then gives a function expression with the theory of mathematical approach.With either mathematical approach or statistics we can make the same conclusion that DEM elevation errors in the condition of the same grid survey data and the same mathematic model have the same property.