抗差趋势面与正交多面函数结合拟合DEM数据  

Combining Fitting Based on Robust Trend Surface and Orthogonal Multiquadrics with Application in DEM Fitting

作　　者：张菊清[1] 刘平芝[2] 

机构地区：[1]长安大学地质工程与测绘学院,陕西西安710054 [2]西安测绘研究所,陕西西安710054

出　　处：《测绘学报》2008年第4期526-530,共5页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(40672173;40774001);地球空间与大地测量教育部重点实验室开放基金(1469990324233-04-11)

摘　　要：空间数据内插是DEM建模中不可缺少的环节。本文提出将趋势面与多面函数结合拟合DEM数据。在趋势面拟合过程中,提出将局部有显著起伏的采样点视为异常观测值,采用抗差估计法,控制显著异常点对曲面拟合的不利影响;针对多面函数拟合中,难以合理地选择节点这一问题,提出基于正交最小二乘法的基本思想,计算各节点核函数对曲面拟合贡献的大小,并依此为依据自适应地选择节点。最后利用新提出的方法,对野外实测的地形数据进行拟合,结果表明进行趋势面拟合后,再进行多面函数拟合,整体上优于直接利用多面函数拟合,而基于正交最小二乘法的多面函数拟合法的精度明显优于常规的多面函数拟合法。Spatial data interpolation is an indispensable process in DEM. A combining fitting with trend surface fitting and multidimensional curve fitting is proposed. In order to control the influence of some outstanding points to surface fitting, a robust fitting of the trend surface by using an equivalent weight is adopted. An a daptive node choosing method is proposed based on the effect of every node to the curve fitting calculated by u sing the orthogonal least squares. Last, a practical example of terrain fitting shows that the proposed combined method is effective in improving the quality of DEM fitting.

关 键 词：趋势面拟合 核函数 节点 拟合 

分 类 号：P217[天文地球—测绘科学与技术]