Propagated error analysis of digital elevation models generated by bi-cubic hermite interpolation methods

Abstract

针对由双三次Hermite插值所生成的DEM数据,提出了一种新的传播误差估计方法。传播误差估计模型所适用的空间对象包括:线、不规则三角网(TIN)和规则格网等DEM数据。基于统计学中的误差传播定律,推导出了由非线性插值方法所生成DEM的误差传播公式。最后,将由双三次Hermite插值方法所生成DEM的传播误差与先前研究中采用线性插值所生成DEM的传播误差进行对比分析,由此可以更加全面地掌握通过线性插值或者非线性插值方法所生成DEM的误差传播规律。该成果可用于指导对实际生产DEM产品过程中插值方法的选择。 This paper presents a new development technique in the estimation of the propagated error of DEMs,interpolated by the Hermite bi-cubic interpolation method.Propagated error estimation models are first identified for spatial objects including line,TIN,and rectangular grid DEM.The approach adopted is based on the error propagation law in statistics so as to derive the propagated error of DEMs from this nonlinear interpolation.Finally,the propagated error of DEMs interpolated by the bi-cubic Hermite method derived from this study is compared with the propagated error of DEMs interpolated by bi-linear methods,given by earlier studies.Hence,a full picture of propagated error of DEMs,regarding error propagated from original nodes,obtained by linear and non-linear methods,is now available.This result can serve as a guideline for interpolation method selection in practical DEM production.