DEM平均误差置信区间估计

Confidence interval estimation for DEM mean error

为了对数字高程模型(DEM)精度准确描述,研究了非参数法的DEM平均误差置信区间估计.以我国6个测区不同地形的高级星载热辐射反射辐射计(ASTER)为研究对象,通过非参数法估计DEM平均误差置信度为95%的置信区间,并与传统的t分布进行精度比较.结果表明:t分布模拟精度受误差母体分布影响较大,当误差母体近似正态分布时,其模拟精度高于非正态分布;t分布模拟精度随着采样数增多有升高趋势.无论采样数为多少,母体服从何种分布,非参数法模拟精度均高于t分布;当采样数大于10时,非参数法获取的DEM平均误差置信区间完全满足精度要求.随着采样数的增多,两种模型的置信区间宽度均大幅度减小;当采样数较少时,非参数置信区间宽度远大于t分布,表明非参数法在较少采样数获取的较高模拟精度是以较大置信区间宽度为代价.根据置信区间估计最优准则,非参数法可作为DEM平均误差置信区间估计的高效方法.

In order to give DEM accuracy an accurate description, this paper developed a non- parameter method to estimate the confidence interval for DEM mean error. ASTERs of six test areas with different terrain topography were employed to comparatively analyze the simulation accuracy of the non-parameter method and the classical student t method. The results indicate that the student t method is clearly influenced by the degree of normality of the DEM error population distribution and the sampling number, i. e, with the increasing of the sampling number, the simulation accuracy is improving; the bigger the degree of the non-normal error population, the less reliable the simulation accuracy. No matter what the error population dis- tribution is and how many the sampling numbers are, the non-parameter method is more accu- rate than the student t method; when the sampling number is bigger than 10, the confidence interval of the non-parameter method completely satisfies the accuracy requirement. The confi- dence interval widths of the two methods indicate that with the increasing of the sampling num- ber, the widths become smaller; under the smaller sampling number, the non-parameter needsbigger confidence interval width to satisfy the accuracy requirement. Based on the optimal theo rem of confidence interval evaluation, the non-parameter method can be considered as an effi cient method for confidence interval estimation.