论文总字数：23828字

摘 要

空间插值是数字高程模型（DEM）建立过程中的关键环节，插值方法及其参数的选择对DEM质量具有重要影响。本文对经验贝叶斯克里金算法（EBK）在DEM建模中的适用性做了初步探讨，可为DEM构建及插值方法的选择提供参考。本文选取平原、丘陵和山地三种不同地形样区，进行了EBK算法半变异函数的适用性分析、搜索方式的优选分析、其他参数对于EBK算法插值的影响以及与常用插值算法的对比分析，采用高程误差统计和等高线套合分析等精度评价指标，主要研究成果如下：（1）平原样区指数函数插值效果最好，薄板样条函数最差；丘陵样区K-Bessel函数插值效果最佳，薄板样条函数次之，指数函数最差；山地样区K-Bessel函数最佳，薄板样条函数次之，指数函数最差；（2）平原样区无方向和四方向且偏移45°的插值效果相对较好；丘陵和山地样区四方向的插值效果最好；搜索点数上限固定为15时，平原和丘陵样区都是搜索点数上下限为11-15时插值效果最好，山地区则是7-15；（3）平原样区子集大小为450-500的插值效果最好，丘陵和山地样区随着子集大小的减小，插值效果越来越好；当重叠系数设置为1-5时，对三种样区插值效果的影响不大。（4）与RBF相比，EBK在平原和山地样区的插值效果更好，RBF中张力样条函数和薄板样条函数表现出相对较好的插值效果，但没有在三种样区中均能够有较好插值效果的核函数；与OK相比，EBK在丘陵和山地样区的插值效果更好，在平原和山地样区中，OK部分半变异函数的插值效果优于EBK;与IDW相比，EBK算法在三种样区中均表现更好。

关键词：经验贝叶斯克里金算法 半变异函数 精度分析 数字高程模型

The DEM interpolation based on Empirical Bayesian Kriging algorithm

Abstract

Spatial interpolation is the key link in the process of DEM establishment. The selection of interpolation method and its parameters has an important influence on DEM quality. In this paper, the applicability of EBK in DEM modeling is discussed, which can provide reference for DEM construction and interpolation method selection. In this paper, the applicability analysis of EBK algorithm semi variogram, the optimization analysis of search method, the influence of other parameters on the interpolation of EBK algorithm and the comparison between EBK algorithm and common interpolation algorithm are carried out. The accuracy evaluation indexes such as elevation error statistics and contour overlay analysis are used. The main research results are as follows: (1)in plain area, exponential function has the best interpolation effect, and the worst thin plate spline function; The interpolation effect of K-Bessel function is the best in hilly area, the second is thin plate spline function, and the worst is exponential function; in mountainous area, K-Bessel function is the best, followed by thin plate spline function, and the worst index function;(2) the interpolation effect of plain sample with no direction and square direction and 45 ° offset is relatively good; the interpolation effect of hill and mountain sample is the fourth The interpolation effect of direction is the best; when the upper limit of search points is fixed at 15, the interpolation effect is best when the upper and lower limits of search points are 11-15 in plain and hilly sample areas, and 7-15 in mountain areas;(3) the interpolation effect of 450-500 is the best for the plain sample area, and the interpolation effect is better and better for the hill and mountain sample area with the decrease of the subset size; when the overlap coefficient is set to 1-5, the influence on the interpolation effect of the three sample areas is not significant. (4) Compared with RBF, the interpolation effect of EBK is better in plain and mountain sample areas. The tension spline function and thin plate spline function in RBF show relatively better interpolation effect, but there is no kernel function with better interpolation effect in all three sample areas. Compared with OK, the interpolation effect of EBK is better in Hilly and mountain sample areas. In plain and mountain sample areas, the OK partial semi Variogram Compared with IDW, EBK algorithm performs better in all three sample areas.

Key Words: Empirical Bayesian Kriging algorithm; Semivariogram; Precision analysis; Digital elevation model

目 录

摘 要 I

ABSTRACT II

第一章 绪论 1

1.1研究背景与意义 1

1.2国内外研究现状 1

1.3研究概述 3

1.3.1研究内容 3

1.3.2研究方法 4

1.3.3技术路线 5

1.3.4论文结构 5

第二章 研究基础 7

2.1经验贝叶斯克里金插值算法简介 7

2.2经验贝叶斯克里金算法中的重要概念 7

2.2.1半变异函数模型 7

2.2.2搜索方式及范围 8

2.2.3其他重要参数 8

2.3经验贝叶斯克里金算法的影响因素 8

第三章 基于经验贝叶斯克里金算法的插值实验 10

3.1实验样区概况 10

3.1.1实验样区及数据 10

3.1.2实验数据预处理 10

3.2精度评价 11

3.2.1交叉验证 11

3.2.2预测误差统计 11

3.3不同变量的插值精度分析 12

3.3.1半变异函数对插值精度的影响 12

3.3.2搜索方式对插值精度的影响 13

3.3.3其他因素对插值精度的影响 16

第四章 经验贝叶斯克里金算法与常用插值算法比较 18

4.1对比插值算法选择 18

4.1.1径向基函数插值算法 18

4.1.2普通克里金插值算 18

4.1.3反距离加权插值算法 19

4.2精度评价 20

4.3对比实验结果分析 20

4.3.1高程误差统计 20

4.3.2地形结构特征 22

第五章 结论与展望 24

5.1结论 24

5.2展望 25

参考文献 27

致 谢 29

第一章 绪论

1.1研究背景与意义

数字高程模型（DEM，Digital Elevation Model）是通过有限的地形高程数据实现对地面地形的数字化模拟（即地形表面形态的数字化表达），它是用一组有序数值阵列形式表示地面高程的一种实体地面模型，是数字地形模型（DTM，Digital Terrain Model）的一个分支，其它各种地形特征值均可由此派生。

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