GIS中线元位置不确定性模型的研究

【作者】 张国芹；

【导师】 朱长青； 王光霞；

【作者基本信息】 解放军信息工程大学 ， 地图制图学与地理信息工程， 2004， 硕士

【摘要】 地理信息系统(GIS)是一种以采集、存储、管理、分析和描述地球表面与空间和地理分布有关的空间信息系统。数据是GIS中最基本和最重要的组成部分，数据的质量直接影响到地理信息系统的经济效益和社会效益。因此，空间数据的质量，尤其是空间数据的不确定性变得越来越重要。对GIS不确定性的研究来说，线元不确定性的研究是一个重点，因为线元不仅是面域不确定性的基础，其本身也是GIG叠置分析、缓冲区分析和空间地址配对分析等的基本元素。本文对GIS中数字化数据误差处理和线元不确定性进行了理论与实验研究，特别着重于不确定性模型的建立和理论的推导。主要成果有： (1) 应用非线性最小二乘平差方法—阻尼最小二乘法，研究了数字化数据误差处理，在处理较大数字化数据误差时，采用阻尼最小二乘平差方法减弱了在条件方程线性化过程中产生的模型误差，提高了计算精度。 (2) 研究了GIS中二维平面直线和三维空间直线不确定性ε_σ模型的几何特征，运用函数的单调性和极值理论，从理论上证明了平面直线和空间直线不确定性ε_σ模型误差的几何特征，同时精确求出线元误差带最小带宽的位置及最小带宽。 (3) 从信息熵的角度提出了三维空间直线的误差熵模型，该模型是由在垂直直线的平面的误差熵为半径的圆柱体和两端点的误差球组成。 (4) 基于不确定性理论和概率统计理论，研究了GIS中三维空间圆曲线不确定性模型。根据所求的三维空间圆曲线上各点在该点法平面上的误差椭圆所构成的误差椭圆族、以及圆曲线两个端点的部分空间误差椭球，形成了以三维空间圆曲线真值为轴心的不确定性域，即空间圆曲线的ε_σ带，从而建立了空间圆曲线不确定性的ε_σ带模型。更多还原

【Abstract】 Geography information system (GIS) are special information system that are used to capture, store, manipulate, retrieval and analysis the all or part surface of the earth and the space. In GIS, the quality of spatial data affects the applicability of data and the reliability of applications directly. Hence, the quality of GIS spatial data, especially the uncertainty of spatial data, is becoming more and more important. For the studies of GIS uncertainty, error band model of a line segment is one of the current focus issues, which reason is not only that there are many open questions for the uncertainty of line segment but also that the uncertainty of line segment is the base of both the uncertainty of the surface element and GIS spatial analysis. The thesis studies the error processing of map digitized data and the uncertainty of line segment in GIS based on the theory and experiment, especially focus on the establishment and the derivation theoretically of the uncertainty models. The main results are as follow:(1) Presents a study on the error processing of map digitized data with nonlinear least square adjustment which is called damped least square method. In the processing of the bigger errors, the damped least square method can reduce the model error in the linearization process of the condition equation and then can improve the calculation accuracy.(2) Studies the geometrical shape of error band for GIS uncertainty mode of two-dimension and three-dimension line segment. Based on the monotone and extreme theory of function, we prove the geometrical shape of error band for line segment modeltheoretically, and obtain the minimum and its position of error band mathematically.(3) Constructs an error entropy model for spatial linear positional uncertainty based on the point of information entropy. The model is composed of a cylinder and an error ball. The cylinder radius is the error entropy in the plane perpendicular to the spatial line.(4) Develops an uncertainty model for three-dimension circular curve in GIS based on theuncertainty and statistic theory. The band of the model is composed of a group of errorellipses, which are in the plane perpendicular to the tangent of the point on the spatial circular curve, and the part error ellipsoid of the extreme point. And the centre axle of the band is theoriginal circular curve.更多还原