空间位置数据不确定性问题的若干理论研究
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摘要
GIS的不确定性理论是GIS界公认的最艰难的基础理论问题之一。它对确定GIS数据的质量标准、评价和控制GIS产品质量、优化空间数据分布结构、改善GIS算法、减少GIS设计与开发的盲目性以及GIS的其它研究领域都有重要作用。
空间数据是GIS的一个重要的组成部分,而其中空间数据的质量直接影响到数据的适用性及其GIS的应用成功。因此,国内外的许多研究人员均把GIS中的不确定性问题作为现代GIS研究的重要方面之一。
GIS空间数据不确定性的研究主要涉及到位置不确定性和属性不确定性两大类问题,其理论和实际的内容十分广泛。由于时间和作者的能力所限,本文主要讨论了若干空间位置数据的不确定性问题。本文主要以概率论与数理统计理论和现代测量数据处理理论为基础,通过大量的实验数据和理论分析,得出了一些有益的成果。其主要研究内容有:
(1)对于AutoCAD软件与MapInfo软件进行数据转换时产生的不确定性作了大量的实验研究。选择这两种软件的原因是:AutoCAD软件为目前微机上应用最为广泛的通用交互式计算机辅助绘图软件包,也是世界上最流行的通用CAD平台;而MapInfo软件是目前微机上应用较为广泛的GIS平台。
通过对AutoCAD软件与MapInfo软件进行数据相互转换的实验分析,发现点、线和面元素在数据相互转换后所产生的不确定性是不可忽视的。特别是线和面元素,由于这两个软件使用的算法和取值精度不一样造成两种软件在计算曲线弧长、多边形面积时可能产生较大的误差。
在AutoCAD与MapInfo进行数据转换时,矢量数据误差不仅来源于数据保存为中间结果(交换格式文件)的精度有关,而且与两者在利用坐标数据生成各自的图形所采用的数学模型、数据的截断、积分方法、积分时的细分程度
Uncertainty theory in GIS is one of the most difficult basic theories. The theory have a important action for confirming the quality standard of GIS data, evaluating and controlling the production quality of GIS, optimizing the distributing structure of space data, improving the arithmetic of GIS, decrease the blindness of GIS design and exploitation in GIS, and other study field in GIS.Spatial data is one of the fundamental parts of GIS. The quality of spatial data directly determines the fitness-for-use of GIS and affects the result of GIS application. Therefore, accuracy analysis and quality control of spatial data in GIS is regarded as one of the fundamental theoretical research issues internationally.Study of GIS spatial data uncertainty is mostly come down to positional and attribute uncertainty. It's content is full abroad..This paper is mostly discussed some spatial data uncertainties. This paper is obtained some study productions by mostlyaccording to the foundation of Probability and Statistics theory, and data processing theory of modern time surveying and mapping. That mostly studies and contributions described as following:(l)Large numbers of experimentations are done for AutoCAD and Maplnfoprocreant uncertainty in data transformation. The reason of to select them is thatAutoCAD and Maplnfo are popularly used.The study is indicated that procreant uncertainty cannot slight for dot, line andsurface elements after data transformation. The software may produce some errordue to the software use different arithmetic and choose different precision in lineand surface elements especially.Vector data error root in not only the precision of data that is saved ininterlocutory result, but also relate to mathematics model, truncation of data and
integral method in AutoCAD and Maplnfo process data transformation. If both software cannot find same geometry figure, they may use approximate figure, the replacement will make some error in data transformation.The paper bring forwards the methods for decrease data transformation error in data transformation. The methods possess directionally function for more study of data transformation.(2) The paper studies and analyses the uncertainty of spatial positional data.The paper discusses the method for using condition adjustment and condition adjustment with parameters to solve coordinates transformation parameters. The method can depress systematic error of digital map in some degree. Both methods are same to solve coordinates, but condition adjustment with parameters is more in reason.Digital map with cheapness and convenient is one of mostly methods for vector GIS spatial data. This paper discovers the error distribution for manual digitization not always normal but to be P-normal distribution, P-normal value is 1.5-1.6. This explains a lot of factors have complexity and syntheses in digitization. Error of digitization includes not only accident error, but also systematic error. Therefore, author brings forward just study random uncertainty is not integrated, the research is more important to systematic uncertainty.Positional error of digitization process is regarded a stationary random process for study the error and quality control. Variance-covariance function of data points can be given by random process theory. Measurement relativity of digitization points can be solved by the theory. This study has theoretical value and practicability, and makes an important action for line and surface elements of spatial data.(3) A theory system and a practical method are given for uncertainty of spatial data.
This paper expatiates the concept and definition of uncertainty in GIS. The uncertainty is divided into random uncertainty synthetical uncertainty, the estimating methods is given respectively. Estimating systematic variance and believe coefficient is needed in GIS positional data.Quantificational index data is given for unknown distributive uncertainty. The index data has an important action for unknown distributive uncertainty. (4)A new method of describing error band is given according to mean square of a point. Excellence of inhere error band is keep in the method, and the computing formula is simple. The new error bands are similar with the old, and the action is same. The new error bands can be described by a uniform formula. This paper points out that the new error bands are dumbbell model in practice.Moreover, model uncertainty is not involved in studied error band that deals with data error of the line elements. The problem of synthetic quantification is brought forward for synthesize to take into account data and model uncertainty, and the method is given as well as the curve. The research indicates the method is feasible. (5) Estimating of uncertainty is studied for spatial positional data.A method of calculation is given for data of digital map used coordinates of the same name point on multiple-lift overlay to estimate uncertainty of the positional data. Main contents include using t test method of dual sub-sample array to do gross error test to manual digitizing data of two lift overlay, and is given the method of synthetic estimating variance of unit weight. The characteristic is to apply the principle of statistical test and statistical estimation, so its result is more reasonable and simple. The method improves on old method of estimating variance of unit weight. (6)The selective standard is given according to the rule of optimization for
systematic error and accident error. The standpoint of synthesize to take into account is brought forward. The method can decrease the influence of model error and data error to influence curve matching. The study develops the theory of uncertainty of spatial data.Because of digitization coordinates X and Y are observation value, so the coordinates contain systematic error and accident error. A formula of calculation to solve parameter of curve matching according to least squares collocation. The problem is solved by to introduce given covariance function in this paper.
空间数据是GIS的一个重要的组成部分,而其中空间数据的质量直接影响到数据的适用性及其GIS的应用成功。因此,国内外的许多研究人员均把GIS中的不确定性问题作为现代GIS研究的重要方面之一。
GIS空间数据不确定性的研究主要涉及到位置不确定性和属性不确定性两大类问题,其理论和实际的内容十分广泛。由于时间和作者的能力所限,本文主要讨论了若干空间位置数据的不确定性问题。本文主要以概率论与数理统计理论和现代测量数据处理理论为基础,通过大量的实验数据和理论分析,得出了一些有益的成果。其主要研究内容有:
(1)对于AutoCAD软件与MapInfo软件进行数据转换时产生的不确定性作了大量的实验研究。选择这两种软件的原因是:AutoCAD软件为目前微机上应用最为广泛的通用交互式计算机辅助绘图软件包,也是世界上最流行的通用CAD平台;而MapInfo软件是目前微机上应用较为广泛的GIS平台。
通过对AutoCAD软件与MapInfo软件进行数据相互转换的实验分析,发现点、线和面元素在数据相互转换后所产生的不确定性是不可忽视的。特别是线和面元素,由于这两个软件使用的算法和取值精度不一样造成两种软件在计算曲线弧长、多边形面积时可能产生较大的误差。
在AutoCAD与MapInfo进行数据转换时,矢量数据误差不仅来源于数据保存为中间结果(交换格式文件)的精度有关,而且与两者在利用坐标数据生成各自的图形所采用的数学模型、数据的截断、积分方法、积分时的细分程度
Uncertainty theory in GIS is one of the most difficult basic theories. The theory have a important action for confirming the quality standard of GIS data, evaluating and controlling the production quality of GIS, optimizing the distributing structure of space data, improving the arithmetic of GIS, decrease the blindness of GIS design and exploitation in GIS, and other study field in GIS.Spatial data is one of the fundamental parts of GIS. The quality of spatial data directly determines the fitness-for-use of GIS and affects the result of GIS application. Therefore, accuracy analysis and quality control of spatial data in GIS is regarded as one of the fundamental theoretical research issues internationally.Study of GIS spatial data uncertainty is mostly come down to positional and attribute uncertainty. It's content is full abroad..This paper is mostly discussed some spatial data uncertainties. This paper is obtained some study productions by mostlyaccording to the foundation of Probability and Statistics theory, and data processing theory of modern time surveying and mapping. That mostly studies and contributions described as following:(l)Large numbers of experimentations are done for AutoCAD and Maplnfoprocreant uncertainty in data transformation. The reason of to select them is thatAutoCAD and Maplnfo are popularly used.The study is indicated that procreant uncertainty cannot slight for dot, line andsurface elements after data transformation. The software may produce some errordue to the software use different arithmetic and choose different precision in lineand surface elements especially.Vector data error root in not only the precision of data that is saved ininterlocutory result, but also relate to mathematics model, truncation of data and
integral method in AutoCAD and Maplnfo process data transformation. If both software cannot find same geometry figure, they may use approximate figure, the replacement will make some error in data transformation.The paper bring forwards the methods for decrease data transformation error in data transformation. The methods possess directionally function for more study of data transformation.(2) The paper studies and analyses the uncertainty of spatial positional data.The paper discusses the method for using condition adjustment and condition adjustment with parameters to solve coordinates transformation parameters. The method can depress systematic error of digital map in some degree. Both methods are same to solve coordinates, but condition adjustment with parameters is more in reason.Digital map with cheapness and convenient is one of mostly methods for vector GIS spatial data. This paper discovers the error distribution for manual digitization not always normal but to be P-normal distribution, P-normal value is 1.5-1.6. This explains a lot of factors have complexity and syntheses in digitization. Error of digitization includes not only accident error, but also systematic error. Therefore, author brings forward just study random uncertainty is not integrated, the research is more important to systematic uncertainty.Positional error of digitization process is regarded a stationary random process for study the error and quality control. Variance-covariance function of data points can be given by random process theory. Measurement relativity of digitization points can be solved by the theory. This study has theoretical value and practicability, and makes an important action for line and surface elements of spatial data.(3) A theory system and a practical method are given for uncertainty of spatial data.
This paper expatiates the concept and definition of uncertainty in GIS. The uncertainty is divided into random uncertainty synthetical uncertainty, the estimating methods is given respectively. Estimating systematic variance and believe coefficient is needed in GIS positional data.Quantificational index data is given for unknown distributive uncertainty. The index data has an important action for unknown distributive uncertainty. (4)A new method of describing error band is given according to mean square of a point. Excellence of inhere error band is keep in the method, and the computing formula is simple. The new error bands are similar with the old, and the action is same. The new error bands can be described by a uniform formula. This paper points out that the new error bands are dumbbell model in practice.Moreover, model uncertainty is not involved in studied error band that deals with data error of the line elements. The problem of synthetic quantification is brought forward for synthesize to take into account data and model uncertainty, and the method is given as well as the curve. The research indicates the method is feasible. (5) Estimating of uncertainty is studied for spatial positional data.A method of calculation is given for data of digital map used coordinates of the same name point on multiple-lift overlay to estimate uncertainty of the positional data. Main contents include using t test method of dual sub-sample array to do gross error test to manual digitizing data of two lift overlay, and is given the method of synthetic estimating variance of unit weight. The characteristic is to apply the principle of statistical test and statistical estimation, so its result is more reasonable and simple. The method improves on old method of estimating variance of unit weight. (6)The selective standard is given according to the rule of optimization for
systematic error and accident error. The standpoint of synthesize to take into account is brought forward. The method can decrease the influence of model error and data error to influence curve matching. The study develops the theory of uncertainty of spatial data.Because of digitization coordinates X and Y are observation value, so the coordinates contain systematic error and accident error. A formula of calculation to solve parameter of curve matching according to least squares collocation. The problem is solved by to introduce given covariance function in this paper.
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