A general framework for error analysis in measurement-based GIS Part 4: Error analysis in length and area measurements

This is the final of a series of four papers on the development of a general framework for error analysis in measurement-based geographic information systems (MBGIS). In this paper, we discuss the error analysis problems in length and area measurements under measurement error (ME) of the defining points. In line with the basic ME model constructed in Part 1 of this series, we formulate the ME models for length and area measurements. For length measurement and perimeter measurement, the approximate laws of error propagation are derived. For area measurement, the exact laws of error propagation are obtained under various conditions. An important result is that area measurement is distributed as a linear combination of independent non-central chi-square variables when the joint ME vectors of vertices coordinates are normal. In addition, we also give a necessary and sufficient condition under which the area measurement estimator is unbiased. As a comparison, the approximate law of error propagation in area measurement is also considered and its approximation is substantiated by numerical experiments.This project was supported by the earmarked grant CUHK 4362/00H of the Hong Kong Research grant Council.     

A general framework for error analysis in measurement-based GIS Part 2: The algebra-based probability model for point-in-polygon analysis

This is the second paper of a four-part series of papers on the development of a general framework for error analysis in measurement-based geographic information systems (MBGIS). In this paper, we discuss the problem of point-in-polygon analysis under randomness, i.e., with random measurement error (ME). It is well known that overlay is one of the most important operations in GIS, and point-in-polygon analysis is a basic class of overlay and query problems. Though it is a classic problem, it has, however, not been addressed appropriately. With ME in the location of the vertices of a polygon, the resulting random polygons may undergo complex changes, so that the point-in-polygon problem may become theoretically and practically ill-defined. That is, there is a possibility that we cannot answer whether a random point is inside a random polygon if the polygon is not simple and cannot form a region. For the point-in-triangle problem, however, such a case need not be considered since any triangle always forms an interior or region. To formulate the general point-in-polygon problem in a suitable way, a conditional probability mechanism is first introduced in order to accurately characterize the nature of the problem and establish the basis for further analysis. For the point-in-triangle problem, four quadratic forms in the joint coordinate vectors of a point and the vertices of the triangle are constructed. The probability model for the point-in-triangle problem is then established by the identification of signs of these quadratic form variables. Our basic idea for solving a general point-in-polygon (concave or convex) problem is to convert it into several point-in-triangle problems under a certain condition. By solving each point-in-triangle problem and summing the solutions, the probability model for a general point-in-polygon analysis is constructed. The simplicity of the algebra-based approach is that from using these quadratic forms, we can circumvent the complex geometrical relations between a random point and a random polygon (convex or concave) that one has to deal with in any geometric method when probability is computed. The theoretical arguments are substantiated by simulation experiments.This project was supported by the earmarked grant CUHK 4362/00H of the Hong Kong Research grants Council.     

A general framework for error analysis in measurement-based GIS Part 3: Error analysis in intersections and overlays

This is the third of a four-part series on the development of a general framework for error analysis in measurement-based geographic information systems (MBGIS). In this paper, we study the characteristics of error structures in intersections and polygon overlays. When locations of the endpoints of two line segments are in error, we analyze errors of the intersection point and obtain its error covariance matrix through the propagation of the error covariance matrices of the endpoints. An approximate law of error propagation for the intersection point is formulated within the MBGIS framework. From simulation experiments, it appears that both the relative positioning of two line segments and the error characteristics of the endpoints can affect the error characteristics of the intersection. Nevertheless, the approximate law of error propagation captures nicely the error characteristics under various situations. Based on the derived results, error analysis in polygon-on-polygon overlay operation is also performed. The relationship between the error covariance matrices of the original polygons and the overlaid polygons is approximately established.This project was supported by the earmarked grant CUHK 4362/00H of the Hong Kong Research grants Council.     

补偿海空重力测量动态效应剩余影响的通用模型

针对目前作业过程中普遍存在的测量动态环境效应剩余影响问题,在深入分析海空重力测量误差源形成机理及其变化特性基础上,提出了一种适用于补偿各类海空重力仪动态效应剩余影响的通用模型;研究探讨了通用模型形式优选和模型参数估计问题,将基于信息论的Akaike信息量准则引入通用模型表达式的优选过程,提出应用互相关分析方法对模型参数进行估计,在双重约束下构建了补偿动态效应剩余影响的优化模型。使用典型动态环境下的海面重力观测数据对该方法的有效性进行了验证,结果显示,海洋重力测量成果内符合精度从原先的±9.35×10^-5 m/s²大幅提升到±1.01×10^-5 m/s²,充分体现了本文方法和模型对消除高动态测量环境效应影响的优良特性。     

A cross-analysis framework for multi-source volunteered,crowdsourced, and authoritative geographic information: The case study of volunteered personal traces analysis against transport network data

Abstract

The paper discusses the need of a high-level query language to allow analysts, geographers and, in general, non-programmers to easily cross-analyze multi-source VGI created by means of apps, crowd-sourced data from social networks and authoritative geo-referenced data, usually represented as JSON data sets (nowadays, the de facto standard for data exported by social networks). Since an easy to use high-level language for querying and manipulating collections of possibly geo-tagged JSON objects is still unavailable, we propose a truly declarative language, named J-CO-QL, that is based on a well-defined execution model. A plug-in for a GIS permits to visualize geo-tagged data sets stored in a NoSQL database such as MongoDB; furthermore, the same plug-in can be used to write and execute J-CO-QL queries on those databases. The paper introduces the language by exemplifying its operators within a real study case, the aim of which is to understand the mobility of people in the neighborhood of Bergamo city. Cross-analysis of data about transportation networks and VGI from travelers is performed, by means of J-CO-QL language, capable to manipulate and transform, combine and join possibly geo-tagged JSON objects, in order to produce new possibly geo-tagged JSON objects satisfying users’ needs.