地球信息科学学报

地球信息科学学报 ›› 2013, Vol. 15 ›› Issue (1): 38-45.doi: 10.3724/SP.J.1047.2013.00038

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基于空间陈述的定位及不确定性研究

张毅1, 邬阳2, 高勇1, 刘瑜1   

  1. 1. 北京大学遥感与地理信息系统研究所, 北京 100871;
    2. 北京建筑工程学院测绘与城市空间信息学院, 北京 100044
  • 收稿日期:2012-10-19 修回日期:2012-12-11 出版日期:2013-02-25 发布日期:2013-02-25
  • 通讯作者: 刘瑜(1971-),男,博士,副教授,主要研究方向为地理信息科学、人类移动模式与空间行为。E-mail:liuyu@urban.pku.edu.cn E-mail:liuyu@urban.pku.edu.cn
  • 作者简介:张毅(1971-),男,博士,讲师,主要研究方向为地理信息系统应用。E-mail:zy@pku.edu.cn
  • 基金资助:

    国家自然科学基金项目(41171295、41271385)。

On the Description-based Spatial Positioning and the Associated Uncertainty

ZHANG Yi1, WU Yang2, GAO Yong1, LIU Yu1   

  1. 1. Institute of Remote Sensing and Geographical Information Systems, Peking University, Beijing 100871, China;
    2. School of Geomatics and Urban Information, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
  • Received:2012-10-19 Revised:2012-12-11 Online:2013-02-25 Published:2013-02-25

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被引次数

19 | 3

摘要：

在地理空间知识的表达中,通常以文本方式描述位置。除了常见的地名以及地址外,许多陈述根据与参照地物的空间关系来表达一个目标地物的位置。由于一个空间陈述只是粗略描述了目标对象的位置,因此具有不确定性。在基于空间陈述的定位问题中,不确定性包括4个层次,分别对应于陈述、参照对象、空间关系和目标对象。这4个层次的不确定性适合于不同的建模方式,如概率方法、模糊集方法,以及证据理论方法等。本文采用不确定性场的概念,对点状目标地物的分布进行了探讨,并利用贝叶斯定理证明了对于给定的空间陈述,其不确定性场分布与做出该陈述概率,以及相应空间关系的模糊性之间的联系,该结论可用于指导不确定性场的建立。

关键词: 空间陈述, 目标对象, 空间定位, 不确定性, 参照对象

Abstract:

In the representation and communication of geographical knowledge of human beings, locations are often textually expressed. In addition to place names and addresses, a spatial assertion, which consists of reference objects and spatial relations, can roughly describe a locality. Typical examples of spatial assertions are "the vicinity of Peking University" and "Between Peking University and Tsinghua University". The objective of spatial positioning is to infer the location of a target object and the associated uncertainty for a given spatial assertion. In this research, we investigate four levels of uncertainty associated with spatial assertions. They are uncertainty of spatial assertions, imperfection of reference objects, imprecision and vagueness of spatial relations, and distribution of target objects. If a target object is abstracted to a point, the concept of an uncertainty field can be used to represent the possible spatial distribution of the target object. An uncertainty field is a 2-dimensional probability density function that satisfies 45p(x,y)dxdy=1 where denotes the field and F is its support. For a point T and a reference object A, if the probability that an observer make a description X is high, then the probability density at O is also high when X is known. This argument is proved using Bayes' theorem and can be viewed as the theoretical foundation to establish an uncertainty field. We also implemented a toolkit to generate uncertainty fields based on a number of spatial assertions.

Key words: target object, spatial positioning, reference object, uncertainty, spatial assertion