熵理论在确定点位不确定性指标上的应用  

Application of Entropy Theory in Determining Indexes of Point's Positional Uncertainty

作　　者：李大军[1] 龚键雅[1] 谢刚生[2] 杜道生[1] 

机构地区：[1]武汉大学测绘遥感信息工程国家重点实验室,湖北武汉430079 [2]东华理工学院测量系,江西抚州344000

出　　处：《测绘学院学报》2002年第4期243-246,共4页Journal of Institute of Surveying and Mapping

基　　金：国家自然科学基金项目 (4 60 710 68)

摘　　要：分析了传统点位不确定性指标的局限性 ,基于信息论中的联合熵和最大熵定理导出了n维随机点熵不确定指标以及落入其内概率的统一公式 ;提出了以熵误差椭圆与熵误差椭球作为 2维、3维GIS中点元的位置不确定性度量指标。提出的熵指标具有唯一确定、不受置信水平选取的主观性影响等特点 ,适合于度量未知分布的点位不确定性。Point is both spatial feature and elementary unit of composing line and polygon in vector GIS, and studying indexes of point's positional uncertainty is the basis of developing line's and polygon's uncertainty models. In this paper, the imitation of tradition indexes is analyzed, and entropy uncertainty index of n-dimensional random point is derivedn based union entropy and maximum entropy principle. Entropy indexes of 2-dimensional and 3-dimensional random point is detailed. Entropy indexes can be solely determined and are independent of a certain confident level, and determination of the indexes don't require the condition of normal distribution. They are very suitable measure indexes of point's positional uncertainty.

关 键 词：信息熵 联合熵 不确定指标 GIS 地理信息系统 点元 空间数据库 

分 类 号：P208[天文地球—地图制图学与地理信息工程]