定向移动基于马尔科夫链的时空不确定性  

Modeling Uncertainty of Directed Movement via Markov Chains

作　　者：尹章才[1] 孙华涛[1] 陈雪菲[1] 刘清全[2] 

机构地区：[1]武汉理工大学资源与环境工程学院,湖北武汉430070 [2]武汉大学中国南极测绘研究中心,湖北武汉430072

出　　处：《测绘学报》2015年第10期1160-1166,1176,共8页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(41071283;41301588;41171319);测绘地理信息公益性行业科研专项(201412014)~~

摘　　要：概率时间地理是经典时间地理基于概率的一种扩展,它采用概率描述移动对象在可达位置的非等可能性。已有的概率时间地理是基于正态分布或布朗桥的,其方差与移动速度无关或随移动速度的增大而发散,因而难以兼顾应用针对性和稳定性。本文提出了一种基于马尔科夫链的概率时间地理方法。首先,构建中间关于两边的双向条件马尔科夫链,它在移动速度足够大时的极限可视为布朗桥,因而具有稳定性数字特征。然后,建立定向移动到马尔科夫链的映射关系,主要是根据定向移动的时空位置、移动速度等信息建立马尔科夫链的步长、状态空间和转移矩阵,这样马尔科夫链与移动速度有关。最后,利用双向马尔科夫链连续计算定向移动在任意时刻的概率分布云,其方差的针对性和稳定性在实例中进行了验证。Probabilistic time geography(PTG)is suggested as an extension of(classical)time geography,in order to present the uncertainty of an agent located at the accessible position by probability.This may provide a quantitative basis for most likely finding an agent at a location.In recent years,PTG based on normal distribution or Brown bridge has been proposed,its variance,however,is irrelevant with the agent's speed or divergent with the increase of the speed;so they are difficult to take into account application pertinence and stability.In this paper,a new method is proposed to model PTG based on Markov chain.Firstly,a bidirectional conditions Markov chain is modeled,the limit of which,when the moving speed is large enough,can be regarded as the Brown bridge,thus has the characteristics of digital stability.Then,the directed movement is mapped to Markov chains.The essential part is to build step length,the state space and transfer matrix of Markov chain according to the space and time position of directional movement,movement speed information,to make sure the Markov chain related to the movement speed.Finally,calculating continuously the probability distribution of the directed movement at any time by the Markov chains,it can be get the possibility of an agent located at the accessible position.Experimental results show that,the variance based on Markov chains not only is related to speed,but also is tending towards stability with increasing the agent's maximum speed.

关 键 词：概率时间地理 马尔科夫链 定向移动 棱柱体 

分 类 号：P208[天文地球—地图制图学与地理信息工程]