全概率公式在时间地理中的应用研究  

Probability Model of Directed Movements Based on Total Probability Theorem

作　　者：尹章才[1] 刘清全[1] 孙华涛[1] 

机构地区：[1]武汉理工大学资源与环境工程学院.武汉市珞狮路122号,430070

出　　处：《武汉大学学报（信息科学版）》2013年第8期954-957,共4页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(41071283,41171319);中央高校基本科研业务费专项资金资助项目(2012-IV-097)

摘　　要：在已知起止点时间和位置及最大速度的条件下,针对移动对象的时空不确定性,利用全概率公式构建了定向移动的概率模型。首先,根据起止点时间和位置计算平均速度(即能到达目的地的最小速度),并在最小与最大速度之间随机离散出若干速度点,同时假设随机速度变量服从麦克斯韦-玻尔兹曼分布。然后,对任一速度值计算移动对象的可达范围及其几何概型,即在该速度取值条件下移动对象的条件概率。最后,在速度概率与基于速度条件的几何概率基础上,利用全概率原理能计算定向移动的时空概率分布。实验结果表明,随最大速度的增大,该概率的方差具有收敛性和稳定性,不同于已有概率模型的方差的分散性。When the locations of an agent at two times, and its maximum velocity are known, the agent＇s location between both those time instances is uncertain. We present a practical method, the total probability theorem, to approximate that uncertainty. First, the minimum （average） velocity from starting point to destination can he computed, and then many dis- crete speed values between the minimum and maximum velocity can be chosen randomly. The random speed variable V follows the Maxwell-Boltzmann distribution that describes par- ticle speeds, and thus the probability density function of V, p（V）, becomes applicable. Sec- ond, for a discrete speed value v, we calculate the agent＇s reachable range （x, y） at any time t in time geography. The range follows a uniform distribution, and so at t we may ob- tain p（x, y I v, t）, which is the conditional probability of （x, y） given the value of the ran- dom variable V, V= v. Finally, according to the total probability theorem, the probability distribution of the agent at time t, p（ x, y/t）, is obtained by the equation p（V-=v） p （x, y / v, t） where the parameter V takes all values. When increasing the maximum veloci- ty, experiments show that the total probability variance has a good convergence and steadi- ness, an improvement over the existing method divergence.

关 键 词：概率时间地理 条件概率 正态分布 均匀分布 麦克斯韦-玻尔兹曼分布 

分 类 号：P208[天文地球—地图制图学与地理信息工程]