一种基于统计流形的定位算法  

A localization algorithm based on statistical manifold

作　　者：夏斌[1] 袁文浩[1] 谢楠[1] 刘倩[1] Xia Bin;Yuan Wenhao;Xie Nan;Liu Qian(School of Computer Science and Technology,Shandong University of Technology,Zibo 255000,Shandong China)

机构地区：[1]山东理工大学计算机科学与技术学院

出　　处：《华中科技大学学报（自然科学版）》2018年第9期21-24,29,共5页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61701286);山东省自然科学基金资助项目(ZR2017MF047,ZR2015FL003)

摘　　要：为了提高传统的统计流形定位算法的精度,提出了一种基于统计流形的新定位算法,充分利用未知节点之间的距离信息,实现多个未知节点的同时定位.该算法建立了包含未知节点之间的距离信息的测距模型,通过自然参数和自然统计量来重新参数化,将测距模型的求解问题转化为弯曲指数分布族的参数估计问题,采用统计流形的自然梯度迭代求解;同时,给出了系数矩阵的一般构造方法,该矩阵的构造除了与未知节点和锚节点之间的距离有关,还与未知节点之间的距离有关.仿真结果表明：与传统算法相比较,新算法定位精度更高,收敛速度更快.In order to further improve the positioning accuracy of conventional localization algorithm based on statistical manifold,a novel localization algorithm based on statistical manifold was proposed in this paper which can make full use of distance information between unknown nodes,realize simultaneous localization of multiple unknown nodes.The algorithm established the ranging model including the distance information between unknown nodes.Through the natural parameters and natural statistic parameterized again,the problem of solving the ranging model was transformed into the parameter estimation problem of curved exponential families.Then a natural gradient iteration based on statistical manifolds was adopted to deal with the parameter estimation problem.At the same time,the general construction method of the coefficient matrix was given.The construction of the matrix was not only related to the distances between unknown nodes and anchor nodes, but also to the distances between unknown nodes.Experimental results indicate that the novel algorithm can improve positioning accuracy,compared with the traditional localization algorithm.

关 键 词：统计流形 自然梯度 定位精度 测距模型 系数矩阵 无线传感器网络 弯曲指数分布族 

分 类 号：TN929.53[电子电信—通信与信息系统]