The Methods Of Information Geometry In Wireless Sensor Networks

Wireless sensor network is a computer network composed of some automatic de-vices on certain space.The devices can be used to monitor the physical or environmen-tal situations of the different locations,collaboratively,such as temperature,pressure,sound,vibration,motion and pollutants.The development of wireless sensor networks is first originated in military applications like battlefield surveillance,and nowadays which has been applied to many civil areas,such as health care,traffic control,home automation,environmental and ecological monitoring.In recent years,as the minia-turization of the micro sensor and microprocessor,as well as the progress of modern network and wireless communication technology,wireless sensor networks technology has obtained a considerable attention,especially in the areas of the practical applica-tions such as in wireless communication,environmental monitoring and forecast,target detection and tracking.In this paper,we mainly use the methods of information ge-ometry to investigate issues of detection and resolution,localization and tracking,and large scale of fast location by themselves in wireless sensor networks.Information geometry is a new discipline developed in nearly 30 years,whose original purpose is by the help of the methods of Riemannian manifold to solve the random problems including statistical inference,random neural networks,and the blind signal separation.With the birth of the matrix information geometry,information geometry theory can also be used to solve the no-random problems,such as signal processing,image processing,the optimal control and optimization on manifolds.It is well known that the practical problems in the linear space can often obtain better results by the linear methods.While for the nonlinear problems,we generally cannot use the linear methods to solve them because it maybe cause larger error in this way.However,geometric methods are often very effective for solving nonlinear problems.The reason is that we can consider the research object as a manifold,and define the metric on every point in the manifold for obtaining Riemannian manifold.According to the geometric and topological properties of Riemannian manifold,we can get the geodesic and geodesic distance connecting any two points.In this background,this paper mainly investigates the applications of information geometry in the wireless sensor networks and provides new approaches for the applications of wireless sensor network in the actual environment.The contents of this thesis include the following aspects.Firstly,we introduce the basic principle and related properties of information ge-ometry,and mainly introduce the theoretical basis of information geometry including classical information geometry,matrix manifold and manifold learning,and so on.The classical information geometry considers a family of probability distributions as a dif-ferential manifold,and uses the Fisher information matrix to define the related metric and connection for computing geodesic and geodesic distance on statistical manifold.Matrix information geometry is proposed by Barbaresco,Nielsen and Pennec recently.The main contents contain the general linear group and its subgroups,such as unitary group,symplectic group,orthogonal group and special Euclidean group,as well as the submanifold of the general linear group,such as the matrix manifold of positive def-inite,the Stiefel manifold,the Granssman manifold,etc,as while as the applications in information fields.As a kind of dimensional reduction method based on topological manifold,manifold learning is a blend of mathematics,computer science,intelligence science and cognitive science.Its basic idea is to establish the local mapping relation-ship,and then spread to the global manifold for finding the low dimensional embedding manifold of the whole high dimensional space,and finally realizing the manifold di-mensional reduction and data visualization.Secondly,we mainly investigate the issues of sensor networks based on the theory of statistical manifold,especially use the differential manifold to solve the problems of target detection and resolution.Meanwhile,we introduce a classical angle distri-bution manifold,namely,von Mises distribution manifold.By virtue of the geometric properties of the statistical manifolds for the sensor measurement models concluding a single distance angle positioning model and double angle positioning model in three dimensional sensor measurement networks,we obtain a novel and effective method for solving related problems in sensor networksFurthermore,we study the applicat,ions of matrix information geometry in the sen-sor networks for target resolution and tracking.We present the definition and related contents about information submanifold.And then,by changing the sensor network measurement model with noise into a multivariate probability distribution density func-tion,we can get the corresponding Fisher information matrix.Furthermore,by means of the theory of matrix manifold consisting of positive definite matrices,we define the matrix information distance and matrix resolution for investigating target resolution and sensor schedulingAt last,we use manifold learning method to resolve fast positioning problem in large scale wireless sensor networks.Localization of many unknown nodes in wire-less sensor networks is an important research field and attracts considerable research interests.In order to estimate the geographic location of nodes without an effective self-positioning functionality,we consider the sensor network measurement data space as a high-dimensional data manifold for solving the rapid positioning and estimation problems of the large scale sensor networks by graph embedding method and manifold dimensional reduction principle.