Research On Distributed Inference Based On Factor Graph In Wireless Sensor Networks

In wireless sensor networks(WSNs),the finite precision of sensor nodes and the noise interference of complex environments,may introduce errors to the data collected by the sensor nodes and lead to various uncertainties.How to obtain the target information as accurate as possible from vast uncertain data distributed in different physical regions,is one of the main issues in WSNs.Information fusion can effectively reduce the uncertainties of the collected data and the amount of transmission load in WSNs,so as to increase the accuracy of the data,save the energy of the sensor nodes,and prolong the network lifetime.However,there are still some defects and deficiencies in the information fusion algorithms for WSNs,such as high computational overhead,poor real-time capability,etc.Therefore,with the application backgrounds of cooperative localization and target tracking in WSNs,this dissertation takes factor graph and probabilistic inference methods as the main technical tools,and studies the distributed inference algorithms in WSNs,considering the computational complexity,convergence,and network communication overhead of the inference algorithms.The research target of this dissertation is to achieve accurate and fast data fusion in WSNs.The main research work and contributions of this dissertation are summarized as follows:First of all,a novel representation method for factor graphs is proposed for distributed inference problems in WSNs.Especially for cooperative localization of mobile sensor nodes and tracking of mobile targets in WSNs,based on the temporal inference model of Markov chains,the time dimension is added to the original factor graph model and a dynamic factor graph is proposed for the time-varying network topology of WSNs.Concerning the high computational complexity of message passing algorithms caused by continuous random variables and nonlinear/non-Gaussian probability distribution functions in factor graphs,a sequential particle-based sum-product algorithm(SPSPA)is proposed for distributed inference problems in WSNs.In SPSPA,message update rules at factor nodes and variable nodes are developed and messages are represented by a set of random sampled particles with associated importance weights.At factor nodes,the Monte Carlo method is used to approximately solve the integral in messages,and the importance sampling method is employed to construct the particle representation of outgoing messages.At variable nodes,the incoming messages are represented nonparametrically using the Gaussian kernel density estimation method,and the importance sampling method is also exploited to sample from message products.The data fusion problem of target tracking in a WSN is explored to verify the performance of SPSPA.The proposed dynamic factor graph is employed to model the distributed target tracking problem.Based on SPSPA,a distributed tracking algorithm is proposed and its corresponding message update rules are designed.Simulation results show that the computational complexity of SPSPA is linear in the number of particles.In order to improve the data fusion accuracy,the number of particles should be increased and SPSPA pays lower computational cost than the message passing algorithms using the Gibbs sampling method,which is quadratic in the number of particles.Then,the convergence problem of data fusion algorithms for cooperative localization in WSNs is considered.The dynamic factor graph is employed to model the spatial correlation of distance observations between mobile nodes,and the temporal correlation of the locations of mobile nodes.Therefore,the factor graph can be mapped onto the time-varying network topology.However,with the increase of the number of mobile nodes and the communication distance,as well as the random movements of sensor nodes,the constructed factor graph may contain many loops and the sum-product algorithm may be faced by a lack of convergence guarantees.The marginal a posterior distribution of the location of a mobile node can only be calculated via iterative updates of the messages.Concerning the convergence problem of data fusion algorithms,a sequential uniformly reweighted sum-product algorithm(SURW-SPA)is proposed for cooperative localization in WSNs.The message update rules of Tree-Reweighted Belief Propagation(TRW-BP)in factor graphs are derived and the edge appearance probabilities of factor nodes are set to be all equal.This reduces the degrees of freedom to a scalar variable and makes SURW-SPA suitable for distributed implementation in WSNs.Some sufficient,though not necessary conditions are analyzed,under which SURW-SPA corresponds to optimized TRW-BP.Furthermore,the sequential message update schedule is exploited to improve the convergence of SURW-SPA.The message update order in SURW-SPA is scheduled according to the ordering of mobile nodes.The selection of node ordering and the construction of monotonic chains are also analyzed.Simulation results show that in both static and mobile WSNs,SURW-SPA can converge faster and achieve higher accuracy than the cooperative localization algorithms using the parallel message update schedule.Finally,the communication cost problem of data fusion algorithms for cooperative localization in WSNs is considered from the perspective of variational approximate inference.The mean field approximation method is adopted to approximate the joint posterior probability distribution of the locations of mobile nodes by a fully factorized distribution.Based on the Kullback-Leibler divergence,the cost function is constructed and the variational message passing algorithms can be used to achieve an approximate solution for the marginal a posterior distribution.However,in the particle-based variational inference algorithms,a large number of particles have to be communicated between neighboring sensor nodes for cooperative localization.In order to improve the localization accuracy,the number of particles should be increased and sensor nodes have to pay higher communication cost.Concerning the communication cost problem of data fusion algorithms,a parametric variational sum-product algorithm(PVSPA)is proposed for cooperative localization in WSNs.In PVSPA,the Gaussian probability density function is used to implement the parametric representation for the approximate marginal posterior(AMP)of the location of a mobile node.In this way,only the AMP parameters have to be transmitted between neighboring sensor nodes.The detailed procedure of PVSPA is proposed as follows:(1)Constructing the particle representation of prediction messages,(2)Extracting the Gaussian parameters from the AMPs,(3)Calculating the parametric measurement messages between neighboring nodes,(4)Updating the particle-based AMPs.Simulation results show that compared to the particle-based variational inference algorithms,PVSPA for cooperative localization has dramatically lower communication requirements,which needs not be at the expense of data fusion accuracy.