Belief Propagation Based Cooperative Localization Algorithm For Wireless Sensor Networks

The rapid development of wireless sensor network(WSN)technology is gradually affecting people's production and life.WSN localization technology is a potential way to provide location services for harsh environments,such as indoors,shopping malls and urban areas.However,in non-cooperative localization,it may fail due to the insufficient number of anchors.Cooperative localization is a promising method to improve both the coverage and accuracy of positioning through peer-to-peer communication and measurement between agents.However,the practical application of the cooperative localization is restricted by two factors: on the one hand,its positioning performance is poor in sparse node scenarios;on the other hand,as the number of agents increases,the computational complexity and communication overhead increase dramatically,which brings heavy burden to the system overhead.In order to improve the practical application ability of cooperative localization in different scenarios,the key technologies as the reducing system overhead,controlling message passing and integrating inertial navigation information are studied.Some innovative contributions are achieved as follows:(1)Aiming at the problem of the high system overhead of the cooperative localization in dense WSN,a distributed Gaussian parametric belief propagation(GPBP)cooperative localization algorithm is proposed.GPBP algorithm maps the problem of agent location on the factor graph,obtains the joint posterior distribution of all nodes by using the iterative update mechanism of the message,and then estimates the approximate optimal solution of the agent position through distributed message computation.In the message initialization phase,the prior information of the agents is firstly estimated by constructing the relative spatial relationship between the target and its neighbors,which is effective to accurately approximate the target distribution with fewer samples.The communication overhead of the network is reduced by Gaussian message passing rule.Then,an efficient message calculation method which exploits the Taylor expansion to linearize the measurement equation is derived.Numerical simulation and experimental results present that the proposed GPBP algorithm has low system overhead and high positioning accuracy.(2)In dense WSN,the system overhead of the BP algorithm increases rapidly with the increase of agent density.To solve this problem,a neighbor node selection strategy based on EFIM is proposed.Considering the prior information of the target,the geometric distribution of its neighbors and their uncertainties,the EFIM of the target is derived by constructing the joint posterior distribution of the target and its neighbors,and then the node selection criterion is formulated.Additionally,a simple and easy-to-implement transmit censoring scheme is put forward to limit the spread of invalid message and further reduce the system overhead of the cooperative localization.Numerical simulation and experimental results show that compared with the existing node selection scheme,the proposed scheme can improve the positioning accuracy.(3)The direction of message passing is bidirectional and uncontrolled in BP algorithm.In order to control the direction of message passing from the high precision to low precision,a novel bootstrap percolation scheme is introduced into GPBP(BP-GPBP)cooperative localization.Taking the number of neighbor reference nodes of the target as the threshold constraint,the target nodes are roughly divided into different layers.In order to eliminate the potential flip ambiguities,an approximate collinear detection criterion is proposed as a geometric constraint to evaluate the quality of the neighbor reference nodes.Combing the geometric constraint with the threshold constraint,the targets are further divided into different layers and all the targets are located in this layer-by-layer manner.Simulation results indicate that the proposed algorithm can control the directional flow of messages while reducing system overhead.(4)The performance of cooperative localization depends heavily on the density of nodes.To alleviate this dependence,an IMU/UWB integrated cooperative localization algorithm is proposed.In the time dimension,the position of the agent is predicted by IMU measurement information,which constructs the relative spatial relationship of the same agent in adjacent time.And in the spatial dimension,the position is corrected by UWB measurement information,which presents the relative spatial relationship between the target and its neighbors.The joint posterior distribution of nodes in sequential estimation is derived,and a factor graph which accounts for both spatial and temporal constraints is established.And then,the message calculation and updating are proceeded by the GPBP algorithm.Benefiting from the assistance of IMU,multiple sets of ranging information between the target and its neighbors are obtained in a time-space-changing manner,reducing the dependence of the cooperative localization on node density.Simulation and experimental results show that,the positioning performance of the proposed algorithm in sparse networks is beteer than that of UWB only algorithm.