Research On Distributed Localization Algorithms In Wireless Networks

Location awareness has become an important feature in wireless networks, and wirelesslocation techniques have been widely used in many fields, including military, commerceand public service. The wireless location techniques can be classified into two categories,which are based on space satellite systems and terrestrial wireless networks, respectively.The location techniques based on space satellite systems are suitable for the open outdoorenvironment, while the location techniques based on terrestrial wireless networks are moresuitable for the harsh environments, such as indoors, urban areas and wooded areas. Inlocalization process, the position uncertainties and insufficient number of anchors can leadto large location error, or even location failure. Conventional localization techniqueimproves the localization error by setting high-density or high-power transmission anchors,while the novel cooperative localization technique improves the localization accuracy aswell as availability and reliability by establishing peer-to-peer communications andinter-measurements among the agents. In addition, centralized localization method has largecommunication overhead in large-scale networks and poor scalability, and is sensitive to thenode failure. Distributed localization has better scalability and is more robust, which makesit more attractive in cooperative localization technique.In this paper, we focus on the research of distributed location algorithms in wirelessnetworks. Firstly, it analyzed the distributed localization with uncertain anchors inconventional location technique. Then, it studied the message passing algorithms for thedistributed cooperative localization. Finally, the research was extended to distributed andjoint localization and tracking. The main novelties and contributions are presented below.1. We proposed a distributed localization algorithm based on the expectationmaximization algorithm to tackle the anchors with position uncertainties in thenetworks. The paper realized the agent’s maximum-likelihood estimator by using theexpectation maximization algorithm. To obtain the closed form in Expectation step, itconverted the posterior distributions of anchors’ position errors into the circularlysymmetric Gaussian distributions. Then, it derived the closed-form estimations inmaximization step through the approximations on the confluent hypergeometric function ofthe first kind by the first-order and second-order Taylor expansions. Finally, theperformance and computational complexity of the proposed algorithm were analyzed. 2. We proposed two Gaussian message passing algorithms for distributedcooperative localization to solve the problem that the agent cannot be located for theinsufficient number and the low transmission power of anchors in conventionallocation technique. Factor graph was created according to the joint location posterior of allthe nodes in the networks, and message passing algorithm was utilized to compute theposition posteriors of each node. The paper derived the messages on factor graph and theposition posteriors of each node with Gaussian forms by message approximation innonlinear model and model linearization, respectively, which reduced the communicationoverhead and computational complexity significantly, and made the cooperativelocalization more infeasible in practical applications. The details of these two proposedalgorithms are:(1) Distributed cooperative localization based on Gaussian message passing in thenonlinear model. By introducing the independent constraint of each dimension in theposition variable and approximating the messages from the factor nodes and variable nodes,the closed forms of all the messages on factor graph and position posterior of each nodewere obtained. It derived the message update expressions of the proposed algorithm in bothnetwork with accurate anchors and network with uncertain anchors, and analyzed theperformance, communication overhead and computational complexity of the proposedalgorithm using both the exact message passing scheme and the broadcast message scheme.(2) Distributed cooperative localization based on Gaussian message passing in thelinearized model. The node’s position was treated as a vector variable. It established thenode’s position state-space model, and linearized the observation function to obtain thelinear system model. Based on the linearized system model, it created the factor graph andderived all messages on factor graph and position posterior of each node as multivariateGaussian distributions. Finally, the performance of the proposed algorithm in both staticand mobile networks, the communication overhead and computational complexity of theproposed algorithm using both the exact message passing scheme and the broadcastmessage scheme were analyzed.3. We proposed a Gaussian message passing algorithm for distributed and jointlocalization and tracking to solve the agents’ localization and targets’ tracking innetworks. According to the joint posterior distribution of all the nodes, a factor graph wascreated. Resorting to the Gaussian message passing algorithm using the broadcast messagescheme for distributed cooperative localization, all the messages on factor graph and all the nodes’ position posteriors were updated. Since the targets were inactive andnon-cooperative, the message computing and transmission on the local factor graph relatedto the targets were required to be completed by other nodes. However, each non-target nodeusually cannot get all the messages related to the target on factor graph. Hence, thenon-target nodes computed the means and variances of targets’ position posteriorsdistributively by using the average consensus algorithm, and realized the message passingon the whole factor graph. Finally, it analyzed the performance of the proposed algorithm.