Cooperative Joint Localization and Clock Synchronization Based on Gaussian Message Passing in Asynchronous Wireless Networks

Abstract

Localization and synchronization are very important in many wireless applications such as monitoring and vehicle tracking. Utilizing the same time of arrival (TOA) measurements for simultaneous localization and synchronization is challenging. In this paper, we present a factor graph (FG) representation of the joint localization and time synchronization problem based on TOA measurements, in which the non-line-of-sight measurements are also taken into consideration. On this FG, belief propagation (BP) message passing and variational message passing (VMP) are applied to derive two fully distributed cooperative algorithms with low computational requirements. Due to the nonlinearity in the observation function, it is intractable to compute the messages in closed form and most existing solutions rely on Monte Carlo methods, e.g., particle filtering. We linearize a specific nonlinear term in the expressions of messages, which enables us to use a Gaussian representation for all messages. Accordingly, only the mean and variance have to be updated and transmitted between neighboring nodes, which significantly reduces the communication overhead and computational complexity. A message passing schedule scheme is proposed to trade off between estimation performance and communication overhead. Simulation results show that the proposed algorithms perform very close to particle-based methods with much lower complexity especially in densely connected networks.

A Distributed Cooperative Localization Strategy in Vehicular-to-Vehicular Networks

“…Algorithm 1 provides a summary of the proposed protocol for the distributed positioning algorithm. for nodes j ∈ N do in parallel 5: calculate the estimate and the accuracy of the message, µ(x j , t) in (11) and (12) 6: end for 7: for l = 1 to L max do {iteration index} 8: for j = 1 to N in parallel do 9: calculate the estimate and the accuracy of the message → µ (x j , l) in (23)-(26) 10: calculate the estimate and the accuracy of the message ← µ (x j , l) in (34)-(37) 11: end for 12: broadcast the estimate and the accuracy of the message ← µ (x j , l) 13: end for 14: end for…”

“…Localization problems have been studied steadily to meet these purposes using various techniques, such as maximum a posteriori (MAP) estimations [11,12], extended Kalman filters (EKF) [13][14][15], particle filters [16], and maximum likelihood (ML) estimations [17]. In References [11,12], factor graph models along with belief propagation algorithm are utilized to reduce complexity requirements in communication and computation and achieve joint cooperative localization and clock synchronization. In References [13][14][15], an extended Kalman filter technique is developed to achieve cooperative localization of large groups of mobile robots and road vehicles.…”

Synchronization of application-driven WSN

“…In [16], two joint synchronization and localization algorithms in both line of seeing (LOS) and in non-line of seeing (NLOS) environments are proposed. They applied Taylor expansions in order to represent factor graphs in closed Gaussian forms where the means and variances of beliefs of node estimates can be easily obtained by simple arithmetic operations.…”

Expectation–Maximization-Based Passive Localization Relying on Asynchronous Receivers: Centralized Versus Distributed Implementations

“…However, this mechanism increases the communications overhead. Recently, the close relationship between localization and synchronization is unveiled by simultaneously solving the two problems [18]- [23]. Passive localization in a synchronous network was studied in [24], [25], and in a quasi-synchronous network (all receivers experience the same clock offset) in [26].…”