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.

Abstract-Synchronization is a key functionality in wireless network, enabling a wide variety of services. We consider a Bayesian inference framework whereby network nodes can achieve phase and skew synchronization in a fully distributed way. In particular, under the assumption of Gaussian measurement noise, we derive two message passing methods (belief propagation and mean field), analyze their convergence behavior, and perform a qualitative and quantitative comparison with a number of competing algorithms. We also show that both methods can be applied in networks with and without master nodes. Our performance results are complemented by, and compared with, the relevant Bayesian Cramér-Rao bounds.

Abstract-Cooperative localization in agent networks based on interagent time-of-flight measurements is closely related to synchronization. To leverage this relation, we propose a Bayesian factor graph framework for cooperative simultaneous localization and synchronization (CoSLAS). This framework is suited to mobile agents and time-varying local clock parameters. Building on the CoSLAS factor graph, we develop a distributed (decentralized) belief propagation algorithm for CoSLAS in the practically important case of an affine clock model and asymmetric time stamping. Our algorithm allows for real-time operation and is suitable for a time-varying network connectivity. To achieve high accuracy at reduced complexity and communication cost, the algorithm combines particle implementations with parametric message representations and takes advantage of a conditional independence property. Simulation results demonstrate the good performance of the proposed algorithm in a challenging scenario with time-varying network connectivity.

This paper considers a passive localization scenario relying on a single transmitter, several receivers and multiple moving targets to be located. The so-called "passive" targets equipped with RFID reflectors are capable of reflecting the signals from the transmitter to the receivers. Existing approaches assume that the transmitter and receivers are synchronous or quasi-synchronous, which is not always realistic in practical scenarios. Hence, an asynchronous wireless network is considered, where different clock offsets are assumed at different receivers. We propose a centralized expectation maximizationbased passive localization method for asynchronous receivers (EMpLaR) by treating the clock offsets as hidden variables. Thereby, the proposed algorithm makes use of Taylor expansions to arrive at a closed-form maximization. Furthermore, to improve the robustness to link failures and to reduce the energy consumption, we propose a distributed localization approach based on average consensus formulation to locate the target at each receiver. By applying a quadratic polynomial approximation of the function on which consensus has to be reached, both the computational complexity and the communications overhead are significantly reduced. The Cramér-Rao bound of the target location is derived as a benchmark of our proposed algorithms. Our simulation results show that the proposed centralized and distributed EMpLaR algorithms match the Cramér-Rao bound and significantly improve the localization performance compared to the conventional methods.

No abstract