Distributed clock synchronization for wireless sensor networks using belief propagation

In this paper, we study the global clock synchronization problem for wireless sensor networks. Based on belief propagation, we propose a fully distributed algorithm which has low overhead and can achieve scalable synchronization. It is also shown analytically that the proposed algorithm always converges for strongly connected networks. Simulation results show that the proposed algorithm achieves better accuracy than consensus algorithms. Furthermore, the belief obtained at each sensor provides an accurate prediction on the algorithm's performance in terms of MSE. © 2011 IEEE.published_or_final_versio

Determining the convergence of variance in Gaussian belief propagation via semi-definite programming

In order to compute the marginal distribution from a high dimensional distribution with loopy Gaussian belief propagation (BP), it is important to determine whether Gaussian BP would converge. In general, the convergence condition for Gaussian BP variance and mean are not necessarily the same, and this paper focuses on the convergence condition of Gaussian BP variance. In particular, by describing the message-passing process of Gaussian BP as a set of updating functions, the necessary and sufficient convergence condition of Gaussian BP variance is derived, with the converged variance proved to be independent of the initialization as long as it is greater or equal to zero. It is further proved that the convergence condition can be verified efficiently by solving a semi-definite programming (SDP) optimization problem. Numerical examples are presented to corroborate the established theories.published_or_final_versio

Belief Consensus Algorithms for Fast Distributed Target Tracking in Wireless Sensor Networks

In distributed target tracking for wireless sensor networks, agreement on the target state can be achieved by the construction and maintenance of a communication path, in order to exchange information regarding local likelihood functions. Such an approach lacks robustness to failures and is not easily applicable to ad-hoc networks. To address this, several methods have been proposed that allow agreement on the global likelihood through fully distributed belief consensus (BC) algorithms, operating on local likelihoods in distributed particle filtering (DPF). However, a unified comparison of the convergence speed and communication cost has not been performed. In this paper, we provide such a comparison and propose a novel BC algorithm based on belief propagation (BP). According to our study, DPF based on metropolis belief consensus (MBC) is the fastest in loopy graphs, while DPF based on BP consensus is the fastest in tree graphs. Moreover, we found that BC-based DPF methods have lower communication overhead than data flooding when the network is sufficiently sparse

Cooperative Synchronization in Wireless Networks

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 Cram\'er-Rao bounds