Distributed Clock Skew and Offset Estimation in Wireless Sensor Networks: Asynchronous Algorithm and Convergence Analysis

Abstract

Abstract-In this paper, we propose a fully distributed algorithm for joint clock skew and offset estimation in wireless sensor networks based on belief propagation. In the proposed algorithm, each node can estimate its clock skew and offset in a completely distributed and asynchronous way: some nodes may update their estimates more frequently than others using outdated message from neighboring nodes. In addition, the proposed algorithm is robust to random packet loss. Such algorithm does not require any centralized information processing or coordination, and is scalable with network size. The proposed algorithm represents a unified framework that encompasses both classes of synchronous and asynchronous algorithms for network-wide clock synchronization. It is shown analytically that the proposed asynchronous algorithm converges to the optimal estimates with estimation mean-square-error at each node approaching the centralized Cramér-Rao bound under any network topology. Simulation results further show that the convergence speed is faster than that corresponding to a synchronous algorithm.

An Overview of a Class of Clock Synchronization Algorithms for Wireless Sensor Networks: A Statistical Signal Processing Perspective

“…Existing fully-distributed algorithms in [22,46,47] are based on the belief propagation method in the Bayesian framework. Under the assumption of Gaussian random delays, [46] proposed a belief-based algorithm to estimate the clock offset in a distributed manner.…”

“…Due to the random packet dropouts, the synchronous algorithm may converge slowly. To account for these aspects, Du et al [47] generalized the belief-based algorithm to jointly estimate the clock offset and skew under Gaussian random delays using both synchronous and asynchronous algorithms. In the asynchronous algorithm, some nodes are allowed to update their beliefs more frequently as long as they receive messages from their neighbors within a preset time period.…”

“…Following the two-way message exchange model in Equations (45) and (46), the authors in [47] eliminated the fixed delay d by adding these two equations together. It turns out that:…”

“…It is illustrated analytically in [47] that the asynchronous algorithm converges regardless of the network topology, and the MSE of the estimation parameters achieves the centralized CRLB asymptotically. Simulation results further show that the asynchronous algorithm converges faster than the synchronous one.…”

“…In parallel to the work in [47], Etzlinger et al [22] proposed a BP algorithm and a mean field (MF) algorithm and adopted a Bayesian model with Gaussian random delays. The MAP estimates of clock offset and skew are derived using some simplifications of the measurement likelihoods and prior distributions.…”