Network Clock Synchronization Based on the Second-Order Linear Consensus Algorithm

In this paper a distributed algorithm for clock synchronization is proposed. This algorithm is based on an extension of the linear consensus algorithm which is able to synchronize a family of identical double integrators. Since in reality the various clocks may have different drifts, the algorithm needs to be designed in such a way that it works correctly also in case of heterogeneous double integrators. We start by reviewing an unrealistic synchronous implementation of the clock synchronization algorithm, that has been recently proposed in the context of noisy double integrators. The main contribution of this paper is to propose a realistic pseudo-synchronous implementation of this algorithm. This pseudo-synchronous algorithm is shown to be a perturbation of the synchronous one and so, through arguments related to the center manifold theorem, it is proved to be locally convergent under the assumption of absence of process noise, measurement noise and propagation delays. However, through numerical simulations, the performance of this algorithm is evaluated also in the case the communication delays are not negligible, the clock drifts are time-varying and the communication channels are unreliable. Moreover, again through numerical simulations, the strategy we propose in this paper is compared with other fully distributed strategies recently proposed in the literature. While being slightly slower to reach the asymptotic synchronization, our strategy seems to significantly outperform the other strategies in terms of robustness to process and measurement noises and time-varying clock drifts.