Clock synchronization in a wireless network based on consensus method that takes into account the noise (uncertainty) in the system, with a nice related work about consensus-based network clock synchronization

Jianping He, Xiaoming Duan, Peng Cheng, Ling Shi, Lin Cai, Accurate clock synchronization in wireless sensor networks with bounded noise, Automatica, Volume 81, July 2017, Pages 350-358, ISSN 0005-1098, DOI: 10.1016/j.automatica.2017.03.009.

It is important and challenging to achieve accurate clock synchronization in wireless sensor networks. Various noises, e.g., communication delay, clock fluctuation and measurement errors, are inevitable and difficult to be estimated accurately, which is the main challenge for achieving accurate clock synchronization. In this paper, we focus on how to achieve accurate clock synchronization by considering a practical noise model, bounded noise, which may not satisfy any known distributions. The principle that a bounded monotonic sequence must possess a limit and the concept of maximum consensus are exploited to design a novel clock synchronization algorithm for the network to achieve accurate and fast synchronization. The proposed algorithm is fully distributed, with high synchronization accuracy and fast convergence speed, and is able to compensate both clock skew and offset simultaneously. Meanwhile, we prove that the algorithm converges with probability one, which means that an accurate clock synchronization is achieved. We further prove that the probability of the complete synchronization converges exponentially fast. Experiments and simulations are conducted to verify the noise model and demonstrate the effectiveness of the proposed algorithm.

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