Consensus-based time synchronization via sequential least squares for strongly rooted wireless sensor networks with random delays

Consensus-based time synchronization, which is built on multi-agent consensus technique, becomes an important synchronization strategy to achieve accurate time synchronization for wireless sensor networks in a fully distributed way. In practical network scenarios, random communication delays are inevitable and have a significant influence on the information exchange procedure. Without dealing with the delays, many synchronization algorithms based on consensus will diverge and the nodes in the network will fail to synchronize with each other. A feasible approach addressing this problem is to design powerful and effective relative skew estimator to suppress the influence caused by delays. In this paper, we propose a sequential least squares algorithm to estimate the skew under delays, which improves the estimation accuracy while reducing the memory requirement. Based on the estimation algorithm and considering the case of the varying skews, we also devise an improved estimation scheme by incorporating a forgetting factor so as to track the skew evolution. By applying the proposed estimation method to average consensus protocol, each node can achieve accurate synchronization in the presence of delays. We theoretically prove the convergence of the whole scheme by using Lyapunov theory and considering strongly rooted topology condition, and provide simulations to show that our scheme outperforms existing consensus-based synchronization schemes under random delays.