Average time synchronization in wireless sensor networks by pairwise messages

Most of previous algorithms for time synchronization choose a specific node's (denoted as a root or leader) local time to be the reference time, which is easily disturbed by many events (e.g. root node's power down or damage). The Gaussian distribution for the nodes' local clocks has been reported by a few authors based on laboratory tests, the average of all nodes' clocks is the best approximation to the ideal time. In this paper, the possibility to realize average time synchronization in wireless sensor networks by pairwise messages exchange is studied, and a simple algorithm (ATSP) is proposed, which synchronizes all the nodes' clocks to their average. For networks with clock skew, the algorithm compensates the frequencies of nodes to their average also. Using the Lyapunov's stability theory, convergence analyses and proofs of the algorithm are given. Synchronization error (accuracy) of the algorithm is estimated by using probability theory also, which indicates that the synchronization error of the algorithm is linearly related to the standard deviation of the message delay. Simulations are performed on a 300 nodes network to examine the performance of the algorithm, which verified the theoretical results. (C) 2011 Elsevier B.V. All rights reserved.