Topological analysis of the time synchronization error for LSTS algorithm in WSNs

This paper analyzes the relationship between the steady state error and the topological structure of a least square estimation bases time synchronization (LSTS) algorithm for wireless sensor networks. Given the presence of random bounded communication delays between nodes, the definition of an error indicator is proposed to describe the impact on the statistical property of the global synchronization error. The error indicators are computed among several network architectures with the existence of root node and paths (or cycles). It is discovered that the more paths or cycles between nodes (except root node) exist, the larger the global synchronization error appears which is against our intuition. Simulation examples have validated analytical results.