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Time synchronization in wireless sensor networks is critical for providing accurate timing service to many applications. This paper presents an Error Statistic based Time Synchronization protocol (ESTS) for wireless sensor networks. ESTS uses a flooding mechanism for basic global time synchronization and delay measurement, and achieves a fine grained synchronization through compensating per hop delay to all the nodes. It is a light weight mechanism for its simplicity in both computation and communication. Experiments show that ESTS obtains a better performance in energy efficiency than most in-situ time synchronization protocols in the same precision level. [ABSTRACT FROM AUTHOR]