Analysis of Least Square Estimation Based Time Synchronization with Random Delay over Wireless Sensor Networks

Abstract

In order to tackle the problem of random communication delays in time synchronization process, this paper has mainly discussed the relationship between the global steady-state error of clock synchronization and the probability distribution of the delays of all the communication links for least square estimation based time synchronization algorithm (LSTS) in wireless sensor networks ( WSNs ). First under the general condition of communication in WSNs, it has been described that the probability distribution of bounded random communication delays has a great influence on the clock synchronization error. Then considering that all round-trip delays can be determined correctly between every pair of sensor nodes, the update rule of clock offset compensation has introduced round-trip delays so as to reduce the adjusting amplitude of the clock offset and the error of clock synchronization. Finally simulations for the improved algorithm has been given. It is shown that the error of clock skew compensation mainly depends on the variance of random communication delays rather than expectation, while the global synchronization error depends on the expectation of communication delays. The introduction of round-trip delay in LSTS algorithm can decrease both the expectation and the variance of clock synchronization error.