Maximum Likelihood Estimation of Clock Skew in Wireless Sensor Networks With Periodical Clock Correction Under Exponential Delays

Time synchronization is crucial for wireless sensor networks (WSNs) since it maintains data consistency, coordination, and enables other fundamental operations. Over the last decade, a number of powerful time synchronization algorithms have been proposed for clock accuracy optimization by using signal processing techniques. However, most of these algorithms attempt to estimate the clock phase offset and skew and do not correct the node's local clock at every timing packet exchange before the clock parameters are jointly estimated, which reduces the network synchronization accuracy during the estimation of clock parameters and limits the applicability of the synchronization algorithms for some practical sensor networks where a global time scale is consistently required. Motivated by this, this paper investigates the synchronization scheme of having inactive nodes overhearing the pairwise sender-receiver time synchronization based on acknowledgement with clock correction at every synchronization. Assuming exponential random delays, the maximum likelihood estimators (MLEs) of clock skew and the corresponding approximate Cramer-Rao lower bounds (CRLBs) for active and overhearing nodes are derived. In addition, we also consider a linear synchronization model that the clock skew is directly estimated. Simulation results verify the efficiency of the clock skew estimators.