Maximum Likelihood Estimation of Relative Clock Skew for Distributed Time Synchronization in Industrial Wireless Sensor Networks

Accurate time synchronization is essential for data fusion, deterministic scheduling, and other fundamental operations in industrial wireless sensor networks (IWSNs). The relative clock skew plays a key role in popular distributed time synchronization and directly affects the estimation accuracy of clock compensations. However, communication delays are inevitable and unpredictable in practical scenarios, which makes an error calculation of the relative clock skew for most synchronization protocols. This article investigates the time synchronization problem with Gaussian distribution delays. A maximum likelihood estimator (MLE) of the relative clock skew is derived, and its Cramer-Rao lower bound (CRLB) is given. Without modifying the synchronization protocol and packet format, the MLE gathers the observed values in the past several synchronization periods to accurately estimate the relative clock skew of the current round. The proposed MLE is independent of the clock skew and clock offset estimations. It can be applied to different distributed protocols. Extensive simulation results indicate that the convergence accuracy of the proposed MLE-based synchronization protocols is better than that of the average timesync (ATS), gradient time synchronization protocol (GTSP), and maximum time synchronization (MTS) protocols. In addition, the accuracy of the estimator depends on the synchronization period and the window length of the MLE, which provides flexible accuracy levels for various industrial applications.