Maximum likelihood estimation of clock skew in sparse one-way packet transmissions for machine type communication applications

Establishing and maintaining time synchronization among the nodes in a distributed wireless network with desired accuracy is challenging. In upcoming machine type communication (MTC) applications a fast, scalable and accurate synchronization method is highly desired. We view the clock synchronization problem as peer-to-peer (P2P) continuously running process where clock master with a stable clock source transmits packets with transmit time stamp. Synchronizing nodes listen these packets and apply receive time stamps. Based on the passive listening framework developed in [1], we propose Passive Sparse Maximum Likelihood Estimator (PSMLE) that uses two observations spaced sufficiently apart in time to estimate clock skew. The PSLME based skew estimate is further used by Passive Maximum Likelihood Estimator (PMLE) to estimate clock offset. The resulting enhanced-PMLE (ePMLE) improves estimation accuracy with fewer packet observations. Random component of the link delay is assumed to be Gaussian distributed. We observe that estimator accuracy is independent of propagation delay and distribution parameter and set them to zero without impacting the estimation accuracy. Further, we show that Cramer-Rao Lower Bound (CRLB) does not exist for PSMLE. However we verify through analysis and simulations that by choosing nearly compact observation window for PSMLE and optimal number of packet observations for ePMLE, sub-millisecond (sub-ms) clock accuracy can be achieved for all practical MTC scenarios.