On maximum likelihood estimation of clock offset and skew in networks with exponential delays

Clock synchronization represents a crucial element in the operation of wireless sensor, networks (WSNs). For any general time synchronization protocol involving a two-way message exchange mechanism, e.g., timing synch protocol for sensor networks (TPSN) [see S. Ganeriwal, R. Kumar, and M. B. Srivastava, "Timing Synch Protocol for Sensor Networks," in Proceedings of the First International Conference on Embedded Network Sensor Systems," 2003, pp. 138-149], the maximum likelihood estimate (MLE) for clock offset under the exponential delay model was derived in [D. R. Jeske, "On the Maximum Likelihood Estimation of Clock Offset," IEEE TRANSACTIONS ON COMMUNICATIONS, vol. 53, no. 1, pp. 53-54, January 2005] assuming no clock skew between the nodes. Since all practical clocks are running at different rates with respect to each other, the skew correction becomes important for achieving long term synchronization since it results in the reduction of the number of message exchanges and hence minimization of power consumption. In this paper, the joint MLE of clock offset and skew under the exponential delay model for a two way timing message exchange mechanism and the corresponding algorithms for finding these estimates are presented. Since any time synchronization protocol involves real time message exchanges between the sensor nodes, ML estimates for other synchronization protocols can be derived by employing a similar procedure. In addition, due to the computational complexity of the MLE, a simple, computationally efficient and easy to implement algorithm is presented as an alternative to the ML estimator which particularly suits the low power demanding regime of wireless sensor networks.