On Minimum Variance Unbiased Estimation of Clock Offset in a Two-Way Message Exchange Mechanism

For many applications, distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time. Most of the widely used clock synchronization algorithms in such systems employ the sender-receiver protocol based on a two-way timing message exchange paradigm. Maximum likelihood estimator (MLE) of the clock offset based on the timing message exchanges between two clocks was derived in D. R. Jeske, On maximum likelihood estimation of clock offset[IEEE Trans. Commun., vol. 53, pp. 53-54, Jan. 2005], when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean. Herein, the best linear unbiased estimate using order statistics (BLUE-OS) of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays, respectively. The Rao-Blackwell-Lehmann-Scheffe¿ theorem is then exploited to obtain the minimum variance unbiased estimate (MVUE) for the clock offset which it is shown to coincide with the BLUE-OS. In addition, it is found that the MVUE of the clock offset in the presence of symmetric network delays also coincides with the MLE. Finally, in the presence of asymmetric network delays, although the MLE is biased, it is shown to achieve lesser mean-square error (MSE) than the MVUE in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified.