  The problem of clock offset estimation in a two way timing message exchange
regime is considered when the likelihood function of the observation time
stamps is Gaussian, exponential or log-normally distributed. A parametrized
solution to the maximum likelihood (ML) estimation of clock offset, based on
convex optimization, is presented, which differs from the earlier approaches
where the likelihood function is maximized graphically. In order to capture the
imperfections in node oscillators, which may render a time-varying nature to
the clock offset, a novel Bayesian approach to the clock offset estimation is
proposed by using a factor graph representation of the posterior density.
Message passing using the max-product algorithm yields a closed form expression
for the Bayesian inference problem. Several lower bounds on the variance of an
estimator are derived for arbitrary exponential family distributed likelihood
functions which, while serving as stepping stones to benchmark the performance
of the proposed clock offset estimators, can be useful in their own right in
classical as well Bayesian parameter estimation theory. To corroborate the
theoretical findings, extensive simulation results are discussed for classical
as well as Bayesian estimators in various scenarios. It is observed that the
performance of the proposed estimators is fairly close to the fundamental
limits established by the lower bounds.
