  IEEE 1588, built on the classical two-way message exchange scheme, is a
popular clock synchronization protocol for packet-switched networks. Due to the
presence of random queuing delays in a packet-switched network, the joint
recovery of the clock skew and offset from the timestamps of the exchanged
synchronization packets can be treated as a statistical estimation problem. In
this paper, we address the problem of clock skew and offset estimation for IEEE
1588 in the presence of possible unknown asymmetries between the {\color{black}
deterministic path delays} of the forward master-to-slave path and reverse
slave-to-master path, which can result from incorrect modeling or
cyber-attacks. First, we develop lower bounds on the mean square estimation
error for a clock skew and offset estimation scheme for IEEE 1588 assuming the
availability of multiple master-slave communication paths and complete
knowledge of the probability density functions (pdf) describing the random
queuing delays. Approximating the pdf of the random queuing delays by a mixture
of Gaussian random variables, we then present a robust iterative clock skew and
offset estimation scheme that employs the space alternating generalized
expectation-maximization (SAGE) algorithm for learning all the unknown
parameters. Numerical results indicate that the developed robust scheme
exhibits a mean square estimation error close to the lower bounds.
