  Clock synchronization has become a key design objective in wireless networks
for its essential importance in many applications. However, as the wireless
link is prone to random network delays due to unreliable channel conditions, it
is in general difficult to achieve accurate clock synchronization among
wireless nodes. This letter proposes robust clock synchronization algorithms
based on low rank matrix approximation, which are able to correct timestamps in
the presence of random network delays. We design a low rank approximation based
maximum likelihood estimator (MLE) to jointly estimate the clock offset and
clock skew under the two-way message exchange mechanism assuming Gaussian delay
distribution. By formulating the timestamp correction problem into a low rank
approximation problem, we can solve the problem in the singular value
decomposition (SVD) domain and also via nuclear norm minimization. Numerical
results show that the proposed schemes can correct noisy timestamps and thus
achieve more robust synchronization performance than the MLE.
