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.
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