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Assuming that the network delays are normally distributed and the network nodes are subject to clock phase offset errors, the maximum likelihood estimator (MLE) and the Kalman filter (KF) have been recently proposed with the goal of maximizing the clock synchronization accuracy in wireless sensor networks (WSNs). However, because the network delays may assume any distribution and the performance of MLE and KF is quite sensitive to the distribution of network delays, designing clock synchronization algorithms that are robust to arbitrary network delay distributions appears as an important problem. Adopting a Bayesian framework, this paper proposes a novel clock synchronization algorithm, called the Iterative Gaussian mixture Kalman particle filter (IGMKPF), which combines the Gaussian mixture Kalman particle filter (GMKPF) with an iterative noise density estimation procedure to achieve robust performance in the presence of unknown network delay distributions. The Kullback-Leibler divergence is used as a measure to assess the departure of estimated observation noise density from its true expression. The posterior Cramér-Rao bound (PCRB) and the mean-square error (MSE) of IGMKPF are evaluated via computer simulations. It is shown that IGMKPF exhibits improved performance and robustness relative to MLE. The prior information plays an important role in IGMKPF. A MLE-based method for obtaining reliable prior information for clock phase offsets is presented and shown to ensure the convergence of IGMKPF.