Wireless sensor networks (WSNs) have received huge attention during the recent years due to their applications in a large number of areas such as environmental monitoring, health and traffic monitoring, surveillance and tracking, and monitoring and control of factories and home appliances. Also, the rapid developments in the micro electro-mechanical systems (MEMS) technology and circuit design lead to a faster spread and adoption of WSNs. Wireless sensor networks consist of a number of nodes featured in general with energy-limited sensors capable of collecting, processing and transmitting information across short distances. Clock synchronization plays an important role in designing, implementing, and operating wireless sensor networks, and it is essential in ensuring a meaningful information processing order for the data collected by the nodes. Because the timing message exchanges between different nodes are affected by unknown possibly time-varying network delay distributions, the estimation of clock offset parameters represents a challenge. This dissertation presents several robust estimation approaches of the clock offset parameters necessary for time synchronization of WSNs via the two-way message exchange mechanism. In this dissertation the main emphasis will be put on building clock phase offset estimators robust with respect to the unknown network delay distributions. Under the assumption that the delay characteristics of the uplink and the downlink are asymmetric, the clock offset estimation method using the bootstrap bias correction approach is derived. Also, the clock offset estimator using the robust Mestimation technique is presented assuming that one underlying delay distribution is mixed with another delay distribution. Next, although computationally complex, several novel, efficient, and robust estimators of clock offset based on the particle filtering technique are proposed to cope with the Gaussian or non-Gaussian delay characteristics of the underlying networks. One is the Gaussian mixture Kalman particle filter (GMKPF) method. Another is the composite particle filter (CPF) approach viewed as a composition between the Gaussian sum particle filter and the KF. Additionally, the CPF using bootstrap sampling is also presented. Finally, the iterative Gaussian mixture Kalman particle filter (IGMKPF) scheme, combining the GMKPF with a procedure for noise density estimation via an iterative mechanism, is proposed.

Clock synchronization between any two nodes in a Wireless Sensor Network (WSNs) is generally accomplished through exchanging messages and adjusting clock offset and skew parameters of each node’s clock. To cope with unknown network message delays, the clock offset and skew estimation schemes have to be reliable and robust in order to attain long-term synchronization and save energy. A joint clock offset and skew estimation scheme is studied and developed based on the Gaussian Mixture Kalman Particle Filter (GMKPF). The proposed estimation scheme is shown to be a more flexible alternative than the Gaussian Maximum Likelihood Estimator (GMLE) and the Exponential Maximum Likelihood Estimator (EMLE), and to be a robust estimation scheme in the presence of non-Gaussian/nonexponential random delays. This study also includes a sub optimal method called Maximum Likelihood-like Estimator (MLLE) for Gaussian and exponential delays. The computer simulations illustrate that the scheme based on GMKPF yields better results in terms of Mean Square Error (MSE) relative to GMLE, EMLE, GMLLE, and EMLLE, when the network delays are modeled as non-Gaussian/non-exponential distributions or as a mixture of several distributions.