Receiver-Only-Based Time Synchronization under Exponential Delays in Underwater Wireless Sensor Networks

In this article, we consider the receiver-only-based time synchronization in underwater wireless sensor networks with exponential delays emerging during the message exchanges. This article is motivated by the fact that 25% of timing messages are discarded in the existing receiver-only-synchronization (ROS)-based schemes to cope with the interaction between the discontinuity of the likelihood function and the unknown clock skews, which would result in a massive waste of energy. To account for this issue, a general ROS model under the exponential delay assumption, with clock skews taken into consideration and all timing messages utilized, is introduced. Following the proposed ROS model, we develop a three-step method to jointly estimate clock offsets and skews of both active and silent nodes, as well as other unknown parameters. Specifically, an estimation on clock offset and skew for the active node using support vector machine is followed by a joint maximum-likelihood estimation of the clock skew and clock offset for the silent node as well as clock offset for the active node, and a minimum variance unbiased estimation of the offsets for both active and silent nodes. Such method further improves the estimation accuracy of the proposed ROS model. The effectiveness and robustness of the proposed method is verified by simulations results.