A low complexity linear regression approach to time synchronization in underwater networks

In sensor networks, linear regression has been applied over a set of sending-receiving timestamps to estimate the clock-skew, assuming a time-invariant propagation delay of the beacons exchanged between the nodes. Due to ocean currents and dispersion, propagation delay between underwater nodes is time-varying. In this paper, we first analyze the effect of time-varying propagation on synchronization performance, demonstrating that the time-invariant assumption could lead to very poor performance in underwater networks. We then present a low complexity Time Synchronization algorithm for time-Varying Propagation underwater networks (TSVP), which accounts for both large and time-varying propagation delay. In contrast to existing work in the literature, where two linear regressions are used (the first regression is to handle the propagation delay and the second regression is to obtain the clock skew and offset), we only apply one regression, thereby significantly reducing the computational complexity. To compensate for the effect of time-varying propagation we employ a simple preprocessing before applying the linear regression by taking the advantage of the fact that a beacon and its response experience similar propagation delay. To investigate the behaviors of synchronization algorithms we use a kinematic mobility model where nodes are allowed to freely follow the ocean currents. Simulation results demonstrate that with much lower computational complexity, the proposed approach achieves similar performance as the competitive approach in the literature.