Exponential convergence of time-of-arrival based network clock synchronization under practical assumptions

This work proposes a distributed gradient descent estimator for clock synchronization in wireless sensor networks and provides an analysis of its convergence behavior under practical assumptions. Based on the clock rigidity theory proposed in our previous work, we first establish the exponential convergence of the estimator and characterize its convergence rate. We then study a non-generic configuration with a commonly adopted broadcast communication scheme and show that practical inter-node distances and a broadcast scheme in a wireless sensor network cause very slow convergence in network clock synchronization. A simple modification of the broadcast scheme is proposed and proved to be able to improve the estimator's convergence rate. Simulation examples are provided to support the analysis.