Adaptive Time Synchronization in Time Sensitive-Wireless Sensor Networks Based on Stochastic Gradient Algorithms Framework

Abstract

This study proposes a novel time-synchronization protocol inspired by stochastic gradient algorithms. The clock model of each network node in this synchronizer is configured as a generic adaptive filter where different stochastic gradient algorithms can be adopted for adaptive clock frequency adjustments. The study analyzes the pairwise synchronization behavior of the protocol and proves the generalized convergence of the synchronization error and clock frequency. A novel closed-form expression is also derived for a generalized asymptotic error variance steady state. Steady and convergence analyses are then presented for the synchronization, with frequency adaptations done using least mean square (LMS), the Newton search, the gradient descent (GraDes), the normalized LMS (N-LMS), and the Sign-Data LMS algorithms. Results obtained from real-time experiments showed a better performance of our protocols as compared to the Average Proportional-Integral Synchronization Protocol (AvgPISync) regarding the impact of quantization error on synchronization accuracy, precision, and convergence time. This generalized approach to time synchronization allows flexibility in selecting a suitable protocol for different wireless sensor network applications.