Distributed Network Time Synchronization: Social Learning Versus Consensus

The objective of this paper is to investigate a social learning-based distributed network time synchronization (SLDNTS) and compare it to a classic approach: consensus-based distributed network time synchronization (CDNTS). An observation random variable (ORV), which is a conditional likelihood (e.g., Gaussian) given a synchronized true time hypothesis, is used to generate clock times at each node and each iteration. A time offset and time quality of each node clock are represented, respectively, by a mean shift from the true time and variance of a Gaussian random variable (RV) to consider a practical environment. Then, this paper proposes a simple method to construct an observation matrix that satisfies both the identifiability condition (IC) and the prevailing observation signal existence condition (POSEC) required for the social learning (SL). Each node quantizes its ORV into a heads and tails Bernoulli RV with
$(1-\varepsilon)$
and
$\varepsilon$
probability, respectively, where
$\varepsilon$
is a control parameter for the SLDNTS convergence speed. Using this proposed observation matrix, each node computes its intermediate belief on each possible time hypothesis, shares the information with its connected neighbor nodes, and updates its belief probabilities. Then, this paper verifies, through simulation, that the proposed SLDNTS shows superior performance compared to the classic CDNTS including average time synchronization (ATS) algorithm, maximum time synchronization (MTS) algorithm, and least square time synchronization (LSTS) algorithm under the same observation environment.