Maximum Time Synchronization Research Articles

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.

RMTS: A robust clock synchronization scheme for wireless sensor networks

In recent years, wireless sensor networks (WSNs) have attracted more and more attention, but some applications of WSNs are still restricted by various factors, one of which is the clock synchronization among nodes. It is difficult to estimate the noises caused by communication delay, clock drift and measurement errors, which makes it challenging to achieve accurate clock synchronization. In this paper, we consider a bounded noise model, which does not need to satisfy any fixed probability distribution, nor does it need to have a fixed mean or variance. Under this noise model, we propose a novel clock synchronization scheme based on maximum consensus, which is called Robust Maximum Time Synchronization (RMTS). The proposed RMTS scheme starts with the estimation of relative skew and offset. On the basis, software parameters are adjusted so that all the nodes in the network can have the same software skew and offset. We theoretically prove that the proposed scheme can guarantee the accuracy of clock synchronization. Simulations are conducted to validate the effectiveness of the proposed scheme. The performance comparison with the other two schemes demonstrates that the RMTS scheme outperforms the existing ones.

Time Synchronization for Random Mobile Sensor Networks

Mobile sensor nodes have a wide spectrum of applications, such as social networks and habitat monitoring. Time synchronization is a critical issue for most applications using mobile sensor networks. However, due to the limited communication range, mobile sensor nodes can only exchange their information when they are sufficiently close for contact. Moreover, random movements of the nodes render the performance analysis of any time synchronization protocols challenging. In this paper, we introduce the relation graph for modeling the random contact of mobile sensor nodes and evaluate the probability that the network can be synchronized within an arbitrary time. We adapt the previous maximum time synchronization (MTS) protocol, which can drive the clocks of all sensor nodes to a common value by utilizing their own neighboring information. We provide an analytical lower bound of the probability that the time synchronization can be finished within any given time. The obtained theories and algorithms are applied for several fundamental problems, and it is proven that a better connectivity is beneficial for convergence. For linearizable graph, we provide an efficient way to calculate the exact probabilities. Extensive numerical examples demonstrate the effectiveness of our results.

Time Synchronization in WSNs: A Maximum-Value-Based Consensus Approach

This paper considers time synchronization in wireless sensor networks. When the communication delay is negligible, the maximum time synchronization (MTS) protocol is proposed by which the skew and offset of each node can be synchronized simultaneously. For a more practical case where the intercommunication delays between each connected node are positive random variables, we propose the weighted maximum time synchronization (WMTS), which is able to counteract the impact of random communication delays. Despite the clock offset that cannot be synchronized, WMTS can synchronize the clock skew completely in expectation and achieve acceptable synchronization accuracy. For both protocols, we provide rigorous proofs of global convergence as well as the upper bounds of their convergence time. Compared with existing consensus-based synchronization protocols, the main advantages of our protocols include: 1) a faster convergence speed so that the synchronization can be achieved in a finite time for MTS, and in a finite time in expectation for WMTS, respectively; 2) simultaneous synchronization of both skews and offsets; and 3) random communication delays can be handled effectively. Numerical examples are presented to demonstrate the effectiveness of the proposed protocols.

Study of consensus-based time synchronization in wireless sensor networks

Recently, various consensus-based protocols have been developed for time synchronization in wireless sensor networks. However, due to the uncertainties lying in both the hardware fabrication and network communication processes, it is not clear how most of the protocols will perform in real implementations. In order to reduce such gap, this paper investigates whether and how the typical consensus-based time synchronization protocols can tolerate the uncertainties in practical sensor networks through extensive testbed experiments. For two typical protocols, i.e., Average Time Synchronization (ATS) and Maximum Time Synchronization (MTS), we first analyze how the time synchronization accuracy will be affected by various uncertainties in the system. Then, we implement both protocols on our sensor network testbed consisted of Micaz nodes, and investigate the time synchronization performance and robustness under various network settings. Noticing that the synchronized clocks under MTS may be slightly faster than the desirable clock, by adopting both maximum consensus and minimum consensus, we propose a modified protocol, MMTS, which is able to drive the synchronized clocks closer to the desirable clock while maintaining the convergence rate and synchronization accuracy of MTS.