A model-based approach to clock synchronization

Abstract

In a network of communicating motes, each one equipped with a distinct clock, a given node is taken as reference and is associated with the time evolution t. We introduce and analyze a stochastic model for clocks in which the relative speedup of a clock with respect to the reference node, called the skew, is characterized by some parametrized stochastic process. We study the problem of synchronizing clocks in a network which amounts to estimating the instantaneous relative skews and relative offsets, i.e., the differences in the clock readouts, by asynchronously communicating time-stamped packets between neighboring nodes. For a given communication link, we develop an algorithm for filtering the time-stamps exchanged between the two nodes in order to obtain Maximum-Likelihood (ML) estimates of the logarithm of the relative skew of one clock with respect to the other. We highlight implementation issues of the optimal filter and further present a scheme for pairwise offset estimation based on the obtained relative skew estimates. We study the properties of the proposed algorithms and provide theoretical guarantees on their performance.We extend the analysis to the problem of network-wide synchronization where the goal is to obtain, for each node and any given time instant, estimates of its skew/offset with respect to the reference time, as well as estimates of its relative skew/offset with respect to any other clock in the network. We leverage Kalman-Bucy filtering to obtain ML estimates of the logarithm of the skews at any given time;this gives rise to an online asynchronous algorithm for optimal filtering of the time-stamps in the entire network, which is however centralized. To tackle this, we propose an efficient distributed suboptimal N. Freris is with the TECHNICAL REPORT 2 online estimator for network-wide synchronization of skews and offsets, and study its performance both analytically and experimentally. We summarize our findings into defining a new distributed model-based clock synchronization protocol (MBCSP), and present a comparative simulation study of its accuracy versus prior art to showcase improvements.

A Recursive Method for Clock Synchronization in Asymmetric Packet-Based Networks

“…Our method estimates the bias for the down-link and up-link separately and similarly, so at this point let us just consider the down-link delay. If the random variable represents the down-link delay, then its PDF is determined by (6). The CDF of the Gamma distribution is (9) where is an incomplete Gamma function and is determined by (10) The expected value of the Gamma distribution is determined by the multiplication of and , so (11) It needs to be emphasized that the values of and are unknown, so we are not able to calculate the expected value of the delay using (11).…”

“…The parameters of the PDF are a function of the traffic load and also the number of hops. The PDF of a Gamma distribution is (6) where and are called the shaping and scale parameters, respectively. The exponential distribution is a special case of the Gamma distribution for the case that the shaping parameter is equal to one.…”

“…This assumption reduces the synchronization process to an unbiased estimation problem and has been studied widely, for example in [2]- [5]. In [6], Freris et al proposed a method to estimate the relative speedup of clocks in a network and subsequently estimate the pairwise offset of them. However, for estimating the offset, it is still required to be assumed that delays are symmetric.…”

A Filter‐based Clock Synchronization Protocol for Wireless Sensor Networks

“…We start by modelling a physically time-varying clock model and stating the objective of a distributed synchronization protocol. Considering an integral clock model [26] for each local clock i:…”

Distributed Time Synchronization in Lossy Wireless Sensor Networks

“…The problem of time synchronization in WSNs has attracted a great deal of attention; it represents a challenge, having in mind multi-hop communications, unpredictable packet losses and high probability of node failures. There are numerous approaches to time synchronization in WSNs starting from different assumptions, e.g., Freris et al (2011Freris et al ( , 2009Carli et al (2011);Xia and Cao (2011);Ganeriwal et al (1999); Elson et al (2002). An important class of time synchronization algorithms is based on full distribution of functions, when there are no reference nodes and when all the nodes run the same algorithm, such as in, e.g., Simeone et al (2008); Solis et al (2006).…”