A factor graph approach to clock offset estimation in wireless sensor networks

Aitzaz Ahmad, Davide Zennaro, Erchin Serpedin, Lorenzo Vangelista

Research output: Contribution to journalArticle

26 Citations (Scopus)


The problem of clock offset estimation in a two-way timing message exchange regime is considered when the likelihood function of the observation time stamps is Gaussian, exponential, or log-normally distributed. A parameterized solution to the maximum likelihood (ML) estimation of clock offset is analytically obtained, which differs from the earlier approaches where the likelihood function is maximized graphically. In order to capture the imperfections in node oscillators, which may render a time-varying nature to the clock offset, a novel Bayesian approach to the clock offset estimation is proposed by using a factor graph representation of the posterior density. Message passing using the max-product algorithm yields an exact expression for the Bayesian inference problem. Several lower bounds on the variance of an estimator are derived for arbitrary exponential family distributed likelihood functions which, while serving as stepping stones to benchmark the performance of the proposed clock offset estimators, can be useful in their own right in classical as well Bayesian parameter estimation theory. To corroborate the theoretical findings, extensive simulation results are discussed for classical as well as Bayesian estimators in various scenarios. It is observed that the performance of the proposed estimators is fairly close to the fundamental limits established by the lower bounds.

Original languageEnglish
Article number6179996
Pages (from-to)4244-4260
Number of pages17
JournalIEEE Transactions on Information Theory
Issue number7
Publication statusPublished - 25 Jun 2012



  • Clock synchronization
  • estimation bounds
  • factor graphs
  • message passing
  • wireless sensor networks (WSNs)

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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