A Factor Graph Approach to Clock Offset Estimation in Wireless Sensor Networks

TL;DR

This paper introduces a novel factor graph and Bayesian approach for estimating clock offsets in wireless sensor networks, accommodating different likelihood distributions and node oscillator imperfections, with theoretical bounds and extensive simulations.

Contribution

It presents a new convex optimization method for maximum likelihood estimation and a Bayesian factor graph approach for dynamic clock offset estimation, improving accuracy and robustness.

Findings

Proposed estimators perform close to theoretical bounds.

Bayesian approach effectively models oscillator imperfections.

Simulation results validate the estimators' accuracy across scenarios.

Abstract

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 parametrized solution to the maximum likelihood (ML) estimation of clock offset, based on convex optimization, is presented, 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 a closed form 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.