Estimation from Relative Measurements in Mobile Networks with Markovian Switching Topology: Clock Skew and Offset Estimation for Time Synchronization

TL;DR

This paper presents a distributed algorithm for estimating clock skew and offset in mobile networks with Markovian switching topology, ensuring convergence and providing asymptotic analysis under realistic mobility models.

Contribution

It introduces a novel estimation algorithm for time synchronization in mobile networks with Markovian topology changes, including convergence proofs and asymptotic expressions.

Findings

Algorithm achieves mean square convergence under weak assumptions.

Provides explicit formulas for asymptotic mean and correlation.

Validates Markovian topology model through empirical entropy measures.

Abstract

We analyze a distributed algorithm for estimation of scalar parameters belonging to nodes in a mobile network from noisy relative measurements. The motivation comes from the problem of clock skew and offset estimation for the purpose of time synchronization. The time variation of the network was modeled as a Markov chain. The estimates are shown to be mean square convergent under fairly weak assumptions on the Markov chain, as long as the union of the graphs is connected. Expressions for the asymptotic mean and correlation are also provided. The Markovian switching topology model of mobile networks is justified for certain node mobility models through empirically estimated conditional entropy measures.