2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133906Time synchronization is an important aspect of sensor network operation. However, it is well known that synchronization error accumulates over multiple hops. This presents a challenge for large-scale, multi-hop sensor networks with a large number of nodes distributed over wide areas. In this work, we present a protocol that uses spatial averaging to reduce error accumulation in large-scale networks. We provide an analysis to quantify the synchronization improvement achieved using spatial averaging and find that in a basic cooperative network, the skew and offset variance decrease approximately as $1/\bar{N}$ where $\bar{N}$ is the number of cooperating nodes. For general networks, simulation results and a comparison to basic cooperative network results are used to illustrate the improvement in synchronization performance.Submitted to the IEEE/ACM Transactions on Networking, October 2006. See also cs.IT/0503031Networking and Internet ArchitectureInformation Theorytext