  Time 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.
