  We perform a protocol for multipartite quantum clock synchronization under
the influence of Unruh thermal noise. The clocks consisting of Unruh-DeWitt
detectors when one of detectors accelerated is obtained. To estimate the time
difference between the clocks, we calculate the time probability and analyze
how the probability is influenced by the Unruh thermal noise and other factors.
It is shown that both relativistic motion and interaction between the atom and
the external scalar field affect the choice of optimal number of excited atoms
in the initial state, which leads to a higher clock adjustment accuracy. Time
probabilities for different types of initial states approach to the same value
in the limit of infinite acceleration, while tend to different minimums with
increasing number of atoms. In addition, the accuracy of clock synchronization
using a pair of entangled clocks in two-party system is always higher than in
an multipartite system, while the optimal $Z$-type multipartite initial state
always perform better than the $W$-type state.
