  Time delay estimation (TDE) is an important step to identify and locate
vibration source. The TDE result can be obtained by cross-correlation method
through seeking the maximum correlation peak of two signals. However, the
cross-correlation method will induce random error when dealing with the
nonstationary signal. We propose a novel time shifting deviation (TSDEV) method
to solve this problem, which has been proved to achieve ultrahigh precision
localization result in the fiber vibration monitoring system. This paper
compares TSDEV method with cross-correlation in detail by simulating TDE
process in different conditions, such as signals with arbitrary intercepted
length, nonstationary drift and correlated noise. Besides, experimental
demonstration has been carried out on 60 km fiber to localize a wide band
vibration signal. The typical localization error is 2 m with standard deviation
of 21.4 m using TSDEV method. It stands in clear contrast to the result of
cross-correlation method, whose localization error is 70 m and the standard
deviation is 208.4 m. Compared with cross-correlation method, TSDEV has the
same resistance to white noise, but has fewer boundary conditions and better
suppression on linear drift or common noise, which leads to more precise TDE
results.
