  The quantum stochastic phase estimation has many applications in the precise
measurement of various physical parameters. Similar to the estimation of a
constant phase, there is a standard quantum limit for stochastic phase
estimation, which can be obtained with the Mach-Zehnder interferometer and
coherent input state. Recently, it has been shown that the stochastic standard
quantum limit can be surpassed with non-classical resources such as the
squeezed light. However, practical methods to achieve the quantum enhancement
in the stochastic phase estimation remains largely unexplored. Here we propose
a method utilizing the SU(1,1) interferometer and coherent input states to
estimate a stochastic optical phase. As an example, we investigate the
Ornstein-Uhlenback stochastic phase. We analyze the performance of this method
for three key estimation problems: prediction, tracking and smoothing. The
results show significant reduction of the mean square error compared with the
Mach-Zehnder interferometer under the same photon number flux inside the
interferometers. In particular, we show that the method with the SU(1,1)
interferometer can achieve the fundamental quantum scaling, the stochastic
Heisenberg scaling, and surpass the precision of the canonical measurement.
