  Since a general Gaussian process is phase-sensitive, a stable phase reference
is required to take advantage of this feature. When the reference is missing,
either due to the volatile nature of the measured sample or the measurement's
technical limitations, the resulting process appears as random in phase. Under
this condition, we consider two single-mode Gaussian processes, displacement
and squeezing. We show that these two can be efficiently estimated using photon
number states and photon number resolving detectors. For separate estimation of
displacement and squeezing, the practical estimation errors for hundreds of
probes' ensembles can saturate the Cram\'{e}r-Rao bound even for arbitrary
small values of the estimated parameters and under realistic losses. The
estimation of displacement with Fock states always outperforms estimation using
Gaussian states with equivalent energy and optimal measurement. For estimation
of squeezing, Fock states outperform Gaussian methods, but only when their
energy is large enough. Finally, we show that Fock states can also be used to
estimate the displacement and the squeezing simultaneously.
