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Since a general Gaussian process is phase-sensitive, a stable phase referenceis 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'stechnical limitations, the resulting process appears as random in phase. Underthis condition, we consider two single-mode Gaussian processes, displacementand squeezing. We show that these two can be efficiently estimated using photonnumber states and photon number resolving detectors. For separate estimation ofdisplacement and squeezing, the practical estimation errors for hundreds ofprobes' ensembles can saturate the Cram\'{e}r-Rao bound even for arbitrarysmall values of the estimated parameters and under realistic losses. Theestimation of displacement with Fock states always outperforms estimation usingGaussian states with equivalent energy and optimal measurement. For estimationof squeezing, Fock states outperform Gaussian methods, but only when theirenergy is large enough. Finally, we show that Fock states can also be used toestimate the displacement and the squeezing simultaneously.

Optical estimation of unitary Gaussian processes without phase reference using Fock states