  The formalism of quantum estimation theory is applied to estimate the
disorders in the positions of two membranes positioned in a driven cavity. We
consider the coupled-cavities and the transmissive-regime models to obtain
effective descriptions of this system for different reflectivity values of the
membranes. Our models consist also high temperatures Brownian motions of the
membranes, losses of the cavity fields, the input-output formalism and a
balanced homodyne photodetection of the cavity output field. In this
two-parameter estimation scenario we compare the classical and quantum Fisher
information matrices and evaluate the accuracies of the estimations. We show
that models prefer very different estimation strategies and the temperature
does not have a detrimental effect on the estimation accuracies, but makes more
difficult to attain the quantum optimal limit. Our analysis also reveals that
best estimation strategies with unit effiecient detectors are measurements of
the quadratures of the output field.
