  We address quantum estimation of displacement and squeezing parameters by the
class of probes made of Gaussian states undergoing Kerr interaction. If we fix
the overall energy available to the probe, without posing any constraint on the
available Gaussian squeezing, then Gaussian squeezing represents the optimal
resource for parameter estimation. On the other hand, in the more realistic
case where the amount of Gaussian squeezing is fixed, or even absent, then Kerr
interaction turns out to be useful to improve estimation, especially for probe
states with large amplitude. Our results indicate that precision achievable
with current technology Gaussian squeezing may be attained and surpassed for
realistic values of the Kerr coupling.
