  We describe a compact and reliable method to calculate the Fisher information
for the estimation of a dynamical parameter in a continuously measured linear
Gaussian quantum system. Unlike previous methods in the literature, which
involve the numerical integration of a stochastic master equation for the
corresponding density operator in a Hilbert space of infinite dimension, the
formulas here derived depends only on the evolution of first and second moments
of the quantum states, and thus can be easily evaluated without the need of any
approximation. We also present some basic but physically meaningful examples
where this result is exploited, calculating analytical and numerical bounds on
the estimation of the squeezing parameter for a quantum parametric amplifier,
and of a constant force acting on a mechanical oscillator in a standard
optomechanical scenario.
