  We derive the filtering equation for Markovian systems undergoing homodyne
measurement in the situation where the output processes being monitored are
squeezed. The filtering theory applies to case where the system is driven by
Fock noise (that, quantum input processes in a coherent state) and where the
output is mixed with a squeezed signal. It also applies to the case of a system
driven by squeezed noise, but here there is a physical restriction to
emission/absorption coupling only. For the special case of a cavity mode where
the dynamics is linear, we are able to derive explicitly the filtered estimate
$\pi_t (a)$ for the mode annihilator $a$ based on the homodyne quadrature
observations up to time $t$.
