  We study the position estimation of a mechanical oscillator undergoing both
detuned parametric amplification and continuous quantum measurement. This
model, which can be utilised to produce squeezed states, is applied to a
general optoelectromechanical system. Using a stochastic master equation
formalism, we derive general formulae for the reduction in position uncertainty
of one quadrature of motion. The filter for extracting the optimal position
estimate from the measurement record is derived. We also find that since this
scheme does not work far into the back-action dominated regime, implementing
resolved-sideband cooling improves the squeezing only marginally.
