  Precision measurements with quantum systems rely on our ability to trace the
differences between experimental signals to variations in unknown physical
parameters. In this Letter we derive the Fisher information and the ensuing
Cramer-Rao sensitivity limit for parameter estimation by continuous
measurements on an open quantum system. We illustrate our theory by application
to resonance fluorescence from a laser driven two-state atom and we show that
photon counting and homodyne detection records yield different sensitivity to
the atomic parameters, while none of them exceed our general result.
