  We demonstrate optimal state estimation for a cavity optomechanical system
through Kalman filtering. By taking into account nontrivial experimental noise
sources, such as colored laser noise and spurious mechanical modes, we
implement a realistic state-space model. This allows us to obtain the
conditional system state, i.e., conditioned on previous measurements, with
minimal least-square estimation error. We apply this method for estimating the
mechanical state, as well as optomechanical correlations both in the weak and
strong coupling regime. The application of the Kalman filter is an important
next step for achieving real-time optimal (classical and quantum) control of
cavity optomechanical systems.
