  This paper investigates waveform estimation (tracking) of the time-varying
force in a two-level optomechanical system with backaction noise by Kalman
filtering. It is assumed that the backaction and measurement noises are
Gaussian and white. By discretizing the continuous-time optomechanical system,
the state of the resulting system can be estimated by the unbiased minimum
variance Kalman filtering. Then an estimator of the time-varying force is
obtained, provided that the external force is also in discrete time.
Furthermore, the accuracy of the force estimation, described by the mean
squared error, is derived theoretically. Finally, the feasibility of the
proposed algorithm is illustrated by comparing the theoretical accuracy with
the numerical accuracy in a numerical example.
