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

Force Tracking in Cavity Optomechanics with a Two-Level Quantum System by Kalman Filtering