Weak-force sensing in optomechanical systems with Kalman filtering

Abstract

We investigate the weak-force sensing in an optomechanical resonator by Kalman filter. By discretizing the continuous-time optomechanical system, the state of the resulting system is estimated by the unbiased minimum variance Kalman filter. Subsequently, the external stochastic force is estimated, provided that all noises in the system are white and Gaussian. Furthermore, the accuracy of force estimation, described by the mean squared error, is derived theoretically. The proposed algorithm is finally illustrated by comparing the theoretical accuracy with the numerical accuracy in an explicit example.