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

## TL;DR

This paper develops a Kalman filtering approach for accurately estimating time-varying forces in cavity optomechanical systems affected by backaction noise, with theoretical analysis and numerical validation.

## Contribution

It introduces a Kalman filtering method for waveform estimation of forces in two-level optomechanical systems, including theoretical accuracy analysis and numerical demonstration.

## Key findings

- Kalman filter effectively estimates time-varying forces
- Theoretical mean squared error matches numerical results
- Proposed method handles backaction noise in optomechanics

## Abstract

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.