This work presents a robust approach to estimate the continuously varying phase of an optical system. Here we extend the adaptive homodyne estimator scheme by using a nonlinear guaranteed cost robust filter in the feedback loop to improve the estimator performance. The nonlinear robust filter is designed by using a copy of the sector bounded nonlinear uncertainty present in the measurement of the adaptive homodyne estimator. Finally, closed loop simulations considering both linear and nonlinear

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... uncertainty are performed and the results are compared with the standard Kalman filter results. Simulation results show a significant improvement using the nonlinear filter which provides a better choice for the time varying phase estimation problem.