Robust nonlinear estimation for a Fabry-Perot optical cavity

This paper applies the theory of a discrete-time robust extended Kalman filter (REKF) to the problem of estimating the ring-down (or decay) time constant for a Fabry-Perot optical cavity with uncertain cavity dynamics. The ring-down time constant (reciprocal of the cavity coupling coefficient) is defined as the time taken by the light inside the cavity to decay to 1/e of its initial intensity. The online estimation of the decay constant for a cavity is a direct indication of the absorbing species contained in it and can be used to detect various chemicals, such as explosives and their related compounds. Due to various artifacts introduced by uncontrollable factors in the experimental setup, unmodeled sensor gains, variations in the frequency of the input laser, and the fluctuations in the resonant frequency of the cavity, it is difficult to perfectly model the dynamics for such an optical cavity. The model uncertainties introduced into the cavity dynamics due to such effects are model as norm-bound uncertainties and the exogenous noise is modeled in terms of a sum quadratic constraint (SQC). The REKF Riccati and filter recursion equations are then applied to estimate the ring-down time constant of the uncertain cavity model.