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Kalman filter based estimation of decay time for a multimode optical cavity

We develop an extended Kalman filter to estimate the ring-down time of a multimode Fabry-Perot optical cavity with a pulse train input. First the extended Kalman filter is applied to data generated from a simulator to show that the estimate of the filter converges to the expected value of the ring-down time. It is also shown that the multimode filter improves the estimation performance, compared to a simplified filter designed from a single-mode model. Then the filter is applied to a set of experimentally obtained output intensity data.