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We consider the problem of estimating unknown parameters in stochasticdifferential equations driven by colored noise, which we model as a sequence ofGaussian stationary processes with decreasing correlation time. We aim to inferparameters in the limit equation, driven by white noise, given observations ofthe colored noise dynamics. We consider both the maximum likelihood and thestochastic gradient descent in continuous time estimators, and we propose tomodify them by including filtered data. We provide a convergence analysis forour estimators showing their asymptotic unbiasedness in a general setting andasymptotic normality under a simplified scenario.

Filtered data based estimators for stochastic processes driven by colored noise