A method is proposed for determining dynamical and observational noise parameters in state and parameter identification from time series using Kalman filters. The noise covariances are estimated in a secondary optimization by maximizing the predictive likelihood of the data. The approach is based on internal consistency; for the correct noise parameters, the uncertainty projected by the Kalman filter matches the actual predictive uncertainty. The method is able to disentangle dynamical and

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... vational noise. The algorithm is demonstrated for the linear, extended, and unscented Kalman filters using an Ornstein-Uhlenbeck process, the noise-driven Lorenz system, and van der Pol oscillator as well as a paleoclimatic ice-core record as examples. The approach is also applicable to the ensemble Kalman filter and can be readily extended to non-Gaussian estimation frameworks such as Gaussian-sum filters and particle filters.