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The extended Kalman filter (EKF) is a popularstate estimation method for nonlinear dynamical models. The model errorcovariance matrix is often seen as a tuning parameter in EKF, which is oftensimply postulated by the user. In this paper, we study the filter likelihoodtechnique for estimating the parameters of the model error covariance matrix.The approach is based on computing the likelihood of the covariance matrixparameters using the filtering output. We show that (a) the importance of themodel error covariance matrix calibration depends on the quality of theobservations, and that (b) the estimation approach yields a well-tuned EKF interms of the accuracy of the state estimates and model predictions. For ournumerical experiments, we use the two-layer quasi-geostrophic model that isoften used as a benchmark model for numerical weather prediction

Estimating model error covariance matrix parameters in extended Kalman filtering