Articles | Volume 21, issue 5
Nonlin. Processes Geophys., 21, 919–927, 2014
https://doi.org/10.5194/npg-21-919-2014
Nonlin. Processes Geophys., 21, 919–927, 2014
https://doi.org/10.5194/npg-21-919-2014

Research article 01 Sep 2014

Research article | 01 Sep 2014

Estimating model error covariance matrix parameters in extended Kalman filtering

A. Solonen1,2, J. Hakkarainen2, A. Ilin3, M. Abbas3, and A. Bibov1 A. Solonen et al.
  • 1Lappeenranta University of Technology, Lappeenranta, Finland
  • 2Finnish Meteorological Institute, Helsinki, Finland
  • 3Aalto University, Helsinki, Finland

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

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