Sequential State and Variance Estimation within the Ensemble Kalman Filter

Jonathan R. Stroud, Thomas Bengtsson

University of Pennsylvania and Bell Laboratories

May 2007

Kalman filter methods for real-time assimilation of observations and dynamical systems typically assume knowledge of the system parameters. However, relatively little work has been done on extending state estimation procedures to include parameter estimation. Here, in the context of the ensemble Kalman filter, a Monte Carlo algorithm is proposed for sequential estimation of the states and an unknown scalar observation variance. A Bayesian approach is adopted which yields analytical updating of the parameter distribution. Our proposed assimilation algorithm extends standard ensemble methods, including serial and square-root assimilation schemes. The method is illustrated on the Lorenz 40-variable system, and is shown to be robust to system nonlinearities, sparse observation networks, and the choice of the initial prior distribution.

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