Sequential State and Variance Estimation within the Ensemble Kalman Filter
Jonathan R. Stroud, Thomas Bengtsson
University of Pennsylvania and Bell Laboratories
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.
The manuscript is available in PDF format.