  This paper proposes new methodology for sequential state and parameter
estimation within the ensemble Kalman filter. The method is fully Bayesian and
propagates the joint posterior density of states and parameters over time. In
order to implement the method we consider two representations of the marginal
posterior distribution of the parameters: a grid-based approach and a Gaussian
approximation. Contrary to existing algorithms, the new method explicitly
accounts for parameter uncertainty and provides a formal way to combine
information about the parameters from data at different time periods. The
method is illustrated and compared to existing approaches using simulated and
real data.
