  Data assimilation is the task to combine evolution models and observational
data in order to produce reliable predictions. In this paper, we focus on
ensemble-based recursive data assimilation problems. Our main contribution is a
hybrid filter that allows one to adaptively bridge between ensemble Kalman and
particle filters. While ensemble Kalman filters are robust and applicable to
strongly nonlinear systems even with small and moderate ensemble sizes,
particle filters are asymptotically consistent in the large ensemble size
limit. We demonstrate numerically that our hybrid approach can improve the
performance of both Kalman and particle filters at moderate ensemble sizes. We
also show how to implement the concept of localization into a hybrid filter,
which is key to its applicability to spatially extended systems.
