Understanding the Ensemble Kalman Filter
Matthias Katzfuss, Jonathan R. Stroud and Christopher K. Wikle
Texas A&M University, Georgetown University, and University of Missouri
December 2016
The ensemble Kalman filter (EnKF) is a computational technique for approximate inference in
state-space models. In typical applications, the state vectors are large spatial fields that
are observed sequentially over time. The EnKF approximates the Kalman filter by representing
the distribution of the state with an ensemble of draws from that distribution. The ensemble
members are updated based on newly available data by shifting instead of reweighting, which
allows the EnKF to avoid the degeneracy problems of reweighting-based algorithms such as the
particle filter. Taken together the ensemble representation and shifting-based updates make
the EnKF computationally feasible for extremely high-dimensional state spaces. The EnKF is
successfully used in data assimilation applications with tens of millions of dimensions. While
it implicitly assumes a linear Gaussian state-space model, it has also turned out to be remarkably
robust to deviations from these assumptions in many applications. Despite it successes, the EnKF
is largely unknown in the statistics community. We aim to change that with the present article,
and to entice more statisticians to work on this topic.
The manuscript is available in PDF format.