What the collapse of the ensemble Kalman filter tells us about particle filters
Provides theoretical insight for meteorologists and data assimilation researchers into why localized particle filters can work in high-dimensional problems.
The paper reconciles the apparent contradiction between the success of the ensemble Kalman filter (EnKF) in high-dimensional meteorology and the known collapse of particle filters, showing that EnKF's performance supports the localization of particle filters in high-dimensional settings.
The ensemble Kalman filter (EnKF) is a reliable data assimilation tool for high-dimensional meteorological problems. On the other hand, the EnKF can be interpreted as a particle filter, and particle filters collapse in high-dimensional problems. We explain that these seemingly contradictory statements offer insights about how particle filters function in certain high-dimensional problems, and in particular support recent efforts in meteorology to "localize" particle filters, i.e., to restrict the influence of an observation to its neighborhood.