Theoretical analysis of the Resampled Ensemble Kalman Filter

Music City Center 

Filtering involves the real-time estimation of a dynamical system's state from incomplete and noisy observations. For high-dimensional systems, ensemble Kalman filters are often the preferred method. These filters use an ensemble of interacting particles to sequentially estimate the system's state as new observations come in. While ensemble Kalman filters are widely successful in practice, their theoretical analysis is complicated by the complex dependencies between particles. This presentation introduces ensemble Kalman filters that include an additional resampling step to break these dependencies. The resulting algorithm allows for a non-asymptotic, dimension-free theoretical analysis that improves and extends existing results for filters without resampling, while maintaining comparable performance in various numerical examples.

ensemble Kalman filter

effective dimension

nonasymptotic error bounds

data assimilation