# The Ensemble Kalman Filter: A Signal Processing Perspective

## TL;DR

This paper reviews the ensemble Kalman filter (EnKF) from a signal processing perspective, explaining its derivation, challenges, and relations to other filters, aiming to facilitate its adoption and inspire new research directions.

## Contribution

It provides a comprehensive, signal processing-oriented overview of EnKF, including derivations, extensions, and a survey of literature, tailored for signal processing researchers.

## Key findings

- EnKF handles high-dimensional, nonlinear, non-Gaussian problems effectively.
- The paper clarifies the relation between EnKF, sigma-point KF, and particle filters.
- Simulation examples demonstrate EnKF's practical performance on benchmark problems.

## Abstract

The ensemble Kalman filter (EnKF) is a Monte Carlo based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear and non-Gaussian state estimation problems. Its ability to handle state dimensions in the order of millions has made the EnKF a popular algorithm in different geoscientific disciplines. Despite a similarly vital need for scalable algorithms in signal processing, e.g., to make sense of the ever increasing amount of sensor data, the EnKF is hardly discussed in our field. This self-contained review paper is aimed at signal processing researchers and provides all the knowledge to get started with the EnKF. The algorithm is derived in a KF framework, without the often encountered geoscientific terminology. Algorithmic challenges and required extensions of the EnKF are provided, as well as relations to sigma-point KF and particle filters. The relevant EnKF literature is summarized in an extensive survey and unique simulation examples, including popular benchmark problems, complement the theory with practical insights. The signal processing perspective highlights new directions of research and facilitates the exchange of potentially beneficial ideas, both for the EnKF and high-dimensional nonlinear and non-Gaussian filtering in general.