# The Ensemble Kalman Filter: A Signal Processing Perspective

arXiv: https://arxiv.org/abs/1702.08061 · HTML: https://mlsanity.com/paper/1702.08061/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2017.

## Built on by (most cited first, 17 of 17)

- [Auto-differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2107.07687/) (2021)
- [A System for Imitation Learning of Contact-Rich Bimanual Manipulation Policies](https://mlsanity.com/paper/2208.00596/) (2022)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Reduced-Order Autodifferentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2301.11961/) (2023)
- [Non-Asymptotic Analysis of Ensemble Kalman Updates: Effective Dimension and Localization](https://mlsanity.com/paper/2208.03246/) (2022)
- [The Rank-Reduced Kalman Filter: Approximate Dynamical-Low-Rank Filtering In High Dimensions](https://mlsanity.com/paper/2306.07774/) (2023)
- [Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference](https://mlsanity.com/paper/2312.05910/) (2023)
- [A unifying framework for generalised Bayesian online learning in non-stationary environments](https://mlsanity.com/paper/2411.10153/) (2024)
- [Regularization-Based Efficient Continual Learning in Deep State-Space Models](https://mlsanity.com/paper/2403.10123/) (2024)
- [Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach](https://mlsanity.com/paper/2504.20319/) (2025)
- [Enhancing Energy Efficiency and Reliability in Autonomous Systems Estimation using Neuromorphic Approach](https://mlsanity.com/paper/2307.07963/) (2023)
- [Learning a Stochastic Differential Equation Model of Tropical Cyclone Intensification from Reanalysis and Observational Data](https://mlsanity.com/paper/2601.08116/) (2026)
- [DBPnet: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Wheel Load Estimation](https://mlsanity.com/paper/2605.24860/) (2026)
- [pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements](https://mlsanity.com/paper/2510.27503/) (2025)
- [Prequential posteriors](https://mlsanity.com/paper/2511.17721/) (2025)
- [Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance](https://mlsanity.com/paper/2601.16425/) (2026)
- [Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2605.13174/) (2026)

## Abstract (arXiv)

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.