2016/10/01 by Elizabeth Hou, Hou, Elizabeth, Earl Lawrence +3 · 2 citations
Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Algorithm #Alpha beta filter #Applications (stat.AP) #Artificial intelligence #Atmospheric and Oceanic Physics (physics.ao-ph) #Climate variability and models #Computer science #Covariance #Covariance intersection #Data Analysis #Data assimilation #Ensemble Kalman filter #Ensemble forecasting #Ensemble learning #Extended Kalman filter #FOS: Computer and information sciences #FOS: Physical sciences #Fast Kalman filter #Filter (signal processing) #Invariant extended Kalman filter #Kalman filter #Mathematics #Meteorological Phenomena and Simulations #Moving horizon estimation #Physics #Plant Water Relations and Carbon Dynamics #Rank (graph theory) #State space #Statistics #Statistics and Probability (physics.data-an) #physics.ao-ph #physics.data-an #stat.AP
paper · pdf · doi:10.48550/arxiv.1610.00195
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2016/10/01 · openalex created_date 2016/10/14 · arxiv created 2021/03/11 · arxiv updated 2021/03/12 · openalex updated_date 2026/08/05
The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the well-known Kalman filter. However, its performance can suffer when the ensemble size is smaller than the state space, as is often necessary for computationally burdensome models. This scenario means that the empirical estimate of the state covariance is not full rank and possibly quite noisy. To solve this problem in this high dimensional regime, we propose a computationally fast and easy to implement algorithm called the penalized ensemble Kalman filter (PEnKF). Under certain conditions, it can be theoretically proven that the PEnKF will be accurate (the estimation error will converge to zero) despite having fewer ensemble members than state dimensions. Further, as contrasted to localization methods, the proposed approach learns the covariance structure associated with the dynamical system. These theoretical results are supported with simulations of several non-linear and high dimensional systems.