Related papers: A Langevinized Ensemble Kalman Filter for Large-Sc…
The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state…
The ensemble Kalman filter is a well-known and celebrated data assimilation algorithm. It is of particular relevance as it used for high-dimensional problems, by updating an ensemble of particles through a sample mean and covariance…
The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here we explore another promising solution in which diffusion models are used to…
Ensemble-based data assimilation (DA) methods have become increasingly popular due to their inherent ability to address nonlinear dynamic problems. However, these methods often face a trade-off between analysis accuracy and computational…
Heavy tails is a common feature of filtering distributions that results from the nonlinear dynamical and observation processes as well as the uncertainty from physical sensors. In these settings, the Kalman filter and its ensemble version -…
The ensemble Kalman filter (EnKF) (Evensen, 2009) has proven effective in quantifying uncertainty in a number of challenging dynamic, state estimation, or data assimilation, problems such as weather forecasting and ocean modeling. In these…
Controlled interacting particle systems such as the ensemble Kalman filter (EnKF) and the feedback particle filter (FPF) are numerical algorithms to approximate the solution of the nonlinear filtering problem in continuous time. The…
A modification scheme to the ensemble Kalman filter (EnKF) is introduced based on the concept of the unscented transform (Julier et al., 2000; Julier and Uhlmann, 2004), which therefore will be called the ensemble unscented Kalman filter…
Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models are involved, derivative-free optimization tools are often…
The Kalman filter is a fundamental tool for state estimation in dynamical systems. While originally developed for linear Gaussian settings, it has been extended to nonlinear problems through approaches such as the extended and unscented…
We present a new type of the EnKF for data assimilation in spatial models that uses diagonal approximation of the state covariance in the wavelet space to achieve adaptive localization. The efficiency of the new method is demonstrated on an…
We propose a new type of the Ensemble Kalman Filter (EnKF), which uses the Fast Fourier Transform (FFT) for covariance estimation from a very small ensemble with automatic tapering, and for a fast computation of the analysis ensemble by…
Although data assimilation originates from control theory, the relationship between modern data assimilation methods in geoscience and model predictive control has not been extensively explored. In the present paper, I discuss that the…
Several variations of the Kalman filter algorithm, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are widely used in science and engineering applications. In this paper, we introduce two algorithms of…
Ensemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequential data assimilation, where state vectors are of huge…
The Bootstrap Particle Filter (BPF) and the Ensemble Kalman Filter (EnKF) are two widely used methods for sequential Bayesian filtering: the BPF is asymptotically exact but can suffer from weight degeneracy, while the EnKF scales well in…
This paper presents the machine learning-based ensemble conditional mean filter (ML-EnCMF) -- a filtering method based on the conditional mean filter (CMF) previously introduced in the literature. The updated mean of the CMF matches that of…
We propose a regularization method for ensemble Kalman filtering (EnKF) with elliptic observation operators. Commonly used EnKF regularization methods suppress state correlations at long distances. For observations described by elliptic…
This paper develops an efficient implementation of the ensemble Kalman filter based on a modified Cholesky decomposition for inverse covariance matrix estimation. This implementation is named EnKF-MC. Background errors corresponding to…
Data assimilation is a method of uncertainty quantification to estimate the hidden true state by updating the prediction owing to model dynamics with observation data. As a prediction model, we consider a class of nonlinear dynamical…