Related papers: Exact nonlinear state estimation
Estimating the state of a dynamical system from partial and noisy observations is a ubiquitous problem in a large number of applications, such as probabilistic weather forecasting and prediction of epidemics. Particle filters are a widely…
Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…
An Ensemble Kalman Filter (EnKF, the predictor) is used make a large change in the state, followed by a Particle Filer (PF, the corrector) which assigns importance weights to describe non-Gaussian distribution. The weights are obtained by…
Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…
This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To…
A novel strategy is proposed to improve the accuracy of state estimation and reconstruction from low-fidelity models and sparse data from sensors. This strategy combines ensemble Data Assimilation (DA) and Machine Learning (ML) tools,…
Data assimilation combines dynamical models with observations to improve state estimates. Ensemble filters sequentially assimilate observations by updating a set of samples over time, alternating between a forecast and an analysis step.…
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…
We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…
Performing Data Assimilation (DA) at a low cost is of prime concern in Earth system modeling, particularly at the time of big data where huge quantities of observations are available. Capitalizing on the ability of Neural Networks…
Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…
Through ensemble-based data assimilation (DA), we address one of the most notorious difficulties in phase-resolved ocean wave forecast, regarding the deviation of numerical solution from the true surface elevation due to the chaotic nature…
We introduce a framework for Data Assimilation (DA) in which the data is split into multiple sets corresponding to low-rank projections of the state space. Algorithms are developed that assimilate some or all of the projected data,…
In this letter, a new filtering technique to solve a nonlinear state estimation problem has been developed. It is well known that for a nonlinear system, the prior and posterior probability density functions (pdf) are non-Gaussian in…
Compressed Estimation approaches, such as the Generalised Compressed Kalman Filter (GCKF), reduce the computational cost and complexity of high dimensional and high frequency data assimilation problems; usually without sacrificing…
Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA…
The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a…
Ensemble Kalman filters are based on a Gaussian assumption, which can limit their performance in some non-Gaussian settings. This paper reviews two nonlinear, non-Gaussian extensions of the Ensemble Kalman Filter: Gaussian anamorphosis (GA)…
Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman…
Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a…