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Ensemble Kalman filter (EnKF) has been widely used in state estimation and parameter estimation for the dynamic system where observational data is obtained sequentially in time. To reduce uncertainty and accelerate posterior inference, a…

Parameter estimation has a high importance in the geosciences. The ensemble Kalman filter (EnKF) allows parameter estimation for large, time-dependent systems. For large systems, the EnKF is applied using small ensembles, which may lead to…

The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an…

In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…

Accurate estimation and prediction of trajectory is essential for the capture of any high speed target. In this paper, an extended Kalman filter (EKF) is used to track the target in the first loop of the trajectory to collect data points…

A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when…

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…

The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…

The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state-observation space. The ensemble Kalman filter (EnKF) approximates this mean-field model with an ensemble of interacting…

Many recent advances in sequential assimilation of data into nonlinear high-dimensional models are modifications to particle filters which employ efficient searches of a high-dimensional state space. In this work, we present a complementary…

Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF, necessary to obtain low variance likelihood and states estimates.…

The decentralized particle filter (DPF) was proposed recently to increase the level of parallelism of particle filtering. Given a decomposition of the state space into two nested sets of variables, the DPF uses a particle filter to sample…

Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice.…

The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in…

The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the…

Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in…

In this article, we present the elitist particle filter based on evolutionary strategies (EPFES) as an efficient approach for nonlinear system identification. The EPFES is derived from the frequently-employed state-space model, where the…

Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the…

A scheme is proposed to improve the performance of the ensemble-based Kalman Filters during the initial spin-up period. By applying the no-cost ensemble Kalman Smoother, this scheme allows the model solutions for the ensemble to be "running…

The extended Kalman filter (EKF) is a cornerstone of nonlinear state estimation, yet its performance is fundamentally limited by noise-model mismatch and linearization errors. We develop a residual-aware distributionally robust EKF that…