Related papers: Dynamical Low-Rank Approximations for Kalman Filte…
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…
The ensemble Kalman filter (EnKF) has become a standard methodology for state estimation in high-dimensional systems, yet its various stochastic and deterministic formulations often appear conceptually disconnected. In this paper, a unified…
Despite the cheap availability of computing resources enabling faster Monte Carlo simulations, the potential benefits of particle filtering in revealing accurate statistical information on the imprecisely known model parameters or modeling…
The numerical method of dynamical low-rank approximation (DLRA) has recently been applied to various kinetic equations showing a significant reduction of the computational effort. In this paper, we apply this concept to the linear…
The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In…
The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and…
Kalman Filter (KF) is an optimal linear state prediction algorithm, with applications in fields as diverse as engineering, economics, robotics, and space exploration. Here, we develop an extension of the KF, called a Pathspace Kalman Filter…
The Kalman filter has been adopted in acoustic echo cancellation due to its robustness to double-talk, fast convergence, and good steady-state performance. The performance of Kalman filter is closely related to the estimation accuracy of…
The high dimensionality and computational constraints associated with filtering problems in large-scale geophysical applications are particularly challenging for the Particle Filter (PF). Approximate but efficient methods such as the…
The Ensemble Kalman Filter (EnKF), as a fundamental data assimilation approach, has been widely used in many fields of the sciences and engineering. When the state variable is of high dimensional accompanied with high resolution…
Despite the importance of sparsity signal models and the increasing prevalence of high-dimensional streaming data, there are relatively few algorithms for dynamic filtering of time-varying sparse signals. Of the existing algorithms, fewer…
This paper studies an output feedback stabilization control framework for discrete-time linear systems with stochastic dynamics determined by an independent and identically distributed (i.i.d.) process. The controller is constructed with an…
The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman…
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…
A physics-based methodology for the determination of the localization function for the Ensemble Kalman Filter (EnKF) is proposed. The spatial features of such function evolve dynamically over time according to the relevant instantaneous…
We discuss properties of hierarchical Bayesian inversion through the ensemble Kalman filter (EnKF). Our focus will be primarily on deriving continuous-time limits for hierarchical inversion in the linear case. An important characteristic of…
We introduce two novel interpolatory dynamical low-rank (DLR) approximation methods for the efficient time integration of the Boltzmann-BGK equation. Both methods overcome limitations of classic DLR schemes based on orthogonal projections…
The ensemble Kalman filter (EnKF) is widely used to sample a probability density function (pdf) generated by a stochastic model conditioned by noisy data. This pdf can be either a joint posterior that describes the evolution of the state of…
Data assimilation has been applied to coastal hydrodynamic models to better estimate system states or parameters by incorporating observed data into the model. Kalman Filter (KF) is one of the most studied data assimilation methods whose…
The ensemble Kalman filter (EnKF) is a popular technique for performing inference in state-space models (SSMs), particularly when the dynamic process is high-dimensional. Unlike reweighting methods such as sequential Monte Carlo (SMC, i.e.…