Related papers: A localization technique for ensemble Kalman filte…
We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter…
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…
This paper addresses the problem of designing the {\it continuous-discrete} unscented Kalman filter (UKF) implementation methods. More precisely, the aim is to propose the MATLAB-based UKF algorithms for {\it accurate} and {\it robust}…
In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this…
Variational inference (VI) combined with Bayesian nonlinear filtering produces state-of-the-art results for latent time-series modeling. A body of recent work has focused on sequential Monte Carlo (SMC) and its variants, e.g., forward…
Data assimilation (DA) integrates observational information with model predictions to improve state estimation in complex systems. While filtering provides the basis for online forecasts by using only past and present observations, it can…
In the process of reproducing the state dynamics of parameter dependent distributed systems, data from physical measurements can be incorporated into the mathematical model to reduce the parameter uncertainty and, consequently, improve the…
This paper studies the distributed state estimation problem for a class of discrete-time stochastic systems with nonlinear uncertain dynamics over time-varying topologies of sensor networks. An extended state vector consisting of the…
Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewed as a derivative-free optimization method. In its most…
The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…
We present a novel variational quantum framework for nonlinear partial differential equation (PDE) constrained optimization problems. The proposed work extends the recently introduced bi-level variational quantum PDE constrained…
The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…
Mathematical modeling and simulation of complex physical systems based on partial differential equations (PDEs) have been widely used in engineering and industrial applications. To enable reliable predictions, it is crucial yet challenging…
Accurate modeling and prediction of complex physical systems often rely on data assimilation techniques to correct errors inherent in model simulations. Traditional methods like the Ensemble Kalman Filter (EnKF) and its variants as well 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…
In data assimilation, an ensemble provides a way to propagate the probability density of a system described by a nonlinear prediction model. Although a large ensemble size is required for statistical accuracy, the ensemble size is typically…
Geometry of the state space is known to play a crucial role in many applications of Kalman filters, especially robotics and motion tracking. The Lie group-centric approach is currently very common, although a Riemannian approach has also…
The objective scaling ensemble approach is a novel two-phase heuristic for integer linear programming problems shown to be effective on a wide variety of integer linear programming problems. The technique identifies and aggregates multiple…
The Ensemble Kalman Inversion (EKI) method is widely used for solving inverse problems, leveraging ensemble-based techniques to iteratively refine parameter estimates. Despite its versatility, the accuracy of EKI is constrained by the…
Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the ensemble Kalman filter to reconstruct an elastic rigid…