Related papers: Filtering methods for coupled inverse problems
We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…
The Ensemble Kalman filter and Ensemble square root filters are data assimilation methods used to combine high dimensional nonlinear models with observed data. These methods have proved to be indispensable tools in science and engineering…
The Ensemble Kalman Filter method can be used as an iterative particle numerical scheme for state dynamics estimation and control--to--observable identification problems. In applications it may be required to enforce the solution to satisfy…
Ensemble Kalman methods were initially developed to solve nonlinear data assimilation problems in oceanography, but are now popular in applications far beyond their original use cases. Of particular interest is climate model calibration. As…
In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate…
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.…
This work proposes ensemble Kalman randomized maximum likelihood estimation, a new derivative-free method for performing randomized maximum likelihood estimation, which is a method that can be used to generate approximate samples from…
In this paper, the ensemble consider Kalman filter is proposed to mitigate the negative effects of uncertain parameters in nonlinear dynamic and measurement models. The ensemble Kalman filter can avoid using the Jacobian matrices and reduce…
Ensemble Kalman methods solve problems in domains such as filtering and inverse problems with interacting particles that evolve over time. For computationally expensive problems, the cost of attaining a high accuracy quickly becomes…
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…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
Nonlinear Bayesian update for a prior ensemble is proposed to extend traditional ensemble Kalman filtering to settings characterized by non-Gaussian priors and nonlinear measurement operators. In this framework, the observed component is…
We describe a convergence acceleration technique for unconstrained optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average…
Several numerical tools designed to overcome the challenges of smoothing in a nonlinear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear…
It has been proposed that classical filtering methods, like the Kalman filter and 3DVAR, can be used to solve linear statistical inverse problems. In the work of Iglesias, Lin, Lu, & Stuart (2017), error estimates were obtained for this…
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…
We propose an affine-mapping based variational Ensemble Kalman filter for sequential Bayesian filtering problems with generic observation models. Specifically, the proposed method is formulated as to construct an affine mapping from the…
This paper introduces a computational framework to incorporate flexible regularization techniques in ensemble Kalman methods for nonlinear inverse problems. The proposed methodology approximates the maximum a posteriori (MAP) estimate of a…
We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors…
Kalman Filtering problems often have inherent and known constraints in the physical dynamics that are not exploited despite potentially significant gains (e.g., fixed speed of a motor). In this paper, we review existing methods and propose…