Related papers: Filtering methods for coupled inverse problems
Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the…
This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and…
The objective is to investigate the advantages and performance of Extended Kalman Filter for the estimation of non-linear system where linearization takes place about a trajectory that was continually updated with the state estimates…
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
In this paper, a new filter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system.…
Ensemble models refer to methods that combine a typically large number of classifiers into a compound prediction. The output of an ensemble method is the result of fitting a base-learning algorithm to a given data set, and obtaining diverse…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…
General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases…
State-space models can be used to incorporate subject knowledge on the underlying dynamics of a time series by the introduction of a latent Markov state-process. A user can specify the dynamics of this process together with how the state…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
This paper uses a probabilistic approach to analyze the converge of an ensemble Kalman filter solution to an exact Kalman filter solution in the simplest possible setting, the scalar case, as it allows us to build upon a rich literature of…
This paper is an attempt to solve an important class of hypersingular integral equations of the second kind. To this end, we apply a new weighted and modified perturbation method which includes some special cases of the Adomian…
We consider the solution of inverse problems in dynamic contrast-enhanced imaging by means of Ensemble Kalman Filters. Our quantity of interest is blood perfusion, i.e. blood flow rates in tissue. While existing approaches to compute blood…
The ensemble Kalman filter (EnKF) is widely used for nonlinear and high-dimensional state estimation because it replaces complex covariance propagation with simple ensemble statistics. However, conventional EnKF implementations can become…
This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter which provides an exact solution for the linear Gaussian…
We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance…
We provide estimators for a large class of inverse problems, including nonlinear inverse problems. Using complexity regularization technics we provide adaptive estimators achieving the best rate over the collection of models.