Related papers: Filter Based Methods For Statistical Linear Invers…
In this paper, we study the inverse acoustic medium scattering problem to reconstruct the unknown inhomogeneous medium from far field patterns of scattered waves. We propose the reconstruction scheme based on the Kalman filter, which…
We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed…
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 an adaptive Kalman filter for a linear dynamic system perturbed by an additive disturbance. The objective is to estimate both of the state and the unknown disturbance concurrently, while learning the disturbance as a…
Stochastic parameterizations are increasingly being used to represent the uncertainty associated with model errors in ensemble forecasting and data assimilation. One of the challenges associated with the use of these parameterizations is…
This paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix Lie group with invariance properties. The problem of an invariant continuous-time model with discrete-time measurements is cast into…
Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data is acquired sequentially. The Kalman filter plays a…
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…
We study the inverse medium scattering problem to reconstruct the unknown inhomogeneous medium from the far-field patterns of scattered waves. The inverse scattering problem is generally ill-posed and nonlinear, and the iterative…
This paper examines learning the optimal filtering policy, known as the Kalman gain, for a linear system with unknown noise covariance matrices using noisy output data. The learning problem is formulated as a stochastic policy optimization…
Recently, the stochastic asymptotical regularization (SAR) has been developed in (\emph{Inverse Problems}, 39: 015007, 2023) for the uncertainty quantification of the stable approximate solution of linear ill-posed inverse problems. In this…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…
In this work, we consider a sensor selection drawn at random by a sampling with replacement policy for a linear time-invariant dynamical system subject to process and measurement noise. We employ the Kalman filter to estimate the state of…
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…
The article is devoted to the problem of synthesis of observers of state variables for linear stationary objects operating under conditions of noise or disturbances in the measurement channel. The paper considers a fully observable linear…
We provide a clear and concise introduction to the subjects of inverse problems and data assimilation, and their inter-relations. The first part of our notes covers inverse problems; this refers to the study of how to estimate unknown model…
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.…
The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization…