Related papers: Unscented Kalman Inversion: Efficient Gaussian App…
The ensemble Kalman filter is a well-known and celebrated data assimilation algorithm. It is of particular relevance as it used for high-dimensional problems, by updating an ensemble of particles through a sample mean and covariance…
The Unscented Kalman Filter (UKF) is a ubiquitous tool for nonlinear state estimation; however, its performance is limited by the static parameterization of the Unscented Transform (UT). Conventional weighting schemes, governed by fixed…
The unscented Kalman filter (UKF) is a commonly used algorithm capable of estimating the states of nonlinear dynamic systems. It carefully chooses a set of sample points, called sigma points that capture the nonlinear system states…
Orientation estimation for 3D objects is a common problem that is usually tackled with traditional nonlinear filtering techniques such as the extended Kalman filter (EKF) or the unscented Kalman filter (UKF). Most of these techniques assume…
Latent variable time-series models are among the most heavily used tools from machine learning and applied statistics. These models have the advantage of learning latent structure both from noisy observations and from the temporal ordering…
We propose a new regularisation strategy for the classical ensemble Kalman inversion (EKI) framework. The strategy consists of: (i) an adaptive choice for the regularisation parameter in the update formula in EKI, and (ii) criteria for the…
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…
Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…
The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilizing a derivative-free higher-order approximation by approximating a Gaussian distribution rather than…
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…
Ensemble Kalman Inversion (EKI) has been a very popular algorithm used in Bayesian inverse problems. It samples particles from a prior distribution, and introduces a motion to move the particles around in pseudo-time. As the pseudo-time…
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…
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the…
Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse…
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…
Black-box variational inference (BBVI) with Gaussian mixture families offers a flexible approach for approximating complex posterior distributions without requiring gradients of the target density. However, standard numerical optimization…
Dynamic operation of biological processes, such as anaerobic digestion (AD), requires reliable process monitoring to guarantee stable operating conditions at all times. Unscented Kalman filters (UKF) are an established tool for nonlinear…
Ensemble Kalman inversion is a parallelizable derivative-free method to solve inverse problems. The method uses an ensemble that follows the Kalman update formula iteratively to solve an optimization problem. The ensemble size is crucial to…
Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems.…