Related papers: An extended sampling-ensemble Kalman filter approa…
Enforcing sparse structure within learning has led to significant advances in the field of data-driven discovery of dynamical systems. However, such methods require access not only to time-series of the state of the dynamical system, but…
Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a…
Many interventional surgical procedures rely on medical imaging to visualise and track instruments. Such imaging methods not only need to be real-time capable, but also provide accurate and robust positional information. In ultrasound…
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…
A complete solution for an inverse problem needs five main steps: choice of basis functions for discretization, determination of the order of the model, estimation of the hyperparameters, estimation of the solution, and finally,…
Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is…
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…
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…
Dynamic Mode Decomposition (DMD) and its extensions (EDMD) have been at the forefront of data-based approaches to Koopman operators. Most (E)DMD algorithms assume that the entire state is sampled at a uniform sampling rate. In this paper,…
A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent…
In this work, we propose an innovative iterative direct sampling method to solve nonlinear elliptic inverse problems from a limited number of pairs of Cauchy data. It extends the original direct sampling method (DSM) by incorporating an…
The use of model order reduction techniques in combination with ensemble-based methods for estimating the state of systems described by nonlinear partial differential equations has been of great interest in recent years in the data…
Nonlinear filtering problems are encountered in many applications, and one solution approach is the extended Kalman filter, which is not always convergent. Therefore, it is crucial to identify conditions under which the extended Kalman…
The reliability and precision of dynamic database are vital for the optimal operating and global control of integrated energy systems. One of the effective ways to obtain the accurate states is state estimations. A novel robust dynamic…
Accurate estimation and prediction of trajectory is essential for the capture of any high speed target. In this paper, an extended Kalman filter (EKF) is used to track the target in the first loop of the trajectory to collect data points…
The ensemble Kalman inversion (EKI), as a derivative-free methodology, has been widely used in the parameter estimation of inverse problems. Unfortunately, its cost may become moderately large for systems described by high dimensional…
This paper addresses the inverse problem of qualitatively recovering a clamped cavity in a thin elastic plate using far-field measurements. We present a strengthened analysis of the linear sampling method by carefully examining the range of…
We present a method of using classical wavelet based multiresolution analysis to separate scales in model and observations during data assimilation with the ensemble Kalman filter. In many applications, the underlying physics of a phenomena…
Bayesian linear inverse problems aim to recover an unknown signal from noisy observations, incorporating prior knowledge. This paper analyses a data-dependent method to choose the scale parameter of a Gaussian prior. The method we study…
The motivation of this work is to improve the performance of standard stacking approaches or ensembles, which are composed of simple, heterogeneous base models, through the integration of the generation and selection stages for regression…