Related papers: A Multiresolution Ensemble Kalman Filter using Wav…
We present two methods for detecting patterns and clusters in high dimensional time-dependent functional data. Our methods are based on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant…
Nanomechanical resonant sensors are used in mass spectrometry via detection of resonance frequency jumps. There is a fundamental trade-off between detection speed and accuracy. Temporal and size resolution are limited by the resonator…
This paper develops efficient ensemble Kalman filter (EnKF) implementations based on shrinkage covariance estimation. The forecast ensemble members at each step are used to estimate the background error covariance matrix via the…
A new generation of wide-field radio interferometers designed for 21-cm surveys is being built as drift scan instruments allowing them to observe large fractions of the sky. With large numbers of antennas and frequency channels the enormous…
Motivated by the challenge of incorporating data into misspecified and multiscale dynamical models, we study a McKean-Vlasov equation that contains the data stream as a common driving rough path. This setting allows us to prove…
This study considers the data assimilation problem in coupled systems, which consists of two components (sub-systems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in…
In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold…
Velocity measurements made from multiple-epoch astronomical images of evolving objects with optically thin continuum emission (e.g. as relativistic jets or expanding supernova shells) may be confused as a result of the overlap of…
The Ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 [10] as a novel method for data assimilation: state estimation for noisily observed time-dependent problems. Since that time it has had enormous impact in many application…
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are…
The use of Kalman filtering, as well as its nonlinear extensions, for the estimation of system variables and parameters has played a pivotal role in many fields of scientific inquiry where observations of the system are restricted to a…
A Kalman filter based sequential estimator is presented in the present work. The estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows. This technique provides an augmented flow state…
Wavelets are closely related to the Schr\"odinger's wave functions and the interpretation of Born. Similarly to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach…
Precise user localization and tracking enhances energy-efficient and ultra-reliable low latency applications in the next generation wireless networks. In addition to computational complexity and data association challenges with…
Motion estimation approaches typically employ sensor fusion techniques, such as the Kalman Filter, to handle individual sensor failures. More recently, deep learning-based fusion approaches have been proposed, increasing the performance and…
It is shown how wavelets may be used to analyse the absorption properties of the Lya forest. The Discrete Wavelet Transform of a QSO spectrum is used to decompose the light fluctuations that comprise the forest into orthogonal wavelets. It…
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…
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…
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman…