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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.…
Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models are involved, derivative-free optimization tools are often…
Ensemble Kalman filter techniques are widely used to assimilate observations into dynamical models. The phase space dimension is typically much larger than the number of ensemble members which leads to inaccurate results in the computed…
Accurate data assimilation (DA) for systems with piecewise-smooth or discontinuous state variables remains a significant challenge, as conventional covariance-based ensemble Kalman filter approaches often fail to effectively balance…
Traditional statements of the celebrated Kalman filter algorithm focus on the estimation of state, but not the output. For any outputs, measured or auxiliary, it is usually assumed that the posterior state estimates and known inputs are…
Continuously monitored atomic spin-ensembles allow, in principle, for real-time sensing of external magnetic fields beyond classical limits. Within the linear-Gaussian regime, thanks to the phenomenon of measurement-induced spin-squeezing,…
This paper studies an output feedback stabilization control framework for discrete-time linear systems with stochastic dynamics determined by an independent and identically distributed (i.i.d.) process. The controller is constructed with an…
State-of-the-art atomic clocks are based on the precise detection of the energy difference between two atomic levels, measured as a quantum phase accumulated in a given time interval. Optical-lattice clocks (OLCs) now operate at or near the…
Motivated by the need for accurate frequency information, a novel algorithm for estimating the fundamental frequency and its rate of change in three-phase power systems is developed. This is achieved through two stages of Kalman filtering.…
Kalman Filter requires the true parameters of the model and solves optimal state estimation recursively. Expectation Maximization (EM) algorithm is applicable for estimating the parameters of the model that are not available before Kalman…
The ensemble empirical mode decomposition (EEMD) and its complete variant (CEEMDAN) are adaptive, noise-assisted data analysis methods that improve on the ordinary empirical mode decomposition (EMD). All these methods decompose possibly…
Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For…
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…
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…
We consider the problem of selecting an optimal set of sensor precisions to estimate the states of a non-linear dynamical system using an Ensemble Kalman filter and an Unscented Kalman filter, which uses random and deterministic ensembles…
The Ensemble Kalman inversion (EKI) method is a method for the estimation of unknown parameters in the context of (Bayesian) inverse problems. The method approximates the underlying measure by an ensemble of particles and iteratively…
The purpose of this review is to present a comprehensive overview of the theory of ensemble Kalman-Bucy filtering for continuous-time, linear-Gaussian signal and observation models. We present a system of equations that describe the flow of…
Data assimilation (DA) integrates numerical model forecasts with observations to achieve the optimal state estimation. Ensemble-based methods, such as the ensemble Kalman filter (EnKF), are widely used for state estimation for…
Creating stable superposed states of matter is one of the most intriguing aspects of quantum physics, leading to a variety of counter-intuitive scenarios along with a possibility of restructuring the way we understand, process and…
Large language models (LLMs) have demonstrated remarkable capabilities in generating programs from natural language descriptions, yet ensuring their correctness without an external oracle remains a critical challenge. To solve the…