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In many physical applications, the system's state varies with spatial variables as well as time. The state of such systems is modelled by partial differential equations and evolves on an infinite-dimensional space. Systems modelled by…
The ensemble Kalman filter (EnKF) is widely used for nonlinear and high-dimensional state estimation because it replaces complex covariance propagation with simple ensemble statistics. However, conventional EnKF implementations can become…
Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters - show performance degradation when applied to nonlinear systems whose uncertainty follows…
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 Kalman filter is a fundamental filtering algorithm that fuses noisy sensory data, a previous state estimate, and a dynamics model to produce a principled estimate of the current state. It assumes, and is optimal for, linear models and…
The phase-field approach to brittle fracture provides a continuum framework for modeling crack initiation and propagation without explicit representation of discrete crack surfaces, provided the spatial discretization is fine enough to…
Autonomous vehicles have gained significant attention due to technological advancements and their potential to transform transportation. A critical challenge in this domain is precise localization, particularly in LiDAR-based map matching,…
The Ensemble Kalman Filter (EnKF) is a popular estimation technique in the geosciences. It is used as a numerical tool for state vector prognosis and parameter estimation. The EnKF can, for example, help to evaluate the geothermal potential…
In conventional distributed Kalman filtering, employing diffusion strategies, each node transmits its state estimate to all its direct neighbors in each iteration. In this paper we propose a partial diffusion Kalman filter (PDKF) for state…
In GNSS-denied underwater environments, individual unmanned underwater vehicles (UUVs) suffer from unbounded dead-reckoning drift, making collaborative navigation crucial for accurate state estimation. However, the severe communication…
An Ensemble Kalman Filter (EnKF, the predictor) is used make a large change in the state, followed by a Particle Filer (PF, the corrector) which assigns importance weights to describe non-Gaussian distribution. The weights are obtained by…
The accuracy of Earth system models is compromised by unknown and/or unresolved dynamics, making the quantification of systematic model errors essential. While a model parameter estimation, which allows parameters to change…
Two central problems in modern control theory are the controller design problem: which deals with designing a control law for the dynamical system, and the state estimation problem (observer design problem): which deals with computing an…
In this paper, the ensemble consider Kalman filter is proposed to mitigate the negative effects of uncertain parameters in nonlinear dynamic and measurement models. The ensemble Kalman filter can avoid using the Jacobian matrices and reduce…
The ensemble random forest filter (ERFF) is presented as an alternative to the ensemble Kalman filter (EnKF) for the purpose of inverse modeling. The EnKF is a data assimilation approach that forecasts and updates parameter estimates…
The most accurate version of the unscented Kalman filter (UKF) involves the construction of two ensembles. To reduce computational cost, however, UKF is often implemented without the second ensemble. This simplification comes at a price,…
We examine the problem of time delay estimation, or temporal calibration, in the context of multisensor data fusion. Differences in processing intervals and other factors typically lead to a relative delay between measurement updates from…
This work addresses the critical lack of precision in state estimation in the Kalman filter for 3D multi-object tracking (MOT) and the ongoing challenge of selecting the appropriate motion model. Existing literature commonly relies on…
A priori state vector and error covariance computation for the Unscented Kalman Filter (UKF) is described. The original UKF propagates multiple sigma points to compute the a priori mean state vector and the error covariance, resulting in a…
The ensemble Kalman filter (EnKF) is a Monte Carlo based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear and non-Gaussian state estimation problems. Its ability to handle state dimensions in the…