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Federated learning (FL), aimed at leveraging vast distributed datasets, confronts a crucial challenge: the heterogeneity of data across different silos. While previous studies have explored discrete representations to enhance model…

Data assimilation is a method of uncertainty quantification to estimate the hidden true state by updating the prediction owing to model dynamics with observation data. As a prediction model, we consider a class of nonlinear dynamical…

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…

It is known that the conventional estimators such as extended Kalman filter (EKF) and unscented Kalman filter (UKF) may provide favorable performance; However, they may not guarantee the robustness against model uncertainty and cyber…

We propose an efficient online approximate Bayesian inference algorithm for estimating the parameters of a nonlinear function from a potentially non-stationary data stream. The method is based on the extended Kalman filter (EKF), but uses a…

Filtering - the task of estimating the conditional distribution for states of a dynamical system given partial and noisy observations - is important in many areas of science and engineering, including weather and climate prediction.…

The Ensemble Kalman Filter (EnKF), as a fundamental data assimilation approach, has been widely used in many fields of the sciences and engineering. When the state variable is of high dimensional accompanied with high resolution…

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…

Advanced driver assistance systems are critically dependent on reliable and accurate information regarding a vehicles' driving state. For estimation of unknown quantities, model-based and learning-based methods exist, but both suffer from…

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 Kalman filter (KF) and its variants are among the most celebrated algorithms in signal processing. These methods are used for state estimation of dynamic systems by relying on mathematical representations in the form of simple…

Inconsistency issue is one crucial challenge for the performance of extended Kalman filter (EKF) based methods for state estimation problems, which is mainly affected by the discrepancy of observability between the EKF model and the…

Pose estimation is important for robotic perception, path planning, etc. Robot poses can be modeled on matrix Lie groups and are usually estimated via filter-based methods. In this paper, we establish the closed-form formula for the error…

Existing uncertainty modeling approaches try to detect an out-of-distribution point from the in-distribution dataset. We extend this argument to detect finer-grained uncertainty that distinguishes between (a). certain points, (b). uncertain…

With the maturation of quantum computing technology, research has gradually shifted towards exploring its applications. Alongside the rise of artificial intelligence, various machine learning methods have been developed into quantum…

An extended Kalman filter (EKF) is developed on the special Euclidean group, SE(3) for geometric control of a quadrotor UAV. It is obtained by performing an extensive linearization on SE(3) to estimate the state of the quadrotor from noisy…

Wireless sensor networks (WSNs) represent a critical research domain within the Internet of Things (IoT) technology. The distributed Kalman filter (DKF) has garnered significant attention as an information fusion method for WSNs. However,…

This paper deals with the implementation of the extended robust Kalman filter (ERKF) which was developed considering uncertainties in the parameter matrices of the underlying state-space model. A key contribution of this work is the…

Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better…

This paper investigates the state estimation problem for unknown linear systems subject to both process and measurement noise. Based on a prior input-output trajectory sampled at a higher frequency and a prior state trajectory sampled at a…