Related papers: Space-Time Decomposition of Kalman Filter
Kernel adaptive filtering (KAF) integrates traditional linear algorithms with kernel methods to generate nonlinear solutions in the input space. The standard approach relies on the representer theorem and the kernel trick to perform…
As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…
The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an…
This article examines state estimation in discrete-time nonlinear stochastic systems with finite-dimensional states and infinite-dimensional measurements, motivated by real-world applications such as vision-based localization and tracking.…
The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the…
Accurate knowledge of time-variation in meridional flow-speed and profile is crucial for estimating a solar cycle's features, which are ultimately responsible for causing space climate variations. However, no consensus has been reached yet…
Dynamic mode decomposition (DMD) is a data-driven method of extracting spatial-temporal coherent modes from complex systems and providing an equation-free architecture to model and predict systems. However, in practical applications, the…
Intelligent vehicles in autonomous driving and obstacle avoidance, the precise relative state of vehicles put forward a higher demand. For a vehicle-borne sensor network with time-varying transmission delays, the problem of coordinate…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this work, we attempt to provide a consistent framework through Koopman theory and its related…
In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a…
The Kalman Filter (KF) is a powerful mathematical tool widely used for state estimation in various domains, including Simultaneous Localization and Mapping (SLAM). This paper presents an in-depth introduction to the Kalman Filter and…
A dynamic weighted directed graph (DWDG) is commonly encountered in various application scenarios. It involves extensive dynamic interactions among numerous nodes. Most existing approaches explore the intricate temporal patterns hidden in a…
This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter,…
The robustness of the Kalman filter to double talk and its rapid convergence make it a popular approach for addressing acoustic echo cancellation (AEC) challenges. However, the inability to model nonlinearity and the need to tune control…
The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cell-centered finite differences. Two localized exponential time differencing methods are…
In this paper, we continue to study the derivative-free extended Kalman filtering (DF-EKF) framework for state estimation of continuous-discrete nonlinear stochastic systems. Having considered the Euler-Maruyama and It\^{o}-Taylor…
Particle filters are computational techniques for estimating the state of dynamical systems by integrating observational data with model predictions. This work introduces a class of Localized Particle Filters (LPFs) that exploit spatial…
This paper focuses on designing a consistent and efficient filter for map-based visual-inertial localization. First, we propose a new Lie group with its algebra, based on which a novel invariant extended Kalman filter (invariant EKF) is…
The cubature Kalman filter (CKF), while theoretically rigorous for nonlinear estimation, often suffers performance degradation due to model-environment mismatches in practice. To address this limitation, we propose CKFNet-a hybrid…