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In this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured porous media. Fluid flow and transport in fractured porous media…
We propose a generalised framework for the updating of a prior ensemble to a posterior ensemble, an essential yet challenging part in ensemble-based filtering methods. The proposed framework is based on a generalised and fully Bayesian view…
The minimum error entropy (MEE) has been extensively used in unscented Kalman filter (UKF) to handle impulsive noises or abnormal measurement data in non-Gaussian systems. However, the MEE-UKF has poor numerical stability due to the inverse…
Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's…
We propose a regularization method for ensemble Kalman filtering (EnKF) with elliptic observation operators. Commonly used EnKF regularization methods suppress state correlations at long distances. For observations described by elliptic…
The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman…
Performing Data Assimilation (DA) at a low cost is of prime concern in Earth system modeling, particularly at the time of big data where huge quantities of observations are available. Capitalizing on the ability of Neural Networks…
Accurate characterization of the equilibrium distributions of complex molecular systems and their dependence on environmental factors such as temperature is essential for understanding thermodynamic properties and transition mechanisms.…
This paper is concerned with the convergence and the error analysis for the feedback particle filter (FPF) algorithm. The FPF is a controlled interacting particle system where the control law is designed to solve the nonlinear filtering…
Kalman filter-based algorithms are fundamental for mobile robots, as they provide a computationally efficient solution to the challenging problem of state estimation. However, they rely on two main assumptions that are difficult to satisfy…
In this paper, the well-known multiplicative extended Kalman filter (MEKF) is re-investigated for attitude estimation using vector observations. From the Lie group theory, it is shown that the attitude estimation model is group affine and…
Nonlinear stochastic differential equation models with unobservable variables are now widely used in the analysis of PK/PD data. The unobservable variables are often estimated with extended Kalman filter (EKF), and the unknown…
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…
This paper presents a novel approach to address the inconsistency problem caused by observability mismatch in visual-inertial navigation systems (VINS). The key idea involves applying a linear time-varying transformation to the error-state…
Motivated by the needs of online large-scale recommender systems, we specialize the decoupled extended Kalman filter (DEKF) to factorization models, including factorization machines, matrix and tensor factorization, and illustrate the…
The ability of ensemble Kalman filter (EnKF) algorithms to extract information from observations is analyzed with the aid of the concept of the degrees of freedom for signal (DFS). A simple mathematical argument shows that DFS for EnKF is…
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon…
In the flow and transport numerical simulation, mesh adaptivity strategy is important in reducing the usage of CPU time and memory. The refinement based on the pressure error estimator is commonly-used approach without considering the flux…
Aerospace design is increasingly incorporating Design Under Uncertainty based approaches to lead to more robust and reliable optimal designs. These approaches require dependable estimates of uncertainty in simulations for their success. The…
Data-driven models of dynamical systems require extensive amounts of training data. For many practical applications, gathering sufficient data is not feasible due to cost or safety concerns. This work uses the Subset Extended Kalman Filter…