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Covariance inflation and localization are two important techniques that are used to improve the performance of the ensemble Kalman filter (EnKF) by (in effect) adjusting the sample covariances of the estimates in the state space. In this…
This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical system. Our reduced-order autodifferentiable ensemble Kalman…
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…
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…
We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic non-linear observer on Lie groups, for continuous-time systems with discrete observations. One of the main…
This paper presents an innovative Reduced-Order Model (ROM) for merging experimental and simulation data using Data Assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our…
Legged robots require knowledge of pose and velocity in order to maintain stability and execute walking paths. Current solutions either rely on vision data, which is susceptible to environmental and lighting conditions, or fusion of…
As 6G networks are developed and defined, offloading of XR applications is emerging as one of the strong new use cases. The reduced 6G latency coupled with edge processing infrastructure will for the first time provide a realistic…
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…
Despite the cheap availability of computing resources enabling faster Monte Carlo simulations, the potential benefits of particle filtering in revealing accurate statistical information on the imprecisely known model parameters or modeling…
An ensemble Kalman filter (EnKF)-based mixed model (EnKF-MM) is proposed for the subgrid-scale (SGS) closure in the large-eddy simulation (LES) of turbulence. The model coefficients are determined through the EnKF-based data assimilation…
We present a new type of the EnKF for data assimilation in spatial models that uses diagonal approximation of the state covariance in the wavelet space to achieve adaptive localization. The efficiency of the new method is demonstrated on an…
In this work, we study the emergence of sparsity and multiway structures in second-order statistical characterizations of dynamical processes governed by partial differential equations (PDEs). We consider several state-of-the-art multiway…
Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The…
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…
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation…
This paper is concerned with optimality and stability analysis of a family of ensemble Kalman filter (EnKF) algorithms. EnKF is commonly used as an alternative to the Kalman filter for high-dimensional problems, where storing the covariance…
The Ensemble Kalman filter assumes the observations to be Gaussian random variables with a pre-specified mean and variance. In practice, observations may also have detection limits, for instance when a gauge has a minimum or maximum value.…
Many real-world problems require one to estimate parameters of interest, in a Bayesian framework, from data that are collected sequentially in time. Conventional methods for sampling from posterior distributions, such as {Markov Chain Monte…
The reconstruction of the dynamics of an observed physical system as a surrogate model has been brought to the fore by recent advances in machine learning. To deal with partial and noisy observations in that endeavor, machine learning…