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This paper concerns Kalman filtering when the measurements of the process are censored. The censored measurements are addressed by the Tobit model of Type I and are one-dimensional with two censoring limits, while the (hidden) state vectors…
For many of the physical phenomena around us, we have developed sophisticated models explaining their behavior. Nevertheless, inferring specifics from visual observations is challenging due to the high number of causally underlying physical…
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…
Ensemble Kalman filter (EnKF) has been widely used in state estimation and parameter estimation for the dynamic system where observational data is obtained sequentially in time. To reduce uncertainty and accelerate posterior inference, a…
This paper tackles the intricate task of jointly estimating state and parameters in data assimilation for stochastic dynamical systems that are affected by noise and observed only partially. While the concept of ``optimal filtering'' serves…
We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter…
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…
Inertial motion capture systems widely use low-cost IMUs to obtain the orientation of human body segments, but these sensors alone are unable to estimate link positions. Therefore, this research used a SLAM method in conjunction with…
This work introduces an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its primary objective is to provide a methodology enabling the evaluation of the precision of existing Kalman filter variants…
This research paper delves into the Linear Kalman Filter (LKF), highlighting its importance in merging data from multiple sensors. The Kalman Filter is known for its recursive solution to the linear filtering problem in discrete data,…
Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…
De Facto, signal processing is the interpolation and extrapolation of a sequence of observations viewed as a realization of a stochastic process. Its role in applied statistics ranges from scenarios in forecasting and time series analysis,…
Applications of free-flying robots range from entertainment purposes to aerospace applications. The control algorithm for such systems requires accurate estimation of their states based on sensor feedback. The objective of this paper is to…
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…
Data assimilation techniques are often confronted with challenges handling complex high dimensional physical systems, because high precision simulation in complex high dimensional physical systems is computationally expensive and the exact…
The combined use of data from different sources can be critical in emergencies, where accurate models are needed to make real-time decisions, but high-fidelity representations and detailed information are simply unavailable. This study…
The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…
In this study, two classes of methods including statistical and variational data assimilation algorithms will be described. In statistical methods, the model state is updated sequentially based on the previous estimate. Variational methods,…
State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these…
This paper presents an approach for simultaneous estimation of the state and unknown parameters in a sequential data assimilation framework. The state augmentation technique, in which the state vector is augmented by the model parameters,…