Related papers: Interacting particle filters for simultaneous stat…
This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To…
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…
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 Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…
This paper presents a new filter for state-space models based on Bellman's dynamic-programming principle, allowing for nonlinearity, non-Gaussianity and degeneracy in the observation and/or state-transition equations. The resulting Bellman…
The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state-observation space. The ensemble Kalman filter (EnKF) approximates this mean-field model with an ensemble of interacting…
Time-scale theory, due to its ability to unify the continuous and discrete cases, allows handling intractable non-uniform measurements, such as intermittent received signals. In this work, we address the state estimation problem of a…
Filtering in spatially-extended dynamical systems is a challenging problem with significant practical applications such as numerical weather prediction. Particle filters allow asymptotically consistent inference but require infeasibly large…
Particle and ensemble filters are increasingly utilized for inference, optimization, and forecast; however, both filtering methods use discrete distributions to simulate continuous state space, a drawback that can lead to degraded…
We address the problem of observation noise misspecification in Bayesian filtering of dynamical systems via recent advances in generalised Bayesian inference. Mis-match in tail decay between the true data generating process and an assumed…
In this article we consider the linear filtering problem in continuous-time. We develop and apply multilevel Monte Carlo (MLMC) strategies for ensemble Kalman-Bucy filters (EnKBFs). These filters can be viewed as approximations of…
Nonlinear model predictive control has become a popular approach to deal with highly nonlinear and unsteady state systems, the performance of which can however deteriorate due to unaccounted uncertainties. Model predictive control is…
In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this…
Geometry of the state space is known to play a crucial role in many applications of Kalman filters, especially robotics and motion tracking. The Lie group-centric approach is currently very common, although a Riemannian approach has also…
Parametric filters, such as the Extended Kalman Filter and the Unscented Kalman Filter, typically scale well with the dimensionality of the problem, but they are known to fail if the posterior state distribution cannot be closely…
An optimal estimator of quantum states based on a modified Kalman's Filter is proposed in this work. Such estimator acts after state measurement, allowing obtain an optimal estimation of quantum state resulting in the output of any quantum…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
Particle filters provide Monte Carlo approximations of intractable quantities such as point-wise evaluations of the likelihood in state space models. In many scenarios, the interest lies in the comparison of these quantities as some…
Kalman Filter requires the true parameters of the model and solves optimal state estimation recursively. Expectation Maximization (EM) algorithm is applicable for estimating the parameters of the model that are not available before Kalman…
Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. The most reliable methods of MCMC are computationally expensive.…