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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.…
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…
The problem of incorporating information from observations received serially in time is widespread in the field of uncertainty quantification. Within a probabilistic framework, such problems can be addressed using standard filtering…
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…
The Derivative-free nonlinear Kalman Filter is proposed for state estimation and fault diagnosis in distributed parameter systems and particularly in dynamical systems described by partial differential equations of the nonlinear wave type.…
Ensemble Kalman methods are widely used for state estimation in the geophysical sciences. Their success stems from the fact that they take an underlying (possibly noisy) dynamical system as a black box to provide a systematic,…
Recursive estimation of nonlinear dynamical systems is an important problem that arises in several engineering applications. Consistent and accurate propagation of uncertainties is important to ensuring good estimation performance. It is…
Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and…
We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…
A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…
Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the…
The extended Kalman filter is perhaps the most standard tool to estimate in real time the state of a dynamical system from noisy measurements of some function of the system, with extensive practical applications (such as position tracking…
Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modeled on the basis of simple assumptions such as bias, white noise, first…
The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…
Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…
Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, but their application to the geosciences has been limited due to their inefficiency in high-dimensional systems in…
Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…
Data assimilation combines dynamical models with observations to improve state estimates. Ensemble filters sequentially assimilate observations by updating a set of samples over time, alternating between a forecast and an analysis step.…
In a variety of problems, the number and state of multiple moving targets are unknown and are subject to be inferred from their measurements obtained by a sensor with limited sensing ability. This type of problems is raised in a variety of…
In this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous time state space model with discrete time observations by an algorithm that combines the Kalman filter and a particle…