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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.…

The use of model order reduction techniques in combination with ensemble-based methods for estimating the state of systems described by nonlinear partial differential equations has been of great interest in recent years in the data…

We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that…

For oceanographic applications, probabilistic forecasts typically have to deal with i) high-dimensional complex models, and ii) very sparse spatial observations. In search-and-rescue operations at sea, for instance, the short-term…

A sequential estimator based on the Ensemble Kalman Filter for Data Assimilation of fluid flows is presented in this research work. The main feature of this estimator is that the Kalman filter update, which relies on the determination of…

Motivated by the maneuvering target tracking with sensors such as radar and sonar, this paper considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state space models.…

A new application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, we here employ numerical solutions of the dual processes…

Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…

We present a method of using classical wavelet based multiresolution analysis to separate scales in model and observations during data assimilation with the ensemble Kalman filter. In many applications, the underlying physics of a phenomena…

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…

Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…

For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewed as a derivative-free optimization method. In its most…

In data assimilation, an ensemble provides a way to propagate the probability density of a system described by a nonlinear prediction model. Although a large ensemble size is required for statistical accuracy, the ensemble size is typically…

For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect the…

In this work, we aim at studying ensemble based optimal control strategies for data assimilation. Such formulation nicely combines the ingredients of ensemble Kalman filters and variational data assimilation (4DVar). In the same way as…

Data assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modelling is an important element in data assimilation algorithms which…

State estimates from weak constraint 4D-Var data assimilation can vary significantly depending on the data and model error covariances. As a result, the accuracy of these estimates heavily depends on the correct specification of both model…

In this paper, the ensemble consider Kalman filter is proposed to mitigate the negative effects of uncertain parameters in nonlinear dynamic and measurement models. The ensemble Kalman filter can avoid using the Jacobian matrices and reduce…