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Autonomous landing of Uncrewed Aerial Vehicles (UAVs) on oscillating marine platforms is severely constrained by wave-induced multi-frequency oscillations, wind disturbances, and prediction phase lags in motion prediction. Existing methods…
Numerical solvers using adaptive meshes can focus computational power on important regions of a model domain capturing important or unresolved physics. The adaptation can be informed by the model state, external information, or made to…
This paper introduces the ensemble directional Kalman filter (EnDKF), an ensemble-based Kalman filtering approach for pose tracking that jointly estimates an object's position and attitude using ideas from directional statistics. The EnDKF…
It is a grand challenge to find a feasible weather modification method to mitigate the impact of extreme weather events such as tropical cyclones. Previous works have proposed potentially effective actuators and assessed their capabilities…
The Extended Kalman Filter (EKF) is both the historical algorithm for multi-sensor fusion and still state of the art in numerous industrial applications. However, it may prove inconsistent in the presence of unobservability under a group of…
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,…
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…
We propose a method to account for model error due to unresolved scales in the context of the ensemble transform Kalman filter (ETKF). The approach extends to this class of algorithms the deterministic model error formulation recently…
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,…
A physics-infused strategy relying on the Ensemble Kalman Filter (EnKF) is here used to augment the accuracy of a continuous Immersed Boundary Method (IBM). The latter is a classical penalty method accounting for the presence of the…
We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus, the computational task is to estimate a time-evolving density $\rho(v, t)$ given noisy observations of the true density…
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface…
A turbulent boundary layer is an essential flow case of fundamental and applied fluid mechanics. However, accurate measurements of turbulent boundary layer parameters (e.g., friction velocity $u_\tau$ and wall shear $\tau_w$), are…
Natural disasters, such as hurricanes and typhoons, pose significant challenges to public safety and infrastructure. While government agencies rely on multi million dollar UAV systems for storm data collection and disaster response, smaller…
Due to the state trajectory-independent features of invariant Kalman filtering (InEKF), it has attracted widespread attention in the research community for its significantly improved state estimation accuracy and convergence under…
Ensemble forecast based on physics-informed models is one of the most widely used forecast algorithms for complex turbulent systems. A major difficulty in such a method is the model error that is ubiquitous in practice. Data-driven machine…
Parameter estimation has a high importance in the geosciences. The ensemble Kalman filter (EnKF) allows parameter estimation for large, time-dependent systems. For large systems, the EnKF is applied using small ensembles, which may lead to…
In many areas of science and engineering, it is a common task to infer physical fields from sparse observations. This paper presents the DAFI code intended as a flexible framework for two broad classes of such inverse problems: data…
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…