Related papers: Smoothing and parameter estimation by soft-adheren…

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…

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.…

Reliable state estimation is essential for autonomous systems operating in complex, noisy environments. Classical filtering approaches, such as the Kalman filter, can struggle when facing nonlinear dynamics or non-Gaussian noise, and even…

We propose analytical mean square error (MSE) expressions for the Kalman filter (KF) and the Kalman smoother (KS) for benchmark studies, where the true system dynamics are unknown or unavailable to the estimator. In such cases, as in…

In this study, we explore data assimilation for the Stochastic Camassa-Holm equation through the application of the particle filtering framework. Specifically, our approach integrates adaptive tempering, jittering, and nudging techniques to…

Observational data are often accompanied by natural structural indices, such as time stamps or geographic locations, which are meaningful to prediction tasks but are often discarded. We leverage semantically meaningful indexing data while…

Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…

This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…

Traditional statements of the celebrated Kalman filter algorithm focus on the estimation of state, but not the output. For any outputs, measured or auxiliary, it is usually assumed that the posterior state estimates and known inputs are…

Data assimilation is the process of estimating the state of a dynamical system over time by combining model predictions with measurements. This task becomes challenging when the system is nonlinear and high-dimensional. To address this,…

Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…

In this work, we consider a sensor selection drawn at random by a sampling with replacement policy for a linear time-invariant dynamical system subject to process and measurement noise. We employ the Kalman filter to estimate the state of…

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…

Smoothing is widely used approach for measurement noise reduction in spectral analysis. However, it suffers from signal distortion caused by peak suppression. A locally self-adjustive smoothing method is developed that retains sharp peaks…

We propose modeling raw functional data as a mixture of a smooth function and a highdimensional factor component. The conventional approach to retrieving the smooth function from the raw data is through various smoothing techniques.…

When measurements from dynamical systems are noisy, it is useful to have estimation algorithms that have low sensitivity to measurement noises and outliers. In the first set of results described in this paper we obtain optimal estimators…

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

Data assimilation techniques, such as ensemble Kalman filtering, have been shown to be a highly effective and efficient way to combine noisy data with a mathematical model to track and forecast dynamical systems. However, when dealing with…

This paper introduces a novel Kalman filter framework designed to achieve robust state estimation under both process and measurement noise. Inspired by the Weighted Observation Likelihood Filter (WoLF), which provides robustness against…

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.…