Related papers: Ensemble transport smoothing. Part II: Nonlinear u…
Vehicle state estimation presents a fundamental challenge for autonomous driving systems, requiring both physical interpretability and the ability to capture complex nonlinear behaviors across diverse operating conditions. Traditional…
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 paper is proposed a novel incremental iterative Gauss-Newton-Markov-Kalman filter method for state estimation of dynamic models given noisy measurements. The mathematical formulation of the proposed filter is based on the…
Kalman filtering has been traditionally applied in three application areas of estimation, state estimation, parameter estimation (a.k.a. model updating), and dual estimation. However, Kalman filter is often not sufficient when experimenting…
A common pipeline in functional data analysis is to first convert the discretely observed data to smooth functions, and then represent the functions by a finite-dimensional vector of coefficients summarizing the information. Existing…
This proposed work introduces a data-assimilation-assisted approach to train neural networks, aimed at effectively reducing epistemic uncertainty in state estimates of separated flows. This method, referred to as model-consistent training,…
Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…
Methods of dynamical system's theory are used for numerical study of transport and mixing of passive particles (water masses, temperature, salinity, pollutants, etc.) in simple kinematic ocean models composed with the main Eulerian coherent…
Modelling exchangeable relational data can be described by \textit{graphon theory}. Most Bayesian methods for modelling exchangeable relational data can be attributed to this framework by exploiting different forms of graphons. However, the…
Spatially extended stationary and traveling states in the strongly nonlinear regime of convection in layers of binary fluid mixtures heated from below are described by a few-mode-model. It is derived from the proper hydrodynamic balance…
The Boltzmann equation for inelastic Maxwell models is used to analyze nonlinear transport in a granular binary mixture in the steady simple shear flow. Two different transport processes are studied. First, the rheological properties (shear…
Trajectory reconstruction is the process of inferring the path of a moving object between successive observations. In this paper, we propose a smoothing spline -- which we name the V-spline -- that incorporates position and velocity…
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…
We propose the application of iterative regularization for the development of ensemble methods for solving Bayesian inverse problems. In concrete, we construct (i) a variational iterative regularizing ensemble Levenberg-Marquardt method…
The dynamic Schr\"odinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as optimal transport problems. It consists of learning non-linear diffusion processes using efficient…
Staged trees are a relatively recent class of probabilistic graphical models that extend Bayesian networks to formally and graphically account for non-symmetric patterns of dependence. Machine learning algorithms to learn them from data…
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…
A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is based on the observation that many dynamic state space models have a relatively small number of static parameters…
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,…
We consider the problem of state estimation in dynamical systems and propose a different mechanism for handling unmodeled system uncertainties. Instead of injecting random process noise, we assign different weights to measurements so that…