Related papers: Dynamical Low-Rank Approximations for Kalman Filte…
Several important learning tasks can be formulated as minimizing an entropy-regularized objective over an appropriate space of probability distributions. Mean-field Langevin dynamics (MFLD) facilitate computation in this general context,…
In this paper, we continue to study the derivative-free extended Kalman filtering (DF-EKF) framework for state estimation of continuous-discrete nonlinear stochastic systems. Having considered the Euler-Maruyama and It\^{o}-Taylor…
Nonlinear Kalman Filters are powerful and widely-used techniques when trying to estimate the hidden state of a stochastic nonlinear dynamic system. In this paper, we extend the Smart Sampling Kalman Filter (S2KF) with a new point symmetric…
We exploit knowledge of linear substructure in the linear-regression Kalman filters (LRKFs) to simplify the problem of moment matching. The theoretical results yield quantifiable and significant computational speedups at no cost of…
The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm…
In this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal discretization is refined, the estimate…
This work proposes a novel low-complexity digital backpropagation (DBP) method, with the goal of optimizing the trade-off between backpropagation accuracy and complexity. The method combines a split step Fourier method (SSFM)-like structure…
The aim of this paper is to propose a new numerical approximation of the Kalman-Bucy filter for semi-Markov jump linear systems. This approximation is based on the selection of typical trajectories of the driving semi-Markov chain of the…
State estimation in heavy-tailed process and measurement noise is an important challenge that must be addressed in, e.g., tracking scenarios with agile targets and outlier-corrupted measurements. The performance of the Kalman filter (KF)…
Recently a deterministic method, frequent directions (FD) is proposed to solve the high dimensional low rank approximation problem. It works well in practice, but experiences high computational cost. In this paper, we establish a fast…
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…
In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The…
In this work, we systematically benchmark two recently developed deep density methods for nonlinear filtering. We model the filtering density of a discretely observed stochastic differential equation through the associated Fokker--Planck…
Ensemble filtering of chaotic, partially observed systems is often performed with ensembles far smaller than the state dimension resulting in empirical covariances that are low rank. Subsequently, stochastic observation perturbations can…
The ensemble Kalman filter (EnKF) is widely used for nonlinear and high-dimensional state estimation because it replaces complex covariance propagation with simple ensemble statistics. However, conventional EnKF implementations can become…
We study the Continuous-Discrete Kalman Filter (CD-KF) for State-Space Models (SSMs) where continuous-time dynamics are observed via multiple sensors with discrete, irregularly timed measurements. Our focus extends to scenarios in which the…
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…
We introduce cooperative sequential state space estimation in the domain of augmented complex statistics, whereby nodes in a network collaborate locally to estimate noncircular complex signals. For rigour, a distributed augmented (widely…
Few real-world systems are amenable to truly Bayesian filtering; nonlinearities and non-Gaussian noises can wreak havoc on filters that rely on linearization and Gaussian uncertainty approximations. This article presents the Bayesian…
This work presents a fast, uncertainty-aware sequential data assimilation framework for estimating key aerodynamic states (e.g., instantaneous vorticity fields and aerodynamic loads) during severe gust encounters, where vortex-gust…