Numerical Gaussian process Kalman filtering

Kalman filtering using pairwise Gaussian models

An important problem in signal processing consists in recursively estimating an unobservable process x = {xn}n∈IN from an observed process y = {yn}n∈IN. This is done classically in the framework of Hidden Markov Models (HMM). In the linear Gaussian case, the classical recursive solution is given by the well-known Kalman filter. In this paper, we consider Pairwise Gaussian Models by assuming tha...

Infinite-Dimensional Kalman Filtering Approach to Spatio-Temporal Gaussian Process Regression

We show how spatio-temporal Gaussian process (GP) regression problems (or the equivalent Kriging problems) can be formulated as infinite-dimensional Kalman filtering and Rauch-Tung-Striebel (RTS) smoothing problems, and present a procedure for converting spatio-temporal covariance functions into infinite-dimensional stochastic differential equations (SDEs). The resulting infinitedimensional SDE...

Gaussian Mixture Model-Based Ensemble Kalman Filtering for State and Parameter Estimation for a PMMA Process

Abstract: Polymer processes often contain state variables whose distributions are multimodal; in addition, the models for these processes are often complex and nonlinear with uncertain parameters. This presents a challenge for Kalman-based state estimators such as the ensemble Kalman filter. We develop an estimator based on a Gaussian mixture model (GMM) coupled with the ensemble Kalman filter ...

On Kalman Filtering for Conditionally Gaussian Systems with Random Matrices

Efficient Spatio-Temporal Gaussian Regression via Kalman Filtering

In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the most powerful estimation approaches also thanks to their universal representing properties. Their extension to dynamical processes has been instead elusive so...