Numerical Gaussian Process Kalman Filtering for Spatiotemporal Systems

Author(s)
Armin Kuper, Steffen Waldherr
Abstract

We present a novel Kalman filter (KF) for spatiotemporal systems called the numerical Gaussian process Kalman filter (NGPKF). Numerical Gaussian processes have recently been introduced as a physics-informed machine-learning method for simulating time-dependent partial differential equations without the need for spatial discretization while also providing uncertainty quantification of the simulation resulting from noisy initial data. We formulate numerical Gaussian processes as linear Gaussian state space models. This allows us to derive the recursive KF algorithm under the numerical Gaussian process state space model. Using two case studies, we show that the NGPKF is more accurate and robust, given enough measurements, than a spatial discretization-based KF.

Organisation(s)
Functional and Evolutionary Ecology
External organisation(s)
Katholieke Universiteit Leuven
Journal
IEEE Transactions on Automatic Control
Volume
68
Pages
3131-3138
No. of pages
8
ISSN
0018-9286
DOI
https://doi.org/10.1109/TAC.2022.3232058
Publication date
05-2023
Peer reviewed
Yes
Austrian Fields of Science 2012
202034 Control engineering, 102019 Machine learning
Keywords
ASJC Scopus subject areas
Control and Systems Engineering, Computer Science Applications, Electrical and Electronic Engineering
Portal url
https://ucris.univie.ac.at/portal/en/publications/numerical-gaussian-process-kalman-filtering-for-spatiotemporal-systems(657e82d3-7f17-4b91-8041-8253d086881d).html