Year: 2023
Author: Rosalba Cacciapuoti, Luisa D’Amore, Rosalba Cacciapuoti
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 4 : pp. 847–882
Abstract
We present an innovative interpretation of Kalman filter (KF) combining the ideas of Schwarz domain decomposition (DD) and parallel in time (PinT) approaches. Thereafter we call it DD-KF. In contrast to standard DD approaches which are already incorporated in KF and other state estimation models, implementing a straightforward data parallelism inside the loop over time, DD-KF ab-initio partitions the whole model, including filter equations and dynamic model along both space and time directions/steps. As a consequence, we get local KFs reproducing the original filter at smaller dimensions on local domains. Also, sub problems could be solved in parallel. In order to enforce the matching of local solutions on overlapping regions, and then to achieve the same global solution of KF, local KFs are slightly modified by adding a correction term keeping track of contributions of adjacent subdomains to overlapping regions. Such a correction term balances localization errors along overlapping regions, acting as a regularization constraint on local solutions. Furthermore, such a localization excludes remote observations from each analyzed location improving the conditioning of the error covariance matrices. As dynamic model we consider shallow water equations which can be regarded a consistent tool to get a proof of concept of the reliability assessment of DD-KF in monitoring and forecasting of weather systems and ocean currents.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0203
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 4 : pp. 847–882
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 36
Keywords: Data assimilation Kalman filter domain decomposition filter localization model reduction numerical algorithm.