@Article{NMTMA-16-847,
author = {D’Amore , Luisa and Cacciapuoti , Rosalba},
title = {Space-Time Decomposition of Kalman Filter},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2023},
volume = {16},
number = {4},
pages = {847--882},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0203},
url = {http://global-sci.org/intro/article_detail/nmtma/22114.html}
}