Information Structures of the Kalman Filter for the Elastic Wave Equation
Author(s)
Arbelaiz, Juncal; Jensen, Emily; Bamieh, Bassam; Hosoi, Anette E.; Jadbabaie, Ali; Lessard, Laurent; ... Show more Show less
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We study the Kalman Filter for the linear elastic wave equation over the real line with spatially distributed partial state measurements. The dynamics of the filter are described by a spatial convolution operator with asymptotic exponential spatial decay rate. This decay rate dictates how measurements from different spatial locations must be exchanged to implement the filter: faster spatial decay implies local measurements are more relevant and the filter is more “decentralized”; slower decay implies farther measurements also become relevant and the filter is more “centralized”. Using dimensional analysis, we demonstrate that this decay rate is a function of one dimensionless group defined from system parameters, such as wave speed and noise variances. We find a critical value of such dimensionless group for which the Kalman Filter is completely decentralized.
Date issued
2022Department
Massachusetts Institute of Technology. Department of Mathematics; Massachusetts Institute of Technology. Department of Mechanical Engineering; Massachusetts Institute of Technology. Institute for Data, Systems, and SocietyJournal
IFAC-PapersOnLine
Publisher
Elsevier BV
Citation
Juncal Arbelaiz, Emily Jensen, Bassam Bamieh, Anette E. Hosoi, Ali Jadbabaie, Laurent Lessard,
Information Structures of the Kalman Filter for the Elastic Wave Equation, IFAC-PapersOnLine, Volume 55, Issue 13, 2022, Pages 1-6.
Version: Final published version
ISSN
2405-8963
Keywords
Control and Systems Engineering