Information Structures of the Kalman Filter for the Elastic Wave Equation
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Author(s)
Arbelaiz, Juncal
Jensen, Emily
Bamieh, Bassam
Hosoi, Anette E.
Jadbabaie, Ali
Lessard, Laurent
Date Issued
2022
Journal
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
Abstract
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.
Subjects
Control and Systems Engineering
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
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Creative Commons Attribution Noncommercial No Derivatives
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DOI of Published Version
https://doi.org/10.1016/j.ifacol.2022.07.226
