Low-rank multi-parametric covariance identification
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10543_2021_867_ReferencePDF.pdf
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Author(s)
Musolas, Antoni
Massart, Estelle
Hendrickx, Julien M.
Absil, P.-A.
Marzouk, Youssef
Date Issued
May 2021
Journal
BIT Numerical Mathematics
Publisher
Springer Netherlands
Citation
Musolas, Antoni, Massart, Estelle, Hendrickx, Julien M., Absil, P.-A. and Marzouk, Youssef. 2021. "Low-rank multi-parametric covariance identification."
Version
Author's final manuscript
Abstract
Abstract
We propose a differential geometric approach for building families of low-rank covariance matrices, via interpolation on low-rank matrix manifolds. In contrast with standard parametric covariance classes, these families offer significant flexibility for problem-specific tailoring via the choice of “anchor” matrices for interpolation, for instance over a grid of relevant conditions describing the underlying stochastic process. The interpolation is computationally tractable in high dimensions, as it only involves manipulations of low-rank matrix factors. We also consider the problem of covariance identification, i.e., selecting the most representative member of the covariance family given a data set. In this setting, standard procedures such as maximum likelihood estimation are nontrivial because the covariance family is rank-deficient; we resolve this issue by casting the identification problem as distance minimization. We demonstrate the utility of these differential geometric families for interpolation and identification in a practical application: wind field covariance approximation for unmanned aerial vehicle navigation.
MIT Department
Massachusetts Institute of Technology. Center for Computational Science and Engineering
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10543-021-00867-y
