Bayesian Inference of Total Least-Squares With Known Precision
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Date
2022-09-06
Authors
Friml, Dominik
Václavek, Pavel
0000-0002-2013-6912Advisor
Referee
Mark
Journal Title
Journal ISSN
Volume Title
Publisher
IEEE
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Abstract
This paper provides a Bayesian analysis of the total least-squares problem with independent Gaussian noise of known variance. It introduces a derivation of the likelihood density function, conjugate prior probability-density function, and the posterior probability-density function. All in the shape of the Bingham distribution, introducing an unrecognized connection between orthogonal least-squares methods and directional analysis. The resulting Bayesian inference expands on available methods with statistical results. A recursive statistical identification algorithm of errors-in-variables models is laid- out. An application of the introduced inference is presented using a simulation example, emulating part of the identification process of linear permanent magnet synchronous motor drive parameters. The paper represents a crucial step towards enabling Bayesian statistical methods for problems with errors in variables.
Description
Citation
Proceedings of the IEEE Conference on Decision and Control. 2022, p. 1-6.
https://ieeexplore.ieee.org/document/9992409
https://ieeexplore.ieee.org/document/9992409
Document type
Peer-reviewed
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Accepted version
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Language of document
en
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Defence
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(C) IEEE