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Confidence assessment for spectral estimation based on estimated covariances
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0001-5158-9255
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2016 (English)In: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Institute of Electrical and Electronics Engineers (IEEE), 2016, 4343-4347 p.Conference paper (Refereed)
Abstract [en]

In probability theory, time series analysis, and signal processing, many identification and estimation methods rely on covariance estimates as an intermediate statistics. Errors in estimated covariances propagate and degrade the quality of the estimation result. In particular, in large network systems where each system node of the network gather and pass on results, it is important to know the reliability of the information so that informed decisions can be made. In this work, we design confidence regions based on covariance estimates and study how these can be used for spectral estimation. In particular, we consider three different confidence regions based on sets of unitarily invariant matrices and bound the eigenvalue distribution based on three principles: uniform bounds; arithmetic and harmonic means; and the Marcenko-Pastur Law eigenvalue distribution for random matrices. Using these methodologies we robustly bound the energy in a selected frequency band, and compare the resulting spectral bound from the respective confidence regions.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2016. 4343-4347 p.
Series
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, ISSN 1520-6149
Keyword [en]
Confidence Regions, Covariance Estimation, Marcenko-Pastur Law, Random Matrices, Spectral Estimation
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-195037DOI: 10.1109/ICASSP.2016.7472497ISI: 000388373404098ScopusID: 2-s2.0-84973366523ISBN: 9781479999880 (print)OAI: oai:DiVA.org:kth-195037DiVA: diva2:1044594
Conference
41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016, Shanghai International Convention Center Shanghai, China, 20 March 2016 through 25 March 2016
Note

QC 20161104

Available from: 2016-11-04 Created: 2016-11-01 Last updated: 2017-01-24Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf