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Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations
Faculty of Cybernetics, Taras Shevchenko National University of Kyiv, Kiev, Ukraine.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
2017 (English)In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 52, no 9, 1129-1139 p.Article in journal (Refereed) Published
Abstract [en]

We investigate the guaranteed estimation problem of linear functionals from solutions to transmission problems for the Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observation errors are supposed to be unknown and belonging to certain sets. It is shown that the optimal linear mean square estimates of the above mentioned functionals and estimation errors are expressed via solutions to the systems of transmission problems of the special type. The results and techniques can be applied in the analysis and estimation of solution to forward and inverse electromagnetic and acoustic problems with uncertain data that arise in mathematical models of the wave diffraction on transparent bodies.

Place, publisher, year, edition, pages
Blackwell Publishing Ltd , 2017. Vol. 52, no 9, 1129-1139 p.
Keyword [en]
Estimation, Helmholtz equation, Indirect noisy observations, Linear functionals, Transmission problems, Uncertain data, Acoustic fields, Guaranteed estimation, Noisy observations, Observation errors, Statistical characteristics, Transmission problem, Uncertain datas, Wave diffractions, Inverse problems
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-25366DOI: 10.1002/2017RS006293ISI: 000413167900008Scopus ID: 2-s2.0-85029350367OAI: oai:DiVA.org:hig-25366DiVA: diva2:1147091
Conference
URSI Commission B International Symposium on Electromagnetic Theory (EMTS), Espoo, Finland, 14-18 August 2016
Available from: 2017-10-04 Created: 2017-10-04 Last updated: 2017-12-06Bibliographically approved

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CiteExportLink to record
Permanent link

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