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- Title
Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations.
- Authors
Podlipenko, Yu. K.; Shestopalov, Yu. V.
- Abstract
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.
- Publication
Radio Science, 2017, Vol 52, Issue 9, p1129
- ISSN
0048-6604
- Publication type
Article
- DOI
10.1002/2017RS006293