Filtering of Multidimensional Stationary Processes with Missing Observations
The problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional continuous time stationary stochastic process from observations of the process with a stationary noise is considered. Formulas for calculating the mean-square error...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2019-03-01
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| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/675309 |
| _version_ | 1797350228513259520 |
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| author | Mikhail Moklyachuk Maria Sidei Oleksandr Masyutka |
| author_facet | Mikhail Moklyachuk Maria Sidei Oleksandr Masyutka |
| author_sort | Mikhail Moklyachuk |
| collection | DOAJ |
| description | The problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional continuous time stationary stochastic process from observations of the process with a stationary noise is considered. Formulas for calculating the mean-square errors and the spectral characteristics of the optimal linear estimates of the functionals are derived under the condition of spectral certainty, where spectral densities of the signal and the noise processes are exactly known. The minimax (robust) method of estimation is applied in the case of spectral uncertainty, where spectral densities of the processes are not known exactly, while some sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and minimax spectral characteristics of the optimal estimates are derived for some special sets of admissible spectral densities. |
| first_indexed | 2024-03-08T12:41:40Z |
| format | Article |
| id | doaj.art-bfb5984075fc4f63b7e7d250e13a3c9e |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T12:41:40Z |
| publishDate | 2019-03-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-bfb5984075fc4f63b7e7d250e13a3c9e2024-01-21T10:07:06ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532019-03-0121243210.32323/ujma.4729291225Filtering of Multidimensional Stationary Processes with Missing ObservationsMikhail Moklyachuk0Maria Sidei1Oleksandr Masyutka2Taras Shevchenko National University of KyivTaras Shevchenko National University of KyivTaras Shevchenko National University of KyivThe problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional continuous time stationary stochastic process from observations of the process with a stationary noise is considered. Formulas for calculating the mean-square errors and the spectral characteristics of the optimal linear estimates of the functionals are derived under the condition of spectral certainty, where spectral densities of the signal and the noise processes are exactly known. The minimax (robust) method of estimation is applied in the case of spectral uncertainty, where spectral densities of the processes are not known exactly, while some sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and minimax spectral characteristics of the optimal estimates are derived for some special sets of admissible spectral densities.https://dergipark.org.tr/tr/download/article-file/675309minimax-robust estimateleast favourable spectral density |
| spellingShingle | Mikhail Moklyachuk Maria Sidei Oleksandr Masyutka Filtering of Multidimensional Stationary Processes with Missing Observations Universal Journal of Mathematics and Applications minimax-robust estimate least favourable spectral density |
| title | Filtering of Multidimensional Stationary Processes with Missing Observations |
| title_full | Filtering of Multidimensional Stationary Processes with Missing Observations |
| title_fullStr | Filtering of Multidimensional Stationary Processes with Missing Observations |
| title_full_unstemmed | Filtering of Multidimensional Stationary Processes with Missing Observations |
| title_short | Filtering of Multidimensional Stationary Processes with Missing Observations |
| title_sort | filtering of multidimensional stationary processes with missing observations |
| topic | minimax-robust estimate least favourable spectral density |
| url | https://dergipark.org.tr/tr/download/article-file/675309 |
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