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Robust filtering of stochastic
processes
Mikhail Moklyachuk, Aleksandr Masyutka Department of Probability Theory and Mathematical Statistics,
Kyiv National Taras Shevchenko University, Kyiv 01033, Ukraine
Аннотация:
The considered problem is estimation of the unknown value of the
functional $A\vec{\xi}=\int^\infty_0\vec{a}(t)\vec{\xi}(-t)dt$ which depends on the unknown values of a multidimensional stationary stochastic process $\vec{\xi}(t)$ based on
observations of the process $\vec{\xi}(t)+ vec{\eta}(t)$ for $t\leq0.$ Formulas are obtained for calculation the mean square error and the spectral characteristic of the optimal estimate of the functional under the condition
that the spectral density matrix $F(\lambda)$ of the signal process $\vec{\xi}(t)$ and
the spectral density matrix $G(\lambda)$ of the noise process $\vec{\eta}(t)$ are known.
The least favorable spectral densities and the minimax-robust spectral characteristic of the optimal estimate of the functional $A\vec{\xi}$ are
found for concrete classes $D = D_F\times D_G$ of spectral densities under
the condition that spectral density matrices $F(\lambda)$ and $G(\lambda)$ are not
known, but classes $D = D_F\times D_G$ of admissible spectral densities are
given.
Ключевые слова:
Stationary stochastic process, filtering, robust estimate,
observations with noise, mean square error, least favorable spectral densities, minimax-robust spectral characteristic.
Образец цитирования:
Mikhail Moklyachuk, Aleksandr Masyutka, “Robust filtering of stochastic
processes”, Theory Stoch. Process., 13(29):2 (2007), 166–181
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/thsp195 https://www.mathnet.ru/rus/thsp/v13/i2/p166
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Страница аннотации: | 65 | PDF полного текста: | 29 | Список литературы: | 17 |
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