Detecting an Unknown Abrupt Change in the Band Center of the Fast-Fluctuating Gaussian Random Process
The generalized maximum likelihood algorithm is introduced for detecting the abrupt change in the band center of a fast-fluctuating Gaussian random process with the uniform spectral density. This algorithm has a simpler structure than the ones obtained by means of common approaches and it can be eff...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2020-08-01
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| Series: | Measurement Science Review |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/msr-2020-0023 |
| _version_ | 1818585823683018752 |
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| author | Chernoyarov Oleg Demina Tatiana Kabanov Yuri Makarov Alexander |
| author_facet | Chernoyarov Oleg Demina Tatiana Kabanov Yuri Makarov Alexander |
| author_sort | Chernoyarov Oleg |
| collection | DOAJ |
| description | The generalized maximum likelihood algorithm is introduced for detecting the abrupt change in the band center of a fast-fluctuating Gaussian random process with the uniform spectral density. This algorithm has a simpler structure than the ones obtained by means of common approaches and it can be effectively implemented on the base of both modern digital signal processors and field-programmable gate arrays. By applying the multiplicative and additive local Markov approximation of the decision statistics and its increments, the analytical expressions are calculated for the false alarm and missing probabilities. And with the help of statistical simulation it is confirmed that the proposed detector is operable, while the theoretical formulas describing its quality and efficiency approximate satisfactorily the corresponding experimental data in a wide range of parameters of the observable data realization. |
| first_indexed | 2024-12-16T08:43:12Z |
| format | Article |
| id | doaj.art-9fdbbdbb32844866b988965f4723874f |
| institution | Directory Open Access Journal |
| issn | 1335-8871 |
| language | English |
| last_indexed | 2024-12-16T08:43:12Z |
| publishDate | 2020-08-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Measurement Science Review |
| spelling | doaj.art-9fdbbdbb32844866b988965f4723874f2022-12-21T22:37:39ZengSciendoMeasurement Science Review1335-88712020-08-0120418719510.2478/msr-2020-0023msr-2020-0023Detecting an Unknown Abrupt Change in the Band Center of the Fast-Fluctuating Gaussian Random ProcessChernoyarov Oleg0Demina Tatiana1Kabanov Yuri2Makarov Alexander3International Laboratory of Statistics of Stochastic Processes and Quantitative Finance, National Research Tomsk State University, Lenin Avenue, 36, 634050, Tomsk, RussiaDepartment of Mathematics, Physics and System Analysis, Faculty of Engineering, Maikop State Technological University, Pervomayskaya st., 191, 385000, Maikop, RussiaDepartment of Probability Theory, Faculty of Mechanics and Mathematics, Moscow State University, Leninskiye Gory, 1, 119991, Moscow, RussiaInternational Laboratory of Statistics of Stochastic Processes and Quantitative Finance, National Research Tomsk State University, Lenin Avenue, 36, 634050, Tomsk, RussiaThe generalized maximum likelihood algorithm is introduced for detecting the abrupt change in the band center of a fast-fluctuating Gaussian random process with the uniform spectral density. This algorithm has a simpler structure than the ones obtained by means of common approaches and it can be effectively implemented on the base of both modern digital signal processors and field-programmable gate arrays. By applying the multiplicative and additive local Markov approximation of the decision statistics and its increments, the analytical expressions are calculated for the false alarm and missing probabilities. And with the help of statistical simulation it is confirmed that the proposed detector is operable, while the theoretical formulas describing its quality and efficiency approximate satisfactorily the corresponding experimental data in a wide range of parameters of the observable data realization.https://doi.org/10.2478/msr-2020-0023fast-fluctuating random processabrupt changemaximum likelihood methoddiscontinuous parameterunknown band centerlocal markov approximation methodfalse alarm probabilitymissing probabilitystatistical simulation |
| spellingShingle | Chernoyarov Oleg Demina Tatiana Kabanov Yuri Makarov Alexander Detecting an Unknown Abrupt Change in the Band Center of the Fast-Fluctuating Gaussian Random Process Measurement Science Review fast-fluctuating random process abrupt change maximum likelihood method discontinuous parameter unknown band center local markov approximation method false alarm probability missing probability statistical simulation |
| title | Detecting an Unknown Abrupt Change in the Band Center of the Fast-Fluctuating Gaussian Random Process |
| title_full | Detecting an Unknown Abrupt Change in the Band Center of the Fast-Fluctuating Gaussian Random Process |
| title_fullStr | Detecting an Unknown Abrupt Change in the Band Center of the Fast-Fluctuating Gaussian Random Process |
| title_full_unstemmed | Detecting an Unknown Abrupt Change in the Band Center of the Fast-Fluctuating Gaussian Random Process |
| title_short | Detecting an Unknown Abrupt Change in the Band Center of the Fast-Fluctuating Gaussian Random Process |
| title_sort | detecting an unknown abrupt change in the band center of the fast fluctuating gaussian random process |
| topic | fast-fluctuating random process abrupt change maximum likelihood method discontinuous parameter unknown band center local markov approximation method false alarm probability missing probability statistical simulation |
| url | https://doi.org/10.2478/msr-2020-0023 |
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