https://oldena.lpnu.ua/handle/ntb/46156| Title: | Analysis of mean function discrete LSM-estimator for biperiodically nonstationary random signals |
| Other Titles: | Аналіз дискретної МНК-оцінки математичного сподіванння біперіодично нестаціонарних випадкових сигналів |
| Authors: | Яворський, І. Дзерин, О. Юзефович, Р. Javorskyj, I. Dzeryn, O. Yuzefovych, R. |
| Affiliation: | Фізико-механічний інститут ім. Г. В. Карпенка НАН України Технологічно-природничий університет, Бидгощ Національний університет “Львівська політехніка” Karpenko Physico-Mechanical Institute of National Academy of Sciences of Ukraine UTP University of Sciences and Technology, Bydgoszcz Lviv Polytechnic National University |
| Bibliographic description (Ukraine): | Javorskyj I. Analysis of mean function discrete LSM-estimator for biperiodically nonstationary random signals / I. Javorskyj, O. Dzeryn, R. Yuzefovych // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 6. — No 1. — P. 44–57. |
| Bibliographic description (International): | Javorskyj I. Analysis of mean function discrete LSM-estimator for biperiodically nonstationary random signals / I. Javorskyj, O. Dzeryn, R. Yuzefovych // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 6. — No 1. — P. 44–57. |
| Is part of: | Mathematical Modeling and Computing, 1 (6), 2019 |
| Issue: | 1 |
| Issue Date: | 26-Feb-2019 |
| Publisher: | Lviv Politechnic Publishing House |
| Place of the edition/event: | Львів Lviv |
| UDC: | 621.391 519.72 |
| Keywords: | біперіодично корельовані випадкові процеси метод найменших квадратів дискретні оцінки параметрів детермінованої складової незміщеність оцінки слушність biperiodically correlated random process the least square method discrete estimators of deterministic part parameters unbiasedness of estimate consistency |
| Number of pages: | 14 |
| Page range: | 44-57 |
| Start page: | 44 |
| End page: | 57 |
| Abstract: | Проаналізовано дискретні оцінки детермінованої складової біперіодично
нестаціонарних випадкових сигналів, отриманих за допомогою методів найменших квадратів
(МНК). Показано, що МНК-оцінювання дає можливість уникнути ефектів просочування.
Визначено умови слушності дискретних оцінок. Проаналізовано формули
для дисперсії оцінок, які описують її залежність від довжини реалізації, інтервалу
дискретизації та кореляційних компонентів сигналу. Discrete estimators of the deterministic part for a biperiodically nonstationary signal obtained by the least square method (LSM) are analysed. It was shown that LSM-estimation allows avoiding the leakage effects. The conditions of consistency for the discrete estimators are obtained. The formulae for variance estimators, which describe their dependencies on a realization length, sampling interval and signal covariance components, are analysed. |
| URI: | https://ena.lpnu.ua/handle/ntb/46156 |
| Copyright owner: | CMM IAPMM NAS © 2019 Lviv Polytechnic National University |
| References (Ukraine): | 1. Javors’kyj I., YuzefovychR., Matsko I., Kravets I. The Stochastic Recurrence Structure of Geophysical Phenomena. 55–88 (2015). In: Chaari F., LeskowJ., NapolitanoA., ZimrozR.,WylomanskaA., DudekA. (eds) Cyclostationarity: Theory and Methods – II. CSTA 2014. Applied Condition Monitoring, vol 3. Springer, Cham. 2. DenysenkoN.A., Hoffman I., Inshekov E.N. Simplified stochastic model of the electric load in electricity system. Russian Electromechanics. 8, 104–108 (1987). 3. NapolitanoA. Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications. John Wiley & Sons, Ltd. IEEE Press (2012). 4. Javorskyj I., Kravets I., Matsko I., YuzefovychR. Periodically correlated random processes: Application in early diagnostics of mechanical systems. Mechanical Systems and Signal Processing. 83, 406–438 (2017). 5. Antoni J. Cyclostationarity by examples. Mechanical Systems and Signal Processing. 23, 987–1036 (2009). 6. Javorskyj I. On period estimate of periodically correlated random processes. Otbor i Peredacha Informatsiyi. 73, 12–21 (1986), (in Russian). 7. DraganY., RozhkovV., Javorskyj I. The Methods of Probabilistic Analysis of Oceanological Rhythms. Leningrad, Gidrometeoizdat (1987), (in Russian). 8. Javorskyj I.Mathematical models and analysis of stochastic oscillations. Lviv, Physico-mechanical institute of NAS of Ukraine (2013), (in Ukrainian). 9. Javorskyj I., YuzefovychR., DzerynO. LSM-harmonic analysis of bi-periodic nonstationary vibration signals. Information extraction and processing. 45 (121), 14–25 (2017), (in Ukrainian). 10. Javorskyj I., Matsko I., YuzefovychR., Zakrzewski Z. Discrete estimators of characteristics for periodically correlated time series. Digital Signal Processing. 53, 25–40 (2016). 11. Javorskyj I., YuzefovychR., Kravets I., Matsko I. Properties of characteristics estimators of periodically correlated random processes in preliminary determination of the period of correlation. Radioelectronics and Communication Systems. 55 (8), 335–348 (2012). |
| References (International): | 1. Javors’kyj I., YuzefovychR., Matsko I., Kravets I. The Stochastic Recurrence Structure of Geophysical Phenomena. 55–88 (2015). In: Chaari F., LeskowJ., NapolitanoA., ZimrozR.,WylomanskaA., DudekA. (eds) Cyclostationarity: Theory and Methods – II. CSTA 2014. Applied Condition Monitoring, vol 3. Springer, Cham. 2. DenysenkoN.A., Hoffman I., Inshekov E.N. Simplified stochastic model of the electric load in electricity system. Russian Electromechanics. 8, 104–108 (1987). 3. NapolitanoA. Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications. John Wiley & Sons, Ltd. IEEE Press (2012). 4. Javorskyj I., Kravets I., Matsko I., YuzefovychR. Periodically correlated random processes: Application in early diagnostics of mechanical systems. Mechanical Systems and Signal Processing. 83, 406–438 (2017). 5. Antoni J. Cyclostationarity by examples. Mechanical Systems and Signal Processing. 23, 987–1036 (2009). 6. Javorskyj I. On period estimate of periodically correlated random processes. Otbor i Peredacha Informatsiyi. 73, 12–21 (1986), (in Russian). 7. DraganY., RozhkovV., Javorskyj I. The Methods of Probabilistic Analysis of Oceanological Rhythms. Leningrad, Gidrometeoizdat (1987), (in Russian). 8. Javorskyj I.Mathematical models and analysis of stochastic oscillations. Lviv, Physico-mechanical institute of NAS of Ukraine (2013), (in Ukrainian). 9. Javorskyj I., YuzefovychR., DzerynO. LSM-harmonic analysis of bi-periodic nonstationary vibration signals. Information extraction and processing. 45 (121), 14–25 (2017), (in Ukrainian). 10. Javorskyj I., Matsko I., YuzefovychR., Zakrzewski Z. Discrete estimators of characteristics for periodically correlated time series. Digital Signal Processing. 53, 25–40 (2016). 11. Javorskyj I., YuzefovychR., Kravets I., Matsko I. Properties of characteristics estimators of periodically correlated random processes in preliminary determination of the period of correlation. Radioelectronics and Communication Systems. 55 (8), 335–348 (2012). |
| Content type: | Article |
| Appears in Collections: | Mathematical Modeling And Computing. – 2019. – Vol. 6, No. 1 |
| File | Description | Size | Format | |
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| 2019v6n1_Javorskyj_I-Analysis_of_mean_function_44-57.pdf | 1.55 MB | Adobe PDF | View/Open | |
| 2019v6n1_Javorskyj_I-Analysis_of_mean_function_44-57__COVER.png | 382.3 kB | image/png | View/Open |
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