Analysis of mean function discrete LSM-estimator for biperiodically nonstationary random signals

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dc.citation.epage57
dc.citation.issue1
dc.citation.spage44
dc.contributor.affiliationФізико-механічний інститут ім. Г. В. Карпенка НАН України
dc.contributor.affiliationТехнологічно-природничий університет, Бидгощ
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationKarpenko Physico-Mechanical Institute of National Academy of Sciences of Ukraine
dc.contributor.affiliationUTP University of Sciences and Technology, Bydgoszcz
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorЯворський, І.
dc.contributor.authorДзерин, О.
dc.contributor.authorЮзефович, Р.
dc.contributor.authorJavorskyj, I.
dc.contributor.authorDzeryn, O.
dc.contributor.authorYuzefovych, R.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2020-02-27T09:45:22Z
dc.date.available2020-02-27T09:45:22Z
dc.date.created2019-02-26
dc.date.issued2019-02-26
dc.description.abstractПроаналізовано 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.
dc.description.abstractDiscrete 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.
dc.format.extent44-57
dc.format.pages14
dc.identifier.citationJavorskyj 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.
dc.identifier.citationenJavorskyj 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.
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/46156
dc.language.isoen
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 1 (6), 2019
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dc.relation.references8. Javorskyj I.Mathematical models and analysis of stochastic oscillations. Lviv, Physico-mechanical institute of NAS of Ukraine (2013), (in Ukrainian).
dc.relation.references9. Javorskyj I., YuzefovychR., DzerynO. LSM-harmonic analysis of bi-periodic nonstationary vibration signals. Information extraction and processing. 45 (121), 14–25 (2017), (in Ukrainian).
dc.relation.references10. Javorskyj I., Matsko I., YuzefovychR., Zakrzewski Z. Discrete estimators of characteristics for periodically correlated time series. Digital Signal Processing. 53, 25–40 (2016).
dc.relation.references11. 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).
dc.relation.referencesen1. 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.
dc.relation.referencesen2. DenysenkoN.A., Hoffman I., Inshekov E.N. Simplified stochastic model of the electric load in electricity system. Russian Electromechanics. 8, 104–108 (1987).
dc.relation.referencesen3. NapolitanoA. Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications. John Wiley & Sons, Ltd. IEEE Press (2012).
dc.relation.referencesen4. 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).
dc.relation.referencesen5. Antoni J. Cyclostationarity by examples. Mechanical Systems and Signal Processing. 23, 987–1036 (2009).
dc.relation.referencesen6. Javorskyj I. On period estimate of periodically correlated random processes. Otbor i Peredacha Informatsiyi. 73, 12–21 (1986), (in Russian).
dc.relation.referencesen7. DraganY., RozhkovV., Javorskyj I. The Methods of Probabilistic Analysis of Oceanological Rhythms. Leningrad, Gidrometeoizdat (1987), (in Russian).
dc.relation.referencesen8. Javorskyj I.Mathematical models and analysis of stochastic oscillations. Lviv, Physico-mechanical institute of NAS of Ukraine (2013), (in Ukrainian).
dc.relation.referencesen9. Javorskyj I., YuzefovychR., DzerynO. LSM-harmonic analysis of bi-periodic nonstationary vibration signals. Information extraction and processing. 45 (121), 14–25 (2017), (in Ukrainian).
dc.relation.referencesen10. Javorskyj I., Matsko I., YuzefovychR., Zakrzewski Z. Discrete estimators of characteristics for periodically correlated time series. Digital Signal Processing. 53, 25–40 (2016).
dc.relation.referencesen11. 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).
dc.rights.holderCMM IAPMM NAS
dc.rights.holder© 2019 Lviv Polytechnic National University
dc.subjectбіперіодично корельовані випадкові процеси
dc.subjectметод найменших квадратів
dc.subjectдискретні оцінки параметрів детермінованої складової
dc.subjectнезміщеність оцінки
dc.subjectслушність
dc.subjectbiperiodically correlated random process
dc.subjectthe least square method
dc.subjectdiscrete estimators of deterministic part parameters
dc.subjectunbiasedness of estimate
dc.subjectconsistency
dc.subject.udc621.391
dc.subject.udc519.72
dc.titleAnalysis of mean function discrete LSM-estimator for biperiodically nonstationary random signals
dc.title.alternativeАналіз дискретної МНК-оцінки математичного сподіванння біперіодично нестаціонарних випадкових сигналів
dc.typeArticle

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Mathematical Modeling And Computing. – 2019. – Vol. 6, No. 1