Home
|
Back to issue
|
ISSN 0474-8662. Information Extraction and Processing. 2017. Issue 45 (121)
Discrete estimators of covariance components of vectorial periodically nonstationary random processes
Matsko I. Y.
Karpenko Physico-Mechanical Institute of the NAS of Ukraine, Lviv
https://doi.org/10.15407/vidbir2017.45.026
Keywords: vectorial periodically correlated random processes, correlation invariants,
discrete estimators, sampling step.
Cite as: Matsko I. Y. Discrete estimators of covariance components of vectorial periodically nonstationary random processes. Information Extraction and Processing. 2017, 45(121), 26-37. DOI:https://doi.org/10.15407/vidbir2017.45.026
Abstract
The properties of estimators for invariants of covariance tensor-function of vectorial periodically correlated random processes, calculated on the base of discrete data, are analyzed. It is shown that aliasing effect of the first kind leads to incorrect estimation of the mean function Fourier coefficients and the second kind leads to decreasing a convergence of covariance components estimator. The conditions of avoidance of the aliasing effect of the first and the
second kinds are obtained. Formulas for the estimator variance and bias, which allow comparing efficiency of the discrete and the continuous estimators, are derived. The consistency of estimators is proved. Dependences of the estimators variances and biases on realization length and signal parameters are found.
References
1. Javorskyj, I.M. Mathematical models and analysis of stochastic oscillations. Karpenko Physico-mechanical institute of NAS of Ukraine: Lviv, 2012; p 802. (in Ukrainian)
2. Javorskyj, I.M.; Matsko, I. Y.; Yuzefovych; R.M.; Kravets, I.B. Vectorial diagnosis of rolling bearing at outer race. Vibrations in Engineering and technology. - 2014; 2 (76), 101-110. (in Ukrainian)
3. Matsko, I.Y.; Yavorsky, I.M.; Yuzefovych, R.M.; Shevchyk, V.B. Invariant correlation analysis of the vibration of the rolling bearing with defects on the outer and inner rings. Phys.-Chem. mechanics of materials. 2016; 52( 6), 109-117. (in Ukrainian)
https://doi.org/10.1007/s11003-017-0033-7
4. Yavorskyj, I. M.; Matsko, I. Y.; Yuzefovych, R. M.; Dzeryn, O. Yu. Vectorial periodically correlated random processes and their covariance invariant analysis. Cyclistationarity: Theory and methods III. Chaari, F.; Leskow, J.; Napolitano, A.; Zimroz, R.; Wylomanska, A. Eds. Switzerland: Springer Int. Publ., 2016; pp 121-150.
https://doi.org/10.1007/978-3-319-51445-1_8
5. Yavorskyj, I.; Isayev I.; Majewski, J.; Yuzefovych, R. Component covariance analysis of periodically correlated random processes. Signal Proc. 2010; 90, 1083-1102.
https://doi.org/10.1016/j.sigpro.2009.07.031
6. Yavorskyj, I.; Isayev, I.; Zakrzewski, Z.; Brooks, S. Coherent covariance analysis of periodically correlated random processes. Signal Proc. 2007; 87, 13-32.
https://doi.org/10.1016/j.sigpro.2006.04.002
7. Javorskyj, I. M.; Yuzefovych, R. M.; Matsko, I. Y.; Shevchyk, V. B. Estimation of correlation invariants of periodically non-stationary random processes. Information expraction and processing. 2013; 89 (115), 14-21. (in Ukrainian)
8. Javorskyj, I. M.; Yuzefovych, R. M.; Matsko, I. Y.; Shevchyk, V. B. Component correlation analysis of vector periodically non-stationary random processes. Izvestiya Vysshikh Uchebnykh Zavedenii. Radioelektronika. 2014; 57( 9), 29-41. (in russian)
https://doi.org/10.3103/S0735272714090039
9. Javorskyj, I. M.; Matsko, I. Y.; Yuzefovych, R. M.; Zakrzewski, Z. Discrete estimators of characteristics for periodically correlated time series. Digital Signal Proc. 2016; 53, 25-40.
https://doi.org/10.1016/j.dsp.2016.03.003