DOI: https://doi.org/10.3103/S0735272711010079
Open Access Open Access  Restricted Access Subscription Access

Least squares method in the statistic analysis of periodically correlated random processes

Ihor N. Yavorskyj, Roman Yuzefovych, I. B. Kravets, Zbigniew Zakrzewski

Abstract


The properties of least-squares estimates of mathematical expectations and correlation function of periodically correlated random processes (mathematical model of stochastic oscillations) have been investigated. The formulas defining the statistical characteristics of estimates were analyzed. In addition, examples were presented for illustrating the analysis of modulated signals.


Keywords


periodically correlated random process; mean; correlation function; least squares estimate; bias; variance

Full Text:

PDF

References


Ya. P. Dragan and I. N. Yavorskii, Rhythmics of Sea Disturbance and Underwater Acoustic Signals (Naukova Dumka, Kyiv, 1982) [in Russian].

Ya. P. Dragan, V. A. Rozhkov, and I. N. Yavorskii, Probabilistic Analysis Methods of the Phythmics of Oceanological Processes (Gidrometeoizdat, Leningrad, 1987) [in Russian].

W. A. Gardner (Ed.), Cyclostationarity in Communications and Signal Processing (IEEE Press, New York, 1994).

W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: Half a Century of Research,” Signal Processing, No. 86, 639 (2006).

H. L. Hurd and A. Miamee, Periodically Correlated Random Sequences: Spectral Theory and Practice (John Wiley & Sons Inc., New Jersey, 2007).

I. M. Yavorskyj, O. P. Drabich, P. P. Drabich, et al., “Methods and New Engineering Tools for Vibration-Based Diagnostics of Bearing Assemblies and Gear Units,” Problems of the Life and Operation Safety of Constructions, Buildings and Machines (PEWI NANU, Kyiv, 2006) [in Ukrainian].

I. M. Yavorskyj, P. P. Drabich, I. Yu. Isaev, et al., “Development of Information-Measuring System for Vibration-Based Diagnostics of Bearings of Large Stationary Assemblies,” Problems of the Life and Operation Safety of Constructions, Buildings and Machines (PEWI NANU, Kyiv, 2009) [in Ukrainian].

I. Javorskyj, I. Isayev, Z. Zakrzewski, and S. P. Brooks, “Coherent Covariance Analysis of Periodically Correlated Random Process,” Signal Processing, No. 87, 13 (2007).

I. Javorskyj, I. Isayev, J. Majewski, and R. Yuzefovych, “Component Covariance Analysis for Periodically Correlated Random Process,” Signal Processing, No. 90, 1083 (2010).







© Radioelectronics and Communications Systems, 2004–2020
When you copy an active link to the material is required
ISSN 1934-8061 (Online), ISSN 0735-2727 (Print)
tel./fax +38044 204-82-31, 204-90-41