ISSN 0474-8662. Information Extraction and Processing. 2017. Issue 45 (121)
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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.


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