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Journal of Automation and Information Sciences
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ISSN Druckformat: 1064-2315
ISSN Online: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v52.i6.40
pages 44-57

Properties of LSM-Estimator of Correlation Function of Biperiodically Correlated Random Processes

Igor N. Javorskyj
G.V. Karpenko Physico-Mechanical Institute of National Academy of Sciences of Ukraine, Lvov, Institute of Telecommunications of University of Science and Technology, Bydgoszcz (Poland)
Roman M. Yuzefovych
G.V. Karpenko Physico-Mechanical Institute of National Academy of Sciences of Ukraine, National University "Lvovskaya Politekhnika", Lvov
Oxana Yu. Dzeryn
G.V. Karpenko Physico-Mechanical Institute of National Academy of Sciences of Ukraine, Lvov
Pavel A. Semenov
Odessa National Maritime University, Odessa


Recurrence and stochasticity are the features of many oscillation processes which occur in the different fields of science and techniques. Nowadays the models in the form of periodically correlated random processes (PCRP) are successfully used for the analysis of these processes. PCRP-approach provided more efficient solution to problem of signal transformation in communication theory, technical and medical diagnosis, energetics, forecasting of geophysical processes. Based on the experimental data coherent and component methods, the least square method, the linear filtration method have been developed for estimating correlation and spectral characteristics of PCRP. However, when analyzing oscillations there are situations when stochastic recurrence of one period interacts with stochastic recurrence of other. To analyze properties of double rythmicity the use is made of its models in the form of biperiodically correlated random processes (BPCRP). With close combination frequencies the application of the component method for estimating BPCRP characteristics can lead to significant leakage errors. As shown in this paper using the least square method helps to avoid these errors. Analysis of features of correlation functions estimates was carried out based on solution of the matrix equation providing the necessary conditions for the quadratic functional minimum. An expression is obtained for biasing estimates arising due to a preliminary definition of mathematical expectation. It is shown that the condition for the asymptotical unbiasedness of estimates is the attenuation of the correlation relationship with an increase in the bias. This condition also provides the mean square convergence of estimates for Gaussian BPCRP. Expression for the variance of LSM-estimator of correlation function compared with the variance of the component estimator contains additional components dependent of combinative frequencies and tending to zero when the length of realization is growing. Consideration was given to the example of LSM-estimating the correlation function of quadrature BPCRP-model and the comparison of efficiency of component and LSM-estimators was carried out.


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