ВЛАСТИВОСТІ МНК-ОЦІНКИ КОРЕЛЯЦІЙНОЇ ФУНКЦІЇ БІПЕРІОДИЧНО КОРЕЛЬОВАНИХ ВИПАДКОВИХ ПРОЦЕСІВ

• Datum: 2020
• Hauptverfasser: Javorskyj, I.N., Yuzefovych, R.M., Dzeryn, O.Yu., Semenov, P.A.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
• Schlagworte: біперіодично корельовані випадкові процеси; оцінка кореляційної функції; метод найменших квадратів; асимптотична незміщеність і слушність; просочування
• Online Zugang: https://jais.net.ua/index.php/files/article/view/467
• Назва журналу: Problems of Control and Informatics

Recurrence and stochasticity are the features of a lot of oscillation processes which occur in the different fields of science and techniques. Nowadays the models in the form of periodically correlated random processes are successfully used for the analysis of this processes. PCRP-approach provides more efficient solution of problems of signal transformation in signal and connection theory, technical and medical diagnosis, energetic, forecasting of geophysical processes. Coherent and component methods, least square method, linear filtration method have been developed for estimating covariance and spectral characteristics of PCRP on the basis of the experimental data. Meanwhile it often occur situations when stochastic recurrence of the one period interacts with stochastic recurrence of the other period when analyzing oscillations of the natural and artificial origin. The models of bi periodically correlated random processes (BPCRP) are used to analyze the features of double rhythmic. Probabilistic characteristics of BPCRP can be defined on the basis of the experimental data through the component method, but using of this method leads to significant leakage errors when combination frequencies are close. As it was shown in the paper that using of the least square method helps to avoid these errors. Analysis of the features of covariance function was made on the basis of the solution of matrix equation providing necessary conditions for the quadratic functional minimum. It was obtained the expression for estimation bias arising from the preliminary definition of the mathematical expectation. It was shown that the damping of correlations with the rising of bias is the condition of asymptotic unbiasedness of estimators. This condition also provides root mean square convergence of estimator for gauss BPCRP. Expression for the variance of LSM-estimator of the covariance function in comparison with the variance of component estimator contain additional components depending on combinative frequencies and tending to zero when the length of realization is rising. It was considered the example of LSMestimator of the covariance function of quadrature BPCRP model and it was made the comparison of efficiency of component and LSM-estimators.