Communications - Scientific Letters of the University of Zilina 2018, 20(1):67-72 | DOI: 10.26552/com.C.2018.1.67-72

On Frequency Estimation for Partially Observed System with Small Noises in State and Observation Equations

Oleg V. Chernoyarov1, Yury A. Kutoyants2, Mariana Marcokova3
1 Department of Electronics and Nanoelectronics, National Research University "Moscow Power Engineering Institute", Russia and International Laboratory of Statistics of Stochastic Processes and Quantitative Finance of Tomsk State University, Russia
2 Laboratoire Manceau de Mathématiques, Le Mans University, France and International Laboratory of Statistics of Stochastic Processes and Quantitative Finance of Tomsk State University, Russia
3 Department of Structural Mechanics and Applied Mathematics, University of Zilina, Slovakia and Department of Electronics and Nanoelectronics, National Research University "Moscow Power Engineering Institute", Russia

We consider the problem of frequency estimation of the periodic signal multiplied by a Gaussian process (Ornstein-Uhlenbeck) and observed in the presence of the white Gaussian noise. We demonstrate the consistency and asymptotic normality of the maximum likelihood and Bayesian estimators in the sense of the small noise asymptotics. The model of observations is a linear nonhomogeneous partially observed system and the construction of the estimators is based on the Kalman-Bucy filtration equations. For the study of the properties of the estimators, we apply the techniques introduced by Ibragimov and Has'minskii.

Keywords: partially observed linear system; stochastic signal; frequency estimator; maximum likelihood method; Bayesian approach; characteristics of estimators; small noise asymptotic

Published: March 31, 2018  Show citation

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Chernoyarov, O.V., Kutoyants, Y.A., & Marcokova, M. (2018). On Frequency Estimation for Partially Observed System with Small Noises in State and Observation Equations. Communications - Scientific Letters of the University of Zilina, 20(1), 67-72. doi: 10.26552/com.C.2018.1.67-72
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