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

Abstract

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