  We consider the problem of frequency estimation of the periodic signal
multiplied by a stationary Gaussian process (Ornstein-Uhlenbeck) and observed
in the presence of the white Gaussian noise. We show the consistency and
asymptotic normality of the maximum likelihood estimator in the asymptotics of
small noise in observations. The model of observations is a linear
nonhomogeneous partially observed system and the construction and study of the
estimator is essentialy based on the asymptotics of the equations of
Kalman-Bucy filtration.
