  We consider the problem of parameter estimation for the partially observed
linear stochastic differential equation. We assume that the unobserved
Ornstein-Uhlenbeck process depends on some unknown parameter and estimate the
unobserved process and the unknown parameter simultaneously. We construct the
two-step MLE-process for the estimator of the parameter and describe its large
sample asymptotic properties, including consistency and asymptotic normality.
Using the Kalman-Bucy filtering equations we construct recurrent estimators of
the state and the parameter.
