  The partially observed linear Gaussian system of stochastic differential
equations with low noise in observations is considered. A kernel-type
estimators are used for estimation of the quadratic variation of the derivative
of the limit of the observed process. Then this estimator is used for
nonparametric estimation of the integral of the square of volatility of
unobservable component. This estimator is also used for construction of
substitution estimators in the case where the drift in observable component and
the volatility of the state component depend on some unknown parameter. Then
this substitution estimator and Fisher-score device allows us to introduce the
One-step MLE-process and adaptive Kalman-Bucy filter.
