  We consider the problem of parameter estimation in a partially observed
linear Gaussian system with small noises in the state and observation
equations. We describe asymptotic properties of the MLE and Bayes estimators in
the setting with state and observation noises of possibly unequal intensities.
It is shown that both estimators are consistent, asymptotically normal with
convergent moments and asymptotically efficient. This model has an unusual
feature: larger noise in the state equation yields smaller estimation error.
The proofs are based on asymptotic analysis of the Kalman-Bucy filter and the
associated Riccati equation in particular.
