  The model of partially observed linear system depending on some unknown
parameters is considered. An approximation of the unobserved component is
proposed. This approximation is realized in three steps. First an estimator of
the method of moments of unknown parameter is constructed. Then this estimator
is used for defining the One-step MLE-process and finally the last estimator is
substituted to the equations of Kalman filter. The solution of obtained
equations provide us the approximation (adaptive Kalman filter). The asymptotic
properties of all mentioned estimators and MLE and Bayesian estimators of the
unknown parameters are described. The asymptotic efficiency of adaptive
filtering is discussed.
