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.

翻译：考虑部分可观测线性系统的模型，该系统依赖于某些未知参数。提出了一种对未观测分量的近似方法。该近似通过三步实现：首先构建未知参数的矩估计量，随后利用该估计量定义一步最大似然估计过程，最后将所得的估计量代入卡尔曼滤波器方程。所获方程的解提供了近似结果（自适应卡尔曼滤波器）。文中描述了所有提及的估计量、最大似然估计量以及未知参数的贝叶斯估计量的渐近性质，并讨论了自适应滤波的渐近效率。