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：本文研究部分观测的线性系统模型，该模型取决于一些未知参数。提出了未被观测到的组件的近似方法，该方法分为三个步骤。首先构建未知参数矩估计的方法，然后使用该估计量定义单步MLE过程，最后将最后一个估计量代入卡尔曼滤波器的方程式中。解决得到的方程提供了逼近（自适应卡尔曼滤波器）。描述了所有提到的估计量和MLE和贝叶斯估计量的渐近性质。讨论了自适应滤波器的渐近效率。