Optimal linear filter for self-tuning application

An optimal linear filter or predictor is described which has the feedback form of a Kalman filter but which involves only an input-output signal model within the feedback loop. The Kalman gain matrix is replaced by a dynamical gain block. The solution to the problem is obtained using a polynomial system approach. This enables adaptive estimators to be constructed since the signal models are normally identified in polynomial matrix (ARMA) form.