Off-line estimation of trajectory in discrete state space using the minimal-covariance adaptive FIR smoothing with extended output vector

The new tool for off-line estimation of the state of discrete linear systems is presented. The algorithm of Finite Impulse Response (FIR) smoother is described and its optimality is proven. The optimality of this smoother means that error covariance matrix of the estimation is minimal. It places this method in the Least Square Estimation (LSE) methods group, which are much better than frequently used Least Mean Square (LMS) methods. This method can also be used as FIR filter or predictor. In the paper the simple simulation, showing the mode of actions of described smoother, is presented. It is compared with others presented in the literature.