Linear adaptive filtering of random sequences on basis of deterministic approach

Abstract

The article studies the technique of synthesis of random sequence filters with unknown prior statistical      information about the parameters of signal and noises. The synthesis uses only current measurements and a limited amount of empirical information, which leads to the necessity of using a deterministic approach based on the least squares method. In order to obtain a recursive filtering algorithm, it is proposed to extend the structure of the method loss function by  including in loss function an additional term that defines the estimate extrapolation for the next measurement period. The optimal current estimate is based on both measurement results and extrapolated values. The extrapolation function is selected based on the desired class of synthesized filter. The paper considers a variant of polynomial extrapolation, taking into account previous estimates and measurements. The use of only previous estimates leads to the structure of the filter with feedback, while the use of only the previous measurements forms a transversal filter. Mathematical modeling was carried out and on particular example and the loss of filtering accuracy by not taking into account a priori statistical information was estimated.