Filtering of infinite sets of stochastic signals: An approach based on interpolation techniques

摘要: We propose an approach to the filtering of infinite sets stochastic signals, K"Y and K"X. The known Wiener-type cannot be applied signals. Even in case when K"X are finite sets, computational work associated with Wiener becomes unreasonably hard. To avoid such difficulties, a new theory is studied. problem addressed as follows. Given two K"X, find single filter F:K"Y->K"X that estimates signals from controlled error. Our based on exploiting signal interpolation idea. proposed F represented form sum p terms, F(y)=@?"j"="1^pT"jR"jQ"j(y). Each term derived three operations presented by matrices, Q"i, R"i T"i i=1,...,p. operation special stage aimed at facilitating numerical work. In particular, Q"1,...,Q"p used transform observable y@?K"Y different Matrices R"1,...,R"p reduce set related matrix equations independent equations. Their solution requires much less effort than would required full T"i,...,T"p determined conditions. show asymptotically optimal. Moreover, model terms pseudo-inverse matrices and, therefore, it always exists.