Recent zbMATH articles in MSC 49K45https://www.zbmath.org/atom/cc/49K452021-07-10T17:08:46.445117ZWerkzeugAn optimal linear filter for estimation of random functions in Hilbert spacehttps://www.zbmath.org/1462.490412021-07-10T17:08:46.445117Z"Howlett, Phil"https://www.zbmath.org/authors/?q=ai:howlett.phil-g"Torokhti, Anatoli"https://www.zbmath.org/authors/?q=ai:torokhti.anatoli-pSummary: Let \(\boldsymbol{f}\) be a square-integrable, zero-mean, random vector with observable realizations in a Hilbert space \(H\), and let \(\boldsymbol{g}\) be an associated square-integrable, zero-mean, random vector with realizations which are not observable in a Hilbert space \(K\). We seek an optimal filter in the form of a closed linear operator \(X\) acting on the observable realizations of a proximate vector \(\boldsymbol{f}_{\epsilon} \approx \boldsymbol{f}\) that provides the best estimate \(\widehat{\boldsymbol{g}}_{\epsilon} = X\boldsymbol{f}_{\epsilon}\) of the vector \(\boldsymbol{g} \). We assume the required covariance operators are known. The results are illustrated with a typical example.