论文标题
最佳线性滤波器，用于估计希尔伯特空间中随机函数
An optimal linear filter for estimation of random functions in Hilbert space
论文作者
论文摘要
Let ${\mbox{$\mbox{\boldmath $f$}$}}$ be a square-integrable, zero-mean, random vector with observable realizations in a Hilbert space $H$, and let ${\mbox{$\mbox{\boldmath $g$}$}}$ be an associated square-integrable, zero-mean, random vector with在Hilbert Space $ k $中，实现是无法观察到的。我们以封闭的线性运算符$ x $的形式寻找最佳过滤器，该$ x $作用于可观察的vector $ {\ mbox {$ \ mbox {$ \ mbox {\ boldmath $ f $ f $} $}}}}}_ε\ y \ mbox {$ \ mbox {$ \ mbox {$ \ mbox {$ \ f $ f $} $} $} $} $} $} $} $ \ wideHat {{\ mbox {$ \ mbox {\ boldmath $ g $} $}}}}_ε= x {\ mbox {$ \ mbox {\ mbox {\ boldmath $ f $ f $} $} $}}_ε$我们假设所需的协方差运营商已知。结果用一个典型的例子说明了结果。
Let ${\mbox{$\mbox{\boldmath $f$}$}}$ be a square-integrable, zero-mean, random vector with observable realizations in a Hilbert space $H$, and let ${\mbox{$\mbox{\boldmath $g$}$}}$ 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 ${\mbox{$\mbox{\boldmath $f$}$}}_ε \approx {\mbox{$\mbox{\boldmath $f$}$}}$ that provides the best estimate $\widehat{{\mbox{$\mbox{\boldmath $g$}$}}}_ε = X {\mbox{$\mbox{\boldmath $f$}$}}_ε$ of the vector ${\mbox{$\mbox{\boldmath $f$}$}}$. We assume the required covariance operators are known. The results are illustrated with a typical example.
