Linear Filtering for Time-Delay Systems

A linear filtering problem is studied in which the signal process(x(t):t 0) is described by a stochastic differential equationwhere time delays are present in both the noise input and thex variable. By means of a transformation new to the filteringliterature, we reduce the signal equation to a delay-free stochasticevolution equation; this permits us to solve the problem byapplication of the theory of infinite-dimensional linear filtering.