Wide band noises: Invariant results

Abstract

In applications wide band noises are observed by autocovariance functions. At the same time there are infinitely many wide band noises having the same autocovariance function. Each of these wide band noises creates its own best estimate and optimal control. Therefore, it is practically important to obtain filtering and control results which depend on autocovariance function and independent on respective wide band noises. Shortly, we call such results as invariant results. In this paper we present two such results related to linear filtering and LQG problems.