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SUMMARYThe paper presents a mathematical theory of handling and working with wideband noises. We demonstrate that a wideband noise can be represented as a distributed delay of a white noise. From this, we deduce that the behavior of a wideband noise is the same as the behavior of an infinite dimensional colored noise along the boundary line. All these are used to deduce a complete set of formulae for the Kalman-type optimal filter and also to derive nonlinear filtering equation for wideband-noise-driven linear and nonlinear systems.

In this paper we consider a linear signal system together with the two linear observation systems. The observation systems differ from each other by the noise processes. The noise of one of them is a constant shift in time of the signal noise. In the other one the shift is neglected. Respectively, we consider two best estimates of the signal corresponding to two different observation systems. The following problem is investigated: whether the effect of the shift on the best estimate becomes negligible as time increases. This leads to a comparison of the asymptotical behaviors of the solutions of respective Riccati equations. It is proved that under a certain relation between the parameters, the effect of the shift is not negligible.