Abstract
The article contains the consideration of a mathematical model of optimal dynamical measurement in the space of differentiated noises. This model is used in solving the problems of dynamically distorted signal recovery. Here, the mathematical model of optimal dynamic measurement is investigated in the presence of a deterministic multiplicative effect, which can be used to describe changes in the time parameters of the measuring transducer. In addition, the model provides for the presence of random additive influence. Main result of this article is a solution of optimal dynamical measurement for such mathematical model. To solve this problem the theory of optimal dynamic measurement is used. This theory is at the intersection of several scientific areas: the theory of dynamic measurements, the theory of optimal control for the Leontief type systems and the theory of the Sobolev type equations.
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