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Optimal Algorithms of Filtration of Non-Markovian Process


A.V. Korennoi, A.M. Mezhuev

The operation is dedicated to a solution of the problem of an optimum filtration of non-Markovian process on the basis of methods of an optimum filtration of casual fields in Gauss approximation. Till now at solving the problem of an optimum filtration of stochastic process was restricted to the Markovian theory. However in some cases the procedure of an information of the process to Markovian reduces to is intolerable rough or composite algoritms for practical embodying, and in the series of cases such procedure is basically impossible. Thus, the filtrations, inlet by the Markovian theory of restriction, do not allow to envelop all class of continuous stochastic process. In operation the optimum algorithm of filtration of continuous non-Markovian process in Gauss approximation is designed. The synthesized algorithm alongside with the problem of a flowing filtration of a Markovian process solves the problem of all three aspects of interpolation (filtration with retardation). On the concrete example of reception of a mixture of non-Markovian process and white Gauss noise with usage of the method of system performances the application of the obtained algorithm is surveyed and the plan of the optimum filter is designed. The surveyed problem testifies that apart from expansion problems of the stochastic process class, algorithm of filtration allows to solve such nonconventional for the Markovian theory, as estimation of a pulse response of a linear stochastic data link and optimum reception of multipath signals at reflection from some extended field. Besides in the class of linear systems it is necessary to mark convenience of exposition of estimated stochastic process with the help of the pulse response of a shaping filter that doesn’t require engaging of the means of the differential equations.
June 24, 2020
May 29, 2020

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