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Robust approach in the synthesis of adaptive nonlinear blocks in view of finite input signal-to-noise ratio

Keywords:

V.M. Artyushenko – Dr.Sc.(Eng.), Professor, Head of Department of Information Technology and Management Systems, Technological University (Korolyov, Moscow region)
E-mail: artuschenko@mail.ru
V.I. Volovach – Dr.Sc.(Eng.), Associate Professor, Head of Department of Information and Electronic Service,
Volga Region State University of Service (Togliatti)
E-mail: volovach.vi@mail.ru


We reviewed and analyzed the issues related to the synthesis of the algorithms of adaptive nonlinear processing in tracking meters implemented through the nonlinear blocks (NLB) based on the use of a robust approach to determine the optimal parameters amplitude transfer characteristic (ATC) by the criterion of the minimum value of root mean square error (RMSE) and with the finite signal-to-noise ratio (SNR) at the output of the NLB taken into account.
It is shown that it is simpler to approximate the characteristics, obtained by the criterion of the minimum RMSE, by sufficiently non-linear dependencies, using a robust approach. It is noted that a NLB has to be adaptive, because in real noise conditions the PDF is unknown whereas the problem of estimating the parameters of the NLB with ATC in the form of a generalized polynomial should be solved as linear regression model. The adaptation algorithm is obtained and the corresponding structural diagram of the NLB on basis of the quadrature generator is presented. We considered a particular case of the limitations of NLB settings when using a servo system based on a multidimensional quadrature generator.
The difference between the measuring signal used for the adaptation of the NLB and the useful signal is shown; the requirements for the ratio of useful signal parameters and measurement signal parameters depending on the parameters of influencing noise are described. It is noted that for the case of nonlinear dependence of the ATC on the optimal settings of the NLB, characterized by a considerable complexity, a probabilistic integral of the Newtonian type can be used.
And the other method of obtaining the finite SNR is considered. This method is based on the optimization of the ATC of the NLB by the minimum generalized RMSE (GRMSE) criterion. The noise reduction criterion, in this case, is also quadratic, whereby it is possible to apply the same adaptation algorithm that is used to minimize RMSE of signal distinguishing. Some necessary mathematical expressions are given to determine the settings of the discriminator. It is shown that to build an adaptive NLB with adaptation algorithms for search, a meter for a current GRMSE should be used.

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May 29, 2020

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