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Synthesis of algorithms of non-linear adaptive signal processing for tracking meters using blocks of non-linear transformation with feed-forward


V.M. Artyushenko – Dr. Sc. (Eng.), Professor, Head of Department of Information Technology and Management Systems, Technological University (Korolyov, Moscow region)
V.I. Volovach – Dr. Sc. (Eng.), Associate Professor, Head of Department of Information and Electronic Service, Volga Region State University of Service (Togliatti)

The issues associated with the synthesis of algorithms of adaptive nonlinear signal processing of the discriminators of tracking meters using the feed-forward blocks of nonlinear transformation are considered and analyzed. It is shown that in real cases, the useful signal is affected by noise with non-Gaussian nature of distribution. In this case the noise often has unknown density of distribution of instantaneous values or its envelope. Non-linear processing of the received signal in these cases should be adaptive, self-consistent with probabilistic properties of influencing noise and with current mismatch between the measured parameters and their estimates.
We considered implementing the adaptive feed-forward blocks of nonlinear transformation (ABNT) with approximation of probability den-sity distribution (PDF) of influencing broad-band noise by using parameter-oriented model. The method of moments is used as a method of estimating parameters of the model. However, only the case of linear approximation of noise of the real PDF with the introduction of a system of orthogonal functions is analyzed. The algorithm of nonlinear processing is obtained, and the block diagram of ABNT, imple-menting it, is proposed. This block diagram uses a linear approximation of the PDF of the instantaneous values of noise.
It is shown by several examples that the accuracy of approximation can be approved by applying non-linear approximation of the PDF of instantaneous values of noise. In particular, such results were obtained for the case when the PDF of noise is described by a generalized Gaussian model. The optimum amplitude characteristic (AC) for such a model is determined by just one parameter of noise (settings). In this case the estimator of the named parameter can be used as adjustment parameter of AC of quasi-optimal block of nonlinear transformation. Analysis of the simulation results for Laplace distributions and Gauss distributions shows the asymptotic approximation of the mean estimator to the true value of settings parameter. It is shown that when the PDF of noise is described by abnormally cluttered model, asymptotic approximation of the parameter estimators also tends to the true values of the parameters of this distribution.
We presented the implementation of feed-forward ABNT with approximation of the PDF for influencing narrowband noise by using a parametric model of its envelope. The case of non-stationary noise with time-varying PDF is analyzed.
The analysis showed that to construct feed-forward ABNT, based on approximating the PDF of noise, one should use the algorithms for estimating the parameters of linear model PDF presented in the form of a generalized polynomial of decomposition in a series of linearly independent functions as well as nonlinear models, such as generalized Gaussian distribution or abnormally cluttered distributions.

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