Journal: Volume 21, No. 4, 2016
Pages: 39 – 45
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Algorithms for calculation of coefficients of the equation of truncated polynomial maximization at the estimation of constant signal parameter on the background of non-gaussian noises

Artem Honcharov, Vitalii Filipov, Anatolii Chepynoga, М. Bezpalyi

Abstract

The features of estimation of constant signal parameter are researched in this article by the method of maximization of truncated stochastic polynomial. The offered method of estimation is based on moment-cumulant description of random variables and the representation of likelihood function in the form of truncated stochastic polynomial of s degree. The additive non-Gaussian random variable is used as a mathematical model of the noise, which is described by the second order cumulant and skewness coefficient. Constant signal is represented as a function of informative parameter J. The method of maximization of truncated stochastic polynomial allows to get simplified algorithms of estimation of parameter J on the background of asymmetric non-Gaussian noises. The basic idea of simplification of the estimated algorithms consists in the following: not all members of a polynomial are used in stochastic polynomial, but only those that allow to simplify the algorithm of estimation. The main materials of the article are devoted to the analysis of methods for simplification of estimation algorithms of constant signal parameter for s > 2 degrees of truncated polynomial. The criterion of simplification of polynomial estimation algorithms and the method for receiving weight coefficients, maximizing truncated stochastic polynomial, are offered in the article. Сoefficients of the increase of the amount of information are pointed for the analysis of the accuracy of simplified estimation algorithms. This allows to choose the optimum method to get truncated polynomial coefficients in terms of minimum variance estimation of constant signal parameter

Keywords

non-Gaussian noises, method of maximization of truncated stochastic polynomial, depth of stochastic polynomial truncation, skewness coefficient

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Suggested citation

Honcharov, A., Filipov, V., Chepynoga, A., & Bezpalyi, M. (2016). Algorithms for calculation of coefficients of the equation of truncated polynomial maximization at the estimation of constant signal parameter on the background of non-gaussian noises. Bulletin of Cherkasy State Technological University, 21(4), 39-45.