Filipov V. Methods of the joint estimations of the parameters of the constant signal and non-gaussian noises with using the truncated stochastic polynomials.

The object of study: the evaluation parameters constant signal received at background of different types of non-gaussian noises. Goal of study: the development of innovate methods and algorithms of joint estimations of the parameters of the constant signal and non-gaussian noises, through the use of the moment-cumulant description of the random variables and stochastic truncated polynomials, which provides a synthesis of both fast and efficient algorithms for evaluation. Methods of study: mathematical apparatus of probability theory, statistics, theory of signals and common methods of mathematical analysis and computational mathematics, stochastic polynomials. Algorithms of joint estimations are obtained in the thesis, based on the use of joint estimations methods of parameters of constant signal and non-gaussian noises, that is based on the methods of maximizing polynomial (method Kunchenko) and maximization of truncated stochastic polynomial. The scientific novelty of the results: for the first estimations methods that allow to synthesize simplified and efficient algorithms for joint estimation of parameters of signal and non-gaussian noises by the use of truncated stochastic polynomials, have been developed. The practical value of the results: the computational algorithms of joint evaluation of parameter of constant signal at background of non-gaussian noises have been synthesized, which allow to vary the speed and accuracy for evaluating degrees of polynomials s=2-6; the quantitative values of efficiency of the synthesized computational algorithms of joint signal parameter and non-gaussian noises estimations have been obtained, by which the accuracy of the developed methods by the joint estimations have been analyzed, which shows that the asymptotic effectiveness of the synthesized algorithms of joint estimations are increases with the degree of the polynomial. The research results implemented in manufacturing and in studying process.