Koval V. Models and methods of polynomial estimation of the signal parameters on the background of multiplicative and multiplicatively additive interferences.

The object of research is the process of estimating the parameters of signals on a background of multiplicative and additive-multiplicative noise. The aim of this study is to develop new models of interaction and interference signals on the basis of moment-cumulant description and computational methods in estimating the parameters of polynomial signals received on the background of multiplicative and additive-multiplicative non-Gaussian noise. To achieve the objectives used mathematical modeling techniques and statistical methods of analysis and synthesis, the use of the mathematical apparatus of the theory of probability and mathematical statistics, simulation (computer) modeling, numerical methods for solving nonlinear equations. Scientific novelty and practical significance of the results: 1. New mathematical model was resulting of the multiplicative and additive-multiplicative constant mixture and radio interference, based on the moment-cumulant description that simplifies the process of estimating the parameters of signals with the non-Gaussian nature of the noise. 2. For the first time the analytical expressions of the information retrieved on the evaluated parameters and coefficients of variance reduction, which does not depend on the type of the signal, but contain components of statistical models describing the additive and multiplicative noise, which indicate an increase precision of the estimates of the method of maximizing the polynomial compared to the classical linear methods. 3. Iterative methods improved for finding the scalar evaluation using the maximization of a polynomial with non-identically distributed random values, thus reducing the computational cost when using a modified procedure of accumulation Fisher. 4. Recursive methods improved, resulting in a synthesized polynomial algorithms for computing estimates of parameters, which gives the opportunity to work with sequential sampling, and the results can be presented on an arbitrary step. 5. Computational methods for estimating the parameters of polynomial signals in multiplicative and additive-multiplicative effect of non-Gaussian noise get further development. Scientific and technical novelty of research supported by publications, patents of Ukraine and acts of implementation. The results obtained have a broad meaning and may be used for develop statistical signal processing devices, parameter estimation information in systems of radar, radio navigation, sonar transmission.