Selin V. Models and Methods of Nonlinear Parameter Estimation of polynomial trend at the non-Gaussian Stochastic Component

The thesis is devoted to building models and methods of nonlinear parameter estimation of polynomial trends, which are in the additive mixture with a stochastic component. In the construction models used unit of power of stochastic polynomials of Kunchenko. The object of research is the process of estimating the parameters of a polynomial trend in the action of the additive non-Gaussian stochastic component. Theoretical studies based on the use of the theory of probability and mathematical statistics, time series analysis, signal theory, the theory of adaptive systems, methods, object-oriented programming, and general methods of computational mathematics. New probabilistic models describing the interaction of the additive polynomial trend and the non-Gaussian stochastic component using moment-cumulant description was proposed. A comparative analysis of the accuracy of the parameter estimates with estimates obtained using the Least Squares Methods. The recurrent and adaptive refinement procedures estimates parameters of polynomial trends in the conditions of a priori uncertainty are developed. Software module parameter estimation of polynomial trends is developed. Results obtained in the thesis should be used in the design of information technology systems for estimating the parameters of trends that are described by a polynomial of a certain order.