Ivchenko O. Mathematical models, methods and tools for estimating the parameters of correlated non-Gaussian stochastic processes

The object of study: the process of estimation the parameters of correlated non-Gaussian processes of information and measurement systems and data links. Goal of study: development of methods and means of mathematical and computer modeling of efficient algorithms for estimating the parameters of correlated non-Gaussian processes and parameter estimation methods of these models to improve the quality of the assessments by improving the accuracy of the latter. Methods of study: mathematical apparatus of the theory of probability, mathematical statistics and the theory of processes, as well as common methods of mathematical correlation analysis. The scientific novelty of the results: created new mathematical modeling methods estimate the parameters of random correlated non-Gaussian processes through the use of moment-cumulant models, an that is based on the methods of maximizing polynomial (method Kunchenko); For the first time invited to: non-Gaussian probability models correlated random processes based on the description of a finite sequence of cumulant functions of higher orders, thereby expanding their classification; Methods for the synthesis of non-linear computational algorithms determine the parameters: variance, skewness and kurtosis for correlated non-Gaussian stationary random processes. This reduced the variance of estimates of random process compared with the known methods; new method of generating pseudo-random sequences. An improved method for maximizing the polynomial based on the use of stochastic polynomials and application of cumulant functions of higher orders that allowed the development of computational algorithms for evaluation of parameters of stochastic processes with smaller variance compared with the known results when the correlation between the sampled value is not considered. The research results implemented in manufacturing and in studying process.