Viediernikov D. Mathematical models, methods and tools of constant signal parameter estimation in non-Gaussian correlated noise

The application of modern theory of random process processing is a necessary condition for the construction of modern information and measurement systems, diagnostic systems, monitoring, control, the development of which is characterized by increased requirements for accuracy and quality of information processing. The improvement of systems of this class is associated with both technological upgrades and the creation of advanced methods for estimating the parameters of random processes that reflect the behaviour of the object of study. The scientific and technical problem of use and development of methods of mathematical and computer modelling of processes of estimation of parameter of a constant signal at additive interaction with correlated non-Gaussian noise of various types and kinds on the basis of development of moment-cumulative models of researched processes and polynomial estimation methods is considered in the dissertation work. Application of a modified method of maximization of a polynomial, which allowed to increase the accuracy of evaluation processes in data reception and processing systems taking into account the parameters and characteristics of non-Gaussian processes and to create algorithmic bases and computer tools for their implementation. In addition, the following results were obtained. It is shown that a promising direction is the approach based on the application of moment-cumulative functions of higher orders to describe random processes. It is proposed to use a modified method of maximizing the polynomial (Kunchenko's method), which allows to create an algorithmic basis for modelling processes and the organization of software modelling tools. New mathematical models of additive interaction of useful signal and correlated non-Gaussian noise on the basis of application of one-moment and two-moment cumulative functions of higher orders are offered. This made it possible to describe the parameters and characteristics of the correlations non-Gaussian noise of the studied random process. Analytical expressions of moment-cumulative models for asymmetric, excess, asymmetric-excess correlated non-Gaussian processes for additive interaction of useful signal and noise are obtained. This allowed to expand the class of solvable problems for the synthesis of signal processing algorithms for statistically dependent sample values. The use of multi-moment cumulative functions to describe statistically dependent non-Gaussian random processes has expanded the class of investigated random variables and the possibility of applying the polynomial maximization method (Kunchenko method) to obtain unknown signal parameters estimation. To implement adaptive algorithms for signal parameters estimation in non-Gaussian correlated noise, methods of a priori determination of higher-order statistics are presented. This provides additional opportunities for the implementation of flexible polynomial estimation algorithms depending on the noise situation. A modification of the polynomial maximization method (Kunchenko method) is based on the use of two-moment cumulative functions of higher orders, which make it possible to take into account the statistical relationships of sample values with given constraints on their complexity and to ensure adequate representation of the studied process. The application of a new modified method allowed to develop new algorithms for signal parameters estimation in information-measuring systems, control systems, monitoring and diagnostics with better accuracy characteristics in comparison with known methods. On the basis of the obtained moment-cumulative models of the description of random correlated non-Gaussian processes, polynomial stochastic methods for unknown signal parameters estimation for processing dependent sample values are proposed. This allowed the synthesis of computational algorithms for processing non-Gaussian asymmetric, excess and asymmetric-excess correlated processes. Based on the proposed methods, the synthesis and analysis of polynomial computational algorithms for constant parameter estimation of the useful signal with better accuracy characteristics in the form of reducing the variance of the estimation compared with the known results are proposed. The results were improved by taking into account additional information about the studied processes in the form of moment-cumulative functions of higher orders. The structural scheme of the polynomial processing system of the investigated correlated non-Gaussian process on the basis of the polynomial maximization method is offered, which allows to modernize the existing technical systems with the best characteristics. The developed software package, its structure and a set of software modules provide computer modelling of the processes of the constant signal parameter estimation in additive interaction with non-Gaussian correlated noise of different types and kinds.