Nonlinear methods for signal parameters estimation in asymmetric-excess non-gaussian correlated noise

In the theory of statistical analysis of multidimensional random variables, the tasks of correlation analysis are quite important in the construction and implementation of many technical systems of control, monitoring and diagnostics. In the process of solving these tasks, the determination of the presence and nature of statistical relationship of the studied random variables is a priority. Based on the results of correlation analysis, conclusions are drawn about the presence and nature of functional dependence of random variables, the preference of the research methods used and the proposed models for describing random multidimensional processes. The application of classical mathematical apparatus of correlation analysis is widely used in the assumption that the observed random process belongs to multidimensional normal distribution law. In practice, such prerequisites for correlation analysis are not always fulfilled and most likely are a convenient mathematical idealization of the processes under study. Studies show that in describing random processes, including nonGaussian ones, an approach based on the use of moment and cumulative functions of higher orders is promising. Such a representation of random processes makes it possible to increase the accuracy of their processing under given restrictions on their algorithmic complexity and to take into account correlation relationships of the studied non-Gaussian random variables. In the proposed paper, we consider the construction of methods for constant signal parameter estimation in asymmetric-excess non-Gaussian correlated noise using the method of polynomial maximization (Kunchenko method) and its adaptation to implement non-linear algorithms and computer-aided means of functioning of signal processing systems. It is shown that polynomial processing of random variables, taking into account the parameters of a non-Gaussian distribution in the form of cumulants of one-dimensional and multidimensional distributions, makes it possible to reduce the variance of the parameter estimation in comparison with the well-known results