Palahin V. Mathematical models, methods and tools for detection and recognition of signals on the background of Non-Gaussian noise

The object of research is the process of detection and recognition of signals on the background of non-Gaussian noise in systems for receiving and processing data. The purpose of this paper is to establish and implement process models to detect and recognition signals on the background of non-Gaussian noise on the basis of moment-cumulant description of the random variables with the formation of moment of quality criteria of statistical hypothesis testing and polynomial decision rules for the synthesis of effective methods and computer tools of processing systems data. To solve the problems of methods were used probability theory and mathematical statistics, mathematical analysis, signal processing theory and statistical hypothesis testing. Offered: 1) Mathematical model for non-Gaussian random variables additive and additive- multiplicative interaction between signal and noise; 2) Method synthesis rules of statistical hypothesis testing based on the development of asymptotically normal quality criteria such as Neyman-Pearson; 3) Method synthesis decision rules of statistical hypothesis testing for correlated non-Gaussian random variables; 4) Methods joint recognition signals and estimation of their parameters; 5) Methods synthesis nonlinear stochastic decision rules for multialternative statistical hypothesis testing. The results obtained may be used for solving the tasks of analysis, synthesis, design and operation of a systems monitoring, control and diagnosis.