Development of Moment Quality Criterion and Polynomial Methods for Signals Detection and Distinction in Non-Gaussian Noise

The paper analyzes the development of innovative models and methods for detecting and distinguishing signals in non-Gaussian noise. The authors propose a new quality criterion for statistical hypothesis testing, based on describing the random process through its moments. The paper suggests the use of stochastic polynomials to develop decision rules, where the optimal coefficients are determined by the new adapted moment quality criterion for multiple hypothesis testing. The paper provides an analysis of the synthesized models and polynomial algorithms used for detecting and distinguishing signals in non-Gaussian noise. A generalized structure of polynomial decision rules for multiple statistical hypothesis testing is suggested. The paper highlight the fact that nonlinear processing of samples, considering parameters of non-Gaussian distribution of random variables such as moments of the third and higher orders, can improve signal processing efficiency. This paper also explores the development of effective methods and algorithms for processing data in non-Gaussian noise. Research has demonstrated that the enhanced effectiveness of nonlinear signal processing, relative to existing results, is contingent upon accounting for the characteristics of non-Gaussian noise.