The authors of this paper study the synthesis of new models and methods for signal detection in additive correlated non-Gaussian noise. A new moment quality criterion decision making is proposed based on a random process description using moments and a formation of polynomial decision rules. Taking into account parameters of non-Gaussian distribution of random variables (such as the moments of third and higher orders and joint cumulants), it is shown that nonlinear processing of samples can increase the signal processing efficiency. A synthesis of effective methods and algorithms of data processing in non-Gaussian noise is also presented in this work.