Regression Algorithms for Detection and Recognition of Non-Centered Non-Stationary Random Signals in the Short-Range Autonomous Information Systems

Abstract

The article forms the rationale for using the regression algorithms to detect and recognize the non-stationary non-centered signals and noise taking into account the specifics of the short-range autonomous information systems (SRAIS) under conditions of unknown mathematical expectations of informative parameters of signals. When representing each sample realization of the non-stationary processes, subordinated to the normal law of distribution of probabilities, in discrete time, based on the approximate Kotelnikov theorem to solve the problems of signal detection and recognition on the background of band white noise were obtained the expressions for the coefficients of private plausibility of the respective hypotheses. The resulting algorithms require computation of quadratic forms and knowledge of the expectations of selected informative parameters. It is shown that taking into consideration the specific SRAIS – equality relations of mathematical expectation to the RMS values in the samples and high correlation coefficients of the parameter estimates of informative parameters – it is possible to proceed from calculating the quadratic forms in the signal processing algorithms to calculating the modules of errors of multiple initial regression representations for linear correlation. The article justifies the regression algorithms to form the areas of decision-making in which relative distances from the initial regression line are restricted, that is, the algorithms have a clear geometric meaning. Such algorithms can be applied regardless of the probability distribution of estimated random parameters of the signals (for unimodal distributions), since a priori information about the coefficients of the initial regression is obtained when investigating the correlations curves of the random parameters of the signal in the entire area of their change in linear correlation. In non-linear correlation in the SRAIS, using the information on the application conditions it is possible to make alterations of parameters of decision-making algorithms. The article investigates the performance and decision-making regression algorithm to detect the correlated two-dimensional non-centered random vectors for the normal distributions of signal and noise with different primary regression specifications. The considered regression algorithms can be applied in SRAIS to improve noise immunity when solving the tasks of detection and recognition of signals and noise.