The paper discusses the major modes of mapping the underlying surface using algorithms synthetic aperture radar antenna system onboard. The causes of the appearance of systematic errors in the mathematical modeling of the synthetic aperture antenna device. A method for reducing these methodological errors, is to increase the number of active reflectors radar signals. It is shown that in this case must take into account correlations between the echoes of individual reflectors. The mathematical model takes into account the spatial and temporal correlation characteristics of the observed signals. The mathematical model is implemented as a simulation algorithm of unsteady, non-Gaussian processes with the specified correlation-spectral characteristics of a given density and distribution of samples of these processes, simulating fluctuations in the amplitude of the observed echo in each bin. The possibility of a significant acceleration of the process simulation using the simplified forms correlations in the form of exponential curves.