The authors summarize the principle underlying the modern satellite altimetry. Careful analysis of the shape of the reflected signal enables estimating the flight altitude of the satellite altimeter above sea level, and other important parameters of the sea surface in the area under study quite reliably. Important in doing so is the reflected signal power model used. The Brown-Hayne model seems to be the most common one. The values of these parameters are determined from measurements using certain optimization methods. It is especially noted that the problem in question can be successfully solved by methods based on modern theory of artificial neural networks. Numerical experiments using real altimetric data were carried out in MATLAB environment. In this regard, the basic concepts of this theory are described and the possibilities of its use as an effective approximation of any dependence are emphasized. The Levenberg-Marquardt method and the genetic algorithm of artificial neural networks show the same results, but the latter does not require setting initial values of parameters, only limits of their possible change.