1 Neiman Yu.M.
2 Sugaipova L.S.

Moscow State University of Geodesy and Cartography (MIIGAiK)

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.
1.   Burakov M. V. Geneticheskii algoritm: teoriya i praktika. SPb.: GUAP, 2008, 164 p.
2.   Burakov M. V. Neironnye seti i neirokontrollery. SPb.: GUAP, 2013, 284 p.
3.   Gill F., Myurrei U., Rait M. Prakticheskaya optimizatsiya. Per. s angl. V. Yu. Lebedeva; pod red. A. A. Petrova. Moskva: Mir, 1985, 509 p.
4.   Kallan R. Osnovnye kontseptsii neironnykh setei. Per. s angl. A. G. Sivaka. Moskva: Vil'yamc, 2001, 287 p.
5.   Pleshakov D. I. Opredelenie vysoty sputnika «GEO-IK-2» nad morskoi poverkhnost'yu. Al'manakh sovremennoi metrologii. – 2015. – 2 (3), 2015, no. 2 (3), pp. 132–141.
6.   Khaikin S. Neironnye seti. Per. s angl. N. N. Kussul'. Moskva: Vil'yams, 2016, 1104 p.
7.   Brown G. S. (1977) The average impulse response of a rough surface and its applications. IEEE Transactions on Antennas and Propagation, AP-25. pp. 67-74.
8.   Hayne G. S. (1980) Radar altimeter mean return waveforms from near-normal-incidence ocean surface scattering. IEEE Transactions on Antennas and Propagation, Volume 28, no. 5, pp. 687-692.
9.   Hornik K., Stinchcombe M., White H. (1989) Multilayer feedforward networks are universal approximators. Neural Network, no. 2, pp. 359366.
10.   Levenberg K. (1944) A Method for the Solution of Certain Problems in Least Squares. Quarterly of Applied Mathematics, no. 2, pp. 164-168.
11.   Marquardt D. (1963) An Algorithm for Least Squares Estimation on Nonlinear Parameters. SIAM Journal on Applied Mathematics, no. 11, pp. 431-441.
12.   Rosmorduc V., Benveniste J., Bronner E., Dinardo S., Lauret O., Maheu C., Milagro M., Picot N., Ambrozio A., Escolà R., Garcia-Mondejar A., Restano M., Schrama E., Terra-Homem M. (2016) Radar Altimetry Tutorial. J. Benveniste and N. Picot (Eds). URL: www.altimetry.info (accessed: 20.08.2019).
13.   Sadollaha A., Sayyaadia H., Yadav A. (2018) A dynamic metaheuristic optimization model inspired by biological nervous systems: Neural network algorithm. Applied Soft Computing, no. 71, pp. 747-782.
Neiman Yu.M., 
Sugaipova L.S., 
(2019) On determining parameters of the returned altimetry signal. Geodesy and cartography = Geodezia i Kartografia, 80(12), pp. 10-19. (In Russian). DOI: 10.22389/0016-7126-2019-954-12-10-19