A.A. Potapov – Member of Russian A.M. Prokhorov Academy of Engineering Sciences, Dr.Sc.(Phys.-Math.),  Professor, Main Research Scientist, Kotel'nikov IRE of RAS (Moscow) E-mail: potapov@cplire.ru

This work represents the first paper from a papers' cycle which are devoted not to energy but textural and fractal detectors of targets in the presence of the high intensity noise and interferences from the surface of earth and sea for low angles of incidence and sliding angles of a probing wave and also for complex weather conditions. According to the author's classification, this new detectors' class is referred to topological ones which are divided into textural, fractal, entropy ones and so on. The main postulate of topological detectors which has been proposed by the author is «Maximum of topology at the minimum of energy». The work is basically based on the available papers of specialists from China and USA. In Russia and in the world the author and his pupils (V.A. Kotelnikov IREE RAS) have priority in development of theory and methods of designing such topological detectors of targets.

This work develops the fractal model on a «simple-to-complex» basis, systematically introduces the fractal theory into regular radar practice of target detection using a one-dimensional sampling and SAR images. Fractal methods of detection of an artificial target on the natural background imply application of the fractal dimension, Hurst exponent, fractal signature, multi-fractal spectrum and other parameters. Due to its development the fractals theory plays an important part in targets detection being the very important complement to the conventional energy target detection now. In the future the fractal theory with no doubts will occupy its worthy individual place in radio location. Results of various applications of fractal methods of target detection using the signal structure function which depends on the signal-to-noise ratio not so much are quite encouraging but as everything fundamentally new (especially in radio location) require its understanding and comprehension by large groups of hardware developers and also overcoming a certain psychological barrier in thinking due to the new mathematical apparatus.

Today, an important factor which restrains using of fractal characteristics in applications to targets detection is the accurate estimation of fractal parameters over big data sets on a real-time basis. By combining the fractals theory and the statistical processing method using transformations from the function theory (Fourier transform, fractional Fourier transform, Hilbert transform and so on) we will get performance of fractal methods improved on a real-time basis. It is of great importance and will actively facilitate the fractal theory development in the target detection field.

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