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On the strategic directions in synthesis of new topological radar detectors of low-contrast objects against the background of high-intensity noise from the ground, sea and precipitations


A.A. Potapov - Dr.Sc. (Phys.-Math.), Professor, Member of Russian A.M. Prokhorov Academy of Engineering Sciences and Russian Academy of Natural Sciences, President of cooperative Chinese-Russian laboratory of informational technologies and signals fractal processing (China, Guanzhou); Chief Research Scientist, V.A. Kotelnikov Intstitute of Radio Engineering and Electronics of RAS, Russia, Moscow. E-mail:

The main ideas and strategic directions in synthesis of fundamentally new topological radar detectors of low-contrast objects have been considered. The objects detection is conducted against the background of reflections from the ground, sea and precipitations. The new topologic signs and methods of detection of low-contrast objects against the background of high-intensity noise are presented. The methods are based on the textural and fractal analysis and also on the theory of deterministic chaos. The main purpose of this work is to interpret the main directions of radio physics, radio engineering and radio location in “fractal” language that makes new ways and generalizations on future promising radio systems. The new kind and approach of up-to-date radiolocation: fractal-scaling or scale-invariant radiolocation has been proposed. It leads to basic changes in the theoretical radiolocation structure itself and also in its mathematical apparatus. The fractal radio systems conception, sampling topology, global fractal-scaling approach and the fractal paradigm underlies the scientific direction established by the author in Russia and over the world for the first time. The author has been investigating these issues for exactly 35 years. In the author\'s works the determinant conception of processing of low-contrast images was from the beginning involved unlike foreign works. The model of the images which are being analyzed has been developed with taking into account additive and multiplicative background interferences during the processing of complex (objects and targets are presented) two-dimensional textural scenes. For the first time in the world a calculation of the complete ensemble of 28 textural signs and its synchronous analysis for real (optical and radar in the millimeter range (MMW) at wavelength 8.6 mm) and also synthesized textures on the basis of autoregressive models was performed by the author in IREE RAS as long ago as early eighties of XX century. In our opinion the obtained researches of the new experimental data in aggregate with the previous data give us enough information for proving of the fundamentals of theory and methods which were put forward by the author as long ago as the end of XX century. Application of fractals, scaling effects and fractional operators may mean the future of radio electronics because all the previous and current radio electronics is based solely (and only!) on the theory of integer-valued functions and does not take into account the fractional measure in information theory. Introduction of the fractal conception into radio physics, radio location, radio engineering and functional radio electronics is not only proved but is required. The author prepared this article during working on the project «Leading Talents of Guangdong Province», № 00201502 (2016-2020) in the JiNan University (China, Guangzhou) in March 2016.
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  11. Potapov A.A. New Conception of Fractal Radio Device with Fractal Antennas and Fractal Detectors in the MIMO-Systems // Book of Abstracts Third Int. Scientific Symp. «The Modeling of Nonlinear Processes and Systems (MNPS-2015)» (22–26 June, 2015, Russia, Moscow). M.: Ianus-K. 2015. P. 33.
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  18. Potapov A.A. The Textures, Fractal, Scaling Effects and Fractional Operators as a Basis of New Methods of Information Processing and Fractal Radio Systems Designing // Proc. SPIE. 2009. V. 7374. P. 73740E-1 - 73740E-14.
  19. Potapov A.A., Galkina T. V., Kolesnikov A.I., Orlova T.I., KHljavich JA. L. Linejjno modelirovannye ehtalony v korreljacionnom opoznavanii statisticheskikh teksturnykh polejj // Tezisy dokladov X Vsesojuznojj NTK «Statisticheskie metody v teorii peredachi i preobrazovanija informacionnykh signalov» (Lvov, 4-6.10.88). Kiev: KIIGA. 1988. S. 143-144.
  20. Potapov A.A. Statisticheskijj podkhod k opisaniju izobrazhenijj tekstur zemnojj poverkhnosti v opticheskom i radiodiapazone // Tez. dokl. Vsess. konf. «Matematicheskie metody raspoznavanija obrazov (MMRO-IV)» (Riga, 24-26 oktjabrja 1989 g.). Riga: MIPKRRiS. 1989. CH. 4. S. 150-151.
  21. Potapov A.A., Galkina T.V. , Orlova T.I., KHljavich JA.L. Dispersionnyjj metod obnaruzhenija determinirovannykh obektov na teksturnykh opticheskikh i radiolokacionnykh izobrazhenijakh zemnojj poverkhnosti // Radiotekhnika i ehlektronika. 1990. T. 35. № 11. S. 2295-2301.
  22. Potapov A.A., Galkina T. V., Orlova T. I., KHljavich JA.L. Mashinnyjj metod obnaruzhenija iskazhenijj teksturnykh kartin // Tez. dokl. I Vsesojuznojj konf. «Fizika i konversija» (Kaliningrad, Moskovskaja obl., 3.01-5.01.91). M.: Izd-vo Fizicheskogo obshhestva SSSR. 1991. S. 97.
  23. Potapov A.A., Galkina T.V, Orlova T.I., KHljavich JA.L. Metod vydelenija konturov protjazhennykh determinirovannykh obektov v stokhasticheskikh poljakh // Radiotekhnika i ehlektronika. 1991. T. 36. № 11. S. 2240-2242.
  24. Potapov A.A. Novye informacionnye tekhnologii na osnove verojatnostnykh teksturnykh i fraktalnykh priznakov v radiolokacionnom obnaruzhenii malokontrastnykh celejj // Radiotekhnika i ehlektronika. 2003. T. 48. № 9. S. 1101-1119.
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  26. Potapov A.A. Fraktaly i khaos kak osnova novykh proryvnykh tekhnologijj v sovremennykh radiosistemakh / Dopolnenie k kn.: Kronover R. Fraktaly i khaos v dinamicheskikh sistemakh / Per. s angl.; pod red. T.EH. Krenkelja. M.: Tekhnosfera. 2006. S. 374-479.
  27. Potapov A.A. Radiofizicheskie ehffekty pri vzaimodejjstvii ehlektromagnitnogo izluchenija millimetrovogo diapazona voln s okruzhajushhejj sredojj // Zarubezhnaja radioehlektronika. 1992. № 8. S. 36-76; № 9. S. 4-28; № 11. S. 23-48; 1993. № 3. S. 36-48; № 7-9. S. 32-49; 1994. № 7/8. S. 11-30; 1995. № 1. S. 27-36.
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  29. Potapov A.A., Kolesnikov A. I. Korreljacionnye kharakteristiki izobrazhenijj zemnojj poverkhnosti // Radiotekhnika i ehlektronika. 1993. T. 38. № 7. S. 1270-1279.
  30. Potapov A.A., Kolesnikov A. I. Spektralnye kharakteristiki izobrazhenijj zemnojj poverkhnosti // Radiotekhnika i ehlektronika. 1993. T. 38. № 10. S. 1851-1862.
  31. Potapov A.A., Wu Hao, Foukzon J., Podosenov S.A., Men’kova E.R.Fields, Fractals, Control and Low-Contrast Target Detection / Ed. by Dr. Sci. Phys.-Math. ProfessorA.A. Potapov. China, 2016.
  32. German V.A. Obnaruzhenie malokontrastnykh radiolokacionnykh celejj, osnovannoe na fraktalnykh parametrakh signalov: Avtoref. dis. kand. fiz.-mat. nauk. M.: IREH RAN. 2001. 130 s.
  33. Potapov A.A., German V.A. EHffekty determinirovannogo khaosa i strannyjj attraktor pri radiolokacii dinamicheskojj sistemy tipa rastitelnogo pokrova // Pisma v ZHTF. 2002. T. 28. № 14. S. 19–25.
  34. Potapov A.A. Determinirovannyjj khaos v radiolokacionnykh izobrazhenijakh zemnojj poverkhnosti i fraktalnye signatury raspoznavanija // Tez. dokl. LII Nauchnojj sessii, posvjashh. Dnju Radio (Moskva, 21-22 maja 1997 g.). M.: Izd. ΡΗΤΟ REHS im. A.S. Popova, 1997. T. 1. S. 169.
  35. Potapov A.A., German V.A.Obnaruzhenie iskusstvennykh obektov s pomoshhju fraktalnykh signatur // Tez. dokl. 3-jj Vseross. konf. s uchastiem stran SNG «Raspoznavanie obrazov i analiz izobrazhenijj: novye informacionnye tekhnologii» (Nizhnijj Novgorod, 1-7 dekabrja 1997 g.). N.Novgorod: Izd.NIIPMKpriNNGU. 1997. CH. 1. S. 213-217.
  36. Potapov A.A., German V.A. Detection of Artificial Objects with Fractal Signatures // Pattern Recognition and Image Analysis. 1998. V. 8. № 2. P. 226–229.
  37. German V.A., Potapov A.A. Ob izmerenii fraktalnykh kharakteristik radiolokacionnykh i opticheskikh izobrazhenijj // Trudy VII Vseross. shkoly-seminara «Fizika i primenenie mikrovoln» (Krasnovidovo Moskovsk. obl., 24-30 maja 1999 g.). M.: Izd-vo MGU. 1999. T. 2. S. 185.
  38. Potapov A.A., German V.A.Fraktalnye signatury v metodakh obnaruzhenija malokontrastnykh obektov na radiolokacionnykh i opticheskikh izobrazhenijakh zemnojj poverkhnosti // Trudy VII Vseross. shkoly-seminara «Fizika i primenenie mikrovoln» (Krasnovidovo Moskovsk. obl., 24-30 maja 1999 g.). M.: Izd-vo MGU. 1999. T. 2. S. 200.
  39. Potapov A.A.,German V.A. Konceptualnye aspekty fraktalnogo obnaruzhenija celejj na radiolokacionnykh, opticheskikh i sintezirovannykh izobrazhenijakh zemnojj poverkhnosti // Tr. VII Vseross. shkoly-seminara «Volnovye javlenija v neodnorodnykh sredakh» (Krasnovidovo Moskovsk. obl., 22–27 maja 2000 g.). M.: Izd-voMGU. 2000. T. 2. S. 58-62.
  40. Potapov A.A., German V.A. Fractal Method of Detection of Weak Signals from Complex Images // Book of abstracts Second Int. Conf. «Modern Trends in Computational Physics», (Russia, Dubna, July 24-29, 2000). Dubna: JINR. 2000. P. 132.
  41. Potapov A.A., German V.A. Fractals, Fractal Target Selection and Fractal Antennas // Proc. 1st Int. Workshop on Mathematical Modeling of Physical Processes in Inhomogeneous Media, (Mexico, Guanajuato, Gto., March 20-22, 2001). Guanajuato. 2001. P. 44-46.
  42. Potapov A.A., German V.A. Fractal Selection of Artificial Objects from Radar Images on Inhomogeneous Background // Proc. the Fourth Int. Symposium «Physics and Engineering of Millimeter and Sub-Millimeter Waves» (MSMW’2001), (Ukraine, Kharkov, June 4 - 9, 2001). Kharkov: Kharkov State University. 2001. V. 1. P. 268–270.
  43. Potapov A.A., German V.A. Fraktaly v klasterizacii radiolokacionnykh izobrazhenijj poverkhnostnykh i podpoverkhnostnykh obektov // Dokl. 4-jj Mezhdunar. konf. «Cifrovaja obrabotka signalov i ee primenenie» (Moskva, 27 fevralja – 1 marta 2002 g.). M.: RNTO REHS im. A.S.Popova. 2002. T. 1. S. 217-219.
  44. Potapov A.A., German V.A. Klassifikacija i raspoznavanie obektov fraktalnymi metodami // Tezisy dokl. 2-go Mezhdunar. kongressa «Nelinejjnyjj dinamicheskijj analiz NDA-2» (Moskva, 3-8 ijunja 2002 g.). M.: MAI. 2002. S. 235.
  45. Potapov A.A. New Information Radiophysical Technologies Fractal in Radiolocation: Fractal and Synergetic // Proc. of 28th ESA Antenna Workshop on pace Antenna Systems and Technologies (Noordwijk, The Netherlands, 31 May – 03 June 2005).- Noordwijk: ESTEC. 2005. Pt. 2. P. 1047-1050.
  46. Potapov A.A., German V.A. Strannye attraktory, determinirovannyjj khaos i ustojjchivye paretiany, kak ehlementy novojj modeli otrazhennogo radiolokacionnogo signala // Tr. KHI-jj Mezhdunar. konf. po spinovojj ehlektronike i girovektornojj ehlektrodinamike (Firsanovka, Moskovsk. obl., 20-22 dekabrja 2002 g.). M.: Izd. MEHI (TU). 2002. S. 263–280.
  47. Potapov A.A., German V.A. Primenenie fraktalnykh metodov dlja obrabotki opticheskikh i radiolokacionnykh izobrazhenijj zemnojj poverkhnosti // Radiotekhnika i ehlektronika. 2000.T. 45. № 8. S. 946-953.
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  49. Potapov A.A. Fraktaly v radiofizike i radiolokacii. EHlementy teorii fraktalov // Radiotekhnika i ehlektronika. 2000. T. 45, № 11. S. 1285-1292.
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  54. Soumeya Cherouat, Faouzi Soltani, Françoise Schmitt, Franck Daout.Using fractal dimension to target detection in bistatic SAR data // Signal, Image and Video Processing. 2015. V. 9. № 2. P. 365–371.
  55. Coopmans C.,Malek H., Spencer E. Radiation and Impedance Characteristics of a Circular Loop Antenna Driven by Fractional Order Electronics // Proc. ASME 2013 Int. Design Engineering Technical Conf. & Computers and Information in Engineering Conf. IDETC/CIE (2013 August 4-7, 2013, Portland, USA). Portland: American Society of Mechanical Engineers. 2013. P. V004T08A028-V004T08A028.
  56. Podosenov S.A., Potapov A.A., Foukzon Dzh., Menkova E.R. Negolonomnye, fraktalnye i svjazannye struktury v reljativistskikh sploshnykh sredakh, ehlektrodinamike, kvantovojj mekhanike i kosmologii: V 3-kh tomakh / pod red. A.A. Potapova. M.: LENAND. 2015. 1200 s.
  57. Potapov A.A., German V.A. O metodakh izmerenija fraktalnojj razmernosti i fraktalnykh signatur mnogomernykh stokhasticheskikh signalov // Radiotekhnika i ehlektronika. 2004. T. 49. № 12. S. 1468–1491.
  58. Guljaev JU.V., Nikitov S.A., Potapov A.A.,German V.A. Primenenie teorii fraktalov, drobnojj mery i skejjlingovykh ehffektov v skhemakh obnaruzhitelejj radiosignalov // Nelinejjnyjj mir. 2006. T. 4. № 4-5. S. 165–171.
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  60. Guljaev JU.V., Nikitov S.A., Potapov A.A., German V.A. Idei skejjlinga i drobnojj razmernosti v skheme fraktalnogo obnaruzhitelja radiosignalov // Radiotekhnika i ehlektronika. 2006. T. 51. № 8. S. 968–975.
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  63. Potapov A.A. K teorii funkcionalov stokhasticheskikh polejj obratnogo rassejanija // Radiotekhnika i ehlektronika. 2007.  T. 52. № 3. S. 261-310.
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  65. Potapov A.A. Can We Build an Adaptive Fractal Radio System? // Proc. PIERS 2009 in Moscow «Progress in Electromagnetics Research Symp.» (18-21 August, 2009, Moscow, Russia). Cambridge, MA: Electromagnetics Academy. 2009. P. 1798–1802. 
  66. Potapov A.A. The Global Fractal Method, Fractal Paradigm and the Fractional Derivatives Method in Fundamental Radar Problems and Designing of Revolutionary Radio Signals Detectors // Zbornik radova Konferencije MIT - Matematicke i informacione tehnologije (Vrnjackoj Banji od 5. do 9. septembra i u Becicima od 10. do 14. septembra 2013. godine). Kosovska Mitrovica: Prirodno-matematicki fakultet Ulverziteta u Pristini (Serbia), 2014. P. 539–552.
  67. Andreev G. A., Potapov A.A. Stokhasticheskijj avtoregressionnyjj sintez izobrazhenijj tekstur zemnykh pokrovov (Preprint № 23 (498)). M: IREH AN SSSR. 1988. 31 s.
  68. Potapov A.A. O primenenii pokazatelja KHersta H v adaptivnojj fraktalnojj obrabotke informacii i sinteze novykh klassov fraktalnykh «N-signalov» //Obozrenie prikladnojj i promyshlennojj matematiki. 2008. T. 15. № 6. S. 1121–1123.
  69. Potapov A.A. Novye vidy i metody sinteza dinamicheskikh fraktalnykh obnaruzhitelejj prostranstvenno-vremennykh signalov // EHlektromagnitnye volny i ehlektronnye sistemy. 2014. T. 19. № 2. S. 24–40.
  70. Potapov A.A., German V.A. Fraktaly v klasterizacii radiolokacionnykh izobrazhenijj poverkhnostnykh i podpoverkhnostnykh obektov // Dokl. 4-jj Mezhdunar. konf. «Cifrovaja obrabotka signalov i ee primenenie» (Moskva, 27 fevralja – 1 marta 2002 g.). M.: RNTO REHS im. A.S. Popova. 2002. T. 1. S. 217-219.
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