Digital Signal Processing 
Russian 
Theoretical Fundamentals of Design of Telecommunication Systems with High Energy Efficiency Abstract 2. Shannon C. Communication in the presence of noise, Proc. IRE, v. 37, 1949, no. 1, pp. 1043. 3. Kotelnikov V.A. Teoria potencialnoi pomehoustoitchivosty. (The theory of a potential noise immunity). Ì.: Gosenergoizdat, 1956, p. 152. 4. J.G. Proakis. Digital Communications. NY, McGrawHill, 1995, p. 800. 5. V.A. Varguasin, I.A. Cikin. Methods of Increase of Power and Spectral Efficiency of a Digital Radio Communication. SPb.: BHBPeterburg, 2013, p. 352. 6. Bykhovskiy M.A. Veroiatnost oshibki dlia optimalnih mnogomernih kodov v gaussovskom kanale sviazi i ih osnovnie harakteristiki (Bit error probability for optimal codes in a gaussian communication ñhannel and their key characteristics.) // Electrosvyaz, 2016, no. 2, pp. 5561 7. Bykhovskiy M.A. Pomehoustojchivost priema optimalnih signalov raspologenih na poverhnosti Nmernoi sferi (Noise immunity of the reception of optimal signals located on a surface of an Ndimensional sphere). // Electrosvyaz, 2016, no. 3, pp. 4046 8. Bykhovskiy M.A. Propusknaia sposobnost kanala sviazi pri peredatche signalov ogranitchenoi dlitelnosti (Bandwidth capacity of telecommunication channel during transmission of signals of limited duration.) // Electrosvyaz, 2016, no. 8, pp. 3742 Energy Efficiency of Telecommunication Systems that use Multidimensional Signal Ensembles and Cascade Source Coding Keywords: cascade source coding, multidimensional signal ensemble, noise immunity of signal reception, ReedSolomon codes, complexity realization of demodulators and decoders. The article contains formulas allowing to determine the probability of error reception of the signals in the investigated telecommunication system; such formulas determine the impact of the SS signals’ length and ReedSolomon codes’ length on the noise immunity of the signal reception. It is shown that in such a system it is possible to provide energy efficiency of message transmission that is fairly close to energy efficiency of an “ideal”, according to Shannon, telecommunication system while using rather simple demodulators of the received signals and decoders of the RS codes. It is also noted that cascade codes are more energy efficient than modern turbocodes. References 2. W. Wesley Peterson, E.J. Weldon, Jr., Error Correcting Codes. The MIT Press Cambridge, Massachhusetts and London, England, 1972, p. 594. 3. Bykhovskiy M.A. Pomehoustojchivost priema optimalnih signalov raspologenih na poverhnosti Nmernoi sferi (Noise immunity of the reception of optimal signals located on a surface of an Ndimensional sphere). // Electrosvyaz, 2016, no. 3, pp. 4046 4. V.A. Varguasin, I.A. Cikin. Methods of Increase of Power and Spectral Efficiency of a Digital Radio Communication. SPb.: BHBPeterburg, 2013, p. 352. 5. J.G. Proakis. Digital Communications. NY, McGrawHill, 1995, p. 800.
Abstract The work is intended to decrease bit error rate (BER) of a singletone HF data modem by introducing guard intervals (GI) between the test and information signals, provided that the data rate is maintained unchanged. The influence of different types of GI on the calculation accuracy of communication channel impulse response (IR) is illustrated in comparison with the one specified in the simulation. Moreover, the simulations showed that application of GI in singletone HF data modems makes it possible to decrease BER in a fading channel maintaining the data rate unchanged. In addition, under certain conditions, it becomes possible to increase the data rate of the modem. 2. ARINC Characteristic 6352. HF Data Link Protocol. Feb. 27, 1998. 3. MILSTD188110C. Interoperability and Performance Standards for Data Modems. Sept. 23, 2011. 4. Manjirov A.V., Polianin A.D. Reference book on integral equations: the methods of solving. M: Faktorial Press, 2000. 384 p. 5. Djigan V.I. Adaptive signals filtering: theory and algorithms. M.: Technosfera, 2013. 528 p. 6. Sayed A.H. Adaptive filters. – New Jersey: Hoboken: John Wiley & Sons, Inc., 2008. 786 p. 7. Tikhonov A.N., Arsenin V.Ja. Methods for solving illposed problems. M.: Nauka, 1986. 288 p. 8. Maslakov M.L., Egorov V.V. Influence of the choice of the regularization parameter on BER on adaptive signal correction problems. IX AllRussian Conference «Radiolocation and Radiocommunication». Moscow, 2015. P. 182187. 9. Nikolaev B.I. Serial transmission of discrete messages over continuous channels with memory. – M.: Radio i svjaz’, 1988. 264 p. 10. Maslakov M.L. Pat. ¹ 2573270. RU. H04L 1/20. Method of adaptive correction with guard interval compensation / Egorov V.V., Katanovich A.A., Lobov S.A., Maslakov M.L., Mingalev A.N., Smal M.S., Timofeev A.E. 2016. 11. Maslakov M.L. Adaptive correction with noise compensation. 16th International Conference «Digital Signal Procesing and Application – DSPA 2014». Moscow, 2014. pp. 220223.
Abstract Let s_{0} be modulation binary sequence, expressed by row vector, with n elements ±1, let s_{0} denote the sequence of length N=n+2m containing s_{0} a central part with m proceeding and m subsequent zeros, and let x be a real row vector of length N of the filter pulse response (reference sequence). Filter output is a crosscorrelation function of sequences x and s: where k is the index of nonzero output sample: k∈ Ω ={(n+m1),...,1,0,1,...,n+m1}. The segment of sidelobe suppression is given by successive indexes k∈ Ψ={a,a+1,...,b},M∉ Ψ, where index M of he main lobe is excluded. Integrated sidelobe level for the problem described is determined by expression and calculated in decibels, where w_{k} is a positive weight equal to unity in the segment and equal to some small value outside the segment. It is shown in the paper that optimal vector x minimizing ISL for a fixed s, is given by the formula x = sR^{1}, where R is a certain N×N matrix, which is a function of s. The paper describes the following properties of filter output for this solution:
Average losses in signaltonoise ratio are calculated as a function of segment width for several families of modulation sequences s_{0}: M sequences [8], Legendre sequences [9], and sequences up to length 271 with best known integrated sidelobe level of autocorrelation function [7]. References 2. A.A. Trukhachev. Radiolokatsionnye signaly i ih primenenie (Radar signals and their applications). Ì. Voenizdat. 2005. 320 p. 3. P. Stoica, J. Li, and M. Xue. Transmit codes and receive filters for radar. IEEE Signal Processing Magazine. Vol. 25. pp. 94–109. November 2008. 4. JungSoo Chung and JongSeon No. Low Correlation Zone Sequences. Sequences and Their Applications – SETA 2010: 6th International Conference, Paris, France, September 1317, 2010. Proceedings. SpringerVerlag Berlin Heidelberg. pp. 129. 5. G.V. Zaytsev, N.S. Kondranina, D.M. Litvinov. Otsenka characteristic metoda nesoglasovannoy filtratsii, minimizirujuschego integral’niy uroven’ bokovih lepestkov fazokodomanipulirovannih signalov (Characterization of mismatched filtering, minimizing integrated sidelobe level for phasecoded pulse). Tsifrovaya obrabotka signalov (Digital signal processing). ¹ 1, 2017. 6. R. A. Horn, C. R. Johnson. Matrix Analysis. Cambridge University Press. 1985. 652 p. 7. J. Knauer. Merit Factor Records. Nov. 2004. Available in oct. 2016 at URL: http://labraj.feri.um.si/en/LowAutocorrelation_Binary_Sequence_Problem. 8. W.W. Peterson, E.J. Weldon. Errorcorrecting codes. MIT Press. 1972. 590 p. 9. J. Jedwab. A Survey of the Merit Factor Problem for Binary Sequences. Sequences and Their Applications. Proceedings of SETA 2004. ed. T. Helleseth et al. Lecture Notes in Computer Science. vol. 3486. pp. 30–55. SpringerVerlag. Berlin Heidelberg. 2005.
Abstract Narrowband rejection filter is implemented method of compensation for noise with figure 1a. The twostage implementation is proposed based on figure 1b. This system is differed using decimation and interpolation effects impulse response when implementing narrowband filter. The method is used for multiple reduction in computing costs. The degree of rejection noise is determined accuracy of approximation desired frequency response of a narrowband filter in the passband. The synthesis of transfer function narrowband filter in the band are made special requirements. Requirements in accuracy of approximation in the passband are weakened. Two methods of effective implementation are possible. The first method is suggested using structure of quadrature modulation. The second method is implemented using complex impulse characteristics. The quadrature modulation is increased computational costs. The impulse response of comb and antialiasing filters are taken real value, when ω_{0}=2πk/ν. The computation costs are becoming commensurate with costs on rejection filter. The total computational efficiency of narrowband rejection filter are determined order of rejection filter in interference compensation circuits. Narrowband rejection filter are realized alternative way with use decimation and interpolation the converted signal. The comparative analysis of characteristic are shown achieve specified properties of selectivity at substantially less computational costs. The multistage realization of narrowband filter are reduced computing costs. References 2. Vityazev V.V., Morozov E.A. Optimal'noe proektirovanie tsifrovykh polosovykh fil'trov na protsessorakh obrabotki signalov // Elektrosvyaz'.  1995. ¹ 12.  S. 2931. 3. Vityazev V.V. Tsifrovaya chastotnaya selektsiya signalov. M.: Radio i svyaz', 1993. 240 s. 4. Vityazev V.V. Mnogoskorostnaya obrabotka signalov.  M.: Goryachaya liniya  Telekom, 2017.  336 s.
Abstract In this article, we present several typical examples of solving the problems of synthesizing integer IIR of minimum data representation capacity, examples illustrating the principal possibilities of this approach to the multifunctional design of digital systems. The stability of the solution for integer IIR filters is guaranteed by the priority implementation of the functional stability conditions in the process of the INPsynthesis. It is possible to set the required maximum pole radius of the transfer function in the synthesis, which allows to effectively control the quality factor of the designed filter in the event of the occurrence of limit cycles of one kind or another. During the synthesis of the cascade integer filter, the necessary scaling of the signal can be provided. There is no need to use indirect scaling techniques, for example, using Lpnorm. References 2. Rabiner R, Gold B. Theory and application of digital signal processing. Moscow, Mir, 1978, 848 p 3. Sergienko À.B. Digital signal processing. St. Petersburg: Peter, 2002. 608 p 4. EzIIR filter design package. http://www.ti.com/tool/sprc072 5. Mingazin A.T. Synthesis of transfer functions of digital filters in the region of discrete values of coefficients (overview). // Electronic equipment. Ser. 10.1993. ¹ 1,2. p. 335. 6. Mathias Lang. Algorithms for the Constrained Design of Digital Filters with Arbitrary Magnitude and Phase Responses. // Vienna, June 1999. 7. Bugrov V.N. Development of digital filters by methods of integer nonlinear programming. // Vestnik Newsletter NNSU, 2009, ¹ 6. p. 61 – 70. 8. Shkelev E.I., Bugrov V.N., Proidakov V.I., Artemev V.V. Integer digital filters  effective solution for 8bits digital platforms. Moscow, Components and technologies, ¹ 10, 2013, p. 104 – 110. 9. Bugrov V.N., Proidakov V.I., Artemev V.V. Synthesis of digital filters by methods of integer nonlinear programming. 17th international conference "Digital signal processing and its applications – DSPA2915", Abstracts. M: NTO RES them. A. S. Popov, 2015, p. 200 – 204. 10. Bugrov V.N. Complex selective problems of integer digital filtering. Moscow, Components and technologies, ¹ 10, 2016, p. 100 – 120. 11. Bugrov V.N, Morozov N.S. Integer design of FIR Filters with linear phase. // DSPA, ¹ 1, 2016, p. 14 – 19. 12. Demðster A.G., Macleod M.D. IIR digital filter design using minimum adder multiplier blocks.//IEEE Trans.on Circuits and SystemsII, 1998, v. 45, N 6. 13. Voinov B.S., Bugrov V.N., Voinov B.B. Informacionnie tekhnologii i sistemi: poisk optimalnih, originalnih i racionalnih resheniy. Moscow.: Science, 2007, 730 p. 14. Semenov B.U. Microcontrollers MSP430. The first acquaintance, Moscow: Publishing house "Solonpress", 2006. 15. Kisel V.A. Analog and Digital Correctors: A Handbook.  M .: Radio and Communication, 1986, 184 p
The specified effect is realized in a multichannel frequency measurement system using several parallel connected signal recirculator with adjustable delay periods in the feedback circuits. The effectiveness of the method has been studied theoretically and experimentally. The accuracy and sensitivity of the method are estimated as a function of the interference intensity at the input of the measurer. It is shown that for a signaltointerference ratio of 20 dB or more, the error of the new method does not exceed (1 ... 2) % of the nominal value of the frequency. It is agrees well with the potentially achievable accuracy under the conditions in question. In conditions of high noise the gain the threshold value of the signaltointerference ratio in comparison with the world analogs is 45 dB or more. The received results and conclusions drawn allow to recommend this method for practical application in systems of the automatic speech processing in the conditions of action of the intensive acoustic noise. 2. Fant G. Akusticheskaya teoriya recheobrazovaniya. – M.: Nauka, 1964. – 304 s. 3. Savchenko V.V. Ocenka kachestva cifrovoj peredachi rechi po konechnoj vyborke rechevogo signala // Ehlektrosvyaz'. 2017. ¹ 3. S. 5257. 4. Lebedeva N.N., Karimova E.D., Kazimirova E.A. Analiz rechevogo signala v issledovaniyah funkcional'nogo sostoyaniya cheloveka // Biomedicinskaya radioehlektronika. 2015. ¹ 2. S. 312. 5. Andreeva N.G., Smirnova T.A. Vospriyatie sintezirovannyh modelej odnoformantnyh glasnyh s raznoj chastotoj osnovnogo tona // Sensornye sistemy. 2014. T. 28. ¹ 4. S. 1321. 6. Chernobel'skij S.I. Sravnenie rezul'tatov akusticheskogo analiza golosa pri razlichnyh sposobah ego zapisi // Vestnik otorinolaringologii. 2014. ¹ 1. S. 4143. 7. Alimuradov A.K. Issledovanie chastotnoizbiratel'nyh svojstv metodov dekompozicii na ehmpiricheskie mody dlya ocenki chastoty osnovnogo tona rechevyh signalov // Trudy Moskovskogo fizikotekhnicheskogo instituta. 2015. T. 7. ¹ 3 (27). S. 5668. 8. Vishnyakova O.A., Lavrov D.N. Gibridnyj algoritm vydeleniya chastoty osnovnogo tona // Matematicheskie struktury i modelirovanie. 2016. ¹ 1 (37). S. 5965. 9. Gaj V.E. Metod ocenki chastoty osnovnogo tona v usloviyah pomekh // Cifrovaya obrabotka signalov. 2013. ¹ 4. S. 6571. 10. Arhipov I.O., Giniyatullin R.R. Avtokorrelyacionnyj vydelitel' osnovnogo tona s predvaritel'nym ocenivaniem chastoty kolebanij golosovyh svyazok // V sbornike: "Molodye uchenye  uskoreniyu nauchnotekhnicheskogo progressa v XXI veke".  Izhevsk: Izdvo: INNOVA, 2016. S. 421428. 11. Savchenko V.V., Savchenko A.V. Information Theoretic Analysis of Efficiency of the Phonetic Encoding–Decoding Method in Automatic Speech Recognition // Journal of Communications Technology and Electronics. 2016. Vol. 61. No. 4. P. 430435. 12. Azarov I.S., Vashkevich M.I., Petrovskij A. Algoritm ocenki mgnovennoj chastoty osnovnogo tona rechevogo signala // Cifrovaya obrabotka signalov. 2012. ¹ 4. S. 4957. 13. Vol'f D.A., Meshcheryakov R.V. Model' i programmnaya realizaciya singulyarnogo ocenivaniya chastoty osnovnogo tona rechevogo signala // Trudy SPIIRAN. 2015. ¹ 6. S. 191209. 14. Savchenko V.V. Testirovanie sluchajnyh vremennyh ryadov na stacionarnost' na osnove principa minimuma informacionnogo rassoglasovaniya // Izvestiya vuzov. Radiofizika. 2017. T. 60. ¹ 1. S. 8996. 15. Savchenko V.V. Enhancement of the Noise Immunity of a VoiceActivated Robotics Control System Based on Phonetic Word Decoding Method // Journal of Communications Technology and Electronics. 2016. Vol. 61. No. 12. P. 1374 1379. 16. 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Abstract When developing a FMCW SAR, the ADC resolution is chosen based on the dynamic range of echo signals output by the receiver. Compared with impulse systems, here the dynamic range is characterised by larger values, because its upper boundary is determined not by the total strength of a separate distance range being resolved, but by the total strength of the echo signal of the whole surface being mapped within the antenna illumination footprint. In addition, in smallsize FMCW SARs, it is not possible to implement the traditional techniques of dynamicrange extension used in impulse radars (sensitivitytime control and cosecant antenna patterns), because distances are measured based on the frequency principle and stringent requirements are set for the weight and sizerelated characteristics of the antenna systems. As a result, the dynamic range of the signals may reach around 70–80 dB, which suggests ADC resolutions of 12–14 bits and sampling rates of up to tenths of MHz. Studies aimed at reducing the amount of information recorded (to enable its transmission via a radio channel from the UAV to the ground station) have shown that a progressive reduction of the ADC resolution from 16 bits to 8, 4, 2 and 1 bits does not lead to a noticeable visual decrease in the quality of radar images created and in their deciphering qualities, due to the oversampling effect. In this paper, we present a method of validating requirements for the ADC resolution in FMCW SARs (given the conditions under which the surface survey must be performed) that takes into account the oversampling effect. The results obtained show that the ADC resolution can be significantly reduced (down to binary quantization) without any loss of the quality of radar images created. This reduction in the amount of information recorded by a FMCW SAR allows us to lower, proportionately to the reduction in the ADC resolution, computing requirements when synthesizing radar images (including on the carrier) and radiochannel throughput requirements when transmitting recorded signals to the ground control station. 2. Sandia National Laboratories // URL: http://www.sandia.gov. 3. ImSAR LLC // URL: http://www.imsar.com. 4. Bogomolov A.V., Kuprjashkin I.F., Lihachev V.P., Rjazancev L.B. Malogabaritnaja dvuhdiapazonnaja RSA dlja bespilotnogo aviacionnogo kompleksa. Trudy XXIX Vserossijskogo simpoziuma «Radiolokacionnoe issledovanie prirodnyh sred» SPb.: VKA imeni A.F.Mozhajskogo, 2015. no 11. pp. 237242. 5. Rjazancev L.B. Obosnovanie konstrukcii antennoj sistemy RLS s sintezirovannoj aperturoj dlja BLA malogo klassa // Antenny. 2016. no 5. pp. 4955. 6. Lajons R. Cifrovaja obrabotka signalov. M.: OOO «BinomPress», 2006. 7. Kester U. Analogocifrovoe preobrazovanie. M.: Tehnosfera, 2007. 8. J.C. Candy, G.C. Temes, “Oversampling Methods for A/D and D/A Conversion,” pp. 129, IEEE Press, 1992. 9. Kuprjashkin I.F, Lihachev V.P. Kosmicheskaja radiolokacionnaja s`emka zemnoj poverhnosti v uslovijah pomeh: monografija. Voronezh: Nauchnaja kniga, 2014. 10. Improving ADC Resolution by Oversampling and Averaging // URL: http://www.silabs.com. 11. Shkol'nyj L.A. Radiolokacionnye sistemy vozdushnoj razvedki, deshifrirovanie radiolokacionnyh izobrazhenij. M.: VVIA im. Prof. N.E. Zhukovskogo, 2008.
Abstract The prediction of the navigation parameter values is carried out for each frame of the video sequence according to the linear models in the finite memory scheme. The optimal estimates of navigational parameters by the correlationextreme algorithm are calculated once when the difference between the forecast and actual values of at least one navigation parameter exceeds the specified error. The comparative tests of the algorithm in comparison with known algorithms of the same type that confirmed the correspondence of the qualitative parameters of the proposed algorithm to the requirements of the corresponding documents were carried out. 2. Baklitsky V.K. Correlationextreme methods of navigation and guidance. Tver: Book club, 2009. 216 p. 3. Babayan P.V., Ershov M.D.. Algoritmyi ustraneniya rassoglosovaniya raznorodnyih izobrazheniy v bortovoy sisteme videniya// Vestnik RSREU, no 54, ñhast 2, Ryazan, 2015. pp. 1520. 4. German E.V., Muratov E.R., Novikov A.I. Matematicheskaya model formirovaniya zonyi neopredelennosti v zadache sovmescheniya izobrazheniy// Vestnik RSREU, no 4, vyip. 46, chast 2. Ryazan, 2013. pp. 1016. 5. Forsythe D.A., Pons J. Computer vision. Modern approach. M .: Williams, 2004. 928 p. 6. Gonzales R., Woods R. Digital image processing. M .: Technosphere, 2005. 1072 p. 7. Efimov A.I., Novikov A.I. Algoritmyi sovmescheniiya izobrazheniy na osnove preobrazovaniya v kompleksnoy ploskosti// Tezisyi nauchno_tehnicheskoy konferentsii «Tehnicheskoe zrenie v sistemah upravleniya», Moskva, 2017. pp. 3436. 8. Novikov A.I., Sablina V.A., Efimov A.I., Nikiforov M.B. Contour Analysis in the tasks of real and virtual images superimposition// Journal Coupled Systems and Multiscale Dynamics, vol 4(4), 2016 pp. 251259. (Doi: 10.1166/jcsmd. 2016.1112 J. Coupled Syst. Multiscale Dyn. vol 4(4)/2330152X/2016/251/009). 9. Canny J.; A computational approach to edge detection; Proc. Of IEEE Transactions on Pattern and Machine Intelligence PAMI8, 679 (1986). 10. Elesina S.I, Lomteva O. A. Increase of image combination performance in combined vision systems using genetic algorithm. Proceedings of the 3rd Mediterranean Conference on Embedded Computing (MECO). Montenegro, Budva, 2014. pp. 158161. 11. Elesina S.I., Efimov A.I. Otbor kriterialnyih funktsiy dlya sistem uluchshennogo i kombinirovannogo videniya// Izvestiya TulGU, tehnicheskie nauki, vyip. 9, ch.1. 2013. pp. 229236.
Abstract As a practical example, the implementation of directionofarrival (DOA) estimator in a passive radar system assembled for position location equipped with active ring array antenna is considered. Modified ANN topology based on multilayer perceptron architecture is used to obtain DOA estimator directly from the output of the network. The results of numerical simulation carried out for the wide range of angles are compared to the optimal numerical solution and the CramerRao Lower Bound. The results indicate that there is no significant dependency of the accuracy of estimator on true parameter value and the standard deviation of estimator increases no more than 10 percent while the consumed computational time decreases no less than 12 times. 2. Haykin S., Neural Networks: A Comprehensive Foundation, 2nd ed. – Prentice Hall; 1998. 3. Baum E., Supervised Learning of Probability Distributions by Neural Networks // American Institute of Physics, 1988, pp. 52–61. 4. Setiono R., A neural network construction algorithm which maximizes the likelihood function // Connection Science, vol. 7, no. 2, 1995, pp. 147–166. 5. C. Cervellera, D. Maccio, M. Muselli, Deterministic learning for maximumlikelihood estimation through neural networks // IEEE Transactions on Neural Networks, vol. 19, no. 8, 2008, pp. 1456–1467. 6. Efimov E.N., Shevgunov T. Ya., Feedforward neural networks synthesis using simple adaptive elements // Journal of Radioelectronics, M.: IRE RAS, No.8, 2012. 7. Efimov E. N., Filimonova D.V., Shevgunov T. Ya. Using feedforward neural networks for implementing maximum likelihood parameter estimators // Naukoemkie Tekhnologii, M.: Radiotehnika. 2015. ¹ 8. pp. 4247. 8. Tatuzov A.L., Application of neural networks in radiolocation. – M.: Radiotehnika. 2009. – 432 p. 9. Strocev A.A., Lomanceva Y.A., Assesment of the influence antenna array topology for direction finder on the quality of neural network generates a peleng estimate // 19th International conference “Digital signal processing and its applications”, M.: IPU RAS, 2931 march 2017, pp. 814–817. 10. Shevgunov T. Ya., Efimov E.N., Filimonova D.V., Synthesis of feedforward artificial neural network approximating a maximum likelihood estimator// 19th International conference “Digital signal processing and its applications”, M.: IPU RAS, 2931 march 2017, pp. 818–822. 11. Kay S.M. Fundamentals of Statistical Signal Processing: Estimation Theory. – Upper Saddle River. – Prentice Hall, 1993. 12. Bolshakov A.A., Karimov R.N., Multidimensional data and time series analysis methods, 2nd ed., M.: Goryachaya LiniyaTelekom, 2014. 13. R. Battiti, First and SecondOrder Methods for Learning: Between Steepest Descent and Newton’s Method // Neural Computation, 1992, Vol. 4, ¹ 2, pp. 141–166. 14. D. W. Marquardt, An algorithm for leastsquares estimation of nonlinear parameters // J. Soc. Ind. Appl. Math., vol. 11, 1963, pp. 431–441. 15. Dubrovin A. V., Sosulin Y. G. Onestage estimation of the position of a radio source by a combined passive system // Journal of Communications Technology and Electronics, 2007, vol. 52, ¹ 4, pp. 415–430. 16. Zekavat R., Buehrer R. M., Handbook of Position Location: Theory, Practice and Advances. – WileyIEEE Press, 2011 17. Dubrovin A. V., Potential directionfinding accuracy of systems with Antenna Arrays Configured as a set of an arbitrary number of rings // Journal of Communications Technology and Electronics, 2006, Vol. 51, No. 3, pp. 252–254.
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