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UDC 62-51 DOI: 10.14529/ctcr150309 The Signals Processing in Radionavigation as a Ill-Posed Inverse Problems with Application of the Method of Regularization E.N. Simonov, South Ural State University, Kyshtym Branch, Kyshtym, Chelyabinsk region, Russian Federation, n.e.simonov@yandex.ruD.V. Ivaneev, South Ural State University, Kyshtym Branch, Kyshtym, Chelyabinsk region, Russian Federation, strato5128@inbox.ruAbstractOn the basis of the existing algorithms for processing of radar signals using the methods of solving ill-posed problems and the analysis has been suggested that the problem of reduction in the definition of the regularized solutions is promising and will allow semi-chit increase in accuracy (resolution) noise immunity is at least two times in comparison with existing processing techniques. Three variants of an inverse ill-posed problem and methods of its regularization (such as Tikhonov regularization method, Kalman filter, and so on) with respect to the radar. Analyzed and studied example of regularized solutions for the Fourier transform, which is built on the basis of a decision of the Fredholm integral control of the first kind of convolution type, which is used for mathematical processing of signals in radar, navigation and other fields. Keywordsthe problem of reduction, inverse problems, ill-posed problems, regularization, noise-immunity References1. Sizikov V.S. Matematicheskie metody obrabotki rezul'tatov izmereniy [Mathematical Methods of Processing the Results of Measurements]. St. Petersburg, Politehnic Publ., 2001. 240 p. 2. Polyanin A.D., Manzhirov A.V. Spravochnik po integral'nym uravneniyam: Tochnye resheniya [Handbook of Integral Equations: Exact Solutions]. Moscow, Factorial Publ., 1998. 432p. 3. Tikhonov A.N., Arsenin V.Ya. Metody resheniya nekorrektnykh zadach [Methods for Solving Ill-Posed Problems]. Moscow, Home Edition of the Physical and Mathematical Literature Publ., 1979. 283 p. 4. Simonov E.N. Fizika vizualizatsii izobrazhenii v rentgenovskoy komp'yuternoy tomografii: monografiya [Physics Visualization Image in X-ray Computed Tomography: a Monograph]. Chelyabinsk, South Ural St. Univ. Publ., 2013. 479 p. 5. Kuriksha A.V. Primenenie metodov resheniya nekorrektnykh zadach dlya sinteza algoritmov povysheniya razreshayushchey sposobnosti v radiolokatsii: dis.kand. teh. nauk [Application Methods for Solving Ill-Posed Problems for the Synthesis Algorithms Increasing Resolution in Radar: Thesis of Candidate of Technical Sciences]. Moscow, MSTI, 2006. 92 p. 6. Plokhuta P.A. Issledovanie metodov resheniya nekorrektnykh zadach mnogosignal'noy radiopelengatsii na odnoy chastote [The Study of Methods for Solving Ill-Posed Problems of Multisignalfinding on the Same Frequency: Thesis of Candidate of Technical Sciences]. Moscow, MSTU of N.A. Bauman, 2009, 162 p. 7. Tikhonov V.I. Optimal'nyy priem signalov [Optimal Signals Reception]. Moscow, Radio and Connection Publ., 1983. 320 p. 8. Sizikov V.S. [The Application of Regularization for Stable Computation of the Fourier Transform]. Mathematics and Physics Journal, 1998, vol. 38, no. 3, pp. 376–386. SourceBulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control, Radio Electronics, 2015, vol. 15, no. 3, pp. 66-74. (in Russ.) (Information and Communication Technologies and Systems) |