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Abstract

The problems of constructing stable algorithms for adaptive estimation of the state of control objects with allowance for parametric perturbations based on the theory of conditional Gaussian filtration are considered. Algorithms for estimating the state of stochastic controllable objects using the regularized method of the Cholesky factorization and pseudo-inversion of perturbed symmetric matrices are given. These algorithms allow us to stabilize the procedure for inversion of matrices in estimating the state of stochastic objects and, thereby, to increase the accuracy of determining the true estimate of the state vector when the parameters of the object and the observer are perturbed.

First Page

47

Last Page

51

References

1. M.A.Ogarkov, Metody' statisticheskogo ocenivaniya parametrov sluchayny'h processov [Methods for statistical estimation of random process parameters]. Moskva: E`nergoatomizdat, 1990, 208 p. (in Russian).

2. S.V.Pervachev, A.I.Perov, Adaptivnaya fil'traciya soobsch'eniy [Adaptive filtering of messages]. Moskva: Radio i svyaz', 1991, 160 p. (in Russian).

3. I.N.Sinicy'n, Fil'try' Kalmana i Pugacheva [Kalman and Pugachev filters]. Moskva: Logos, 2006, 640 p. (in Russian).

4. H.Z.Igamberdiev, A.N.YUsupbekov, O.O.Zaripov, Regulyarny'e metody' ocenivaniya i upravleniya dinamicheskimi ob`ektami v usloviyah neopredelennosti [Regular methods for evaluating and managing dynamic objects under uncertainty]. Tashkent: TashGTU, 2012, 320 p.

5. A.A.CHernov, V.D.YAstrebov, “Vozmusch'eniya processa kalmanovskoy fil'tracii” [Perturbations of the Kalman filtration process], Kosm. Issledovaniya, vol. 22, no. 4, pp. 537-542, 1984 (in Russian).

6. K.T.Leondesa, Fil'traciya i stohasticheskoe upravlenie v dinamicheskih sistemah [Filtering and stochastic control in dynamic systems]. Moskva: Mir, 1980, 407 p. (in Russian).

7. A.A.CHernov, V.D.YAstrebov, “Metod ocenki vozmusch'eniy v algoritmah resheniya navigacionny'h zadach” [Methods for evaluating capabilities in algorithms for solving navigation problems], Kosm. Issledovaniya, vol. 22, no. 3, pp. 361-368, 1984 (in Russian).

8. S.V.Sokolov, “O fil'tracii parametricheskih vozmusch'eniy pri lineynom ocenivanii stohasticheskogo ob`ekta” [Filtering parametric features for linear estimation of a stochastic object], Izvestiya vuzov - Priborostroenie, pp. 3-10, 1991 (in Russian).

9. R.SH.Lipcer, A.N.SHiryaev, Statistika sluchayny'h processov [Statistics of random processes]. Moskva: Nauka, 1974, 697 p. (in Russian).

10. M.S.YArly'kov, M.A.Mironov, Markovskaya teoriya ocenivaniya sluchayny'h processov [Markov theory of random process estimation]. Moskva: Radio i svyaz', 1993, 464 p. (in Russian).

11. A.V.Bulinskiy, A.N.SHiryaev, Teoriya sluchayny'h processov [Theory of random processes]. Moskva: Fizmatlit, 2003, 362 p. (in Russian).

12. F.R.Gantmaher, Teoriya matric [Matrix theory]. Moskva: Nauka, 1988, 552 p. (in Russian).

13. Dj.Demmel', Vy'chislitel'naya lineynaya algebra. Teoriya i prilojeniya [Computational linear algebra. Theory and applications]. Moskva: Mir, 2001, 430 p. (in Russian).

14. Dj.Golub, Van CH.Louch, Matrichny'e vy'chisleniya [Matrix calculations]. Moskva: Mir, 1999, 548 p. (in Russian).

15. V.V.Voevodin, YU.A.Kuznecov, Matricy' i vy'chisleniya [Matrix calculations]. Moskva: Mir, 1984, 318 p. (in Russian).

16. CH.Louson, R.Henson, CHislennoe reshenie zadach metoda naimen'shih kvadratov [Numerical solution of least squares problems]. Moskva: Nauka, 1986, 232 p. (in Russian).

17. V.I.Meleshko, “O regulyarizovanny'h neortogonal'ny'h faktorizaciyah i psevdoobrasch'eniyah vozmusch'enny'h matric” [On regularized non-orthogonal factorizations and pseudo-conversions of perturbed matrices], J. vy'chisl. matem. i matem. fiz., vol. 26, no. 4, pp. 485-498, 1986 (in Russian).

18. V.M.Verjbickiy, Vy'chislitel'naya lineynaya algebra [Computational linear algebra]. - Moskva: Vy'ssh. shk., 2009, 351 p. (in Russian).

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