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Volumn 45, Issue 11, 2000, Pages 2028-2046

Minimal realization and dynamic properties of optimal smoothers

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CASCADE CONTROL SYSTEMS; ERROR ANALYSIS; MARKOV PROCESSES; MATHEMATICAL MODELS; MATRIX ALGEBRA; POLES AND ZEROS; RICCATI EQUATIONS; SIGNAL FILTERING AND PREDICTION; STATE ESTIMATION; STATE SPACE METHODS;

EID: 0034318326     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.887625     Document Type: Article
Times cited : (10)

References (31)
  • 1
    • 0021493808 scopus 로고
    • Linear estimation of boundary value stochastic processes - Part II: 1-D smoothing problems
    • M. B. Adams, A. S. Willsky, and B. C. Levy, "Linear estimation of boundary value stochastic processes - Part II: 1-D smoothing problems," IEEE Trans. Automat. Contr., vol. AC-29, pp. 811-821, 1984.
    • (1984) IEEE Trans. Automat. Contr. , vol.AC-29 , pp. 811-821
    • Adams, M.B.1    Willsky, A.S.2    Levy, B.C.3
  • 2
    • 0001076547 scopus 로고
    • A system theory criteria for positive real matrices
    • B. D. O. Anderson, "A system theory criteria for positive real matrices," SIAM J. Contr., vol. 5, pp. 171-182, 1967.
    • (1967) SIAM J. Contr. , vol.5 , pp. 171-182
    • Anderson, B.D.O.1
  • 3
    • 0004702092 scopus 로고
    • The inverse problem of stationary convariance generation
    • _, "The inverse problem of stationary convariance generation," J. Statist. Phys, vol. 1, pp. 133-147, 1969.
    • (1969) J. Statist. Phys , vol.1 , pp. 133-147
  • 5
    • 0018681624 scopus 로고
    • A stochastic realization approach to the smoothing problem
    • F. Badawi, A. Lindquist, and M. Pavon, "A stochastic realization approach to the smoothing problem," IEEE Trans. Automat. Contr., vol. AC-24, pp. 878-888, 1979.
    • (1979) IEEE Trans. Automat. Contr. , vol.AC-24 , pp. 878-888
    • Badawi, F.1    Lindquist, A.2    Pavon, M.3
  • 6
    • 34250491432 scopus 로고
    • Controlled and conditioned invariant subspaces in linear system theory
    • G. Basile and G. Marro, "Controlled and conditioned invariant subspaces in linear system theory," J. Optim. Theory Appl., vol. 3, pp. 306-316, 1973.
    • (1973) J. Optim. Theory Appl. , vol.3 , pp. 306-316
    • Basile, G.1    Marro, G.2
  • 8
    • 0028524134 scopus 로고
    • A prametrization of minimal stochastic realizations
    • A. Ferrante, "A prametrization of minimal stochastic realizations," IEEE Trans. Automat. Contr., vol. 39, no. 10, pp. 2122-2126, 1994.
    • (1994) IEEE Trans. Automat. Contr. , vol.39 , Issue.10 , pp. 2122-2126
    • Ferrante, A.1
  • 9
    • 0020089575 scopus 로고
    • On the structure of minimal square spectral factors
    • L. Finesso and G. Picci, "On the structure of minimal square spectral factors," IEEE Trans. Automat. Contr., vol. AC-27, pp. 122-127, 1982.
    • (1982) IEEE Trans. Automat. Contr. , vol.AC-27 , pp. 122-127
    • Finesso, L.1    Picci, G.2
  • 11
    • 0003502435 scopus 로고
    • A. Gelb, Ed., Cambridge, MA: MIT Press
    • A. Gelb, Ed., Applied Optimal Estimation. Cambridge, MA: MIT Press, 1974.
    • (1974) Applied Optimal Estimation
  • 12
    • 0010354847 scopus 로고
    • Englewood Cliffs, NJ: Prentice-Hall
    • T. Kailath, Linear System Theory. Englewood Cliffs, NJ: Prentice-Hall, 1980.
    • (1980) Linear System Theory
    • Kailath, T.1
  • 13
    • 84941526864 scopus 로고
    • An innivations approach to least-squares estimation - Part II: Linear smoothing in additive noise
    • T. Kailath and P. A. Frost, "An innivations approach to least-squares estimation - Part II: Linear smoothing in additive noise," IEEE Trans. Automat. Contr., vol. AC-13, pp. 655-660, 1968.
    • (1968) IEEE Trans. Automat. Contr. , vol.AC-13 , pp. 655-660
    • Kailath, T.1    Frost, P.A.2
  • 14
    • 0025480304 scopus 로고
    • Modeling and estimation of discrete-time Gaussian reciprocal processes
    • Sept.
    • B. C. Levy, R. Frezza, and A. J. Krener, "Modeling and estimation of discrete-time Gaussian reciprocal processes," IEEE Trans. Automat. Contr., vol. 35, pp. 1013-1023, Sept. 1990.
    • (1990) IEEE Trans. Automat. Contr. , vol.35 , pp. 1013-1023
    • Levy, B.C.1    Frezza, R.2    Krener, A.J.3
  • 16
    • 0018468516 scopus 로고
    • On the stochastic realization problem
    • A. Lindquist and G. Picci, "On the stochastic realization problem," SIAM J. Contr. Optim., vol. 17, pp. 365-389, 1979.
    • (1979) SIAM J. Contr. Optim. , vol.17 , pp. 365-389
    • Lindquist, A.1    Picci, G.2
  • 17
    • 0029272296 scopus 로고
    • Zeros of spectral factors, the geometry of splitting subspaces, and the algebraic Riccati inequality
    • A. Lindquist, Gy. Michaletzky, and G. Picci, "Zeros of spectral factors, the geometry of splitting subspaces, and the algebraic Riccati inequality," SIAM J. Contr. Optim., vol. 33, no. 401, p. 365, 1995.
    • (1995) SIAM J. Contr. Optim. , vol.33 , Issue.401 , pp. 365
    • Lindquist, A.1    Michaletzky, Gy.2    Picci, G.3
  • 18
    • 0000097466 scopus 로고
    • A geometric approach to modeling and estimation of linear stochastic systems
    • A. Lindquist and G. Picci, "A geometric approach to modeling and estimation of linear stochastic systems," J. Math. Syst., Estim. Contr., vol. 1, pp. 241-333, 1991.
    • (1991) J. Math. Syst., Estim. Contr. , vol.1 , pp. 241-333
    • Lindquist, A.1    Picci, G.2
  • 19
    • 33749889372 scopus 로고    scopus 로고
    • Geometric methods for state-space identification
    • S. Bittanti and G. Picci, Eds. Berlin, Germany: Springer-Verlag
    • _, "Geometric methods for state-space identification," in Identification, Adaptation, Learning, S. Bittanti and G. Picci, Eds. Berlin, Germany: Springer-Verlag, 1996.
    • (1996) Identification, Adaptation, Learning
  • 20
    • 0002174025 scopus 로고
    • A solution of the smoothing problem for linear dynamic systems
    • D. Q. Mayne, "A solution of the smoothing problem for linear dynamic systems," Automatica, vol. 4, pp. 73-92, 1966.
    • (1966) Automatica , vol.4 , pp. 73-92
    • Mayne, D.Q.1
  • 21
    • 0000915211 scopus 로고
    • The time-invariant linear-quadratic optimal-control problem
    • B. P. Molinari, "The time-invariant linear-quadratic optimal-control problem," Automatica, vol. 13, pp. 347-357, 1977.
    • (1977) Automatica , vol.13 , pp. 347-357
    • Molinari, B.P.1
  • 22
    • 0017483257 scopus 로고
    • Least-squares estimation of discrete linear dynamical systems using orthogonal transformations
    • C. C. Paige and M. A. Sauders, " Least-squares estimation of discrete linear dynamical systems using orthogonal transformations," SIAM J. Numer. Anal., vol. 14, pp. 180-193, 1977.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 180-193
    • Paige, C.C.1    Sauders, M.A.2
  • 23
    • 0030150960 scopus 로고    scopus 로고
    • New square-root smoothing algorithms
    • P. Park and T. Kailath, " New square-root smoothing algorithms," IEEE Trans. Automat. Contr., vol. 41, pp. 727-732, 1996.
    • (1996) IEEE Trans. Automat. Contr. , vol.41 , pp. 727-732
    • Park, P.1    Kailath, T.2
  • 24
    • 0018995623 scopus 로고    scopus 로고
    • Stochastic realization and invariant directions of the matrix Riccati equation
    • M. Pavon, "Stochastic realization and invariant directions of the matrix Riccati equation," SIAM J. Contr. Optim., vol. 18, pp. 155-180.
    • SIAM J. Contr. Optim. , vol.18 , pp. 155-180
    • Pavon, M.1
  • 25
    • 43949159970 scopus 로고
    • A causal modes and balanced realizations of stationary processes
    • G. Picci and S. Pinzoni, "A causal modes and balanced realizations of stationary processes," Linear Algebra Applicat., vol. 205-206, pp. 997-1043, 1994.
    • (1994) Linear Algebra Applicat. , vol.205-206 , pp. 997-1043
    • Picci, G.1    Pinzoni, S.2
  • 26
    • 21644483999 scopus 로고
    • Maximum likelihood estimates of linear dynamic systems
    • H. E. Rauch, F. Tung, and C. T. Striebel, " Maximum likelihood estimates of linear dynamic systems," AIAA J., vol. 3, pp. 1445-1450, 1965.
    • (1965) AIAA J. , vol.3 , pp. 1445-1450
    • Rauch, H.E.1    Tung, F.2    Striebel, C.T.3
  • 28
    • 0016987023 scopus 로고
    • New smoothing algorithms based on reversed-time lumped models
    • G. S. Sidhu and U. B. Desai, " New smoothing algorithms based on reversed-time lumped models," IEEE Trans. Automat. Contr., vol. AC-21, pp. 538-541, 1976.
    • (1976) IEEE Trans. Automat. Contr. , vol.AC-21 , pp. 538-541
    • Sidhu, G.S.1    Desai, U.B.2
  • 29
    • 0019599168 scopus 로고
    • On complementary models and fixed-interval smoothing
    • H. L. Weinert and U. B. Desai, "On complementary models and fixed-interval smoothing," IEEE Trans. Automat. Contr., vol. AC-26, 1981.
    • (1981) IEEE Trans. Automat. Contr. , vol.AC-26
    • Weinert, H.L.1    Desai, U.B.2
  • 30
    • 0015206454 scopus 로고
    • Least squares stationary optimal control and the algebraic Riccati equation
    • J. C. Willems, "Least squares stationary optimal control and the algebraic Riccati equation," IEEE Trans. Automat. Contr., vol. AC-16, pp. 621-634, 1971.
    • (1971) IEEE Trans. Automat. Contr. , vol.AC-16 , pp. 621-634
    • Willems, J.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.