메뉴 건너뛰기




Volumn 44, Issue 3, 2006, Pages 1019-1039

Solution of filtering problem with nonlinear observations

Author keywords

DMZ equation; Filtering problem; Kolmogorov equation; Nonlinear observations; Real time computation

Indexed keywords

DMZ EQUATION; FILTERING PROBLEM; KOLMOGOROV EQUATION; NONLINEAR OBSERVATIONS; REAL TIME COMPUTATION;

EID: 33646554492     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902411970     Document Type: Article
Times cited : (5)

References (27)
  • 1
    • 33646561356 scopus 로고
    • Approximation of the Zakai equation by the splitting up method
    • (Warsaw, 1988) (J. Zabczyk, ed.), Springer-Verlag, Berlin
    • A. BENSOUSSAN, R. GLOWINSKI AND A. RASCANU, Approximation of the Zakai equation by the splitting up method, in Stochastic Systems and Optimization (Warsaw, 1988) (J. Zabczyk, ed.), Springer-Verlag, Berlin, (1989), pp. 257-265.
    • (1989) Stochastic Systems and Optimization , pp. 257-265
    • Bensoussan, A.1    Glowinski, R.2    Rascanu, A.3
  • 3
    • 0002237314 scopus 로고
    • The geometry of the conditional density functions
    • O. L. R. Jacobs, et al., eds., Academic Press, New York
    • R. W. BROCKETT AND J. M. C. CLARK, The geometry of the conditional density functions, in Analysis and Optimization of Stochastic Systems, O. L. R. Jacobs, et al., eds., Academic Press, New York, 1980, pp. 299-309.
    • (1980) Analysis and Optimization of Stochastic Systems , pp. 299-309
    • Brockett, R.W.1    Clark, J.M.C.2
  • 4
    • 0021463341 scopus 로고
    • Des resultats de non-existence de filtre de dimension finie
    • M. CHALEYAT-MAUREL AND D. MICHEL, Des resultats de non-existence de filtre de dimension finie, Stochastics, 13 (1984), pp. 83-102.
    • (1984) Stochastics , vol.13 , pp. 83-102
    • Chaleyat-Maurel, M.1    Michel, D.2
  • 5
    • 0030354533 scopus 로고    scopus 로고
    • Finite dimensional filters with nonlinear drift VI: Linear structure of Ω
    • J. CHEN AND S. S.-T. YAU, Finite dimensional filters with nonlinear drift VI: Linear structure of Ω, Math. Control Signals Systems, 9 (1996), pp. 370-385.
    • (1996) Math. Control Signals Systems , vol.9 , pp. 370-385
    • Chen, J.1    Yau, S.S.-T.2
  • 6
    • 0028272761 scopus 로고
    • Finite-dimensional filters with nonlinear drift II: Brockett's problem on classification of finite-dimensional estimation algebra
    • W. L. CHIOU AND S. S.-T. YAU, Finite-dimensional filters with nonlinear drift II: Brockett's problem on classification of finite-dimensional estimation algebra, SIAM J. Control Optim., 32 (1994), pp. 297-310.
    • (1994) SIAM J. Control Optim. , vol.32 , pp. 297-310
    • Chiou, W.L.1    Yau, S.S.-T.2
  • 7
    • 0001610264 scopus 로고
    • On a multiplicative functional transformation arising in nonlinear filtering theory
    • M. H. A. DAVID, On a multiplicative functional transformation arising in nonlinear filtering theory, Z. Wahrsch Verw. Gebiete, 54 (1980), pp. 125-139.
    • (1980) Z. Wahrsch Verw. Gebiete , vol.54 , pp. 125-139
    • David, M.H.A.1
  • 8
    • 0000123636 scopus 로고
    • Approximations to solutions of the Zakai filtering equation
    • R. J. ELLIOTT AND R. GLOWINSKI, Approximations to solutions of the Zakai filtering equation, Stochastic Anal. Appl., 7 (1988), pp. 145-168.
    • (1988) Stochastic Anal. Appl. , vol.7 , pp. 145-168
    • Elliott, R.J.1    Glowinski, R.2
  • 9
    • 33646568246 scopus 로고    scopus 로고
    • Time-discretization of the Zakai equation for diffusion processes observed in correlated noise, Analysis and Optimization of Systems
    • A. Bensoussan and J.J. Lions, eds., Springer-Verlag, Berlin
    • P. FLORCHINGER AND F. LEGLAND, Time-discretization of the Zakai equation for diffusion processes observed in correlated noise, Analysis and Optimization of Systems, A. Bensoussan and J.J. Lions, eds., Lecture Notes in Inform. Sci. and Control, 144, Springer-Verlag, Berlin, pp. 228-237,
    • Lecture Notes in Inform. Sci. and Control , vol.144 , pp. 228-237
    • Florchinger, P.1    Legland, F.2
  • 11
    • 84972561398 scopus 로고
    • Stochastic differential equations for the nonlinear filtering problem
    • M. FUJISAKI, G. KALLIANPUR AND H. KUNITA, Stochastic differential equations for the nonlinear filtering problem, Osaka J. Math., 1 (1972), pp. 19-40.
    • (1972) Osaka J. Math. , vol.1 , pp. 19-40
    • Fujisaki, M.1    Kallianpur, G.2    Kunita, H.3
  • 12
    • 85024423711 scopus 로고
    • New results in linear filtering and prediction theory
    • R. E. KALMAN AND R. S. BUCY, New results in linear filtering and prediction theory, Trans. ASME Ser. D. J. Basic Engrg., 83 (1961), pp. 95-108.
    • (1961) Trans. ASME Ser. D. J. Basic Engrg. , vol.83 , pp. 95-108
    • Kalman, R.E.1    Bucy, R.S.2
  • 14
    • 0001272602 scopus 로고
    • On the analogy between mathematical problems of nonlinear filtering and quantum physics
    • S. K. MITTER, On the analogy between mathematical problems of nonlinear filtering and quantum physics, Ricerche Automat., 10 (1979), pp. 163-216.
    • (1979) Ricerche Automat. , vol.10 , pp. 163-216
    • Mitter, S.K.1
  • 15
    • 0025256772 scopus 로고
    • On a necessary and sufficient condition for finite dimensionality of estimation algebras
    • L.-F. TAM, W. S. WONG, AND S. S.-T. YAU, On a necessary and sufficient condition for finite dimensionality of estimation algebras, SIAM J. Control Optim., 28 (1990), pp. 173-185.
    • (1990) SIAM J. Control Optim. , vol.28 , pp. 173-185
    • Tam, L.-F.1    Wong, W.S.2    Yau, S.S.-T.3
  • 16
    • 0025551914 scopus 로고
    • Recent results on nonlinear filtering: New class of finite dimensional filters
    • Honolulu
    • S. S.-T. YAU, Recent results on nonlinear filtering: New class of finite dimensional filters, in Proceedings of the 29th Conf. Decision and Control, Honolulu, 1990, pp. 231-233.
    • (1990) Proceedings of the 29th Conf. Decision and Control , pp. 231-233
    • Yau, S.S.-T.1
  • 17
    • 0000943914 scopus 로고
    • Finite dimensional filters with nonlinear drift I: A class of filters including both Kalman-Bucy filters and Benes filters
    • S. S.-T. YAU, Finite dimensional filters with nonlinear drift I: A class of filters including both Kalman-Bucy filters and Benes filters, J. Math. Syst., Estimation and Control, 4(2) (1994), pp. 181-203.
    • (1994) J. Math. Syst., Estimation and Control , vol.4 , Issue.2 , pp. 181-203
    • Yau, S.S.-T.1
  • 18
    • 0008289982 scopus 로고    scopus 로고
    • Brockett's problem on nonlinear filtering theory
    • Lectures on Systems, Control and Information, AMS/IP
    • S. S.-T. YAU, Brockett's problem on nonlinear filtering theory, in Lectures on Systems, Control and Information, AMS/IP, Stud. Adv. Math., 17 (2000), pp. 177-212.
    • (2000) Stud. Adv. Math. , vol.17 , pp. 177-212
    • Yau, S.S.-T.1
  • 19
    • 0002436645 scopus 로고    scopus 로고
    • Direct method without Riccati equation for Kalman-Bucy filtering system with arbitrary initial conditions
    • San Francisco, CA
    • S.-T. YAU AND G.-Q. Hu, Direct method without Riccati equation for Kalman-Bucy filtering system with arbitrary initial conditions, in Proceedings of the 13th World Congress IFAC, vol. II, San Francisco, CA, 1996, pp. 469-474.
    • (1996) Proceedings of the 13th World Congress IFAC , vol.2 , pp. 469-474
    • Yau, S.-T.1    Hu, G.-Q.2
  • 20
    • 0035114853 scopus 로고    scopus 로고
    • Finite dimensional filters with nonlinear drift. X: Explicit solution of DMZ equation
    • S. S.-T. YAU AND G. Q. Hu, Finite dimensional filters with nonlinear drift. X: Explicit solution of DMZ equation, IEEE Trans. Automat. Control, 46 (2001), pp. 142-148.
    • (2001) IEEE Trans. Automat. Control , vol.46 , pp. 142-148
    • Yau, S.S.-T.1    Hu, G.Q.2
  • 22
    • 0033235847 scopus 로고    scopus 로고
    • Hessian matrix non-decomposition theorem
    • S. S.-T. YAU, X. Wu AND W. S. WONG, Hessian Matrix non-decomposition theorem, Math. Res. Lett., 6 (1999), pp. 663-673.
    • (1999) Math. Res. Lett. , vol.6 , pp. 663-673
    • Yau, S.S.-T.1    Wu, X.2    Wong, W.S.3
  • 23
    • 0031258187 scopus 로고    scopus 로고
    • Finite dimensional filters with nonlinear drift III: Duncan-Mortensen- Zakai equation with arbitrary initial condition for linear filtering system and the Benes filtering system
    • S. S.-T. YAU AND S.-T. YAU, Finite dimensional filters with nonlinear drift III: Duncan-Mortensen-Zakai equation with arbitrary initial condition for linear filtering system and the Benes filtering system, IEEE Trans. Aerosp. Elec. Syst., 33, 1997, pp. 1277-1294.
    • (1997) IEEE Trans. Aerosp. Elec. Syst. , vol.33 , pp. 1277-1294
    • Yau, S.S.-T.1    Yau, S.-T.2
  • 24
    • 0028758480 scopus 로고
    • New direct method for Kalman-bucy filtering system with arbitrary initial condition
    • Lake Buena Vista, FL
    • S. S.-T. YAU AND S.-T. YAU, New direct method for Kalman-Bucy filtering system with arbitrary initial condition, in Proceedings of the 33rd Conf. Decision and Control, Lake Buena Vista, FL, 1994, pp. 1221-1225.
    • (1994) Proceedings of the 33rd Conf. Decision and Control , pp. 1221-1225
    • Yau, S.S.-T.1    Yau, S.-T.2
  • 25
    • 0030296239 scopus 로고    scopus 로고
    • Explicit solution to a Kolmogorov equation
    • S. S.-T. YAU AND S.-T. YAU, Explicit solution to a Kolmogorov equation, Appl. Math. Optim., 34 (1996), pp. 231-266.
    • (1996) Appl. Math. Optim. , vol.34 , pp. 231-266
    • Yau, S.S.-T.1    Yau, S.-T.2
  • 26
    • 0034348672 scopus 로고    scopus 로고
    • Real time solution of nonlinear filtering problem without memory, i
    • S.-T. YAU AND S. S.-T. YAU, Real time solution of nonlinear filtering problem without memory, I, Math. Res. Lett., 7 (2000), pp. 671-693.
    • (2000) Math. Res. Lett. , vol.7 , pp. 671-693
    • Yau, S.-T.1    Yau, S.S.-T.2
  • 27
    • 0001548031 scopus 로고    scopus 로고
    • Existence and uniqueness and decay estimates for the time dependent parabolic equation with application to Duncan-Mortensen-Zakai equation
    • S.-T. YAU AND S. S.-T. YAU, Existence and uniqueness and decay estimates for the time dependent parabolic equation with application to Duncan-Mortensen-Zakai equation, Asian J. Math., 2 (1998), pp. 1079-1149.
    • (1998) Asian J. Math. , vol.2 , pp. 1079-1149
    • Yau, S.-T.1    Yau, S.S.-T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.