Real time solution of nonlinear filtering problem without memory I

Mathematical Research Letters

Volumn 7, Issue 5-6, 2000, Pages 671-693

  Yau, Shing Tung ^a   Yau, Stephen S T ^a  

^a NONE

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[No Author keywords available]

Indexed keywords

EID: 0034348672     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/mrl.2000.v7.n6.a2     Document Type: Article

References (13)

1. [Ch] J. Chen, On uniquity of Yau filters, Proceedings of the American Control Conference (Baltimore, Maryland), June 1994, 252-254.
2. [Ch-Ya1] J. Chen and S. S.-T. Yau, Finite-dimensional filters with nonlinear drift VI: Linear structure of Ω, Math. Control Signals Systems 9 (1996), 370-385.
3. [Ch-Ya2] _, Finite-dimensional filters with nonlinear drift VII: Mitter conjecture and structure of η, SIAM J. Control Optim. 35 (1997), 1116-1131.
4. [C-Y-L1] J. Chen, Stephen S.-T. Yau, and C. W. Leung, Finite-dimensional filters with nonlinear drift IV: Classification of finite-dimensional estimation algebras of maximal rank with state space dimension 3, SIAM J. Control Optim. 34 (1996), 179-198.
5. [C-Y-L2] _, Finite-dimensional filters with nonlinear drift VIII: Classification of finite-dimensional estimation algebras of maximal rank with state-space dimension 4, SIAM J. Control Optim. 35 (1997), 1132-1141.
6. [Ch-Ya] W. L. Chiou and S. S.-T. Yau, Finite-dimensional filters with nonlinear drift II: Brockett's problem on classification of finite-dimensional estimation algebras, SIAM J. Control Optim. 32 (1994), 297-310.
7. [Fl-Mi] W. H. Fleming and S. K. Mitter, Optimal control and nonlinear filtering for non degenerate diffusion processes, Stochastics 8 (1982), 63-77.
8. [Hu-Ya] G. W. Hu and S. S.-T. Yau, Finite dimensional filters with nonlinear drift X: Explicit solution of DMZ equation, IEEE Trans. Automat. Control, to appear.
9. [Ya-Hu] G.-Q. Hu and S. S.-T. Yau, Finite dimensional filters with nonlinear drift XIV: Classification of finite dimensional estimation algebras of maximal rank with arbitrary state space dimension and Mitter conjecture, Preprint.
10. [Ma] S. Marcus, Algebraic and geometric methods in nonlinear filtering, SIAM J. Control Optim. 22 (1984), 817-844.
11. [T-W-Y] 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), 173-185.
12. [Ya-Ya1] S. T. Yau and S. S.-T. Yau, Finite dimensional filters with nonlinear drift III: Duncan-Mortensen-Zakai equation with arbitrary initial condition for Kalman-Bucy filtering system and Benes filtering system, IEEE Transactions on Aerospace and Electronic Systems 33 (1997), 1277-1294.
13. [Ya-Ya2] _, Existence and uniqueness and decay estimates for the time dependent parabolic equation with application to Duncan-Mortensen-Zakai equation, Asian J. Math. 2 (1998), 1079-1149.