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研究生:彭明新
論文名稱:有限維過濾系統的構造
論文名稱(外文):The Construction of Finite Dimensional Filter.
指導教授:邱文齡郭仲成許建明許建明引用關係林克保
學位類別:碩士
校院名稱:輔仁大學
系所名稱:數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:24
中文關鍵詞:Duncan-Mortensen-Zakai
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自從Kalman-Bucy過濾在工業上普及化後,大家對找出新的有限維過濾的有了濃厚的興趣.推廣
Kalman過濾至非線性過濾之各式新想法中藉由Duncan-Mortensen-Zakai(DMZ)方程式求取條件密度函數的方法,更為吸引大家.
在這篇論文中,我們研究Yau與Hu所考慮非線性過濾系統其DMZ方程式的明顯解,並呈現出在Hu-Yau條件下,藉由解聯立一階常微分方程組
及一Kolmogorov型方程式,來構造出有限維過濾.
Ever since the technique of Kalman-Bucy filter was popularized, there has been an intense interest in finding
new classes of finite dimensional filters. Among new ideas for extending Kalman filtering to nonlinear filtering, the conditional density approach, via the Duncan-Mortensen-Zakai(DMZ) equation , is more attractable. In this thesis, we study the explicit solution of DMZ equation for the nonlinear filtering system considered by Hu and Yau and exhibit a finite dimensional recursive filter under Hu-Yau conditions by solving a system of first order ordinary differential equations and a Kolmogorov-type equation.
一.引言.............................................1
二.基本觀念.........................................6
三.一個直接構造有限維基本過濾的方法................11
References
[1] Ludwig Arnold, Stochastic Differential Equation: Theory and Applica-tions,
1974, pp. 202-210.
[2] R. W. Brockett, Nonlinear systems and nonlinear estimation theory, in
The Mathematics of Filtering and Identification and Application, M.
Hazewinkel and J. S. Willems, eds., Reidel, Dordrecht, 1981.
[3] 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.
[4] R. W. Brockett, Nonlinear control theory and differential geometry, In
Proc. Internat. Conf. Mathematicians, 1983, pp. 1357-1368.
[5] J. Chen, S. S.-T. Yau and C. W. Leung, Finite-dimensional filters with
nonlinear drift VIII: Classification of finite-dimensional estimation alge-bras
of maximal rank with state-space dimension 4, 1993, pp. 2126-2130.
[6] J. Chen and S. S. -T. Yau, Finite dimensional Filters with nonlinear
drift VII: Mitter conjecture and structure of , SIAM J. Control and
Optimization, Vol. 35, No. 4, July 1997, pp 1116-1131.
[7] J. Chen, S. S.-T. Yau and C. W. Leung, Finite-dimensional filters with
nonlinear drift VI: classification of finite-dimensional estimation algebras
of maximal rank with state-space dimension 3, SIAM J. Control and
Optimization, Vol. 34, No. 1, 1996, pp. 179-198.
[8] J.Chen,On uniquity of Yau filters,Proceedings of the American Control
Conference(Baltimore,Maryland), June 1994, pp. 252-254.
[9] W. L. Chiou and S. S. -T. Yau, Finite-dimensional filters with nonlin-ear
drift II: Brockett’s problem on classification of finite-dimensional
estimation algebras,SIAM J. Control and Optimization, Vol. 32, No. 1,
January 1994, pp. 297-310.
[10] W. L. Chiou, A note on estimation algebras on nonlinear filtering theory,
Systems and Control Letters, Vol. 28, 1996, pp. 55-63.
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