臺灣博碩士論文加值系統

卡門-巴希(Kalman-Bucy)濾波器之初值的統計值若以任意區域作為模型時，會使得線性濾波器改變為非線性濾波器，增加其電路系統的複雜。基於此，邱成棟[1]提出一種新的方法，以解決卡門-巴希濾波器的缺點。因此依據邱教授之理論可得到下列優點：1)不須解Riccati方程式，2)可以任意設定初始資料，不須以高斯分布為設定值。
本論文中，我們提出邱式濾波系統之結構設計方法，並採取硬體和軟體合併設計的理論來設計此系統。根據邱教授的理論所得到的常微分方程式並不適合數位化處理，為使其理論能應用至實際電路中，針對其中常微分方程式我們提出了平行化改良方法，改良後的公式不僅更簡明易懂，而且更適合平行化處理。除此之外，我們根據其理論方法，做進一步的探討與分析。

Kalman-Bucy filter is nonlinear and complicated because the initial statistical data is assumed to be in an arbitrary region. Therefore, a new method was proposed by Stephen S.T. Yau [1] to overcome this problem. There are two advantages with his method: (1) no need to solve the Riccati equation by trial-and-error, and (2) the initial data can be arbitrarily assigned without the Gaussian distribution.
The architecture for the Yau filtering system is schemed in this thesis. We intended hardware-software co-design methodology to be used for the system. New formulas suitable for parallel processing are proposed. The formula based on Yau's theory for the ODE-solvers are not suitable for digital computation. To put his theory into practice, we proposed an ODE-solver for the Yau filering system in this thesis. The improved formula is an simple and suitable for parallel processing. Moreover, according to this improved result, further investigation and analysis has been made.

CHAPTER 1 INTRODUCTION
CHAPTER 2 FILTER DESIGN
CHAPTER 3 THE YAU FILTER
CHAPTER 4 Experimental Results
CHAPTER 5 Conclusions
REFERENCES

[1] S.S.-T. Yau and S.T. Yau. "New direct method for Kalman-Bucy filtering system with arbitrary initial condition", Proceedings of 33ed CDC at Lake Buena Vista, Florida, pages 1221-1225, Dec. 1994.
[2] S.S.-T. Yau and S.T. Yau. "Finite-Dimensional Filters with Nonlinear Drift Ⅲ:Duncan-Mortensen-Zakai Equation with Arbitrary Initial Condition for the Linear Filtering System and the Benes Filtering System", IEEE Transactions on Aerospace and Electronic System,4,10(1997),1277-1294
[3] 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. Systems, Estimation and Control 4, no. 2 (1994), 181-203.
[4] S.S.-T. Yau, "Recent results on nonlinear filtering: New class of finite dimensional filters", Proceedings of the 29th Conference on Decision and Control at Honolulu, Hawaii, Dec. 1990, 231-233.
[5] S.S.-T. Yau and G.Q. Hu. "Direct method without Riccati equation for Kalman-Bucy filtering system with arbitrary initial condition.", IFAC 13th Word Congress, San Franciso, pages 469-474.
[6] H.W. Cheng. "Parallel ODE-Solvers for Kalman-Bucy Filter with Arbitrary Initial Condition", Proceedings of the 35th, Conference on Decision and Control Kobe, Japan, December 1996.
[7] R.T. Dong, L.-F. Tam, W.-S. Wong, and S.S.-T. Yau, "Structure and classification theorems of finite-dimensional exact estimation algebras", SIAM J. Control and Optimization 29, no. 4(1991), 866-877.