臺灣博碩士論文加值系統

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

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