自從卡門濾波器的技術被普及化之後，一直以來有對有限維度的遞迴濾波器有一種強烈的關注。在一九九○年，邱成棟博士提出一個新的有限為度的遞迴濾波器。他認為在濾波系統中對所有的 都必須滿足 constant 更證明這個條件完全符合線性要領加上一個滿足Benses條件的非線性要領。此外他精確的建構出一個包含獨特性的初始條件的有限維度濾波器，我們將它叫做邱氏濾波器。
　　在邱氏濾波系統之中，在某個條件下DMZ方程式能夠被化減成線性的Kolmogorov方程式。藉由Kolmogorov方程式的線性，經過解一個包含高斯初始條件的有限個數的Kolmogorov方程式我們可以得到一個近似解 。
　　在本論文為中，我們使用DMZ方程式來算出邱氏濾波系統的狀態機率密度，並且利用此狀態機率密度來算出我們所要求的狀態輸出。我們是用軟體來完成它。

　　Even since the technique of the Kalman filter was popularized, there has been an intense interest in filtering new classes of finite dimensional recursive filters. In 1990, Yau introduced a new class of finite dimensional recursive filter. He considered the filtering system with drift term satisfying constant for all . He proved that this corresponds to exactly the linear drift plus a nonlinear one satisfying Benses condition. He constructed explicitly finite dimensional filter with arbitrarily initial condition. Henceforth, we will name these filters after Yau.
　　In the Yau filtering system, under certain condition, the DMZ equation can be reduced to the linear Kolmogorov equation. By the linearity of the Kolmogorov equation, an approximate solution can be obtained by solving a finite number of kolmogorov equation with Gaussian initial condition.
　　In this thesis, we use the solution of DMZ equation to calculate the conditional probability density of the Yau filtering system and use the condition probability density to calculate the output of state in software.

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