在這篇碩士論文中，我們首先介紹線性的卡爾曼濾波，這也是卡爾曼最先推導出來的形式，接著我們介紹非線性的卡爾曼濾波：擴張卡爾曼濾波、無先導式卡爾曼濾波。無先導式卡爾曼濾波是這篇論文注重的部分，論文中將無先導式卡爾曼濾波與擴張卡爾曼濾波做詳細的比較，在論文的後半我們簡單介紹混沌同步的概念，利用混沌同步的概念我們發展了一種新型態的卡爾曼濾波：兩階段卡爾曼濾波。最後一章我們簡介 MATLAB Simulink ，將擴張卡爾曼濾波在 Simulink 上實現。

In this thesis, we firstly give a brief introduction to the linear Kalman filter, which is the beginning approach of Kalman filter. Next we introduce two Kalman filters for the nonlinear case: extended Kalman filter and unscented Kalman filter. Unscented Kalman filter is emphasized in this thesis. We compare extended Kalman filter and unscented Kalman filter in details. In Chapter 4, we illustrate the concept of synchronization of dynamical system, and use the synchronization technique to develop a new Kalman filter algorithm, named two stage Kalman filter. In the end of the thesis, we demonstrate numerical implement of the extended Kalman filter on MatLab SimuLink.

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