訊號模式及觀測模式通常用來描述一個動態系統模型的認定或估測，如卡門濾波器。訊號模式常用來描述由生成雜訊組成的線性動態方程式，而觀測模式是由線性轉換訊號及高斯白雜訊組成。在本論文中，我們將生成雜訊假設為二元序列。
這離散的生成雜訊使得生成訊號離散。相對的，常見的生成訊號是連續的，而離散的訊號是比連續訊號容易的。然而，離散的訊號還是有許多狀態。因此，定義狀態及減少狀態個數是重要的工作。本論文中，我們利用樹狀結構來定義狀態。集中於最可能的工作狀態來減少狀態個數。再來，我們利用觀測資料，使用兩種方法來還原二元序列。一種是威特比作法，另一個是延伸卡門作法，這兩個方法都是基於訊號狀態的觀念。最後，和連續相位調變方法產生的訊號比較錯誤率。

Signal model and observation model are commonly used to describe a dynamic system model in system identification or estimation such as Kalman filtering. The signal model is usually described by a linear dynamical equation driven by generating noise. The observation model is composed of a linear transformed signal and an additive white Gaussian noise. In this thesis, we set the generating noise to be a white binary sequence.
This discrete generating noise makes the generating signal to be discrete. In contrast, the conventional generating signal is continuous. Discrete signal is simpler than the continuous signal. However, there still are too many states for this discrete signal. Therefore, defining the states and reducing the number of states are important in our work. In this thesis, we apply the tree structure to define the states. The number of states is reduced by focusing on the most probable working states. Afterwards, we apply two methods to recover the white sequence using the observation data. One is the Viterbi method; the other is Extended Kalman filter. Both methods are based upon the concept of signal states. Finally, we compare the error rates with the signal generated by continues phase modulation method.

第1章 引言 1
第2章 CPM(連續相位調變)簡介與其距離頻譜計算 3
2.1 連續相位頻率鍵移CPFSK（Continuous-phase FSK） 3
2.2 連續相位調變CPM（Continuous-Phase Modulation） 5
2.3 GMSK訊號介紹 10
第3章 信號生成與威特比(Viterbi)解碼介紹 13
3.1 信號生成 13
3.1.1 理論： 13
3.1.2 製作： 14
3.2 威特比解碼演算法(Viterbi Algorithm)介紹 18
3.2.1 簡介 18
3.2.2 原理 18
3.2.3 威特比解碼例子 21
第4章 卡門濾波器(Kalman Filter)及延伸卡門濾波器(Extended Kalman Filter)簡介及還原方式介紹 27
4.1 一維卡門濾波器 27
4.1.1 理論 27
4.1.2 在非因果性模型下的卡門濾波 30
第5章 實驗結果與討論 34
5.1 生成信號之錯誤率的比較 34
5.2 不同系統之錯誤率比較 36
5.3 頻譜比較 43
第6章 結論 51
參考文獻 52

[1] Simon Haykin “Communication System”, 4th Edition, JOHN WILEY AND SONS, INC 2001
[2] A. J. Viterbi, “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm,” IEEE Trans. Inform. Theory, IT-13, pp. 260-269, Apr. 1967.
[3] G. D. Forney, Jr,. “Review of random tree codes,” NASA Ames Research Center, Moffett Field, Calif., Appendix A of Final Report on Contract NAS2-3637, NASA CR73176, Dec. 1967.
[4] John B. Anderson, Tor Aulin, Carl-Erik Sunberg, “Digital Phase Modulation,” Plenum press, 1986.
[5] Carl-Erik Sunberg, “Continuous Phase Modulation,” IEEE Communications Magazine, Vol. 24, No. 4, pp 25-35, April 1986.
[6] Kazuaki Murota, Kemkichi Hirade, “GMSK Modulation for Digital Mobile Radio Telephony,” IEEE Transactions on Communications. Vol. COM-29, no. 7, July 1981.
[7] J.W. Woods, ”Two-dimensional Discrete Markovian Fields,” IEEE Trans. Inform. Theory IT-18,232-240(1972)