本篇論文主旨在於探討結合二維模擬退火法與改良式廣義最大概似演算法之訊號抵達時間估測架構。在稠密的多重路徑超寬頻傳輸環境裡，接收訊號中第一個抵達路徑的估測可以使用廣義最大概似(Generalized Maximum Likelihood, GML) 演算法，由於GML 演算法的運算複雜度高，花費時間亦較長，有時候甚至無法收斂，因此可以採用簡化的改良式廣義最大概似演算法來估測訊號抵達時間。在上述之估測演算法之中都需設定兩個臨界值參數，其中一個參數用於界定搜尋路徑的抵達時間範圍，另一個振幅參數則做為判別路徑真偽的臨界值，臨界值的選定對於估測結果有直接的影響。一般而言，臨界值的設定可使用最小錯誤機率法，透過誤判(false alarm) 機率與遺失(miss)機率相加總合之最小值來設定。為了消除密集多重路徑的影響並降低演算法的複雜度，我們使用均方根誤差統計值來進行最佳臨界值的搜尋。將兩個臨界值限定在一個合適的範圍內隨機變動，在計算所有臨界值組合所得到的均方根誤差值之後，選擇最小均方根誤差所對應的最佳臨界值組做為訊號抵達時間估測演算法之所需。不同於上述類似網格的全盤搜尋方式，我們利用二維模擬退火法，逐步尋找最小的均方根誤差值，以解決必須完全計算臨界值變動區域內每一個均方根誤差值後才能選定最佳臨界值組的問題。模擬退火法相較於最陡坡降法(gradient descent)，能避免區域最小值(local minimum)的情況，並以自動搜尋臨界值的方式，逐步找到較佳的臨界值並改善訊號抵達時間的估測結果。電腦模擬結果顯示，在超寬頻環境中，結合二維模擬退火法與改良式廣義最大概似演算法之架構對於訊號抵達時間的估測準確度，有更佳的結果表現。

The main purpose of this thesis is to combine modified GML algorithm with 2-D simulated annealing for estimation of signal arrival time in the UWB systems.In a dense multipath environment, the generalized maximum-likelihood (GML) algorithm can be used for the time-of-arrival (TOA) estimation. Nevertheless, the GML algorithm usually takes a long period of time, and sometimes fails to converge. Hence, a modified GML (MGML) algorithm is investigated. Two threshold parameters need to be determined in using the estimation algorithm. One threshold is to decide the arrival time range of estimated path, and the other, an amplitude threshold, is to judge whether the estimated path is true. Generally, the decision rule of thresholds may be based on the minimum error probability, which is defined as the sum of false alarm probability and miss probability. To mitigate the effects from noise and dense multipath interference, and to reduce the computational complexity of the algorithm, a method of threshold settings based on the minimum root mean square error (RMSE) criteria is discussed. In this scheme, the RMSE value for each candidate threshold pair in an appropriate region is computed. Constructing an accurate RMSE table and performing a full-scale grid search of adequate threshold settings can be very time-consuming. A 2-D simulated annealing process is adopted for finding the best pair of thresholds for use in the modified GML algorithm. The simulated annealing, different from the gradient descent, can avoid trapping into a local minimum in finding the best threshold pair. The resulting threshold pair makes the modified GML algorithm become more efficient in estimating the signal arrival time with an automatic search manner. Simulation results show that the proposed scheme can achieve better performance than the grid search approaches in UWB environments.

誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....i
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....iv
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..vi
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..viii
1 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......1
1.2 文獻探討及研究動機. . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...3
2 訊號抵達時間估測法及估測演算法臨界值設定. . . . 4
2.1 室內環境之距離量測及定位. . . . . . . . . . . . . . . . . . 4
2.2 超寬頻系統之訊號模型. . . . . . . . . . . . . . . . . . . . . . 7
2.3 訊號抵達時間估測法. . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 廣義最大概似演算法(GML Algorithm) . . . . . . . .10
2.3.2 改良式廣義最大概似演算法(Modified GML Algorithm) . . . 14
2.4 估測演算法的臨界值設定. . . . . . . . . . . . . . ................15
2.4.1 最小錯誤機率法. . . . . . . . . . . . . . . . . . . . . . . . . ......16
2.4.2 均方根誤差統計法. . . . . . . . . . . . . . . . . . . . . . . . ....18
3 結合二維模擬退火法與改良式廣義最大概似法於訊號抵達時間之估測. . . . . 19
3.1 訊號抵達時間估測架構. . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 模擬退火法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......19
3.2.1 模擬退火法的背景及原理介紹. . . . . . . . . . . . . . . . . .19
3.2.2 適用於估測演算法臨界值設定之二維模擬退火法. . . . . . . . . ...22
4 電腦模擬與分析. . . . ...........................................................27
4.1 IEEE 802.15.4 系統之訊號模式. . . . . . . . . . . . . . . . . . 27
4.2 均方根誤差統計法. . . . . . . . . . . . . . . . . . . . . . . . . .........31
4.3 二維模擬退火法用於估測之臨界值設定. . . . . . . . . . . .32
5 結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ..39
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ...40

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