本論文使用基於廣義概似比的兩種檢定統計法，分別為算術平均數與幾何平均數法以及訊號子空間特徵值法，結合操作在5.8 GHz ISM頻段的調頻相位自我注入鎖定雷達。論文中所提出的雷達系統結合演算法運用於判斷環境中是否存在移動物體，以克服其他感測器誤判率高且無法偵測靜止不動物體的缺點。具有測距能力的調頻相位自我注入鎖定雷達可進一步偵測移動物體距離天線的距離，並且透過第二次檢定統計判斷環境中存在1或2名受測者。
在運算過程中，對於雷達系統的輸出訊號僅需進行傅立葉轉換、共變異數運算以及特徵值分解，相對於傳統的方法動輒二至三個周期以上，本論文所使用的演算法僅需要一個周期的時間即可進行判斷。在人體存在感測實驗中，感測距離為3至5公尺，判斷準確率可達95%，誤判率最低僅為0.4%，訊號週期平均約為5秒時，所需判斷時間為5秒。

This thesis uses two different types of test statistics methods based on the generalized likelihood ratio, respectively arithmetic to geometric mean method and the signal-subspace eigenvalues method. These methods are applied to a frequency-modulated phase-and self-injection-locked radar operating in the 5.8 GHz ISM band. The radar system, integrated with the algorithms presented in this thesis, is used to detect the presence of moving objects in the environment, overcoming the limitations of other sensors with high false alarm rates and inability to detect stationary objects.
The frequency-modulated phase-locked radar with ranging capability is able to measure the distance between the radar and the moving objects. Furthermore, by applying a second statistical test, the algorithm can determine the presence of either one or two targets in the environment.
In terms of computation, the radar system's output signal only requires Fourier transform, covariance calculation, and eigenvalue decomposition. Compared to traditional methods, which often take two to three cycles or more, the algorithm used in this thesis only requires one cycle for detection. In human presence experiments, with sensing distances ranging from 3 to 5 meters, the detection accuracy reaches 95%, and the lowest false alarm rate is only 0.4%. With an average signal period of approximately 5 seconds, the required detection time is 5 seconds.

論文審定書 i
誌謝 ii
摘要 iii
Abstract iv
目錄 v
圖次 vii
表次 x
第一章 序論 1
1.1研究背景 1
1.2偵測文獻探討 2
1.3雷達系統 5
1.3.1正交相位自我注入鎖定雷達 5
1.3.2頻率調變相位自我入鎖定雷達 7
第二章 存在感測理論與雷達訊號處理流程 10
2.1假設檢驗 10
2.1.1二元假設檢驗 10
2.1.2最大概似估計 11
2.1.3廣義概似比檢驗 12
2.1.4接收者操作特徵曲線 13
2.2檢定統計量之數學推導及證明 14
2.2.1雜訊分析 15
2.2.2算術平均數與幾何平均數法 16
2.2.3訊號子空間與特徵值法 18
2.3雷達系統之訊號處理 20
2.3.1正交相位自我注入鎖定雷達 20
2.3.2頻率調變相位自我注入鎖定雷達 24
第三章 雷達系統設置與理論驗證 29
3.1系統架構 29
3.1.1正交相位自我注入鎖定雷達 29
3.1.2頻率調變相位自我注入鎖定雷達 33
3.2系統與環境雜訊 35
3.3雷達訊號模擬 37
3.4 雷達訊號結合GLRT模擬 40
第四章 人體存在感測實驗 43
4.1致動器實驗 43
4.2 人體存在感測實驗設置 45
4.3 人體量測結果 46
4.3.1 QPSIL雷達量測結果 46
4.3.2 FMPSIL雷達量測結果 48
4.4 閥值統計 53
第五章 結論 58
參考文獻 59

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