針對同化量化器分散式偵測次佳性之充分條件分析

Abstract

在設計最佳分散式偵測系統的挑戰之一，就是可能的設計組合會隨著偵測器的個數增加而成指數成長。反之，找出最佳的同化量化器系統設計(Identical Quantizer System or IQS)是比較容易的，因為可能的組合是隨著偵測器的個數呈線性成長。因此衍生一個在此 領域很重要的研究課題，就是在什麼條件下，最佳的同化量化器系統(IQS)可達到最佳分散式偵測系統設計的效能？ 在這篇碩士論文中，我們嘗試用不同的方式思考此一問題：在什麼條件下，IQS僅能 達到次佳的整體效能。運用參考論文[4]中的推導方式，我們比較了同化量化器系統設計(IQS)和只改變一個偵測器量化方式的非同化量化器系統設計(Non-identical Quantizer System or NQS)的錯誤率，然後理論證明出在局部觀察值的機率符合某些特定的線段區域條件，IQS僅能達到次佳的效能。我們同樣也嘗試運用數值模擬的方式，來驗證同化量化器系統設計(IQS)僅能達到次佳效能的區域，結果顯示我們的方法應可再推廣至更多的區段。

One engineering challenge in designing an optimal distributed detection system is that the number of all possible designs (i.e., the combinations of local likelihood-ratio quantizers(LRQs) and the fusion rule) grows exponentially with the number of local sensors. Instead, finding the best identical quantizer design is a much easier task because the number of possibilities only increase linearly with the number of sensors. This then arises the long-standing query on the condition under which the best identical quantizer system (IQS) is also globally optimal. In this thesis, we try to revisit the same query by asking a different but related question: when the IQS is only suboptimal. Using the technique in [4], we compare the performances between the best IQS and the NQS with one different local quantizer, and determine theo-retically a few line regions that give affirmative answer to our question. We also numerically identify certain regions that make the best IQS only suboptimal. Observations on patterns of these regions are subsequently made and remarked.