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姓名 黃崇瑋(Chung-Wei Huang) 查詢紙本館藏 畢業系所 通訊工程學系 論文名稱 以高斯-牛頓與內爾德-米德非線性最小平方法用於無線感測網路之目標物定位
(Gauss-Newton and Nelder-Mead Nonlinear Least Squares Methods for Target Localization in Wireless Sensor Networks)相關論文 檔案 [Endnote RIS 格式]
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摘要(中) 無線感測網路(WSNs) 是由具有感測能力、計算能力及無
線通信能力的感測器所組成,這些感測器具備著體積小、低成本、
低功耗的特性,在感測器有著前述的特性之下,本篇研究是以接
收訊號強度(RSS) 等數據並且對其做量化(Quantization),處理中心
(Fusion center) 以此量化訊號(Quantized data) 並利用最小平方估計
法做定位,當量化階數少的時候,為了降低量化誤差造成目標函式
過多的誤差,在最小平方估計裡加入μ − law 壓縮原始訊號,得到
不錯的效果;這裡的問題屬於非線性最小平方估計,研究中也依
據高斯-牛頓法以及NM-單純形搜索法解決此最佳化問題;在量化臨界值(Quantization threshold) 上,利用Numirical 方式提出適合最
小平方估計的最佳量化臨界值,其均方根(Root Mean Square, RMS)
位置誤差也接近MLE 以及CRLB;此外,並延伸出找到適合所有
位置的量化臨界值,使用在此最小平方估計問題中。摘要(英) Wireless sensor networks (WSNs) conventionally consist of
a large number of low-cost, low-power, densely distributed, and mostly heterogeneous sensors. For the localization application, the target signal strength in a WSN is usually reported by sensors with quantized levels and all quantized data are collected in a fusion center to estimate the target
location based on a nonlinear relationship between distance and signal strength. Instead of using the computation-intensive maximum likelihood (ML) method, we study the least squares method by which the least squares cost function is significantly deteriorated due to nonlinear parameter estimation. To solve this problem, the μ-law compression technique is considered for robust position estimation. Two nonlinear least squares estimation methods, Gauss-Newton and Nelder-Mead, are discussed in our work. Numerical results show that the proposed method can achieve
a good mean square error performance close to the ML method with lower computation loading.關鍵字(中) ★ 無線感測網路
★ 最小平方法
★ 高斯牛頓法
★ 目標物定位關鍵字(英) 論文目次 中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
第1 章序論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 章節架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第2 章系統架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 功率衰減模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 利用量化訊號做位置估計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 最大概似估計(MLE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
第3 章非線性最小平方估計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 利用量化訊號做非線性最小平方估計. . . . . . . . . . . . . . . . . . . . . 11
3.2 非線性最小平方估計的最佳化方法. . . . . . . . . . . . . . . . . . . . . . . 22
3.2.1 依疊代法-高斯牛頓法解決非線性最小平方估計問題. . . . 23
3.2.2 依搜索法-單純型搜索法解決非線性最小平方估計問題. . 25
3.3 量化臨界值. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.1 適合最大概似估計法的量化臨界值. . . . . . . . . . . . . . . . . . . 29
3.3.2 適合最小平方估計法的量化臨界值. . . . . . . . . . . . . . . . . . . 30
第4 章系統模擬與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1 Simulation Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 模擬結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3 演算法複雜度比較. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
第5 章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
附錄A:高斯-牛頓法雅可比矩陣微分過程. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
附錄B:CRLB 證明. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
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339 –349, Jan. 2008.指導教授 張大中(Dah-Chung Chang) 審核日期 2013-1-4 推文 plurk
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