無線感測網路之分散式估測最佳二元量化閘值

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研究生：	王藝霖 Yi-Lin Wang
論文名稱：	無線感測網路之分散式估測最佳二元量化閘值 Optimal Binary Quantization Thresholds for Distributed Estimation in Wireless Sensor Networks
指導教授：	蔡育仁 Yuh-Ren Tsai
口試委員:
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 通訊工程研究所 Communications Engineering
論文出版年：	2008
畢業學年度：	96
語文別：	英文
論文頁數：	47
中文關鍵詞：	無線感測網路、分散式估測、最佳量化閘值
外文關鍵詞：	wireless sensor network, distributed estimation, optimal quantization threshold
相關次數：	點閱：3 下載：0
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在這篇論文中，我們討論無線感測網路的分散式估計問題。在無線感測網路中，包含有多個負責觀測和量化的感測器與一個負責估計的資料收集中心，我們設計在感測器端的量化函數，並固定資料收集中心是特定的估計法。假設每個感測器只能傳送一個位元給資料收集中心，並且也考慮當感測器與資料收集中心的通道是二元對稱通道的情況。我們也考慮感測雜訊是均勻或是高斯分佈。我們先推導出系統的均方差函數，並使用牛頓法去找出讓系統有最小均方差的最佳量化閘值。由結果發現，當系統的感測雜訊越大時，量化閘值集會互相靠近，而所找到的最佳閘值相當接近均勻分散於感測範圍的閘值，我們稱為均勻分散閘值，因此我們也將結果與均勻分散閘值作比較，並發現我們找到的均方差不會大於均勻分散閘值的均方差，也就是說我們提出的方法較均勻分散閘值有較好的效能。若是二元對稱通道的錯誤率越大時，也會越往中間靠近，也就是將所有閘值都設定相同，並且就是在正中間，就是接近於傳統的方法。另外，當系統的感測雜訊不大，或是二元對稱通道的錯誤率不大的時候，我們所提出的方法較傳統的方式都可以得到較低的均方差。另外，針對不同分佈的感測雜訊，在沒有二元對稱通道的情況，可得到相似的最佳閘值，但是在有二元對稱通道的情況就有明顯的差異。

In this work, a distributed estimation problem for wireless sensor networks is considered. A wireless sensor network involves numbers of sensors and a fusion center. We design the compression functions in the sensor nodes and apply a certain estimator in the fusion center. Let each sensor transmit only one bit to the fusion center. We consider the sensing noise distribution is uniform or Gaussian. And both the noise-free communication channels and binary symmetric channels are also considered. First, we evaluate the mean square error (MSE) function of the system. Then the optimal binary quantization thresholds for sensors can be found by using the Newton’s Method based on minimizing the MSE. Finally, we find that when the sensing noise is getting large, the optimal thresholds will approach to each other. When the communication noise is getting large, the optimal thresholds will converge to the conventional method (the same threshold for each sensor setting in the middle of the sensing range). In conclusion, when the sensing noise or the communication noise variance are not too large, the proposed method has better performance, or we say less MSE, than the conventional one.

Chapter 1 Introduction    1
1 Introduction to Distributed Estimation in WSN    1
2 Related Works    3
Chapter 2 System Model    5
1 Distributed Estimation in Wireless Sensor Networks    5
1.1 Sensing Model    5
1.2 Communication Channel Model    6
2 Fusion Rule    7
Chapter 3 Optimal Quantization Thresholds for WSN with Uniform Sensing Noise    10
1 The Conditional MSE and the MSE Evaluation    10
2 MSE Evaluation for Two Nodes in Uniform Sensing Noise Case    12
3 MSE Evaluation for N Nodes in Uniform Sensing Noise Case    15
4 Analysis the Convexity of the MSE in Uniform Noise Case    17
5 Newton’s Method    21
6 Numerical Results of the Optimal Thresholds    22
Chapter 4 Optimal Quantization Thresholds for WSN with Gaussian Sensing Noise    26
1 MSE Evaluation for Two Nodes in Gaussian Sensing Noise Case    26
2 Approximate MSE by Gauss-Legendre Integration    27
3 Analysis the Convexity of the MSE in Gaussian Noise Case    29
4 Numerical Results of the Optimal Thresholds    31
Chapter 5 Optimal Quantization Thresholds for WSN with Sensing Noise and BSC    34
1 Consider BSC with Nonzero Transition Probability    34
2 MSE Analysis with BSC considered    35
3 Convexity of the MSE for Uniform Sensing Noise and BSC Channel    37
4 Convexity of the MSE for Gaussian Sensing Noise and BSC Channel    39
5 Numerical Results of the Optimal Thresholds    41
Chapter 6 Conclusions    46
References    47

                                

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