在本論文中，我們考慮了在分散式參數估測系統中之取樣設計問題，此系統中含有多個距離遙遠且位置固定的感測器，每個感測器皆可事先處理接收到之訊號並且傳送處理後之資料至資料融合中心，以得到最終之估測結果。我們考量兩個議題於此系統中，其一為在一感測器中，對於一參數估測問題之取樣方法設計，而另一個為當所有感測器之總取樣個數被限制時，該如何分配適當的取樣數目給每一感測器。在此，我們提出最大化費雪資訊或最小化費雪資訊損失為設計此兩種議題之準則，內文中會說明取樣設計過程以及提出一些數值模擬做為驗證。

In this thesis, we consider a sampling design problem for a distributed parameter estimation
system. The system contains a number of remotely located local sensors that can preprocess
the observed signal and convey the processed data to a data fusion center to make the final
estimate. Two issues are considered for this system. One is a sampling scheme design for a
parameter estimation problem in a single context. The other is how to assign the appropriate
number of sampling points to each of the sensors when a constraint on the total sample size
is assumed. Here we propose to design this two issues by maximizing the criterion of Fisher's
information or minimizing the Fisher's information loss . A sampling design procedure will be
established and some numerical simulations will be also carried out for illustration purpose.

1 Introduction 1
1.1 Parameter Estimation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Distributed Parameter Estimation System . . . . . . . . . . . . . . . . . . . . . 2
1.3 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 System Model And Theory Basis 5
2.1 Gaussian Estimation Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The Best Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Distributed Gaussian Parameter Estimation Problem . . . . . . . . . . . . . . . 7
2.4 Ali-Silvay Distance Measures (ASDM) . . . . . . . . . . . . . . . . . . . . . . . 8
3 Signal Sampling Design 12
3.1 Sampling Design For Parameter Estimation In The Single Sensor Context . . . . 12
3.2 Iterative Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Numerical Simulation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3.1 Raised-Cosine Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3.2 Simulation Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 Allocation For The Number Of Sampling Points 20
4.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1.1 Problem Formulation For Sample Size Allocation . . . . . . . . . . . . . 20
4.1.2 Demonstration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5 Conclusion 28

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