臺灣博碩士論文加值系統

目前利用GNSS建構電離層垂直全電子含量(Vertical Total Electron Content, VTEC)模型與電子密度(Electron Density, ED)模型的方法可以分為基於函數(function-based)的方法與基於像素(pixel-based)的方法。基於函數的方法其建模的關鍵在於選擇一個適當的數學函數來表示電離層VTEC或ED於建模區域的分布情形，進而有效的估計接收儀差分硬體延遲偏差(Receiver Differential Code Bias, RDCB)、衛星差分硬體延遲偏差(Satellite Differential Code Bias, SDCB)、VTEC或ED，然而電離層電子含量的分佈與變化極為複雜，除了隨時間與空間有週期性的變化外，亦常有不規則擾動的情況發生，因此同一數學函數不見得適合迥異的電離層條件，此外事先該選擇何種數學函數，而其階(degree)與次(order)的訂定，亦時常造成研究人員的困擾。為克服上述問題，本研究提出一套名為LS-MARS的建模方法。LS-MARS首先應用統計學習領域中的多元適應性雲形迴歸(Multivariate Adaptive Regression Splines, MARS)技術先行建構出電離層VTEC或ED的近似函數結構，再利用此函數結構組成法方程式隨後應用最小二乘法(Least Squares Method, LSM)進行參數估計，此方法與傳統基於函數的方法相較，其優點在於無需事先選擇一個描述建模區域電離層分布的函數型態而能自動地、精確地、彈性地與適應性地建構模型，此外因MARS可以應用於高維度資料的建模，而此特性將使得利用LS-MARS可以簡單地建構出不同維度的電離層VTEC(2D、3D)與ED(3D、4D)，或者更高維度的電離層模型，大大提升基於函數方法的建模效能與便利性並有助於對電離層的進一步研究。本文分別對LS-MARS於建構區域性二維電離層VTEC模型與三維ED模型的效能與可靠性進行測試，由本研究成果顯示本研究所提出的LS-MARS演算法於建構區域性電離層VTEC模型與ED模型具有很好的效能與可靠性，此方法可成為相關研究人員從事此方面研究的一種具吸引力的替代方法。

At present, all proposed method for ionospheric vertical total electron content (VTEC) and electron density (ED) modeling using GNSS could be classified into two different categories: function-based and pixel-based. The key point of function-based method is to select an appropriate mathematical function for the distribution of ionospheric VTEC or ionospheric ED over modeling region thus effectively estimates the differential code bias of the receiver (RDCB), the differential code bias of the satellite (SDCB), VTEC or ED. However, the ionosphere not only varies periodically with the time and space, but also has short-term irregular disturbances because of solar activity and geomagnetic variations. The same function model is therefore unlikely to fit different ionospheric behaviors. And it has always bothered researchers for the selection of mathematical function with appropriate degree and order over modeling region. In order to solve these problems, this study proposed a novel function-based approach called LS-MARS. The LS-MARS uses Multivariate Adaptive Regression Splines (MARS) from the field of statistical learning to estimate the VTEC or ED approximate model first and then substitutes this model in the observation equation to form the normal equation. The Least Squares Method (LSM) is used to solve the unknown parameters. Compared with the conventional function-based method, the advantage of LS-MARS is that the optimal approximate model can be found automatically, precisely, flexibly and adaptively from the observations using MARS without a priori knowledge of the ionospheric VTEC or ED distribution mathematical function. The LS-MARS can simply construct VTEC (2D, 3D) and ED (3D, 4D) for different dimensions, or higher dimensional ionospheric model since MARS can model high dimensional data. The LS-MARS can enhance the function-based method for modeling performance and convenience and help to further research on the ionosphere. In this paper, the performance and reliability of the regional two-dimensional VTEC and three-dimensional ED modeled by using LS-MARS were studied. The results showed that the LS-MARS has good modeling effectiveness and reliability for modeling regional ionospheric VTEC and ED. Therefore, this method can serve as an attractive and alternative method for researchers in the field of ionosphere.

誌謝 I
摘要 II
ABSTRACT III
目錄 V
表目錄 VIII
圖目錄 XI
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 研究動機與目的 4
1.4 論文架構 5
第二章 電離層介紹與GPS觀測量 7
2.1 電離層介紹 7
2.1.1 電離層性質與結構 7
2.1.2 電離層變化特性 8
2.1.3 電離層對無線電波的影響 9
2.1.4 IGS maps與IRI 14
2.2 GPS觀測量 17
2.2.1虛擬距離觀測量 18
2.2.2載波相位觀測量 20
2.2.3載波相位平滑電碼觀測量 21
2.2.4 無幾何距線性組合觀測量 21
第三章 LS-MARS建構電離層模型 23
3.1 LS-MARS 演算法介紹 23
3.1.1 Multivariate Adaptive Regression Splines(MARS) 23
3.1.2 Least Squares Adjustment Recapitulated 27
3.2 LS-MARS建構VTEC 33
3.2.1 單層模型(Single Layer Model)的假設 33
3.2.2 全電子含量的映射函數 35
3.2.3 單層模型穿刺點計算 35
3.2.4 全電子含量的函數化 36
3.2.5 參數估計 40
3.3 LS-MARS進行CIT 43
3.3.1 電子密度的函數化 44
3.3.2 參數估計 47
第四章 LS-MARS建構VTEC研究成果及分析 54
4.1 實驗區Ⅰ(經度119°-123°E,緯度21°-26°N) 57
4.1.1 模型殘差分析 58
4.1.2 RDCB估計成果分析 62
4.1.3 VTEC估計成果分析 64
4.2實驗區Ⅱ(經度105°-135°E,緯度15°-45°N) 73
4.2.1 模型殘差分析 74
4.2.2 RDCB估計成果分析 78
4.2.3 VTEC估計成果分析 81
4.3實驗區Ⅲ(經度70°-150°E,緯度30S°-30°N) 89
4.3.1 模型殘差分析 90
4.3.2 RDCB估計成果分析 94
4.3.3 VTEC估計成果分析 97
4.4 小結 105
第五章 LS-MARS進行CIT研究成果及分析 108
5.1 電子密度近似模型的建立 109
5.2 成果分析 110
5.3 小結 117
第六章 結論與建議 118
6.1 結論 118
6.2 未來研究方向與建議 119
參考文獻 121
附錄 126
A1 實驗區Ⅰ(119°-123°E, 21°-26°N) RDCB估計值 126
A2實驗區Ⅱ(105°-135°E, 15°-45°N) RDCB估計值 129
A3實驗區Ⅲ(90°-150°E, 25S°-30°N) RDCB估計值 140
B1實驗區Ⅰ:中興大學(120°40'35"E, 24°07'10"N) VTEC估計值 154
B2實驗區Ⅱ:中興大學(120°40'35"E, 24°07'10"N) VTEC估計值 160
B3實驗區Ⅲ:中興大學(120°40'35"E, 24°07'10"N) VTEC估計值 172
C1實驗區Ⅰ(119°-123°E, 21°-26°N) VTEC分布圖 184
C2實驗區Ⅱ(105°-135°E, 15°-45°N)VTEC分布圖 208
C3實驗區Ⅲ(90°-150°E, 25S°-30°N)VTEC分布圖 220

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