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研究生:陳國華
研究生(外文):Kwo-Hwa Chen
論文名稱:整合TWVD2001水準及GPS資料改進台灣區域性大地水準面模式以應用於GPS高程測量
論文名稱(外文):Improving Local Geoid Model of Taiwan Using TWVD2001 Leveling and GPS Data with Application to GPS Heighting
指導教授:楊 名
指導教授(外文):Ming Yang
學位類別:博士
校院名稱:國立成功大學
系所名稱:測量工程學系碩博士班
學門:工程學門
學類:測量工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:154
中文關鍵詞:大地水準面模式
外文關鍵詞:Geoid Model
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  近年來,GPS衛星定位技術已達成熟發展階段,可提供公分等級之橢球高精度。相較於以水準測量獲得正高之方式,GPS高程測量(GPS Heighting)兼具了施測快速與降低經濟成本等優點。其正高成果之優劣,主要取決於所使用之大地水準面模式精度。目前台灣地區使用的重力法大地水準面模式受限於實測重力點分佈密度較疏以及觀測資料品質之影響,其精度尚有改善的空間。民國89年至92年間,台灣地區分兩階段進行2065個一等水準點之水準、GPS以及重力測量等工作,第一階段完成1010個一等一級水準點之施測與計算,據此建立台灣新的高程基準(Taiwan Vertical Datum 2001, TWVD2001),第二階段則加密於TWVD2001之下,完成1055個一等二級水準點的測量與平差計算。若能藉由分析此2065個水準點的觀測資料以獲得高精度的正高及GPS橢球高成果,並整合此二者進行高程網的聯合平差計算,對於區域性大地水準面模式精度之改善將有重大貢獻。
  本論文主要的研究課題為:(1)利用水準網的觀測資料進行系統誤差改正參數之分析;(2)以Generalized Gauss-Markoff Model平差模式分析一等水準網最小約制平差成果之精度;(3)以多測站-多時段平差法進行一等水準網的GPS測量網之解算與其精度分析;(4)運用最小二乘配置法(Least-squares Collocation, LSC)技術整合一等水準以及GPS資料進行區域性大地水準面模式精度之改善,並探討兩種不同平差模式對於大地水準面精度的改善程度。
  本論文研究得到下列成果:(1)一等水準網觀測資料之後驗單位權觀測精度介於 ~ 之間,水準點正高成果的平均精度為 ± 8.9 mm,山區最大僅達 ± 10 mm;(2)GPS測量網之橢球高成果,一等一級網的平均精度為 ± 3.6 cm,一等二級網平均精度為 ± 2.5 cm;(3)由24小時之GPS檢驗資料驗證得知,山區點的橢球高精度受環境透空遮蔽的影響,精度平均約降低了2 ~ 3倍;(4)以帶有附加參數之「高程值」平差模式進行平差計算,其改善幅度可達74 %,未帶有附加參數之「高程差」平差模式,改善幅度為69 %;(5)以獨立檢驗資料之16個GPS高程測量成果分析修正後模式的改善程度,顯示出本文之研究成果確可有效提昇台灣大地水準面模式之精度,原模式的精度為 ± 13.5 cm,改善後可提昇至 ± 3.4 cm。
  Developments in Global Positioning System(GPS), which can be applied to the cm-level ellipsoidal height, have reached a mature stage in recent years. In comparison with conventional leveling technique, GPS heighting has the advantages of saving time and cost while doing field surveying. However, the accuracy of an orthometric height by GPS heighting is subjected to the existing Taiwan geoid model, which can’t reach to the cm-level. To solve this problem, we use Taiwan Vertical Datum 2001(TWVD2001) instead, which was established through the calculation of 1010 first-order first-class leveling lines. Based on it, they finished further the calculation of 1055 first-order second-class leveling lines. Thus, we obtained 2065 observations of geodetic leveling, GPS and surface gravity. If we can get highly accurate orthometric and ellipsoidal height by using this 2065 data, we will be able to improve the accuracy of Taiwan local geoid model by least-squares collocation(LSC) technique.
  The major themes of this research are:(1)Using leveling data to analyze the systematic error-correction parameters in the leveling networks; (2)Analyzing the accuracy of leveling data by using Generalized Gauss-Markoff Model; (3)Using the multistation-multisession GPS geodetic network adjustment model to analyze the accuracy of GPS data; (4)Combining the leveling and GPS data to improve the accuracy of Taiwan local geoid model by using two different LSC techniques.
  This thesis has obtained conclusions as follows: (1)The posteriori accuracy of unit weight of the leveling observations is ~ . The average accuracy of the orthometric height is ±8.9 mm, and all the accuracy of the orthometric height are smaller than ±10 mm in the mountain area. (2)The average accuracy of ellipsoidal height is ±3.6 cm in the first-order first-class network, and ± 2.5 cm in the first-order second-class network. (3)In comparison with the 24 hours GPS data result, we find that the accuracy of ellipsoidal height within the mountain area is weaker than the plane area in 2 ~ 3 orders. (4)The improvement of the local geoid accuracy is 74 % by using the additional parameters LSC adjustment model, and 69 % in none additional parameter one. (5)The results are then compared with the independent leveling and GPS data obtained from 16 monitoring points. Comparison results show that the accuracy of the improved model has reached ± 3.4 cm in the test area, where a worse level of ± 13.5 cm is obtained from the existing model.
目 錄 1
表 目 錄 4
圖 目 錄 5

第一章 緒論 7
§ 1-1 研究動機與目標 7
§ 1-2 文獻回顧 8
§ 1-3 研究方法 12

第二章 高程系統 14
§ 2-1 大地位數與高程系統之定義 14
§ 2-1-1 大地位數之概念 14
§ 2-1-2 正高系統 15
§ 2-1-3 正常高系統 17
§ 2-1-4 力高系統 18
§ 2-1-5 橢球高系統 18
§ 2-2 台灣高程基準 19
§ 2-2-1 早期之台灣高程基準 19
§ 2-2-2 TWVD2001台灣高程基準 21
§ 2-3 台灣地區重力法大地水準面模式 22
§ 2-3-1 全球大地位模式 22
§ 2-3-2 台灣區域性重力法大地水準面模式之計算 25


第三章 高程測量之系統誤差 28
§ 3-1 水準測量之系統誤差 28
§ 3-1-1 與視距以及觀測時間有關的系統誤差 29
§ 3-1-2 與測站兩尺間高程差有關的系統誤差 34
§ 3-1-3 與水準測量行進方向有關的系統誤差 36
§ 3-1-4 其餘他項的系統誤差 37
§ 3-1-5 正高改正 38
§ 3-2 GPS衛星定位測量之系統誤差 40
§ 3-2-1 與GPS衛星有關的誤差 41
§ 3-2-2 與訊號傳播有關的誤差 42
§ 3-2-3 與接收儀有關的誤差 44
§ 3-2-4 人為控制的SA與AS效應 45
§ 3-2-5 對流層折射延遲誤差對於GPS高程測量的影響 46

第四章 平差計算之數學模式 48
§ 4-1 Generalized Gauss-Markoff 模式 48
§ 4-2 水準測量系統誤差之線性迴歸分析 52
§ 4-2-1 系統誤差線性迴歸分析模式 53
§ 4-2-2 線性迴歸模式之變異性分析 58
§ 4-2-3 線性迴歸模式之參數估值顯著性分析 60
§ 4-2-4 線性迴歸模式與資料之符合程度分析 60
§ 4-3 GPS大地網之多測站-多時段平差模式 61
§ 4-3-1 GPS載波相位觀測量 61
§ 4-3-2 GPS載波相位差分觀測方程式 63
§ 4-3-3 多測站-多時段GPS大地網平差模式 67
§ 4-4 高程控制網最小二乘配置平差模式 69
§ 4-4-1 帶有附加參數之高程值平差模式 69
§ 4-4-2 未帶有附加參數之高程差平差模式 72

第五章 資料處理與成果分析 75
§ 5-1 水準觀測資料之處理 75
§ 5-2 水準測量系統誤差之線性迴歸分析 77
§ 5-3 水準測段往返閉合差分佈之分析 88
§ 5-4 水準觀測網之平差計算與精度分析 90
§ 5-4-1 水準原點K999高程值之賦予 90
§ 5-4-2 水準網最小約制平差計算與精度分析 91
§ 5-5 GPS大地網之平差計算與精度分析 96
§ 5-5-1 多測站-多時段GPS大地網平差計算與精度分析 96
§ 5-5-2 使用24小時的獨立GPS觀測量進行精度之檢驗 99
§ 5-6 整合高程系統之平差計算與精度分析 103
§ 5-6-1 高程控制網聯合平差計算與精度分析 103
§ 5-6-2 獨立觀測資料之檢驗分析 118

第六章 結論與建議 121

參考文獻 123

附錄 131

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