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研究生:黃立信
研究生(外文):Lih-Shinn Hwang
論文名稱:利用低軌衛星負載之定軌資料測定高精度之軌道及地球位模式
論文名稱(外文):Precision orbit determination and gravity models from tracking data of Low-Earth-Orbiting ( LEO ) satellites
指導教授:黃金維黃金維引用關係
指導教授(外文):Cheinway Hwang
學位類別:博士
校院名稱:國立交通大學
系所名稱:土木工程系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:174
中文關鍵詞:線性軌道理論
外文關鍵詞:linear orbit perturbation theory
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本文主要的內容:從衛星定軌資料的前期處理、各座標轉換資料庫的建立、軌道積分參數與條件的設定,GEODYN II軟體積分計算,線性軌道理論數學關係式與程式的建立,到各項實例(如中華一、三號衛星、CHAMP)的應用等。
本文先從衛星運動方程與定軌問題的認識著手,驗證自行開發的座標轉換程式計算,與OASYS積分軟體相較,座標值經由程式在地固(CTS)與慣性(CIS)框架之間的轉換,其各軸最大誤差約在5、6公尺範圍以內。本文並對GEODYN軟體應用從事深入探討,同時藉由對該軟體之應用,建立各項星曆資料庫及積分參數的設定,以此為基礎,實際對衛星定軌數據做程序處理(如一號衛星的range rate 資料、GPS資料和 CHAMP模擬資料等)。同時提出推論:如以都卜勒資料測定中華一號衛星軌道時,推論中華一號衛星之距離變化率觀測中誤差應該約在1 cm 等級,而本研究計算求得中華一號衛星軌道位置及速度之精度為35.17m和3.76 cm 上下。
本文利用Kaula(1966)之線性軌道理論及平差理論,以先前處理過之人造衛星定軌數據,求得衛星之位置擾動,再由其位置擾動反推求得地球重力位之球諧係數差值,從事各項案例的試驗:如計算中華一號衛星的range rate 資料、GPS資料在徑向、沿軌跡方向、橫向三方向擾動分量,發現其最大最小值,與設定的最大階數成正比,且在橫向方向的擾動分量,震幅幅度最大;沿軌跡方向的擾動,圖形變化最激烈。如一年份之一號GPS資料分兩部分處理,一為原始狀態,一為以OSU91A地位模式等擾動力為改正考量,求出的軌道積分資料,兩者經由線性軌道理論的計算,正可求出相對於OSU91A球諧係數的差值,由此差值與各月份繪製的圖表,正可研判重力球諧係數之時間變化。如對分組CHAMP模擬資料試驗,利用線性軌道理論推導之估算係數與EGM96係數(設為真值)相較,計算兩組係數展開至各階繪製之大地起伏網格差之RMS值,以驗證該軌道理論之精度及可行性。如以Kaula 的解析理論推導中華三號衛星之地位球諧係數,利用EGM96球諧係數分析大地位模式對於三號400公里與800公里兩個時期之軌道誤差。三分量的誤差皆以沿軌跡方向最大,徑向次之,而橫向方向最小,其量級主要受衛星高度影響,在總誤差量上,RMS值則分別為64.091公尺與1.691公尺,誤差量的大小亦與高度成反比關係。
本文之貢獻歸納成以下幾點:
一、實際對低軌衛星之定軌資料作程序處理。
二、建立球諧函數與衛星軌道參數之數學觀測方程式,並由其方程式推導求得估算之係數,作為日後改進地球重力場的參考。
三、則是將此觀測方程式實際應用於各項案例試驗,驗證線性軌道理論的可行性。
This work includes preparing tracking data of satellite , establishing coordinate transformation database, setting up orbit integral parameters, experimenting with GEODYN II software, writing linear orbit theory programs and testing various cases ( ROCSAT-1, ROCSAT-3 and CHAMP ) in gravity recovery.
This work primarily investigates the theory of equations of motion ( EOM ) and orbit determination. A set of programs are applied to coordinate transformation between CTS ( conventional inertial system ) and CIS ( conventional terrestrial system ). Compared with the result from OASYS software, the largest differences are about 5-6m . Then, the work studies the structure of the NASA/GSFC orbit determination software-- GEODYN II, and use this software as a basis to process satellite tracking data and to determine orbits of various satellites. For three-day arc, the result of the solutions indicates that the accuracy of ROCSAT-1 of range rate is about 1 cm . For orbit passes near Taiwan, the RMS discrepancies at one-day overlapping arcs are 35.17m and 3.76 cm , which are about the standard errors of ROCSAT-1 orbit determined with range rate.
The orbit perturbation theory of Kaula (1966) was used to derive an approximate analytical formula for near circular orbit and the order-zero formula which is suitable for assessing perturbation in the radial, along-track and cross-track directions.
With this theory, we experiment with different cases of gravity recovery and tests; for example, computing perturbation components in the radial, along-track and cross-track directions, distinguishing time variation of geopotential coefficients, exploring gravity field ( geoid ) determination from orbit perturbations and using linear theory to estimate geopotential model error. The RMS orbit errors due to the EGM96 model error are estimated to be 64.091m for ROCSAT-3 at a 400-km altitude, and 1.691m for ROCSAT-3 at a 800-km altitude, respectively.
In conclusion, the work contributes to:
(1) Practically processing the tracking data of low-earth-orbiting satellites ( range rate and GPS data of ROCSAT-1 and simulated data of CHAMP et al.).
(2) Establishing the relationship of the geopotential coefficients and satellite orbit parameters.
(3) Applying the linear orbit theory to various cases.
中文摘要 i
英文摘要ii
致謝 v
目錄 vi
表目錄 viii
圖目錄 x
第一章 緒論 1
1-1 研究動機與目的 1
1-2 文獻回顧 1
1-3 研究方法 3
第二章 衛星運動方程及定軌問題 5
2-1 二體問題 5
2-1-1 克卜勒座標與直角座標的轉換 8
2-2 衛星擾動運動 10
2-3 擾動力 13
2-3-1 地球引力位擾動 13
2-4 軌道積分 14
2-5 定軌問題 16
第三章 座標轉換 18
3-1 座標系統 18
3-1-1 傳統慣性座標系 18
3-1-2 地球固定座標系 18
3-1-3 衛星軌道座標系 19
3-2 地固座標與慣性座標之轉換 19
3-2-1 座標變動量改正 19
3-2-2 座標轉換程序 25
3-2-3 轉換程式製造與測試 26
3-3 衛星旋轉座標系與慣性直角座標系之轉換 28
第四章 高精度定軌程式─GEODYNII 34
4-1 時間系統 34
4-2 計算流程 36
4-3 執行程序 38
4-4 GEODYN中的模組設定 42
第五章 中華衛星及CHAMP衛星簡介 48
5-1 中華一號衛星 48
5-2 中華三號衛星 49
5-3 CHAMP衛星 50
第六章 以都卜勒資料測定中華一號衛星軌道 58
6-1 S波段的Range Rate資料 58
6-1-1中華一號S波段訊號 58
6-1-2 都卜勒觀測 59
6-1-3 Range Rate資料處理 60
6-2 以GEODYN計算三天軌道 61
6-2-1 觀測資料之先期準備工作 61
6-2-2 計算ROCSAT-1三天軌道 62
6-3 軌道精度評估 63
6-3-1 殘差統計值 63
6-3-2 重疊軌道差異 64
第七章 線性軌道理論介紹 74
7-1 克卜勒函數表達之地球引力位擾動 74
7-2 線性軌道擾動 75
7-3 徑向、沿、橫向擾動 79
7-3-1 零階擾動 83
7-4 高階和共振效應 84
7-5 線性軌道理論計算流程 85
第八章 線性軌道理論應用 93
8-1 軌道數值積分的線性理論應用 93
8-2 中華一號衛星的線性理論應用 105
8-2-1用華衛一號之兩種定軌資料求取擾動力分量 105
8-2-2用華衛一號資料求重力係數之時間變化 106
8-3 CHAMP衛星的線性理論應用 114
8-4 由地位球諧係數誤差引起之軌道誤差 128
第九章 結論與建議 134
9-1 結論 134
9-2 建議 136
參考文獻 137
附錄A 非地球引力位擾動力模式 142
附錄B-1輸入檔ftn05之介紹 149
附錄B-2 ftn05範本(以CHAMP衛星軌道積分為例) 153
附錄C 都卜勒資料定軌格式 164
附錄D GPS資料定軌格式 167
附錄E 程式簡介 169
作者簡歷 173
學術著作目錄 174
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