臺灣博碩士論文加值系統

近年來衛星大地測量發展之重要趨勢之一為利用低軌衛星進行即時氣象監測與地球重力場之研究，如德國的CHAMP衛星（高度400公里，週期約為92分鐘），以及中美合作的COSMIC衛星（高度800公里，週期約為100分鐘）。高精度軌道計算對大地測量衛星而言，是非常重要的一環，而對具有氣象研究任務之衛星計劃而言，近即時精密軌道計算更是必須具備的條件。以具有氣象預報任務之COSMIC衛星為例，精密軌道必須於3小時內計算求得，且預計之實質計算時間大約只有10至30分鐘。以傳統動力法計算衛星軌道需估計軌道擾動力參數，再經由數值積分求得軌道，軌道積分的成果將視擾動力模式的完善與否而定，且耗用之時間過長，故不盡適合於近即時軌道計算。
本文之研究目標在於採用Colombo經驗模式表示COSMIC與CHAMP衛星的軌道擾動，以取代軌道擾動之積分計算，提昇近即時軌道計算之效率。實驗的部分考慮地位模式存在誤差與否的狀況，結果顯示，當不考慮先驗地位模式誤差時，COSMIC衛星的表示時間段為四倍軌道週期（約為400分鐘），其表示精度可達到3公分以內之等級；同樣的精度要求對CHAMP衛星而言則可達三倍軌道週期（約為276分鐘）；相對地，當考慮先驗地位模式誤差時，結果COSMIC在三倍週期的表示精度則可達到3公分以內之等級，此時之精度為2.8公分，而CHAMP衛星在二倍週期內可達到3公分以內的表示精度。由本研究成果可知，在考慮先驗地位模式誤差的二倍週期內，以Colombo經驗模式表示COSMIC和CHAMP衛星軌道擾動與傳統數值積分法具有3公分的符合度，可適用於未來以簡動力法（reduce-dynamic method）計算COSMIC和CHAMP衛星之近即時軌道。

In recent year, the research in real-time meteorology monitor and earth’s gravity field by using low-earth-orbit（LEO）satellite has become one of the important development in Satellite Geodesy. Such as CHAMP（CHAllenging Minisatellite Payload）in Germany and U.S.-Taiwan bilateral COSMIC（Constellation Observing System for Meteorology, Ionosphere, and Climate）. For Satellite Geodesy, precise orbit determination is important. For COSMIC, real-time orbit determination is also important because of it’s projection. For example, the primary goal of COSMIC is atmospheric research. In order to forecast the weather, precise orbit must be obtained in 3 hours but it may only have 10 to 30 minutes for orbit determination. The traditional dynamic method for orbit determination doesn’t apply to real-time orbit determination because it expended too much time.
The purpose of this research to represent the orbit perturbations of the COSMIC and CHAMP satellites by using the Colombo empirical model, for efficiency promotion, over the traditional integration method. In process, it would consider geopotential model whether contain error or not. The result show that, if request of precision is 3 cm and ignore the error of geopotential model, the representing time reach 4 cycles of period for COSMIC (about 400 min) and 3 cycles for CHAMP (about 276 min). When we consider that geopotential model contain error, the representing time reach 3 cycles of period of COSMIC of 2 cycles for CHAMP at the same request of precision. So we can know that, the representing precision of orbit perturbations by using the Colombo empirical model is commensurate with traditional method in 2 cycles. And it will be apply to reduce-dynamic method for near real-time orbit determination of the COSMIC and CHAMP satellites.

第一章 緒論………………………………………………………………1
§1-1 前言…………………………………………………………1
§1-2 文獻回顧……………………………………………………1
§1-3 研究動機與方法……………………………………………3
第二章 衛星運動理論……………………………………………………5
§2-1 二體問題……………………………………………………5
§2-2 衛星擾動理論………………………………………………6
§2-2-1 地球引力位擾動……………………………………8
§2-2-2 多體擾動……………………………………………11
§2-2-3 海潮…………………………………………………14
§2-2-4 地球固體潮…………………………………………17
§2-2-5 大氣阻力……………………………………………19
§2-2-6 太陽輻射壓…………………………………………22
§2-2-7 地球輻射壓…………………………………………25
§2-2-8 其他造成軌道擾動的原因…………………………27
第三章 Colombo軌道誤差理論…………………………………………28
§3-1 Colombo理論………………………………………………28
§3-2 以Colombo經驗模式表示軌道擾動的原理………………36
第四章 實驗敘述…………………………………………………………38
§4-1 GEODYNⅡ軟體………………………………………………38
§4-2 實驗流程……………………………………………………40
§4-3 精度評估的方法……………………………………………43
§4-4 新加入的參數型態…………………………………………44
§4-5 計算過程發生的問題及因應之道…………………………46
第五章 實驗分析…………………………………………………………47
§5-1 COSMIC衛星之測試…………………………………………47
§5-1-1 忽略先驗地球引力位模式誤差的狀況……………47
§5-1-2 考慮先驗地球引力位模式誤差的狀況……………58
§5-2 CHAMP衛星之測試…………………………………………60
§5-2-1 忽略先驗地球引力位模式誤差的狀況……………60
§5-2-2 考慮先驗地球引力位模式誤差的狀況……………72
第六章 結論與建議………………………………………………………74
參考文獻……………………………………………………………………76

林敏傑，1997。低軌衛星近似圓形軌道快速計算法，國立交通大學土木工程學系研究所碩士論文，新竹。
陳俊德，1998。以GEODYNⅡ模擬精密軌道計算，國立交通大學土木工程學系研究所碩士論文，新竹。
劉佾博，1999。近即時動態法中華三號衛星星曆之測定：使用Microlab-1資料，國立成功大學測量工程研究所碩士論文，台南。
曾清涼、儲慶美，1999。GPS衛星測量原理與應用，第二版，國立成功大學衛星資訊研究中心，台南。
Cefola, P. J., 1972. Equinoctial orbit elements - application to artificial satellite orbits. AIAA PAPER 72-0937. Washington, D. C. U.S.A.
Christodoulidis, D. C. et al., 1988. Observed tidal braking in the Earth/Moon/Sun System. J. Geophys. Res., 93, 6216-6236.
Colombo, O. L., 1986. Ephemeris error of GPS satellites. Bull Geod., 60（1）, 64-84.
Colombo, O. L., 1989. The dynamic of Global Positioning System orbits and the determination of precise ephemeris. J. Geophys. Res., 94, 9167-9182.
Cui, C. and M. Mareyen, 1992. Gauss’s equations of motion in terms of Hill variables and first application tonumerical integration of satellite orbits. Manu. Geod., 17, 155-163
Golub, H. G. and Loan, C. F. V., 1996. Matrix Computations, 3rd ed, The Johns Hopkins University Press, Baltimore, MD, U.S.A.
GFZ, 2001：http://www.gfz-potsdam.de/。
Heiskanen, W. A., Moritz, H., 1967. Physical Geodesy. W. H. Freeman and Co., San Francisco, CA, U.S.A.
Hwang, C. W. and M. J. Lin, 1998. Fast intergration of low orbit’s trajectory perturbed by Earth’s non-sphericity, J. Geod., 72, 578-585.
Knocke, P. J., J. C. Ries, and B. D. Tapley, 1988. Earth radiation preasure effects on satellites. Proceedings of the AIAA/ASS Astrodynamic Conference, 577-587.
Lemonine, F. G. et al., 1998. The development of the NASA GSFC and NIMA joint geopotential model EGM96. NASA’s Goddard Space Flight Center, Greenbelt, MD, U.S.A.
McCarthy, J. J. et al., 1993. GEODYNⅡ System Operation Manual , Vols.1-5, NASA/Goddard Space Flight Center, Greenbelt, MD, U.S.A.
NSPO，2001。http://www.nspo.gov.tw/。
Press, H. W. et al. 1992. Numerical recipes in Fortran : the art of scientific computing, 2nd ed., Cambridge University Press, New York, NY, U.S.A.
Rothacher, M., 1992. Orbits of Satellite System in Space Geodesy. 46, Astronomical Institue, University of Berne, Bern, Switzerland.
Seeber, G., 1993. Satellite Geodesy, Walter de Gruyter, Berlin, Germany.
Torge, W., 1991. Geodesy, 2nd ed., Walter de Gruyter, Berlin, New York, NY, U.S.A
Yang, M., 1995. New GPS Measurement Modeling Techniques of Orbit Determination and Precise Kinematic Positioning. Report 431, Department of Geodetic Science and Surveying, The Ohio State University, Columbus, OH, U.S.A.