在現今導航定位系統越來越多個人化產品的當下，使用者對導航的定位要求也越來越高，而最為要求的則是定位時間速度及定位精度。於目前若僅靠單一GPS衛星系統進行導航，在都會市區遮蔽較為嚴重的地方常常造成接收上的困境，或者根本無法鎖定及定位，大大降低衛星導航服務的功能。因此，在近年GLONASS衛星系統已經正式營運並提供全球服務的當下，2G (GPS+GLONASS)衛星導航概念亦已經實現，提供2G衛星導航服務是目前國際不可避免的趨勢。
本研究採取將IGS(International GNSS Service)所提供的GLONASS精密星曆與廣播星曆利用加權最小二乘方法(WLS)演算法則與擴展型卡爾曼濾波器(Extended Kalman Filter;EKF)，將其星曆中之衛星位置、速度、加速度觀測量轉換成內含15個軌道參數之GPS廣播星曆格式，並藉由狀態誤差與觀測量誤差等，驗證其極度複雜之速度項與加速度項偏微分模型推導之正確性。最後，利用所得之軌道參數預估下段時間之衛星位置後並與原始精密星曆與廣播星曆做比較。在預估廣播星曆時，若採用預估精密星曆當觀測量，其位置平均誤差由原本廣播星曆之4.5公尺降至0.4公尺以內，而若使用廣播星曆為觀測量，其即時預估30分內之星曆亦可保有和廣播星曆相同之精度。

Nowadays there are more and more personalized products equipped with Global Navigation Satellite System (GNSS) on the market, and users start to raise their requests on these devices, especially on positioning time and accuracy issues. If we only rely on a single Global Positioning System (GPS) for searching, users may often encounter reception obstacles in the metropolitan area or even face positioning problems. These issues are significantly reducing the service and functions of a GNSS. To tackle these problems, GLONASS satellite system has been officially operated and provided global service in recent years. As a result, the 2G(GPS+GLONASS) satellite navigation concept has been achieved, and provision of 2G satellite navigation service has also become inevitable tendency in the world now.
This study adopts GLONASS precise ephemeris and broadcast ephemeris provided by International GNSS Service (IGS). Using Weighted Least Squares (WLS) and Extended Kalman Filter (EKF) algorithms, we convert the measurement of ephemeris’ satellite position, velocity and acceleration into GPS broadcast ephemeris format which contains 15 orbit elements. Further, we employ state error and measurement error to improve the accuracy of its extremely complicated partial differential derivation model. Finally, we predict the satellite’s position at the sequential epochs by using orbit element and compare it with true precise orbit. If we take precise ephemeris as our measurement, its average position error declines from 4.5 meters to less than 0.4 meters. However, if we take broadcast ephemeris as the measurement, its instant 30 minutes’ ephemeris prediction also keeps same accuracy as broadcast ephemeris does.

[1]M. Ficco, R. Pietrantuono, and S. Russo, “Supporting Ubiquitous Location Information in Interworking 3G and Wireless Networks”, COMMUNICATIONS of the ACM, Vol. 53, No. 11, pp. 116-123, November 2010.
[2]L. Wanninger, “The Future is Now GPS + GLONASS + SBAS = GNSS”, GPS World, pp. 42-48, July 2008.
[3]Wikipedia(2013),Global Navigation Satellite System,
From: http://en.wikipedia.org/wiki/Global_Navigation_Satellite_System
[4]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，頁2-31~2-32，4-5，第五章。
[5]Frank van Diggelen(2009),A-GPS:assisted GPS,GNSS,and SBAS,ARTECH HOUSE,BOSTON.
[6]張清義(2011)，應用GPS速度加強廣播星曆，碩士論文，國立成功大學航空太空工程學系。
[7]Ching-Shun Ho(2009),Theory and Experiment of Navigation with Satellite handout s, NCKU IAA. Unpublished manuscript.
[8]International GNSS Service(2013),IGS Product Availability,
From: ftp://igscb.jpl.nasa.gov/pub/
[9]Rolf Dach,Urs Hugentobler,Pierre Fridez,Michael Meindl,Bernese GPS Software Version 5.0,AIUB.
[10]張玴華(2012)，GPS廣播星曆延伸研究，碩士論文，國立成功大學航空太空工程學系。
[11]Kalman R.E.(1960),A New Approach to Linear Filtering and Prediction Problems,Journal of Basic Engineering,vol.82,pp.35-45.
[12]Minkler G., Minkler J.(1993), Theory and Application of Kalman Filtering, Palm Bay, FL:Magellan Book Company.
[13] A. Gelb, “Applied Optimal Estimation”, The M.I.T. Press, Massachusetts, U.S.A., 1974.
[14]W. Gurtner, “RINEX: The Receiver Independent Exchange Format Version 2.10”, From:ftp://igscb.jpl.nasa.gov/pub/data/format/rinex210.txt, December 10, 2007.
[15]ICD_GLONASS_5.1_(2008)_en
[16]張裕松，GLONASS衛星導航系統的發展和現狀
[17]李建文，GLONASS衛星導航系統及GPS/GLONASS組合應用研究，碩士論文，中國人民解放軍信息工程大學測繪學院
[18]Navigation Center,IS-GPS-200E,From:http://www.navcen.uscg.gov/
[19] H. Hu, C. Yuan, and L. Fang, “Extrapolation and Fitting Algorithms for GLONASS Satellite Orbit”, 2009 Third International Symposium on Intelligent Information Technology Application (IITA 2009), Nanchang, China, pp. 282-285, November 21-22, 2009.
[20] The Insterstate Aviation Committee,IAC from: http://www.glonass-center.ru/GLONASS/
[21]J. Zhang, K. Zhang, R. Grenfell, and R. Deakin, “GPS Satellite Velocity and Acceleration Determination using the Broadcast Ephemeris”, Journal of Navigation, Vol. 59, Issue 2, pp. 293-305, 2006.
[22] H. Hu, C. Yuan, and L. Fang, “Extrapolation and Fitting Algorithms for GLONASS Satellite Orbit”, 2009 Third International Symposium on Intelligent Information Technology Application (IITA 2009), Nanchang, China, pp. 282-285, November 21-22, 2009.
[23]Bucy R.S. and Senne K.D.(1971),Digital Synthesis of Non-Linear Filters,vol.7,Automatica,pp.287.
[24]Ching-Shun Ho(2007),Optimal Filtering Theory and Its Applications handout.Unpublished manuscript,IAA NCKU.
[25]Guochang Xu(2007),GPS Theory,Algorithm and Applications 2nd ed.,Springer,pp.248-249.
[26] Guo Jiming , Meng Xiangguang , Li Zonghua , Nie Zhaosheng(2011), ACCURACY ANALYSIS OF GLONASS SATELLITES BROADCAST EMPHEMERIS
[27]International GNSS Service(2013),Broadcast Ephemeris Product Availability, From: ftp://igs.ensg.ign.fr/pub/igs/data/