目前北斗GEO的星历拟合算法和用户卫星位置算法均引进了人为设置的5°倾角旋转，此外，少数星历参数还有超限现象。取消GEO的旋转倾角和抑制参数超限能够统一北斗混合星座的用户算法。基于第一类无奇点根数，分析了无旋转倾角的GEO两步法星历参数拟合算法。讨论了GEO的参数超限原因，提出采用固定1至2个超限参数取值的缩减参数拟合法。北斗GEO卫星在非地影期和地影期的拟合试验表明，拟合成功率和拟合精度能够保证，拟合用户距离误差（URE）的平均值优于3mm；缩减参数拟合法能够抑制特定时段下的参数超限问题，但是拟合URE放大到2cm。
The GPS-type broadcast ephemerides are currently used by BDS constellation. However, a 5°-rotation added on the original orbital inclination is needed in the GEOs ephemeris parameters fitting algorithm as well as in the user satellite position computation because of the singularity due to small inclination. Besides, the phenomena of exceeding the given boundary happen occasionally for some ephemeris parameters of GEOs. In order to unify the user ephemerides algorithm for the hybrid constellation, a two-step GEO broadcast ephemerides fitting algorithm was analyzed based on the first class nonsingular orbital elements. After the investigation on the reason for the variations of some ephemeris parameters out of limited range, a reduced fitting parameter set was adopted by giving the underlying one or two parameters with fixed values. Fit simulations for 5 GEOs during both eclipsing and non-eclipsing periods show that the two-step fitting algorithm has considerable robustness to ensure the success rate and fitting accuracy. The mean fitting user range error of GEOs with 2 h for NAV and 3 h data set for CNAV are better than 3 mm. For specific fit arcs with the boundary-exceeding problem, it can be fully avoided by using the fitting algorithm with a reduced fitting parameter set. However, the fitting URE will increase to 2 cm.
[1] 杨元喜. 综合PNT体系及其关键技术[J]. 测绘学报, 2016, 45(5):505-510. DOI:10.11947/j.AGCS.2016.2016 0127. YANG Yuanxi. Concepts of Comprehensive PNT and Related Key Technologies[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(5):505-510. DOI:10.11947/j.AGCS.2016.20160127.
[2] 杨元喜, 陆明泉, 韩春好. GNSS互操作若干问题[J]. 测绘学报, 2016, 45(3):253-259. DOI:10.11947/j.AGCS.2016.20150653. YANG Yuanxi, LU Mingquan, HAN Chunhao. Some Notes on Interoperability of GNSS[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(3):253-259. DOI:10.11947/j.AGCS.2016.20150653.
[3] 何峰, 王刚, 刘利, 等. 地球静止轨道卫星广播星历参数拟合与试验分析[J]. 测绘学报, 2011, 40(S):52-58. HE Feng, WANG Gang, LIU Li, et al. Ephemeris Fitting and Experiments Analysis of GEO Satellite[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(S):52-58.
[4] 陈刘成, 韩春好, 陈金平. 广播星历参数拟合算法研究[J]. 测绘科学, 2007, 32(3):12-14. CHEN Liucheng, HAN Chunhao, CHEN Jinping. The Research of Satellites Broadcast Ephemeris Parameters Fitting Arithmetic[J]. Science of Surveying and Mapping, 2007, 32(3):12-14.
[5] 阮仁桂, 贾小林, 吴显兵, 等. 关于坐标旋转法进行地球静止轨道导航卫星广播星历拟合的探讨[J]. 测绘学报, 2011, 40(S):145-150. RUAN Rengui, JIA Xiaolin, WU Xianbing, et al. Broadcast Ephemeris Parameters Fitting for GEO Satellites Based on Coordinate Transformation[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(S):145-150.
[6] 张中凯, 杜兰, 刘利, 等. GEO广播星历参数设计的无奇点根数法[J]. 测绘学报, 2014, 43(5):452-457. DOI:10.13485/j.cnki.11-2089.2014.0076. ZHANG Zhongkai, DU Lan, LIU Li, et al. Parameter Design of GEO Broadcast Ephemeris Based on the Nonsingular Orbital Elements[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(5):452-457. DOI:10.13485/j.cnki.11-2089.2014.0076.
[7] DU Lan, ZHANG Zhongkai, ZHANG Jin, et al. An 18-element GEO Broadcast Ephemeris Based on Non-singular Elements[J]. GPS Solutions, 2015, 19(1):49-59.
[8] 韩星远, 向开恒, 王海红. 第一类无奇点变量的广播星历参数拟合算法[J]. 航天器工程, 2011, 20(4):54-59. HAN Xingyuan, XIANG Kaiheng, WANG Haihong. Research on Broadcast Ephemeris Parameters Fitting Algorithm Based on the First Class of no Singularity Variables[J]. Spacecraft Engineering, 2011, 20(4):54-59.
[9] 刘林, 胡松杰, 王歆. 航天动力学引论[M]. 南京:南京大学出版社, 2006. LIU Lin, HU Songjie, WANG Xin. An Introduction of Astrodynamics[M]. Nanjing:Nanjing University Press, 2006.
[10] 杜兰, 张中凯, 刘利, 等. GEO卫星广播星历的拟合参数设计[J]. 中国空间科学技术, 2013, 33(3):46-51. DU Lan, ZHANG Zhongkai, LIU Li, et al. Fitting Parameters Design for GEO Broadcast Ephemeris[J]. Chinese Space Science and Technology, 2013, 33(3):46-51.
[11] IS-GPS-200G (2012) Navstar GPS Space Segment/Navigation User Interface[EB/OL].[2012-07-18]. Global Positioning System Wing, Space and Missile Systems Center. http://www.navcen.uscg.gov.
[12] IS-GPS-800C (2012) Navstar GPS Space Segment/User Segment L1C Interface[EB/OL].[2012-08-31]. Global Positioning System Wing, Space and Missile Systems Center. http://www.navcen.uscg.gov.
[13] IS-GPS-705C (2012) Navstar GPS Space Segment/User Segment L5 Interfaces[EB/OL].[2012-07-18]. Global Positioning System Wing, Space and Missile Systems Center. http://www.navcen.uscg.gov.
[14] 黄华, 刘林, 周建华, 等. 18参数广播星历分析研究[J]. 飞行器测控学报, 2012, 31(3):80-84. HUANG Hua, LIU Lin, ZHOU Jianhua, et al. Research on 18 Elements Broadcast Ephemeris Model[J]. Journal of Spacecraft TT&C Technology, 2012, 31(3):80-84.
[15] BDS-SIS-ICD (2016) BeiDou Navigation Satellite System Signal in Space Interface Control Document Open Service Signal B1I-2.1[EB/OL].[2016-08-31]. Administrator Office of China Satellite Navigation. http://www.beidou.gov.cn.
[16] 李恒年. 地球静止卫星轨道与共位控制技术[M]. 北京:国防工业出版社, 2010. LI Hengnian. Geostationary Satellite Orbital Analysis and Collocation Strategies[M]. Beijing:National Defense Industry Press, 2010.
[17] KUZNETSOV E D. The Effect of the Radiation Pressure on the Orbital Evolution of Geosynchronous Objects[J]. Solar System Research, 2011, 45(5):433-446.
[18] SOOP E M. 地球静止轨道手册[M]. 王正才, 译. 北京:国防工业出版社, 1999. SOOP E M. Handbook of Geostationary Orbits[M]. WANG Zhengcai, trans. Beijing:National Defense Industry Press, 1999.
[19] XU Guochang. GPS:Theory, Algorithms, and Applications[M]. Berlin:Springer-Verlag, 2007.
[20] MONTENBRUCK O, GILL E. Satellite Orbits:Models, Methods, and Applications[M]. Berlin:Springer-Verlag, 2000.
[21] TAPLEY B D, SCHUTZ B E, BORN G H. Statistical Orbit Determination[M]. New York:Elsevier Academic Press, 2004.
