LEO卫星轨道根数型星历参数与接口设计
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摘要
低轨卫星是导航增强系统发展的新兴力量,具有独特优势。广播星历参数是其实现星基增强的重要指标。中轨GPS星历采用16/18参数模型,若直接用于LEO的星历参数拟合,卫星沿迹方向的位置分量拟合误差大,且对小偏心率近圆轨道有潜在的拟合法矩阵病态问题。基于第一类无奇点根数,通过增加或修改轨道沿迹向和径向摄动参数,设计了适用于近圆低轨卫星的16～19参数的5种星历模型。基于300～1500 km高度LEO的拟合试验表明:提出的16/17/18/18~*/19参数星历,URE最大值分别优于10/6/4/5/2.5 cm。最后,根据拟合参数的变化范围,对5个星历模型进行了接口设计。在数据截断对URE的影响为毫米量级要求下,总比特位分别为329/343/376/379/396,其中16/17参数星历模型比GPS16参数模型减少了29/15个,18/18~*/19参数星历模型比GPS18参数星历模型减少了64/61/41个。
Low earth orbit satellites, with unique advantages, are prosperous types of navigation augmentation satellites for the GNSS satellites constellations. The broadcast ephemeris element needs to be designed as an important index of the augmented LEOs. The GPS ephemerides of 16/18 elements cannot be directly applied to the LEOs because of the poor fitting accuracies in along-track positional component. Besides, the ill-conditioned problem of the normal-matrix exists in fitting algorithm due to the small eccentricity of the LEO orbits. Based on the nonsingular orbital elements, 5 sets of ephemerides with element numbers from 16 to 19 were designed respectively by adding or modifying orbital elements magnifying the along-track and radial positional components. The fitting experiments based on the LEO of 300 to 1500 km altitudes show that the fitting UREs of the proposed 16/17/18/18~*/19-element ephemerides are better than 10/6/4/5/2.5 cm, respectively. According to the dynamical range of the fitting elements, the interfaces were designed for the 5 sets of ephemerides. The effects of data truncation on fitting UREs are at millimeter level. The total bits are 329/343/376/379/396, respectively. 29/15 bits are saved for the 16/17-element ephemerides compared with the GPS16 ephemeris, while 64/61/41 bits can be saved for the 18/18~*/19-element ephemerides compared with the GPS18 elements ephemeris.
Low earth orbit satellites, with unique advantages, are prosperous types of navigation augmentation satellites for the GNSS satellites constellations. The broadcast ephemeris element needs to be designed as an important index of the augmented LEOs. The GPS ephemerides of 16/18 elements cannot be directly applied to the LEOs because of the poor fitting accuracies in along-track positional component. Besides, the ill-conditioned problem of the normal-matrix exists in fitting algorithm due to the small eccentricity of the LEO orbits. Based on the nonsingular orbital elements, 5 sets of ephemerides with element numbers from 16 to 19 were designed respectively by adding or modifying orbital elements magnifying the along-track and radial positional components. The fitting experiments based on the LEO of 300 to 1500 km altitudes show that the fitting UREs of the proposed 16/17/18/18~*/19-element ephemerides are better than 10/6/4/5/2.5 cm, respectively. According to the dynamical range of the fitting elements, the interfaces were designed for the 5 sets of ephemerides. The effects of data truncation on fitting UREs are at millimeter level. The total bits are 329/343/376/379/396, respectively. 29/15 bits are saved for the 16/17-element ephemerides compared with the GPS16 ephemeris, while 64/61/41 bits can be saved for the 18/18~*/19-element ephemerides compared with the GPS18 elements ephemeris.
引文
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[4] MAINE K, DEVIEUX C, SWAN P. Overview of IRIDIUM satellite network[C]//Conference Record. ‘Microelectronics Communications Technology Producing Quality Products Mobile and Portable Power Emerging Technologies’. San Francisco, CA: IEEE, 1995: 483.
[5] FOSSA C E, RAINES R A, GUNSCH G H, et al. An overview of the IRIDIUM (R) low earth orbit (LEO) satellite system[C]//Proceedings of the IEEE 1998 National Aerospace and Electronics Conference. Dayton, OH: IEEE, 1998: 152-159.
[6] JOERGER M, NEALE J, PERVAN B. Iridium/GPS carrier phase positioning and fault detection over wide areas[C]//Proceedings of the 22nd International Technical Meeting of the Satellite Division of the Institute of Navigation. Savannah, GA: ION, 2009: 1371-1385.
[7] JOERGER M, GRATTON L, PERVAN B, et al. Analysis of iridium-augmented GPS for floating carrier phase positioning[J]. Navigation, 2010, 57(2): 137-160.
[8] YANG Yuanxi, LI Jinlong, XU Junyi, et al. Contribution of the Compass satellite navigation system to global PNT Users[J]. Chinese Science Bulletin, 2011, 56(26): 2813-2819.
[9] 胡松杰. GPS和GLONASS广播星历参数分析及算法[J]. 飞行器测控学报, 2005, 24(3): 37-42.HU Songjie. Research on the broadcast ephemeris parameters of GPS and GLONASS[J]. Journal of Spacecraft TT&C Technology, 2005, 24(3): 37-42.
[10] 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(S1): 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(S1): 145-150.
[11] 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. 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.
[12] 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.
[13] 王鼎蔚, 杜兰, 郑勇, 等. LEO广播星历参数设计的无奇点根数法[J]. 测绘科学技术学报, 2017, 34(1): 31-37.WANG Dingwei, DU Lan, ZHENG Yong, et al. Parameter design of LEO broadcast ephemeris based on the nonsingular orbital elements[J]. Journal of Geomatics Science and Technology, 2017, 34(1): 31-37.
[14] 郭睿, 周建华, 胡小工, 等. 一种地球静止轨道卫星的快速恢复定轨方法[J]. 测绘学报, 2011, 40(S1): 19-25.GUO Rui, ZHOU Jianhua, HU Xiaogong, et al. A strategy of rapid orbit recovery for the geostationary satellite[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(S1): 19-25.
[15] 罗璠, 李建文, 黄海, 等. BDS广播星历的轨道误差分析[J]. 测绘通报, 2015(2): 70-72, 91. DOI: 10.13474/j.cnki.11-2246.2015.0045.LUO Fan, LI Jianwen, HUANG Hai, et al. Error analysis of orbit determined by BDS broadcast ephemeris[J]. Bulletin of Surveying and Mapping, 2015(2): 70-72, 91. DOI: 10.13474/j.cnki.11-2246.2015.0045.
[16] 袁晓波, 张超, 杜兰. 基于第一类无奇点根数的LEO历书参数设计[J]. 测绘科学技术学报, 2016, 33(6): 572-576.YUAN Xiaobo, ZHANG Chao, DU Lan. Parameter design of LEO almanac ephemeris based on the first class of non-singularity variables[J]. Journal of Geomatics Science and Technology, 2016, 33(6): 572-576.
[17] 杜兰, 刘泽军, 周佩元, 等. 无旋转倾角的NAV/CNAV型GEO广播星历拟合[J]. 测绘学报, 2017, 46(3): 297-306. DOI: 10.11947/j.AGCS.2017.20160393. DU Lan, LIU Zejun, ZHOU Peiyuan, et al. GEO NAV/CNAV-type broadcast ephemeris fitting without rotation of inclination[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(3): 297-306. DOI: 10.11947/j.AGCS.2017.20160393.
[18] 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.
[19] 黄华. 导航卫星广播星历参数模型及拟合算法研究[D]. 南京: 南京大学, 2012.HUANG Hua. Research on the broadcast ephemeris parameters model and its fitting algorithm[D]. Nanjing: Nanjing University, 2012.
[20] 方善传, 杜兰, 周佩元, 等. 低轨导航增强卫星的轨道状态型星历参数设计[J]. 测绘学报, 2016, 45(8): 904-910. DOI: 10.11947/j.AGCS.2016.20160091. FANG Shanchuan, DU Lan, ZHOU Peiyuan, et al. Orbital list ephemerides design of LEO navigation augmentation satellite[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(8): 904-910. DOI: 10.11947/j.AGCS.2016.20160091.
[21] 赵小阳, 李建成, 金涛勇, 等. ENVISAT-1卫星测高数据编辑标准的研究[J]. 海洋测绘, 2006, 26(6): 65-67.ZHAO Xiaoyang, LI Jiancheng, JIN Taoyong, et al. The research on data editing criteria of ENVISAT-1 satellite altimeter[J]. Hydrographic Surveying and Charting, 2006, 26(6): 65-67.
[22] 常志巧, 胡小工, 杜兰, 等. 第二类无奇点根数的北斗历书参数设计[J]. 宇航学报, 2016, 37(11): 1298-1303.CHANG Zhiqiao, HU Xiaogong, DU Lan, et al. Almanac designing with second class of nonsingular orbital elements for BeiDou navigation satellite system[J]. Journal of Astronautics, 2016, 37(11): 1298-1303.
[23] 陈刘成, 李静, 马瑞, 等. 工程化广播星历参数拟合算法与接口设计[J]. 武汉大学学报(信息科学版), 2011, 36(1): 18-23.CHEN Liucheng, LI Jing, MA Rui, et al. The Engineering design for broadcast ephemeris parameters fitting arithmetic and their interfaces[J]. Geomatics and Information Science of Wuhan University, 2011, 36(1): 18-23.
[24] 肖琴琴. 广播星历参数及拟合算法性能研究[D]. 长沙: 中南大学, 2013.XIAO Qinqin. The performance study of broadcast ephemeris parameters and fitting method[D]. Changsha: Central South University, 2013.
[2] DE SELDING P B. SpaceX to build 4,000 broadband satellites in seattle[EB/OL]. (2015-01-20). https://www.space.com/28305-spacex-satellite-internet-seattle.html
[3] REID T G R, NEISH A M, WALTER T F, et al. Leveraging commercial broadband LEO constellations for navigation[C]//Proceedings of the 29th International Technical Meeting of the Satellite Division of the Institute of Navigation. Portland, OR: [s.n.], 2016.
[4] MAINE K, DEVIEUX C, SWAN P. Overview of IRIDIUM satellite network[C]//Conference Record. ‘Microelectronics Communications Technology Producing Quality Products Mobile and Portable Power Emerging Technologies’. San Francisco, CA: IEEE, 1995: 483.
[5] FOSSA C E, RAINES R A, GUNSCH G H, et al. An overview of the IRIDIUM (R) low earth orbit (LEO) satellite system[C]//Proceedings of the IEEE 1998 National Aerospace and Electronics Conference. Dayton, OH: IEEE, 1998: 152-159.
[6] JOERGER M, NEALE J, PERVAN B. Iridium/GPS carrier phase positioning and fault detection over wide areas[C]//Proceedings of the 22nd International Technical Meeting of the Satellite Division of the Institute of Navigation. Savannah, GA: ION, 2009: 1371-1385.
[7] JOERGER M, GRATTON L, PERVAN B, et al. Analysis of iridium-augmented GPS for floating carrier phase positioning[J]. Navigation, 2010, 57(2): 137-160.
[8] YANG Yuanxi, LI Jinlong, XU Junyi, et al. Contribution of the Compass satellite navigation system to global PNT Users[J]. Chinese Science Bulletin, 2011, 56(26): 2813-2819.
[9] 胡松杰. GPS和GLONASS广播星历参数分析及算法[J]. 飞行器测控学报, 2005, 24(3): 37-42.HU Songjie. Research on the broadcast ephemeris parameters of GPS and GLONASS[J]. Journal of Spacecraft TT&C Technology, 2005, 24(3): 37-42.
[10] 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(S1): 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(S1): 145-150.
[11] 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. 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.
[12] 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.
[13] 王鼎蔚, 杜兰, 郑勇, 等. LEO广播星历参数设计的无奇点根数法[J]. 测绘科学技术学报, 2017, 34(1): 31-37.WANG Dingwei, DU Lan, ZHENG Yong, et al. Parameter design of LEO broadcast ephemeris based on the nonsingular orbital elements[J]. Journal of Geomatics Science and Technology, 2017, 34(1): 31-37.
[14] 郭睿, 周建华, 胡小工, 等. 一种地球静止轨道卫星的快速恢复定轨方法[J]. 测绘学报, 2011, 40(S1): 19-25.GUO Rui, ZHOU Jianhua, HU Xiaogong, et al. A strategy of rapid orbit recovery for the geostationary satellite[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(S1): 19-25.
[15] 罗璠, 李建文, 黄海, 等. BDS广播星历的轨道误差分析[J]. 测绘通报, 2015(2): 70-72, 91. DOI: 10.13474/j.cnki.11-2246.2015.0045.LUO Fan, LI Jianwen, HUANG Hai, et al. Error analysis of orbit determined by BDS broadcast ephemeris[J]. Bulletin of Surveying and Mapping, 2015(2): 70-72, 91. DOI: 10.13474/j.cnki.11-2246.2015.0045.
[16] 袁晓波, 张超, 杜兰. 基于第一类无奇点根数的LEO历书参数设计[J]. 测绘科学技术学报, 2016, 33(6): 572-576.YUAN Xiaobo, ZHANG Chao, DU Lan. Parameter design of LEO almanac ephemeris based on the first class of non-singularity variables[J]. Journal of Geomatics Science and Technology, 2016, 33(6): 572-576.
[17] 杜兰, 刘泽军, 周佩元, 等. 无旋转倾角的NAV/CNAV型GEO广播星历拟合[J]. 测绘学报, 2017, 46(3): 297-306. DOI: 10.11947/j.AGCS.2017.20160393. DU Lan, LIU Zejun, ZHOU Peiyuan, et al. GEO NAV/CNAV-type broadcast ephemeris fitting without rotation of inclination[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(3): 297-306. DOI: 10.11947/j.AGCS.2017.20160393.
[18] 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.
[19] 黄华. 导航卫星广播星历参数模型及拟合算法研究[D]. 南京: 南京大学, 2012.HUANG Hua. Research on the broadcast ephemeris parameters model and its fitting algorithm[D]. Nanjing: Nanjing University, 2012.
[20] 方善传, 杜兰, 周佩元, 等. 低轨导航增强卫星的轨道状态型星历参数设计[J]. 测绘学报, 2016, 45(8): 904-910. DOI: 10.11947/j.AGCS.2016.20160091. FANG Shanchuan, DU Lan, ZHOU Peiyuan, et al. Orbital list ephemerides design of LEO navigation augmentation satellite[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(8): 904-910. DOI: 10.11947/j.AGCS.2016.20160091.
[21] 赵小阳, 李建成, 金涛勇, 等. ENVISAT-1卫星测高数据编辑标准的研究[J]. 海洋测绘, 2006, 26(6): 65-67.ZHAO Xiaoyang, LI Jiancheng, JIN Taoyong, et al. The research on data editing criteria of ENVISAT-1 satellite altimeter[J]. Hydrographic Surveying and Charting, 2006, 26(6): 65-67.
[22] 常志巧, 胡小工, 杜兰, 等. 第二类无奇点根数的北斗历书参数设计[J]. 宇航学报, 2016, 37(11): 1298-1303.CHANG Zhiqiao, HU Xiaogong, DU Lan, et al. Almanac designing with second class of nonsingular orbital elements for BeiDou navigation satellite system[J]. Journal of Astronautics, 2016, 37(11): 1298-1303.
[23] 陈刘成, 李静, 马瑞, 等. 工程化广播星历参数拟合算法与接口设计[J]. 武汉大学学报(信息科学版), 2011, 36(1): 18-23.CHEN Liucheng, LI Jing, MA Rui, et al. The Engineering design for broadcast ephemeris parameters fitting arithmetic and their interfaces[J]. Geomatics and Information Science of Wuhan University, 2011, 36(1): 18-23.
[24] 肖琴琴. 广播星历参数及拟合算法性能研究[D]. 长沙: 中南大学, 2013.XIAO Qinqin. The performance study of broadcast ephemeris parameters and fitting method[D]. Changsha: Central South University, 2013.