Single-Beam Differential Relative Navigation of DRO Satellite Formation

Abstract

This paper proposes a single-beam differential relative navigation method to solve the relative navigation requirements of Distant Retrograde Orbit (DRO) satellite formation in cislunar space. The formation of two DRO satellites can be covered by a beam of measurement sent by a Low Earth Orbit (LEO) satellite, thus establishing two Satellite-to-Satellite Tracking (SST) links with the LEO satellite at the same time. Then differential measurement data can be obtained by these two SST links. This method can get relative states of the DRO satellite information by combining the differential measurement data and three-body orbital dynamics model. DRO is in the space with high asymmetry of the Earth-Moon three-body gravitational field, according to the LiAISON principle, a SST link established between the satellite running on this orbit and an LEO satellite can realize autonomous navigation, thus determining the absolute orbit states of one of the DRO formation satellites and the LEO satellite. The single-beam differential relative navigation method uses the absolute states of two satellites as constraints, and the advantage of using differential measurement data to eliminate common errors can obtain high-precision relative states of DRO satellite formation. In the simulation test, the relative navigation performance of the single-beam differential relative navigation method of the short-distance DRO satellite formation (inter-satellite distance of 50 km) and the long-distance DRO satellite formation (the distance between the satellites is about tens of thousands of kilometers) is tested. And the results show that, when the inter-satellite ranging noise is 0.5 m, the relative navigation accuracy calculated by the method proposed in this paper is 5 m (1 σ), which is 4 times higher than the relative navigation accuracy calculated by differencing the absolute orbit.

Keywords

cislunar space / relative navigation / Satellite-to-Satellite Tracking (SST) / Distant Retrograde Orbit (DRO) / LiAISON

References

[1] 陈冠华,杨驰航,张晨,等. 地月空间的远距离逆行轨道族及其分岔研究[J]. 北京航空航天大学学报,2022,48(12):2576-2588
CHEN G H,YANG C H,ZHANG C,et al. Distant retrograde orbits and its bifurcations in Earth-Moon system[J]. Journal of Beijing University of Aeronautics and Astronautics,2022,48(12):2576-2588
[2] 徐明,徐世杰. 绕月飞行的大幅值逆行轨道研究[J]. 宇航学报,2009,30(5):1785-1797
XU M,XU S J. Stability analysis and transiting trajectory design for retrograde orbits around Moon[J]. Journal of Astronautics,2009,30(5):1785-1797
[3] 曾豪,李朝玉,彭坤,等. 地月空间NRHO与DRO在月球探测中的应用研究[J]. 宇航学报,2020,41(7):910-919
ZENG H,LI Z Y,PENG K,et al. Research on application of Earth- Moon NRHO and DRO for lunar exploration[J]. Journal of Astronautics,2020,41(7):910-919
[4] ZHANG R K，WANG Y，ZHANG H，et al. Transfers from distant retrograde orbits to low lunar orbits[J]. Celestial Mechanics and Dynamical Astronomy：An International Journal of Space Dynamics，2020，132（8）：41-71.
[5] 刘鹏. 基于天基探测器的月球卫星定轨问题[D]. 南京：南京大学，2014.
LIU P. Orbit determination of lunar satellites based on space stations[D]. Nanjing：Nanjing University，2014.
[6] 王猛,单涛,王盾. 高轨航天器GNSS技术发展[J]. 测绘学报,2020,49(9):1158-1167
WANG M,SHAN T,WANG D,et al. Development of GNSS technology for high Earth orbit spacecraft[J]. Acta Geodaetica et Cartographica Sinica,2020,49(9):1158-1167
[7] MO S M,JIN X J,LIN C,et al. Multi-satellite relative navigation scheme for microsatellites using inter-satellite radio frequency measurements[J]. Sensors,2021,21(11):3725
[8] HUI L，SHU B，XU L W，et al. Accounting for inter-system bias in DGNSS Positioning with GPS/GLONASS/BDS/Galileo[J]. Journal of Navigation，2017，70（4）: 686-698.
[9] 刘金海. 多频多模GNSS高精度差分定位模型研究[D]. 北京：中国科学院大学（中国科学院国家授时中心），2020.
LIU J H. Study on the precise differential positioning model based on the multi-frequency and multi-system GNSS[D]. Beijing：University of Chinese Academy of Sciences，2020.
[10] RENGA A，GRASSI M，TANCREDI U. Relative navigation in LEO by carrier-phase differential GPS with intersatellite ranging augmentation[J]. International Journal of Aerospace Engineering，2013，2013：1-11.
[11] 柴嘉薪,王新龙,俞能杰,等. 高轨航天器GNSS信号传播链路建模与强度分析[J]. 北京航空航天大学学报,2018,44(7):1496-1503
CHAI J X,WANG X L,YU N J,et al. Modeling and intensity analysis of GNSS signal link for high-orbit spacecraft[J]. Journal of Beijing University of Aeronautics and Astronautics,2018,44(7):1496-1503
[12] 卢克文,王新龙,申亮亮,等. 高轨GNSS信号可用性分析[J]. 航空兵器,2021,28(1):77-86
LU K W,WANG X L,SHEN L L,et al. Availability analysis of GNSS signal in high orbit[J]. Aero Weaponry,2021,28(1):77-86
[13] 刘林. 航天器定轨理论与应用[M]. 北京：电子工业出版社，2015.
LIU L. Spacecraft orbit determination theory and application[M]. Beijing：Publishing House of Electronics Industry，2015.
[14] 李博. 基于星间定向观测的导航星座长期自主定轨技术研究[D]. 南京：南京航空航天大学，2010.
LI B. Research on long-term autonomous orbit determination for navigation constellation based on inter-satellite orientation observation[D]. Nanjing：Nanjing University of Aeronautics & Astronautics，2010.
[15] WANG J W，BUTCHER E A，TANSEL Y. Space-based relative orbit estimation using information sharing and the consensus Kalman filter[J]. Journal of Guidance，Control，and Dynamics，2019，42（3）: 491-507.
[16] 倪淑燕,陈帅,李春月. 仅测距信息可用的编队卫星自主相对导航简化无损卡尔曼滤波方法[J]. 科学技术与工程,2017,17(33):193-199
NI S Y,CHEN S,LI C Y. Simplified unscented Kalman filter method for autonomous relative navigation for satellite formation with ranging information only[J]. Science Technology and Engineering,2017,17(33):193-199
[17] KILIC C，CHRISTIAN J A. Spacecraft relative navigation using only range-rate measurements[C]// Proceedings of AIAA Guidance，Navigation，and Control Conference. [S. l. ]：AIAA，2017.
[18] 韩飞,刘付成,王兆龙,等. 空间多机器人协同的多视线仅测角相对导航[J]. 航空学报,2021,42(1):316-326
HANG F,LIU F C,WANG Z L,et al. Multiple line-of-sight angles-only relative navigation by multiple collaborative space robots[J]. Acta Aeronautica et Astronautica Sinica,2021,42(1):316-326
[19] KOENIG A W，JUSTIN K，SULLIVAN J，et al. ARTMS：enabling autonomous distributed angles-only orbit estimation for spacecraft swarms[C]//Proceedings of 2021 American Control Conference (ACC), New Orleans, LA, USA: ACC, 2021: 4282-4289,
[20] HILL K,GEORGE H. Autonomous interplanetary orbit determination using satellite-to-satellite tracking[J]. Journal of Guidance,Control,and Dynamics,2007,30(3):679-686
[21] PARKER J，ANDERSON R，BORN G，et al. Navigation between geosynchronous and lunar L1 orbiters[C]//Proceedings of AIAA Astrodynamics Specialist Conference. [S. l. ]：AIAA，2006.
[22] LEONARD J M. Supporting crewed missions using LiAISON navigation in the Earth-Moon system[D]. Boulder，CO：University of Colorado at Boulder，2015.
[23] HESAR S G，PARKER J S，LEONARD J M，et al. Lunar far side surface navigation using Linked Autonomous Interplanetary Satellite Orbit Navigation （LiAISON）[J]. Acta Astronautica，2015，117: 116-129.
[24] 刘江凯. 地月空间DRO航天器自主导航技术仿真研究 ——基于脉冲星、GNSS、LEO星间链路[D]. 北京：中国科学院大学，2022.
LIU J K. Simulation research on autonomous navigation technology for spacecraft in cislunar DROs —based on pulsar，GNSS，and LEO-Linking[D]. Beijing：University of Chinese Academy of Sciences，2022.
[25] 王文彬. 基于DRO-LEO编队的地月航天器自主导航和授时研究[D]. 北京：中国科学院大学，2020.
WANG W B. Autonomous navigation and timing in cislunar space enabled by DRO-LEO formation[D]. Beijing：University of Chinese Academy of Sciences，2020.
[26] LI S L，PU J H，GAO Y，et al. High-fidelity autonomous navigation based on DRO-LEO Inter-Satellite Links[C]//Proceedings of the 28th International Symposium on Space Flight Dynamics. Beijing：[s. n. ]，2022.
[27] WANG W B，SHU L Z，LIU J K，et al. Joint navigation performance of distant retrograde orbits and cislunar orbits via LiAISON considering dynamic and clock model errors[J]. Navigation，2019; 66: 781- 802.
[28] CHRISTIAN J A. Relative navigation using only intersatellite range measurements[J]. Journal of Spacecraft and Rockets，2017, 54(1): 13-28.
[29] 穆静,陈芳. 似然迭代平方根容积卡尔曼滤波算法的克拉美罗下界分析[J]. 西安工业大学学报,2014,34(7):538-542
MU J,CHEN F. Analysis of Cramer-Rao lower bound of likelihood based iterated square root cubature Kalman filter[J]. Journal of Xi'an Technological University,2014,34(7):538-542