Preliminary Numerical Analysis of Precise Orbit Determination for a Multi-Way Microwave Measurement Mode in the Lunar and Mars Missions

Abstract

Precise orbit determination and lander positioning have important scientific meaning in deep-space mission. In this paper，preliminary numerical simulations for a multi-way microwave measurement mode in the Lunar and Mars missions are conducted and analyzed. The measurement model of this tracking mode is derived and its advantages are evaluated. Simulation results show that this model has the potential to improve orbit accuracy，and the position of the lander can also be obtained. The quantitative analysis shows that at the noise level of 1 mm/s，for the Lunar spacecraft，the orbit accuracy can be up to several meters and the positioning accuracy of the lander is expected to reach the decimeter level，considering the coordinate system conversion error，the gravitational field error，the ephemeris error and the transponder error. For the Mars spacecraft，the orbit accuracy can reach tens of meters and the lander positioning accuracy reaches the meter level.

Keywords

multi-way Doppler / multiple objects / precise orbit determination / lander positioning / measurement model

References

[1] 刘庆会,吴亚军,黄勇,等. 基于同波束VLBI 的火星车测定位技术[J]. 中国科学:物理学 力学 天文学,2015,45(9):1-8
LIU Q H,WU Y J,HUANG Y,et al. Mars rover positioning technology based on same-beam VLBI[J]. SCIENTIA SINICA Physica,Mechanica & Astronomica,2015,45(9):1-8
[2] ZHENG W,XU H Z,ZHONG M,et al. Precise recovery of the Earth’s gravitational field with GRACE:intersatellite range-rate interpolation approach[J]. IEEE Geoscience and Remote Sensing Letters,2012,9(3):422-426
[3] ZUBER M T,SMITH D E,WATKINS M M,et al. Gravity field of the Moon from the gravity recovery and interior laboratory(GRAIL)mission[J]. Science,2013,339(6120):668-671
[4] GOOSSENS S,MATSUMOTO K,ISHIHARA Y,et al. Results for orbit determination of the three satellites of Kaguya[J]. Journal of the Geodetic Society of Japan,2009,55(2):255-268
[5] LIU Q,KIKUCHI F,MATSUMOTO K,et al. Same-beam VLBI observations of SELENE for improving lunar gravity field model[J]. Radio Science,2010,45(1):1-16
[6] NAMIKI N,IWATA T,MATSUMOTO K,et al. Farside gravity field of the Moon from four-way Doppler measurements of SELENE(Kaguya)[J]. Science,2009,323(5916):900-905
[7] MOYER T D. Formulation for observed and computed values of deep space network data types for navigation[M]. USA：John Wiley & Sons，2005.
[8] SHAPIRO I I. Fourth test of general relativity[J]. Physical Review Letters,1964,13(26):789
[9] TOMMEI G,MILANI A,VOKROUHLICKÝ D. Light-time computations for the BepiColombo radio science experiment[J]. Celestial Mechanics and Dynamical Astronomy,2010,107(1-2):285-298
[10] 叶茂,李斐,鄢建国,等. 国内外深空探测器精密定轨软件研究综述及WUDOGS简介[J]. 飞行器测控学报,2017,36(1):45-55
YE M,LI F,YAN J G,et al. Review of deep space orbit determination software and introduction to WUDOGS[J]. Journal of Spacecraft TT&C Technology,2017,36(1):45-55
[11] YAN J G,YANG X,YE M,et al. Independent Mars spacecraft precise orbit determination software development and its application[J]. Astrophysics and Space Science,2017,362,(47):181-190
[12] 杨轩，鄢建国，叶茂，等. 火星探测器精密定轨软件研制及MEX数据处理[J]. 武汉大学学报信息科学版（已接收）.
YANG X，YAN J G，YE M，et al.，Development of precise orbit determination software and data processing for MEX[J]. Geomatics and Information Science of Wuhan University，accepted.
[13] 鄢建国,李斐,平劲松. 基于MGS测图段部分弧段的精密定轨及火星重力场模型解算[J]. 测绘学报,2010,39(5):484-490
YAN J G,LI F,PING J S. Precision orbit determination of mgs mapping phase arcs and martian gravity field model solution[J]. Acta Geodaetica et Cartographica Sinica,2010,39(5):484-490
[14] BERTONE S,PONCIN-LAFITTE C L,ROSENBLATT P,et al. Impact analysis of the transponder time delay on radio-tracking observables[J]. Advances in Space Research,2018,61(1):89-96
[15] RAMBAUX N,WILLIAMS J G. The Moon’s physical librations and determination of their free modes[J]. Celestial Mechanics and Dynamical Astronomy,2011,109(1):85-100
[16] WILLIAMS J G,SLADE M A,ECKHARDT D H,et al. Lunar physical librations and laser ranging[J]. Earth,Moon,and Planets,1973,8(4):469-483
[17] WILLIAMS，J G，BOGGS D H，FOLKNER W M. DE430 lunar orbit，physical librations and surface coordinates[R]. USA：JPL Interoffice Memorandum， Jet Propulsion Laboratory，California Institute of Technology，Pasadena，California，2013，19.
[18] LI F,YE M,YAN J G,et al. A simulation of the four-way lunar lander–orbiter tracking mode for the Chang’E-5 mission[J]. Advances in Space Research,2016,57(11):2376-2384
[19] 曹建峰,张宇,胡松杰,等. 嫦娥三号着陆器精确定位与精度分析[J]. 武汉大学学报(信息科学版),2016,41(2):274-278
CAO J F,ZHANG Y,HU S J,et al. An analysis of precise positioning and accuracy of the CE-3 lunar lander soft landing[J]. Geomatics and Information Science of Wuhan University,2016,41(2):274-278
[20] FOLKNER W M，WILLIAMS J G，BOGGS D H，et al. The planetary and lunar ephemerides DE430 and DE431[R]. [S.l]：Interplanetary Network Progress Report，2014，196：1-81.
[21] KONOPLIV A S,PARK R S,FOLKNER W M. An improved JPL Mars gravity field and orientation from Mars orbiter and lander tracking data[J]. Icarus,2016(274):253-260