SCIENTIA SINICA Informationis, Volume 50 , Issue 12 : 1932(2020) https://doi.org/10.1360/SSI-2019-0279

Compensation for time-tag bias of Doppler measurement from Chang'e-3 probe

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  • ReceivedDec 13, 2019
  • AcceptedFeb 6, 2020
  • PublishedOct 20, 2020


Data analysis shows there are periodic systematic errors in the Doppler measurement of the Chang'e-3 lunar probe. According to the Doppler measurement model and orbit information, as well as analysis of the Doppler information, periodic variation in the residuals is related to bias of the time-tag of the measurements. In this paper, self-calibration and differential statistical calibration methods are proposed to compensate this time-tag bias. The time-tag biases of the Jiamusi and Kashi deep space station estimated by these methods were 25 ms and 10 ms, respectively. The root mean square of the Doppler residual was reduced from 1.5 cm/s to 0.3 mm/s after the time-tag bias was compensated. The periodic variation in the residual was removed. In addition, the application of Doppler data in orbit determination was analyzed. Based on the orbit determination of ranging and VLBI data, the position error was only 2.5 m of the orbit determination using the compensated Doppler and VLBI data. The position deviation of the orbit determination obtained using the Doppler and ranging data was 25 m, and the position error of the orbit determination via Doppler data was 200 m.


[1] 孟 , 张 , 叶 . 嫦娥二号卫星技术成就与中国深空探测展望. Sci Sin Tech, 2013, 43: 467-477 CrossRef Google Scholar

[2] Wu X Y, Zhang H H, Zhang T X. The technical design and achievements of Chang’E-3 probe. Sci Sin Tech, 2014, 44: 331-343 CrossRef Google Scholar

[3] Chen C L, Zhang Z F, Peng J. Technique design and realization of the circumlunar return and reentry spacecraft of 3rd phase of Chinese lunar exploration program. Sci Sin Tech, 2015, 45: 111-123 CrossRef Google Scholar

[4] Huang Y, Li P J, Fan M. Orbit determination of CE-5T1 in Earth-Moon L2 libration point orbit with ground tracking data. Sci Sin-Phys Mech Astron, 2018, 48: 079501 CrossRef ADS Google Scholar

[5] Zhang L H, Xiong L, Sun J. Technical characteristics of the relay communication satellite “Queqiao” for Chang’e-4 lunar farside exploration mission. Sci Sin Tech, 2019, 49: 138-146 CrossRef Google Scholar

[6] Ye P J, Sun Z Z, Zhang H. Mission design of Chang’e-4 probe system. Sci Sin Tech, 2019, 49: 124-137 CrossRef Google Scholar

[7] Dong G L, Li H T, Hao W H, et al. Development and future of China's deep space TT&C system(in Chinese). J Deep Space Explor, 2018, 5: 99--114. Google Scholar

[8] 胡 , 郑 , 李 . “嫦娥三号”月球探测器的轨道确定和月面定位. Chin Sci Bull, 2014, 59: 2268-2277 CrossRef Google Scholar

[9] Iess L, Stevenson D J, Parisi M. The Gravity Field and Interior Structure of Enceladus. Science, 2014, 344: 78-80 CrossRef ADS Google Scholar

[10] Armstrong J. Low-frequency Gravitational Wave Searches using Spacecraft Doppler Tracking. Living Reviews in Relativity, 2006, 9(1): 1-2. Google Scholar

[11] 胡 , 马 , 黄 . 利用中国VLBI网实现对“火星快车”的测定轨. Chin Sci Bull, 2010, 55: 2659-2666 CrossRef Google Scholar

[12] Liu C K, Zhou J L, Wang B F. 嫦娥三号“玉兔号”巡视器遥操作中的关键技术. Sci Sin-Inf, 2014, 44: 425-440 CrossRef Google Scholar

[13] Li P J, Zheng X, Liu Q H. Analysis of VLBI observation for Tianma radio telescope in Chang'E-3 orbit determination. Sci Sin-Phys Mech Astron, 2015, 45: 039501 CrossRef ADS Google Scholar

[14] Li H T, Zhou H, Hao W H, et al. Development of radio interferometry and its prospect in deep space navigation (in Chinese). J Spacecr TT&C Technol, 2013, 32: 470--478. Google Scholar

[15] Cao J F, Huang Y, Hu X G, et al. Modeling and application of Doppler data in deep space exploration (in Chinese). J Astronautics, 2011, 32: 1583--1589. Google Scholar

[16] Cao J F, Huang Y, Liu L, et al. Modeling and algorithm realization of three-way Doppler for deep space exploration (in Chinese). J Astronautics, 2017, 38: 304--309. Google Scholar

[17] Huang Y, Hu X G, Cao J F, et al. The Mars satellite orbit determination software at Shanghai Astronomical Observatory (in Chinese). J Spacecr TT&C Technol, 2009, 28: 83--89. Google Scholar

[18] Konopliv A, Park S, Yuan D. The JPL lunar gravity field to spherical harmonic degree 660 from the GRAIL Primary Mission. Journal of Geophysical Research, 2013, 118(7):1415-1434. Google Scholar

[19] Folkner W, Williams J, Boggs D. The planetary and lunar ephemeris DE 421. Interplanetary Network Progress Report, 2009, 178: 1-34. Google Scholar

[20] Ulvestad J., Thurman S. Orbit-Determination Performance of Doppler Data for Interplanetary Cruise Trajectories Part I: Error Analysis Methodology. TDA Progress Report, 1992, 42-108: 31-48. Google Scholar

[21] Hamilton T, Melbourne W. Information Content of A Single Pass of Doppler Data from A Distant Spacecraft. Jet Propulsion Laboratory, 1966. Google Scholar

[22] Liu L, Hu S J, Cao J F, et al. Theory and Application of Spacecraft Orbit Determination. Beijing: Publishing House of Electronics Industry, 2015. Google Scholar

[23] Fan M. Researches of GNSS-based navigation for lunar missions. Dissertation for Ph.D. Degree. Shanghai: Shanghai Astronomical Observatory, 2018. Google Scholar

[24] Liu L S, Zhao H, Liu Y. On methods of accuracy validation for TT&C systems with a calibration satellite (in Chinese). J Spacecr TT&C Technol, 2014, 33: 275--282. Google Scholar

[25] Mao S S, Lv X L. Mathematical Statistics. Beijing: China Renmin University Press, 2011. Google Scholar

[26] Duan J F, Zhang Y, Chen M, et al. Application of GRAIL lunar gravity field model in attitude and orbit control for CE-3 satellite (in Chinese). J Spacecr TT&C Technol, 2014, 33: 342--347. Google Scholar

  • Figure 1

    Post-fit residuals of orbit determination using ranging, Doppler, and VLBI data. (a) Residuals of ranging data; (b) residuals of Doppler data

  • Figure 2

    Post-fit residuals of orbit determination using ranging + VLBI data and Doppler + VLBI data, respectively. (a) Residuals of ranging data; (b) residuals of Doppler data

  • Figure 3

    Post-fit residuals of orbit determination using ranging data and the Doppler data after the calibration of time-tag bias. (a) Residuals of ranging data; (b) residuals of Doppler data

  • Figure 4

    The difference (a) and time-tag bias (b) of the Doppler data obtained from deep space stations for CE-3 probe in lunar orbit

  • Figure 5

    QQ charts of time-tag bias calibrated by differential statistical method for Doppler data obtained from protectłinebreak (a) Jiamisi and (b) Kashi deep space stations

  • Figure 6

    Post-fit residuals of orbit determination by Doppler data after the calibration of time-tag bias

  • Table 1   Specific description of the measurement data
    Type of measurement Station/baseline Tracking arc
    2013-12-09 04:17$\sim$2013-12-09 05:17
    2013-12-09 06:00$\sim$2013-12-09 07:15
    Range/range rate Jiamusi 2013-12-09 07:59$\sim$2013-12-09 09:12
    2013-12-09 09:56$\sim$2013-12-09 11:10
    2013-12-09 11:54$\sim$2013-12-09 13:07
    Range/range rate Kashi 2013-12-09 13:52$\sim$2013-12-09 15:05
    2013-12-09 15:49$\sim$2013-12-09 17:02
    Time delay/time delay rate Beijing-Kunming 2013-12-09 07:02$\sim$2013-12-09 07:13
    Shanghai-Kunming 2013-12-09 07:59$\sim$2013-12-09 09:07
    Beijing-Urumqi2013-12-09 09:56$\sim$2013-12-09 11:04
    Kunming-Urumqi 2013-12-09 11:54$\sim$2013-12-09 13:02
    Shanghai-Urumqi 2013-12-09 13:52$\sim$2013-12-09 15:00
  • Table 2   Statistics of time-tag bias for Doppler data
    Station Mean $(\mu,\rm{ms})$ Standard deviation $(\sigma,\rm{ms})$ Skewness Kurtosis
    Jiamusi $-$24.76 0.72 0.14560 $-$0.03582
    Kashi $-$10.16 1.27 $-$0.28430 0.05471