On an Autonomous Pulsar Observation–Based Timekeeping Method for Deep Space
This article is part of Special Issue:
Shibin Song,
Xiaowei Jin,
Haixia Wang,
Shibin Song
College of Electrical Engineering and Automation , Shandong University of Science and Technology , Qingdao , Shandong , China , sdust.edu.cn
Search for more papers by this authorXiaowei Jin
College of Electrical Engineering and Automation , Shandong University of Science and Technology , Qingdao , Shandong , China , sdust.edu.cn
Search for more papers by this authorCorresponding Author
Haixia Wang
College of Electrical Engineering and Automation , Shandong University of Science and Technology , Qingdao , Shandong , China , sdust.edu.cn
Search for more papers by this authorShibin Song,
Xiaowei Jin,
Haixia Wang,
Shibin Song
College of Electrical Engineering and Automation , Shandong University of Science and Technology , Qingdao , Shandong , China , sdust.edu.cn
Search for more papers by this authorXiaowei Jin
College of Electrical Engineering and Automation , Shandong University of Science and Technology , Qingdao , Shandong , China , sdust.edu.cn
Search for more papers by this authorCorresponding Author
Haixia Wang
College of Electrical Engineering and Automation , Shandong University of Science and Technology , Qingdao , Shandong , China , sdust.edu.cn
Search for more papers by this authorFirst published: 20 February 2025
Academic Editor: Giovanni Palmerini
Abstract
To provide autonomous and accurate time service for deep space missions, a pulsar observation–based timekeeping method is documented in this paper, which utilizes pulsars as the time information source. Firstly, the pulsar observation noise is remodeled as the combination of the Gaussian noise and colored noise, and the detailed expression of the colored noise is presented in the paper. An improved Grey model (GM) is proposed to describe the onboard clock evolution, which models the grey action quantity as a time-varying coefficient and attenuates the dependence of the model on the initial state. On the basis of the modified observation noise model and GM, an unscented Kalman filtering (UKF) is adopted to estimate the onboard clock error. Numerical experiments are conducted to analyze the validity of the proposed method and the impact of spacecraft positioning error and pulsar selection on the proposed method. The proposed method offers an autonomous solution for onboard timekeeping in deep space missions.
Conflicts of Interest
The authors declare no conflicts of interest.
Open Research
Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
- 1 National Research Council of the National Academies, NASA Space Technology Roadmaps and Priorities: Restoring NASA’s Technological Edge and Paving the Way for a New Era in Space, 2012, NASA Technical Reports, National Academies Press, https://doi.org/10.17226/13354.
- 2 Lewandowski W., Azoubib J., and Klepczynski W. J., GPS: primary tool for time transfer, Proceedings of the IEEE. (1999) 87, no. 1, 163–172, https://doi.org/10.1109/5.736348, 2-s2.0-0032715746.
- 3
Re E.,
Di Cintio A.,
Busca G.,
Giunta D., and
Sanchez M., Novel time synchronization techniques for deep space probes, 2009 IEEE International Frequency Control Symposium Joint with the 22nd European Frequency and Time forum, 2009, Besancon, France, 205–210, https://doi.org/10.1109/FREQ.2009.5168170, 2-s2.0-70449487109.
10.1109/FREQ.2009.5168170 Google Scholar
- 4 Tjoelker R. L., Time and Frequency Activities at the NASA Jet Propulsion Laboratory, 2007, Jet Propulsion Laboratory, Pasadena, CA, USA, https://www.ion.org/publications/abstract.cfm?articleID=10578.
- 5 Tjoelker R. L., Prestage J. D., Burt E. A., Chen P., Chong Y. J., Chung S. K., Diener W., Ely T., Enzer D. G., Mojaradi H., Okino C., Pauken M., Robison D., Swenson B. L., Tucker B., and Wang R., Mercury ion clock for a NASA technology demonstration mission, EEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. (2016) 63, no. 7, 1034–1043, https://doi.org/10.1109/TUFFC.2016.2543738, 2-s2.0-84978699337, 27019481.
- 6
Yi L.,
Burt E. A., and
Tjoelker R. L., Mercury lamp studies in support of trapped ion frequency standards, 2015 Joint Conference of the IEEE International Frequency Control Symposium & the European Frequency and Time Forum, April 2015, Denver, CO, USA, https://doi.org/10.1109/FCS.2015.7138820, 2-s2.0-84943232179.
10.1109/FCS.2015.7138820 Google Scholar
- 7 Hinkley N., Sherman J. A., Phillips N. B., Schioppo M., Lemke N. D., Beloy K., Pizzocaro M., Oates C. W., and Ludlow A. D., An atomic clock with 10–18 instability, Science. (2013) 341, no. 6151, 1215–1218, https://doi.org/10.1126/science.1240420, 2-s2.0-84883791947.
- 8 Lu X., Yin M., Li T., Wang Y., and Chang H., Demonstration of the frequency-drift-induced self-comparison measurement error in optical lattice clocks, Japanese Journal of Applied Physics. (2020) 59, no. 7, 070903, https://doi.org/10.35848/1347-4065/ab98d8.
- 9
Manchester R. N., Pulsar timing and its applications, Journal of Physics: Conference Series. (2017) 932, 012002, https://doi.org/10.1088/1742-6596/932/1/012002, 2-s2.0-85039425135.
10.1088/1742-6596/932/1/012002 Google Scholar
- 10 Chen P. T., Speyer J. L., and Majid W. A., Frequency stability analysis of pulsar-aided clocks, Navigation. (2019) 66, no. 3, 621–632, https://doi.org/10.1002/navi.325, 2-s2.0-85070752367.
- 11 Sun H. F., Sun X., Fang H. Y., Shen L. R., Cong S. P., Liu Y. M., Li X. P., and Bao W. M., Building X-ray pulsar timing model without the use of radio parameters, Acta Astronautica. (2018) 143, 155–162, https://doi.org/10.1016/j.actaastro.2017.11.014, 2-s2.0-85037157257.
- 12 Huang L., Shuai P., Zhang X., and Chen S., A new explorer mission for soft X-ray timing - observation of the Crab pulsar, Acta Astronautica. (2018) 151, 63–67, https://doi.org/10.1016/j.actaastro.2018.05.060, 2-s2.0-85048192576.
- 13 Hobbs G., Coles W., Manchester R. N., Keith M. J., Shannon R. M., Chen D., Bailes M., Bhat N. D. R., Burke-Spolaor S., Champion D., Chaudhary A., Hotan A., Khoo J., Kocz J., Levin Y., Oslowski S., Preisig B., Ravi V., Reynolds J. E., Sarkissian J., van Straten W., Verbiest J. P. W., Yardley D., and You X. P., Development of a pulsar-based time-scale, Monthly Notices of the Royal Astronomical Society. (2012) 427, no. 4, 2780–2787, https://doi.org/10.1111/j.1365-2966.2012.21946.x, 2-s2.0-84885244830.
- 14 Melatos A. and Link B., Pulsar timing noise from superfluid turbulence, Monthly Notices of the Royal Astronomical Society. (2014) 437, no. 1, 21–31, https://doi.org/10.1093/mnras/stt1828, 2-s2.0-84890021910.
- 15 Rodin A. E. and Chen D., Optimal filtration and a pulsar time scale, Astronomy Reports. (2011) 55, no. 7, 622–628, https://doi.org/10.1134/S1063772911070055, 2-s2.0-79959915638.
- 16 Wang Y., Zheng W., Sun S., and An X., Algorithm for the pulsar timing system with the system bias, Journal of National University of Defense Technology. (2013) 35, no. 2, 12–16, http://journal.nudt.edu.cn/gfkjdxxben/article/abstract/201302003?st=article_issue.
- 17 Hobbs G., Guo L., Caballero R. N., Coles W., Lee K. J., Manchester R. N., Reardon D. J., Matsakis D., Tong M. L., Arzoumanian Z., Bailes M., Bassa C. G., Bhat N. D. R., Brazier A., Burke-Spolaor S., Champion D. J., Chatterjee S., Cognard I., Dai S., Desvignes G., Dolch T., Ferdman R. D., Graikou E., Guillemot L., Janssen G. H., Keith M. J., Kerr M., Kramer M., Lam M. T., Liu K., Lyne A., Lazio T. J. W., Lynch R., McKee J. W., McLaughlin M. A., Mingarelli C. M. F., Nice D. J., Osłowski S., Pennucci T. T., Perera B. B. P., Perrodin D., Possenti A., Russell C. J., Sanidas S., Sesana A., Shaifullah G., Shannon R. M., Simon J., Spiewak R., Stairs I. H., Stappers B. W., Swiggum J. K., Taylor S. R., Theureau G., Toomey L., van Haasteren R., Wang J. B., Wang Y., and Zhu X. J., A pulsar-based time-scale from the International Pulsar Timing Array, Monthly Notices of the Royal Astronomical Society. (2020) 491, no. 4, 5951–5965, https://doi.org/10.1093/mnras/stz3071.
- 18
Sheikh S. I.,
Hanson J. E.,
Graven P. H., and
Pines D. J., Spacecraft navigation and timing using X-ray pulsars, Navigation. (2011) 58, no. 2, 165–186, https://doi.org/10.1002/j.2161-4296.2011.tb01799.x, 2-s2.0-80052326145.
10.1002/j.2161-4296.2011.tb01799.x Google Scholar
- 19 Mitchell J. W., Hassouneh M. A., Winternitz L. M., Valdez J. E., Ray P. S., Arzoumanian Z., and Gendreau K. C., Station explorer for X-ray timing and navigation technology architecture overview, Proceedings of the 27th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2014), September 2014, Tampa, FL, USA, 3194–3200, https://www.ion.org/publications/abstract.cfm?articleID=12401.
- 20 Liu J., Wang W., Zhang H., Shu L., and Gao Y., Autonomous orbit determination and timekeeping in lunar distant retrograde orbits by observing X-ray pulsars, Navigation. (2021) 68, no. 4, 687–708, https://doi.org/10.1002/navi.451.
- 21 Liu Y., Xu B., Zheng Z., Chen Z., and Zhu X., Research on the joint timekeeping of pulsars and atomic clocks based on Vondrak-Cepek filtering, Monthly Notices of the Royal Astronomical Society. (2023) 521, no. 2, 2553–2559, https://doi.org/10.1093/mnras/stad613.
- 22 Zhu X., Zhang Z., Zhao C., Li B., Tong M., Gao Y., and Yang T., Research on establishing a joint time-scale of pulsar time and atomic time based on a wavelet analysis method, Monthly Notices of the Royal Astronomical Society. (2024) 529, no. 2, 1082–1090, https://doi.org/10.1093/mnras/stae331.
- 23 Wang L., Zhang Z., Zhao C., Li Z., and Tong M., Study on the one-year accuracy of pulsar time-scale, Research in Astronomy and Astrophysics. (2025) 25, no. 1, https://doi.org/10.1088/1674-4527/ada05f.
- 24 Zhou Q., Wei Z. Q., Yan L. L., Sun P. F., Liu S. W., Feng L. P., Jiang K., Wang Y. D., Zhu Y. X., Liu X. G., Ming F., Zhang F., and He Z. N., Space/ground based pulsar timescale for comprehensive PNT system, Acta Physica Sinica. (2021) 70, no. 13, 139701, https://doi.org/10.7498/aps.70.20210288.
- 25 Coles W., Hobbs G., Champion D. J., Manchester R. N., and Verbiest J. P. W., Pulsar timing analysis in the presence of correlated noise, Monthly Notices of the Royal Astronomical Society. (2011) 418, no. 1, 561–570, https://doi.org/10.1111/j.1365-2966.2011.19505.x, 2-s2.0-81055156773.
- 26 Lyne A. G., Shemar S. L., and Graham Smith F., Statistical studies of pulsar glitches, Monthly Notices of the Royal Astronomical Society. (2000) 315, no. 3, 534–542, https://doi.org/10.1046/j.1365-8711.2000.03415.x, 2-s2.0-0042350959.
- 27 Emadzadeh A. A. and Speyer J. L., On modeling and pulse phase estimation of X-ray pulsars, IEEE Transactions on Signal Processing. (2010) 58, no. 9, 4484–4495, https://doi.org/10.1109/TSP.2010.2050479, 2-s2.0-77955592785.
- 28 Sheikh S. I., The Use of Variable Celestial X-Ray Sources for Spacecraft Navigation, 2005, University of Maryland, College Park, Ann Arbor.
- 29 Salas J. D., Applied Modeling of Hydrologic Time Series, 1980, Water Resources Publication, Michigan.
- 30 Shannon R. M. and Cordes J. M., Assessing the role of spin noise in the precision timing of millisecond pulsars, Astrophysical Journal. (2010) 725, no. 2, 1607–1619, https://doi.org/10.1088/0004-637X/725/2/1607, 2-s2.0-78650094663.
- 31
Kedong Y.,
Yan G., and
Xuemei L., Improved grey prediction model based on exponential grey action quantity, Journal of Systems Engineering and Electronics. (2018) 29, no. 3, 560–570, https://doi.org/10.21629/JSEE.2018.03.13, 2-s2.0-85049743908.
10.21629/JSEE.2018.03.13 Google Scholar
- 32 Cilden D., Soken H. E., and Hajiyev C., Nanosatellite attitude estimation from vector measurements using SVD-aided UKF algorithm, Metrology and Measurement Systems. (2017) 24, no. 1, 113–125.
- 33 Song S., Xu L., Zhang H., and Bai Y., Novel X-ray communication based XNAV augmentation method using X-ray detectors, Sensors. (2015) 15, no. 9, 22325–22342, https://doi.org/10.3390/s150922325, 2-s2.0-84940987520, 26404295.
