# A New Space-to-Ground Microwave-Based Two-Way Time Synchronization Method for Next-Generation Space Atomic Clocks

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## Abstract

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^{−17}) and will leverage advantages of the space environment such as microgravity and low interference to operate a new generation of high-performance time-frequency payloads on low-orbit spacecraft. Moreover, using the high-precision time-frequency system of ground stations, low-time-delay high-performance time-frequency transmission networks, which have the potential to achieve ultrahigh-precision time synchronization, will be constructed. By considering full link error terms above the picosecond level, this paper proposes a new space-to-ground microwave two-way time synchronization method for scenarios involving low-orbit spacecraft and ground stations. Using the theoretical principles and practical application scenarios related to this method, a theoretical and simulation verification platform was developed to research the impact of the attitude, phase center calibration, and orbit determination errors on the single-frequency two-way time synchronization method. The effectiveness of this new method was verified. The results showed that when the attitude error is less than 72 arc seconds (0.02°), the phase center calibration error is less than 1 mm, and the precision orbit determination (POD) error is less than 10 cm (three-axis). After disregarding nonlink error terms such as equipment noise, this method can attain a space-to-ground time synchronization accuracy of better than 1.5 ps, and the time deviation (TDEV) of the transfer link is better than 0.7 ps @ 100 s, which results in ultrahigh-precision space-to-ground time synchronization.

## 1. Introduction

## 2. A New Method for Space-to-Ground Two-Way Time Synchronization

#### 2.1. New Generation of Space Time-Frequency Loads

- High-performance space atomic clock (Allan deviation better than 10
^{−17}@ 1 day); - Precise orbit determination of Global Navigation Satellite System (GNSS) receivers;
- Microwave link module for code and carrier phase measurements;
- Laser link module.

#### 2.2. Space-to-Ground Two-Way Time Synchronization Principle Based on a Single Frequency Mode

_{3}; the center point of the signal-receiving antenna installation surface of the microwave link module is A

_{1}, and the center point of the signal-transmitting antenna installation surface is A

_{2}. To avoid signal interference, the transmitting and receiving antennas need to be separated. As a result, there is a fixed safe distance (a few centimeters) between A

_{1}and A

_{2}, and the antennas are installed relative to the ground to achieve high-precision time synchronization with ground equipment; A is the center of mass of the spacecraft. As the GNSS receiver antenna and the microwave link module antenna are connected by a rigid body, the coordinate conversion relationship between A, A

_{1}, A

_{2}, and A

_{3}can be obtained through calibration on the ground beforehand (see the red line in Figure 1). Coordinates of the other three positions can then be calculated based on any one of these coordinates.

#### 2.3. Various Error Corrections of High-Precision Space-to-Ground Time Synchronization

^{−17}@ 1 day) atomic clocks mounted on high-speed low-orbit spacecraft, precision adjustments must be performed on every error-generated term during the space-to-ground two-way time synchronization process to achieve higher-precision time transmission requirements. In Equation (5), the equipment time delay can be accurately calibrated in orbit [25]; the phase center error can be compensated for by performing an accurate calibration along with the corresponding modeling in advance [26]; space-to-ground link measurement noise appears as a random error, for which filtering operations must be conducted based on the statistical properties of the error. Therefore, based on the link accuracy requirements of ultrahigh-precision time synchronization, the main error correction terms considered for space-to-ground two-way time synchronization in single-frequency mode include error corrections for motion delay, periodic relativistic effects, and gravitational delay.

#### 2.3.1. Motion Delay Error Correction

#### 2.3.2. Correction of Periodic Relativistic Error Effect

#### 2.3.3. Gravitational Time Delay Error Correction

## 3. Simulation Test and Performance Analysis

#### 3.1. Low-Orbit Spacecraft-to-Ground Station Simulation Experiment

^{−17}.

#### 3.2. Space-to-Ground Time Synchronization Performance Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Yuan, Y.; Wang, B.; Wang, L. Fiber-based joint time and frequency dissemination via star-shaped commercial telecommunication network. Chin. Phys. B
**2017**, 26, 080601. [Google Scholar] [CrossRef] - Pan, J.; Hu, X.; Zhou, S.; Tang, C.; Guo, R.; Zhu, L.; Tang, G.; Hu, G. Time synchronization of new-generation BDS satellites using inter-satellite link measurements. Adv. Space Res.
**2018**, 61, 145–153. [Google Scholar] [CrossRef] - Yang, W.; Meng, W.; Han, W.; Xie, Y.; Ren, X.; Hu, X.; Dong, W. Advances in Atomic Clock Ensemble in Space of Europe and Ultraprecise Time and Frequency Transfer. Prog. Astron.
**2016**, 34, 221. [Google Scholar] - Laurent, P.; Abgrall, M.; Jentsch, C.; Lemonde, P. Design of the cold atom PHARAO space clock and initial test results. Appl. Phys. B.
**2006**, 84, 683–690. [Google Scholar] [CrossRef] - Cacciapuoti, L.; Salomon, C. Space clocks and fundamental tests: The ACES experiment. Eur. Phys. J. Spec. Top.
**2009**, 172, 57–68. [Google Scholar] [CrossRef] - Zhang, X. System design and key technologies of high accuracy time and frequency microwave link for spaces station. Telecommun. Eng.
**2017**, 57, 407–411. [Google Scholar] - Laurent, P.; Massonnet, D.; Cacciapuoti, L.; Salomon, C. The ACES/PHARAO space mission. Comptes Rendus Phys.
**2015**, 16, 540–552. [Google Scholar] [CrossRef] - Savalle, E.; Guerlin, C.; Delva, P.; Meynadier, F.; Poncin-Lafitte, C.L.; Wolf, P. Gravitational redshift test with the future ACES mission. Class. Quantum Gravity
**2019**, 36, 245004. [Google Scholar] [CrossRef][Green Version] - Heb, M.P.; Stringhetti, L.; Hummelsberger, B.; Hausner, K.; Stalford, R.; Nasca, R.; Cacciapuoti, L.; Much, R.; Feltham, S.; Vudali, T. The ACES mission: System development and test status. Acta Astronaut.
**2011**, 29, 929–938. [Google Scholar] - Cacciapuoti, L.; Much, R.; Feltham, S.; Nasca, R.; Vudali, T.; Hess, M.P.; Stringhetti, L.; Salomon, C. ACES status at completion of the engineering models phase. In Proceedings of the 2010 European Frequency and Time Forum, Noordwijk, The Netherlands, 13–16 April 2010; pp. 1–10. [Google Scholar] [CrossRef]
- Delva, P.; Meynadier, F.; Le Poncin-Lafitte, C.; Laurent, P.; Wolf, P. Time and frequency transfer with a MicroWave Link in the ACES/PHARAO mission. In Proceedings of the 2012 European Frequency and Time Forum, Gothenburg, Sweden, 23–27 April 2012; pp. 28–35. [Google Scholar]
- Origlia, S.; Pramod, M.S.; Schiller, S.; Singh, Y.; Viswam, S.; Bongs, K.; Hafner, S.; Berbers, S.; Dorscher, S.; Al-Masoudi, A. An optical lattice clock breadboard demonstrator for the I-SOC mission on the ISS. In Proceedings of the Lasers & Electro-optics Europe & European Quantum Electronics Conference IEEE, Munich, Germany, 25–29 June 2017; p. 1. [Google Scholar]
- Xu, M.; Shi, W. Development of Deep Space Radio Ranging and Velocity Measurement Technology. J. Deep. Space Explor.
**2018**, 5, 140–146. [Google Scholar] - Michalak, G.; Glaser, S.; Neumayer, K.H.; König, R. Precise orbit and Earth parameter determination supported by LEO satellites, inter-satellite links and synchronized clocks of a future GNSS. Adv. Space Res.
**2021**, 68, 4753–4782. [Google Scholar] [CrossRef] - Seidel, A.; Hess, M.P.; Kehrer, J.; Schafer, W.; Kufner, M.; Siccardi, M.; Cacciapuoti, L.; Aguilar Sanches, I.; Feltham, S. The ACES Microwave Link: Instrument Design and Test Results. In Proceedings of the 2007 IEEE International Frequency Control Symposium Joint with the 21st European Frequency and Time Forum, Geneva, Switzerland, 29 May–1 June 2007; p. 1295. [Google Scholar]
- Liu, Y.; Li, X. Super-high accurate new metho d of common-view time comparison based on space station. Acta Phys. Sin.
**2018**, 67, 68–79. [Google Scholar] - Bai, Y.; Guo, Y.; Wang, X.; Lu, X. Satellite-ground two-way measuring method and performance evaluation of BDS-3 inter-satellite link system. IEEE Access
**2020**, 8, 157530–157540. [Google Scholar] [CrossRef] - Liu, Y.; Li, X. Effect of Orbit Error on Space Station Time Comparison and Calibrating Method. J. Astronaut.
**2019**, 40, 345–351. [Google Scholar] - Meynadier, F.; Delva, P.; Le Poncin Lafitte, C.; Guerlin, C.; Laurent, P.; Wolf, P. ACES Micro-wave link data analysis: Status update. In Proceedings of the Journées Systèmes De Référence Spatio Temporels Scientific Developments from Highly Accurate Space Time Reference Systems, Paris, France, 16–18 September 2013; pp. 134–135. [Google Scholar]
- Cacciapuoti, L. I-SOC Scientific Requirement. 2017. Available online: http://www.exphy.uni-duesseldorf.de/PDF/SCI-ESA-HRE-ESR-ISOC_Iss.1.1_Approved.pdf (accessed on 1 December 2021).
- Pütz, C.; He, M.P.; Hummelsberger, B.; Hausner, K.; Prochazka, I. Aces mission status and outlook. In Proceedings of the 62nd International Astronautical Congress, Cape Town, South Africa, 3–7 October 2011; Volume 1, pp. 495–508. [Google Scholar]
- Cacciapuoti, L.; Armano, M.; Much, R.; Sy, O.; Salomon, C. Testing gravity with cold-atom clocks in space: The ACES mission. Eur. Phys. J. D
**2020**, 74, 164. [Google Scholar] [CrossRef] - Yang, D.; Liu, Y.; Li, G.; Zhao, Q.; Yang, Z. Research on Communication Delay Model for Narrow Beam Inter-satellite Links in a TDMA System. In Proceedings of the China Satellite Navigation Conference (CSNC) 2017 Proceedings, Shanghai, China, 23–25 May 2017; pp. 3–9. [Google Scholar]
- Hobiger, T.; Piester, D.; Baron, P. A correction model of dispersive troposphere delays for the ACES microwave link. Radio Sci.
**2013**, 48, 131–142. [Google Scholar] [CrossRef] - Pan, J.; Hu, X.; Tang, C.; Zhou, S.; Li, R.; Zhu, L.; Tang, G.; Hu, G.; Chang, Z.; Wu, S. System error calibration for time division multiple access inter-satellite payload of new-generation Beidou satellites. Chin. Sci. Bull.
**2017**, 62, 2671–2679. [Google Scholar] [CrossRef][Green Version] - Zhu, J. Research on Determination and Time Synchronizing of Navigation Satellite Based on Crosslinks; National University of Defense Technology: Changsha, China, 2011. [Google Scholar]
- Guo, Y.; Bai, Y.; Gao, S.; Pan, Z.; Han, Z.; Gao, Y.; Lu, X. A SatelliteGround Precise Time Synchronization Method and Analysis on Time Delay Error Caused by Motion. In Proceedings of the China Satellite Navigation Conference (CSNC) 2021 Proceedings, Nanchang, China, 26–28 May 2021; Volume 3, pp. 158–171. [Google Scholar]
- Huang, W.; Kang, J.; Zhang, L.; Li, J. The Principle and Method of Beidou Satellite Navigation and Positioning; Science Press: Beijing, China, 2019; p. 123. [Google Scholar]
- Sun, L.; Gao, S.; Yang, J.; Xiao, F.; Fang, Y.; Feng, S. Relativistic Effect in the Two-Way Time Comparison Between Navigation Satellites. In Proceedings of the China Satellite Navigation Conference (CSNC) 2021 Proceedings, Nanchang, China, 26–28 May 2021; Volume 3, pp. 95–104. [Google Scholar]
- Chen, H.; Wu, H.; Zhou, M.; Qi, J. Orbit Engineering Application and STK Simulation for Microsatellite; Science Press: Beijing, China, 2016; p. 63. [Google Scholar]
- Lv, H. Research on method of Satellite-Ground Time Synchronization Base on Ka Band ISL System of BDS; University of Chinese Academy of Sciences: Beijing, China, 2017. [Google Scholar]
- Li, K.; Zhou, X.; Wang, W.; Gao, Y.; Zhao, G.; Tao, E.; Xu, K. Centimeter-Level Orbit Determination for TG02 Spacelab Using Onboard GNSS Data. Sensors
**2018**, 18, 2671. [Google Scholar] [CrossRef] [PubMed][Green Version] - Meynadier, F.; Delva, P.; Poncin-Lafitte, C.L.; Guerlin, C.; Wolf, P. Atomic clock ensemble in space (ACES) data analysis. Class. Quantum Gravity
**2018**, 35, 035018. [Google Scholar] [CrossRef][Green Version] - Weinbach, U.; Schon, S. Improved GPS receiver clock modeling for kinematic orbit determination of the GRACE satellites. In Proceedings of the 2012 European Frequency and Time Forum, Gothenburg, Sweden, 23–27 April 2012; pp. 157–160. [Google Scholar]

**Figure 3.**Platform architecture of the space-to-ground time synchronization simulation verification.

**Figure 4.**(

**a**) Largest single observation arc of F1 frequency and (

**b**) various delay components in the signal transmission process.

**Figure 5.**Time synchronization error under different error settings. (

**a**) The time synchronization error distribution of different attitude errors when the control phase center calibration error is 1 mm and the orbit determination error is 10 cm. (

**b**) The time synchronization error distribution of different phase center calibration errors when the control attitude error is 0.02° (72 as) and the orbit determination error is 10 cm. (

**c**) The time synchronization error distribution of different orbit determination errors when the control attitude error is 0.02° (72 as) and the phase center calibration error is 1 mm.

**Figure 6.**Space-to-ground time synchronization result. (

**a**) Relative clock difference between the space clock and the ground clock. (

**b**) Fitting residuals of the relative clock difference.

**Figure 7.**Performance objective of the space-to-ground time and frequency transfer expressed in time deviation (TDEV).

**Table 1.**Observations of the low-orbit spacecraft-ground station chain construction on 1 January 2020.

Arc | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Chain Construction Start Time | 04:46:49 | 06:24:10 | 08:02:08 | 09:38:54 | 11:15:38 |

Chain Construction End Time | 04:53:08 | 06:29:42 | 08:06:38 | 09:44:40 | 11:21:26 |

Number of Epochs (s) | 380 | 333 | 271 | 347 | 359 |

Attitude Error (as) | 0 | 60 | 70 | 80 | 90 | 100 |
---|---|---|---|---|---|---|

Two-Way Time Synchronization Accuracy (ps) | 1.2732 | 1.2733 | 1.2822 | 1.3111 | 1.3167 | 1.3272 |

**Table 3.**Two-way time synchronization accuracy (RMS) under different phase center calibration errors.

Phase Centre Calibration Error (mm) | 0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 |
---|---|---|---|---|---|---|

Two-Way Time Synchronization Accuracy (ps) | 1.2295 | 1.2776 | 1.2930 | 1.3102 | 1.3469 | 1.3860 |

Orbit Determination Error (cm) | 0 | 5 | 10 | 15 | 20 | 25 |
---|---|---|---|---|---|---|

Two-Way Time Synchronization Accuracy (ps) | 1.2707 | 1.2825 | 1.2930 | 1.3495 | 1.3874 | 1.4352 |

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**MDPI and ACS Style**

Guo, Y.; Gao, S.; Bai, Y.; Pan, Z.; Liu, Y.; Lu, X.; Zhang, S.
A New Space-to-Ground Microwave-Based Two-Way Time Synchronization Method for Next-Generation Space Atomic Clocks. *Remote Sens.* **2022**, *14*, 528.
https://doi.org/10.3390/rs14030528

**AMA Style**

Guo Y, Gao S, Bai Y, Pan Z, Liu Y, Lu X, Zhang S.
A New Space-to-Ground Microwave-Based Two-Way Time Synchronization Method for Next-Generation Space Atomic Clocks. *Remote Sensing*. 2022; 14(3):528.
https://doi.org/10.3390/rs14030528

**Chicago/Turabian Style**

Guo, Yanming, Shuaihe Gao, Yan Bai, Zhibing Pan, Yinhua Liu, Xiaochun Lu, and Shougang Zhang.
2022. "A New Space-to-Ground Microwave-Based Two-Way Time Synchronization Method for Next-Generation Space Atomic Clocks" *Remote Sensing* 14, no. 3: 528.
https://doi.org/10.3390/rs14030528