# Measuring Height Difference Using Two-Way Satellite Time and Frequency Transfer

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## Abstract

**:**

## 1. Introduction

^{−19}and frequency stability of 1.2 × 10

^{−15}/$\sqrt{\tau}$ [8]. However, OACs are often bulky and can only work in laboratory environments, which significantly limits their application scope and makes it difficult to conduct a clock-transportation experiment. It has always been the wish of scientists to realize a transportable, reliable, and quasi-continuous high-precision OAC, but it is also challenging. To broaden the application scope of OAC, many research groups in the worldwide have been devoted to the development of transportable optical-atomic clocks (TOCs). In 2014, a group reported a TOC based on laser-cooled strontium atoms trapped in an optical lattice, and this TOC fits within a volume of <2 m

^{3}, and its relative uncertainty is 7 × 10

^{−15}[9]. Three years later, a group from Physikalisch-Technische Bundesanstalt (PTB) reported a TOC with

^{87}Sr, with its characterization against an OAC resulting in a systematic uncertainty of 7.4 × 10

^{−17}[10]. With the development of TOC, many scientists started to conduct clock-transportation experiments. Grotti et al. (2018) reported the first field measurement campaign with a

^{87}Sr TOC with an uncertainty of 1.8 × 10

^{−16}and a

^{171}Yb OAC with an uncertainty of 1.6 × 10

^{−16}. They used these clocks and fiber link to determine the geopotential difference between the middle of a mountain and a location 90 km away with a height difference of 1000 m. Their experimental result of potential difference of 10,034(174) m

^{2}s

^{−2}agrees well with value of 10,032.1(16) m

^{2}s

^{−2}determined independently by the conventional geodetic approach [3].

^{−16}level after 12 h was achieved [24]. Riedel et al. (2020) conducted a 26-day comparison of five simultaneously operated OACs and six MACs located at SYRTE, NPL, INRIM, LNE, and PTB by using TWSTFT and GPSPPP. Considering the correlations and gaps of measurement data, they improved the statistical analysis procedure; combined overall uncertainties in the range of 1.8 × 10

^{−16}to 3.5 × 10

^{−16}for the OAC comparisons were found [25]. To investigate the feasibility of transportable atomic clock comparison using TWSTFT, we conducted a MAC comparison experiment at the Beijing Institute of Radio Metrology and Measurement (BIRMM), Beijing [26,27].

## 2. Methods

#### 2.1. Height Measurement Based on Time Difference

^{2}) [7,29,30,31]

_{A}and t

_{B}denote the times at sites A and B, respectively, after a standard time period of T; W

_{A}and W

_{B}are the geopotential at sites A and B, respectively (note that we apply the definition of geopotential given by geodetic community); and $c$ is the speed of light in the vacuum. From Equation (1), we can determine the geopotential difference $\Delta {W}_{AB}={W}_{B}-{W}_{A}$ based on $\Delta {t}_{AB}/T$.

#### 2.2. One Pulse Per Second (1 PPS) Signal

^{7}cycles of the reference signal are one second. The generated 1 PPS signal rises from a low electrical level at the beginning of one reference signal cycle, and keeps the high electrical level for a short time (generally the pulse width is 20 $\mathsf{\mu}\mathrm{s}$), then declines to a low electrical level and keeps the site until the end of the 10

^{7}cycles (calculated from the first rise). This is a complete cycle (1 s) of 1 PPS signal. When the 1 PPS signal is used for time signal comparison, the rising edge of the signal will be used as the point to trigger the timer. Usually, the electrical level of the trigger is a predetermined value between the lowest electrical level and the highest electrical level. Ideally, when the electrical level rises to this predetermined value, the switch is triggered immediately, and the timing starts. However, there is a trigger delay during the process of the trigger switch. In fact, the switch can only be triggered when the actual electrical level is slightly higher than the predetermined value, so the trigger time will be within the time corresponding to the red oblique line [36]. Hence, the rising time duration $\delta t$ is very important for precise time synchronization. Usually, $\delta t$ should be smaller than 10 ns, since if $\delta t$ is too large, the rising edge’s slope (the blue slope line at the bottom of Figure 2) will become too small, which will increase the uncontrollable duration (red line) and reduce the time synchronization precision.

#### 2.3. Transmission of 1 PPS Signal

#### 2.4. Time Difference Calculation in TWSTFT

## 3. Error Analysis and Corrections

#### 3.1. Equipment Delay Error

#### 3.2. Propagation Path Delay Error

#### 3.3. Sagnac Effect Error

## 4. Experiments and Data Processing

#### 4.1. Experiments

^{−15}in one day. The TWSTFT was used as the time-transfer technique, one of the most accurate time-transfer methods than other GNSS-related techniques [50]. Time transfer by satellite does not have higher stability than fiber link, but it has better performance for long-distance time transfer.

#### 4.2. Data Processing

- (1)
- Through the data analysis with a large magnitude of change, we found that the data had some jumps, so we used fitting to restore them to the correct positions to ensure the continuity of all data.
- (2)
- To avoid the influence of outliers on the calculation results, we adopted 3σ criterion (PauTa criterion) to identify and eliminate outliers. The occasional outliers might be due to the fact that during its propagation, the radio frequency signal will suffer from various influences, which causes its distortion. Therefore, in the demodulation process, the sampling decision device cannot accurately reproduce the original 1 PPS signal, leading to outliers.
- (3)
- During continuous observation, some missing data may be caused by accidental failure of touch elements in TIC. We used linear interpolation to supplement the missing data.
- (4)
- We used singular spectrum analysis (SSA) [51] to remove periodic terms. This allows better extraction of trend items.

**Figure 6.**Comparison between two clocks. (

**a**) Row data of two clocks on different floors. (

**b**) Row data of two clocks on the same ground floor. (

**c**) Residual data of two clocks on different floors after processing. (

**d**) Residual data of two clocks on the same ground floor after processing.

## 5. Results

^{−15}and ${k}_{zero}=$−0.93617 × 10

^{−15}, respectively. The slope of the zero-baseline measurement is the constant system shift; therefore, subtracting it from that of the geopotential comparison experiment could determine the difference of the clock running rates between C

_{A}and C

_{B}. To calculate the difference of the clock running rates ($\frac{\Delta {t}_{AB}}{T}$), we differenced the two slopes:

^{−15}and ${u}_{zero}=$0.52 × 10

^{−15}, respectively. On the basis of the propagation law of errors, the uncertainty of the difference of the clock running rates ($\frac{\Delta {t}_{AB}}{T}$) is

## 6. Conclusions

^{−15}, which has better accuracy than period 2 (zero-baseline comparison measurement) 0.52 × 10

^{−15}. The reason for this result may be that the observation time of period 1 is longer than period 2; a longer observation time is helpful to weaken the influence of observation noise on experimental results.

^{−15}and matches the final measurement accuracy. The current result is only exploratory research on this method, which may not be directly applied, but this result proves the feasibility of the method. Although the results reached expectations, there are still some problems worth further exploration. We cannot explain why there is strong periodicity in the observed data, but it is conjectured that these are connected with the atomic clock’s performances and the relative motion of the satellite. The temperature could significantly influence the running rate of the atomic clock [53,54]. Due to the limitation of the experiment conditions, the ambient temperature of the atomic clock is not completely constant, and there is a certain fluctuation, which may be the reason for the jump in the observed data. In addition, the change of satellite orbit may also have an impact on the results. As described in Section 3.3, the satellite’s orbit with a daily period, which is not fixed and changes every day.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Einstein, A. Die Feldgleichungen der Gravitation; Sitzungsberichte der Preussischen Akademie der Wissenschaften: Berlin, Germany, 1915; pp. 844–847. [Google Scholar]
- Takamoto, M.; Ushijima, I.; Ohmae, N.; Yahagi, T.; Kokado, K.; Shinkai, H.; Katori, H. Test of general relativity by a pair of transportable optical lattice clocks. Nat. Photonics
**2020**, 14, 411–415. [Google Scholar] [CrossRef] - Grotti, J.; Koller, S.; Vogt, S.; Häfner, S.; Sterr, U.; Lisdat, C.; Denker, H.; Voigt, C.; Timmen, L.; Rolland, A.; et al. Geodesy and metrology with a transportable optical clock. Nat. Phys.
**2018**, 14, 437–441. [Google Scholar] [CrossRef] [Green Version] - Bondarescu, R.; Bondarescu, M.; Hetényi, G.; Boschi, L.; Jetzer, P.; Balakrishna, J. Geophysical applicability of atomic clocks: Direct continental geoid mapping. Geophys. J. Int.
**2012**, 191, 78–82. [Google Scholar] [CrossRef] [Green Version] - Shen, W.B.; Ning, J.; Chao, D.; Liu, J. A proposal on the test of general relativity by clock transportation experiments. Adv. Space Res.
**2009**, 43, 164–166. [Google Scholar] [CrossRef] - Shen, W.; Chao, D.; Jin, B. On relativistic geoid. Boll Geod. Sci. Affini.
**1993**, 52, 207–216. [Google Scholar] - Bjerhammar, A. On a relativistic geodesy. Bull. Géodésique
**1985**, 59, 207–220. [Google Scholar] [CrossRef] - Chen, J.S.; Hankin, A.M.; Clements, E.R.; Chou, C.W.; Wineland, D.J.; Hume, D.B.; Leibrandt, D.R.; Brewer, S.M. An
^{27}Al^{+}Quantum-Logic Clock with a Systematic Uncertainty below 10^{−18}. Phys. Rev. Lett.**2019**, 123, 33201. [Google Scholar] - Poli, N.; Schioppo, M.; Vogt, S.; Falke, S.; Sterr, U.; Lisdat, C.; Tino, G.M. A transportable strontium optical lattice clock. Appl. Phys. B
**2014**, 117, 1107–1116. [Google Scholar] [CrossRef] [Green Version] - Koller, S.B.; Grotti, J.; Vogt, S.; Al-Masoudi, A.; Dörscher, S.; Häfner, S.; Sterr, U.; Lisdat, C. Transportable Optical Lattice Clock with 7×10
^{−17}Uncertainty. Phys. Rev. Lett.**2017**, 118, 73601. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Rovera, G.D.; Abgrall, M.; Courde, C.; Exertier, P.; Fridelance, P.; Guillemot, P.; Laas-Bourez, M.; Martin, N.; Samain, E.; Sherwood, R.; et al. A direct comparison between two independently calibrated time transfer techniques: T2L2 and GPS Common-Views. J. Physics. Conf. Ser.
**2016**, 723, 12037. [Google Scholar] [CrossRef] - Siu, S.; Wang, J.-L.; Tseng, W.-H.; Liao, C.-S.; Hu, H.-F. Primary reference time clocks performance monitoring using GNSS common-view technique in telecommunication networks. In Proceedings of the 2016 18th Asia-Pacific Network Operations and Management Symposium (APNOMS), Kanazawa, Japan, 5–7 October 2016; pp. 1–4. [Google Scholar]
- Hang, Y.; Hongbo, W.; Shengkang, Z.; Haifeng, W.; Fan, S.; Xueyun, W. Remote time and frequency transfer experiment based on BeiDou Common View. In Proceedings of the 2016 European Frequency and Time Forum (EFTF), York, UK, 4–7 April 2016; pp. 1–4. [Google Scholar]
- Petit, G.; Defraigne, P. The performance of GPS time and frequency transfer: Comment on ‘A detailed comparison of two continuous GPS carrier-phase time transfer techniques’. Metrologia
**2016**, 53, 1003–1008. [Google Scholar] [CrossRef] - Lee, S.W.; Schutz, B.E.; Lee, C.; Yang, S.H. A study on the Common-View and All-in-View GPS time transfer using carrier-phase measurements. Metrologia
**2008**, 45, 156–167. [Google Scholar] [CrossRef] - Kirchner, D. Two-way time transfer via communication satellites. Proc. IEEE
**1991**, 79, 983–990. [Google Scholar] [CrossRef] - Steele, J.M.; Markowitz, W.; Lidback, C.A. Telstar Time Synchronization. IEEE Trans. Instrum. Meas.
**1964**, IM-13, 164–170. [Google Scholar] [CrossRef] - Jiang, Z.; Konaté, H.; Lewandowski, W. Review and preview of two-way time transfer for UTC generation—From TWSTFT to TWOTFT. In Proceedings of the 2013 Joint European Frequency and Time Forum & International Frequency Control Symposium (EFTF/IFC), Prague, Czech Republic, 21–25 July 2013; pp. 501–504. [Google Scholar]
- Bauch, A. Time and frequency comparisons using radiofrequency signals from satellites. Comptes Rendus Phys.
**2015**, 16, 471–479. [Google Scholar] [CrossRef] - Hanson, D.W. Fundamentals of two-way time transfers by satellite. In Proceedings of the 43rd Annual Symposium on Frequency Control, Denver, CO, USA, 31 May–2 June 1989; pp. 174–178. [Google Scholar]
- Imae, M.; Hosokawa, M.; Imamura, K.; Yukawa, H.; Shibuya, Y.; Kurihara, N.; Fisk, P.; Lawn, M.A.; Li, Z.; Li, H. Two-way satellite time and frequency transfer networks in Pacific Rim region. IEEE Trans. Instrum. Meas.
**2002**, 50, 559–562. [Google Scholar] [CrossRef] - Fujieda, M.; Gotoh, T.; Nakagawa, F.; Tabuchi, R.; Aida, M.; Amagai, J. Carrier-phase-based two-way satellite time and frequency transfer. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2012**, 59, 2625–2630. [Google Scholar] [CrossRef] [PubMed] - Jing, W.; Wang, J.; Zhao, D.; Lu, X.; Wu, J. A measurement method of the GEO satellite local oscillator error. In Proceedings of the 2013 Joint European Frequency and Time Forum & International Frequency Control Symposium (EFTF/IFC), Prague, Czech Republic, 21–25 July 2013; pp. 339–342. [Google Scholar]
- Fujieda, M.; Yang, S.; Gotoh, T.; Hwang, S.; Hachisu, H.; Kim, H.; Lee, Y.K.; Tabuchi, R.; Ido, T.; Lee, W.; et al. Advanced Satellite-Based Frequency Transfer at the 10
^{−16}Level. IEEE Trans. Ultrason. Ferroelectr. Freq. Control**2018**, 65, 973–978. [Google Scholar] [CrossRef] [Green Version] - Riedel, F.; Al-Masoudi, A.; Benkler, E.; Dörscher, S.; Gerginov, V.; Grebing, C.; Häfner, S.; Huntemann, N.; Lipphardt, B.; Lisdat, C.; et al. Direct comparisons of European primary and secondary frequency standards via satellite techniques. Metrologia
**2020**, 57, 45005. [Google Scholar] [CrossRef] [Green Version] - Wu, K.; Shen, Z.; Shen, W.B.; Sun, X.; Wu, Y. A preliminary experiment of determining the geopotential difference using two hydrogen atomic clocks and TWSTFT technique. Geod. Geodyn.
**2020**, 11, 229–241. [Google Scholar] [CrossRef] - Shen, W.; Sun, X.; Cai, C.; Wu, K.; Shen, Z. Geopotential determination based on a direct clock comparison using two-way satellite time and frequency transfer. Terr. Atmos. Ocean. Sci.
**2019**, 30, 21–31. [Google Scholar] [CrossRef] [Green Version] - Weinberg, S. Gravitation and cosmology: Principles and Applications of the General Theory of Relativity. Am. J. Phys.
**1972**, 41, 598–599. [Google Scholar] [CrossRef] - Pavlis, N.; Weiss, M. The relativistic redshift with 3×10
^{−17}uncertainty at NIST, Boulder, Colorado, USA. Metrologia**2003**, 40, 66. [Google Scholar] [CrossRef] - Dittus, H.; Lämmerzahl, C.; Peters, A.; Schiller, S. OPTIS—A Satellite test of Special and General Relativity. Adv. Space Res.
**2007**, 39, 230–235. [Google Scholar] [CrossRef] - Vessot, R.; Levine, M.; Mattison, E.; Blomberg, E.; Hoffman, T.; Nystrom, G.; Farrel, B.; Decher, R.; Eby, P.; Baugher, C. Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser. Phys. Rev. Lett.
**1981**, 45, 2081–2084. [Google Scholar] [CrossRef] - Shen, Z.; Shen, W.; Peng, Z.; Liu, T.; Zhang, S.; Chao, D. Formulation of Determining the Gravity Potential Difference Using Ultra-High Precise Clocks via Optical Fiber Frequency Transfer Technique. J. Earth Sci. China
**2018**, 30, 422–428. [Google Scholar] [CrossRef] - Heiskanen, W.A.; Moritz, H. Physical Geodesy; Freeman and Company: San Francisco, CA, USA, 1967. [Google Scholar]
- Saburi, Y.; Yamamoto, M.; Harada, K. High-precision time comparison via satellite and observed discrepancy of synchronization. IEEE Trans. Instrum. Meas.
**1976**, IM-25, 473–477. [Google Scholar] [CrossRef] - Asami, K. An Algorithm to Improve the Performance of M-Channel Time-Interleaved A-D Converters. IEICE Trans. Fundam. Electron. Commun. Comput. Sci.
**2007**, E90-A, 2846–2852. [Google Scholar] [CrossRef] - Ridders, C. Accurate determination of threshold voltage levels of Schmitt trigger. IEEE Trans. Circuits Syst.
**1985**, 32, 969–970. [Google Scholar] [CrossRef] - Dinan, E.H.; Jabbari, B. Spreading codes for direct sequence CDMA and wideband CDMA cellular networks. IEEE Commun. Mag.
**1998**, 36, 48–54. [Google Scholar] [CrossRef] - Celano, T.P.; Francis, S.P.; Gifford, G.A. Continuous satellite two-way time transfer using commercial modems. In Proceedings of the 2000 IEEE/EIA International Frequency Control Symposium and Exhibition (Cat. No.00CH37052), Kansas City, MO, USA, 9 June 2000; pp. 607–611. [Google Scholar]
- Barrow, B.B. Error Probabilities for Telegraph Signals Transmitted on a Fading FM Carrier. Proc. IRE
**1960**, 48, 1613–1629. [Google Scholar] [CrossRef] - Piester, D.; Bauch, A.; Becker, J.; Staliuniene, E.; Schlunegger, C. On measurement noise in the European TWSTFT network. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2008**, 55, 1906–1912. [Google Scholar] [CrossRef] [PubMed] - Goldsmith, A. Wireless Communications; Cambridge University Press: Cambridge, UK, 2005. [Google Scholar]
- ITU-R. The Operational Use of Two-Way Satellite Time and Frequency Transfer Employing Pseudorandom Noise Codes. TF Series: Time Signals and Frequency Standards Emissions, Recommendation ITU-R TF.1153- 3 (08/2015), International Telcomunication Union. 2015. Available online: https://www.itu.int/rec/R-REC-TF.1153-4-201508-I/en (accessed on 5 September 2021).
- Lin, H.T.; Huang, Y.J.; Tseng, W.H.; Liao, C.S.; Chu, F.D. The TWSTFT links circling the world. In Proceedings of the 2014 IEEE International Frequency Control Symposium (FCS), Taipei, Taiwan, 19–22 May 2014; pp. 1–4. [Google Scholar]
- Hopfield, H.S. Tropospheric effect on electromagnetically measured range: Prediction from surface weather data. Radio Sci.
**1971**, 6, 357–367. [Google Scholar] [CrossRef] - Sastamoinen, J. Atmospheric correction for troposphere and stratosphere in radio ranging of satellites, in the Use of Artifical Satellites for Geodesy. Geophys. Monogr. Ser.
**1972**, 15, 247–251. [Google Scholar] - Penna, N.; Dodson, A.; Chen, W. Assessment of EGNOS Tropospheric Correction Model. J. Navigation.
**2001**, 54, 37–55. [Google Scholar] [CrossRef] [Green Version] - Rose, J.A.R.; Watson, R.J.; Allain, D.J.; Mitchel, N.C. Ionospheric corrections for GPS time transfer. Radio Sci.
**2014**, 49, 196–206. [Google Scholar] [CrossRef] - Tseng, W.; Feng, K.; Lin, S.; Lin, H.; Huang, Y.; Liao, C. Sagnac Effect and Diurnal Correction on Two-Way Satellite Time Transfer. IEEE Trans. Instrum. Meas.
**2011**, 60, 2298–2303. [Google Scholar] [CrossRef] - Bidikar, B.; Rao, G.; Laveti, G. Sagnac Effect and SET Error Based Pseudorange Modeling for GPS Applications. Procedia Comput. Sci.
**2016**, 87, 172–177. [Google Scholar] [CrossRef] [Green Version] - Hackman, C.; Levine, J. A Long-Term Comparison of GPS Carrierphase Frequency Transfer and Two-Way Satellite Time/Frequency Transfer. In Proceedings of the 38th Annual Precise Time and Time Interval (PTTI) Meeting, Reston, VA, USA, 7–9 December 2006; pp. 1–15. [Google Scholar]
- Vautard, R.; Yiou, P.; Ghil, M. Singular-spectrum analysis: A toolkit for short, noisy chaotic signals. Phys. D Nonlinear Phenom.
**1992**, 58, 95–126. [Google Scholar] [CrossRef] - Hocking, R. Methods and Applications of Linear Models. In Regression and the Analysis of Variance; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2005. [Google Scholar]
- Ascarrunz, F.G.; Jefferts, S.R.; Parker, T.E. Environmental effects on errors in two-way time transfer. In Proceedings of the 20th Biennial Conference on Precision Electromagnetic Measurements, Braunschweig, Germany, 17–21 June 1996; pp. 518–519. [Google Scholar]
- Ascarrunz, F.G.; Jefferts, S.R.; Parker, T.E. Earth station errors in two-way time and frequency transfer. IEEE Trans. Instrum. Meas.
**1997**, 46, 205–208. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Principle of determining the orthometric heights. W

_{A}and W

_{B}are the geopotentials at point A and B, O

_{A}and O

_{B}are the projection points on the geoid (bold dashed curve) corresponding to point A and B along the plumb lines (light-blue dashed curves), red dashed curve denotes equipotential surface passing through point A, ${\mathrm{W}}_{0}$ is the geopotential on the geoid.

**Figure 3.**Principle of the two-way satellite time and frequency transfer (TWSTFT). There are two same TWSTFT observation systems located at two sites A and B. Every system include clock, emitter, receiver, etc. (see text) (modified after ITU-R 2015).

**Figure 4.**The influence of small periodic movement of satellite on TWSTFT. Two antennas ${T}_{A}$ and ${T}_{B}$ located, respectively, at station A and B, are connected with clocks. S is the geostationary satellite.

**Figure 5.**Time difference measurement. (

**a**) Geopotential difference measurement. (

**b**) Zero-baseline measurement. ${T}_{A}$ and ${T}_{B}$ are the antennas connected to clock ${C}_{A}$ and clock ${C}_{B}$, respectively. ICC is integrated control cabinet, which includes modulation, upconvertor, downconvertor, demodulation, time interval counter, etc. S is the geostationary satellite used in the experiments.

Error Sources | Error Magnitude/ps (Two-Way) | Correction Model | Residual Error/ps |
---|---|---|---|

Time interval counter delay | 10~100 | Zero-baseline calibration | 5 |

Modems delay | 100 | Zero-baseline calibration | 10 |

Satellite transparent transponder delay | 80 | Zero-baseline calibration | 10 |

Transmission and receiving system delay | 200~500 | Zero-baseline calibration | 30 |

Propagation path geometry delay | <10 | Neglected | <10 |

Tropospheric delay | 10 | Neglected | 10 |

Ionospheric delay | 100 | Model correction | <10 |

Asymmetry of station and satellite position delay | 30 | Delay transmission compensation | <1 |

Sagnac effect delay | 1~2 × 10^{5} | Model correction | 10~100 |

Geopotential Comparison | Zero-Baseline | |
---|---|---|

Slope | 2.11639 × 10^{−15} | −0.93617 × 10^{−15} |

The uncertainty of the slope | 0.26 × 10^{−15} | 0.52 × 10^{−15} |

Measured height difference between A and B (m) | 28.0 $\pm $ 5.4 | |

True value (m) | 22.8 | |

Deviation (m) | 5.2 $\pm $ 5.4 |

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**MDPI and ACS Style**

Cheng, P.; Shen, W.; Sun, X.; Cai, C.; Wu, K.; Shen, Z.
Measuring Height Difference Using Two-Way Satellite Time and Frequency Transfer. *Remote Sens.* **2022**, *14*, 451.
https://doi.org/10.3390/rs14030451

**AMA Style**

Cheng P, Shen W, Sun X, Cai C, Wu K, Shen Z.
Measuring Height Difference Using Two-Way Satellite Time and Frequency Transfer. *Remote Sensing*. 2022; 14(3):451.
https://doi.org/10.3390/rs14030451

**Chicago/Turabian Style**

Cheng, Peng, Wenbin Shen, Xiao Sun, Chenghui Cai, Kuangchao Wu, and Ziyu Shen.
2022. "Measuring Height Difference Using Two-Way Satellite Time and Frequency Transfer" *Remote Sensing* 14, no. 3: 451.
https://doi.org/10.3390/rs14030451