Chinese Journal of Lasers, Volume. 52, Issue 2, 0204003(2025)
Calculation Model and Error Analysis of Lunar Laser Time-Frequency Transfer Based on General Relativity
Figures & Tables(16)
Fig. 2. Differences in the calculation of light travel time using BCRS/TDB and GCRS/TT coordinate and time systems
Fig. 3. Light time corrections in DRO one-way laser time-frequency transfer. (a) Instantaneous Euclidean distance from the ground station to the satellite corresponding to the epoch of laser emission; (b) first-order and second-order light time corrections
Fig. 4. First-order and second-order light time corrections in DRO two-way laser time-frequency transfer
Fig. 5. Position correction between detector and reflector for DRO laser time-frequency transfer
Fig. 6. Atmospheric refraction-induced effects in DRO one-way/two-way laser time-frequency transfer
Fig. 8. Relativistic frequency time-delay in DRO one-way/two-way laser time-frequency transfer
Fig. 9. Simulation results of DRO two-way laser time-frequency transfer. (a) Stability corresponding to link residual; (b) residual of link correction
Fig. 10. Simulation results of DRO one-way laser time-frequency transfer. (a) Stability corresponding to link residual; (b) residual of link correction
Fig. 11. Simulation results of DRO one-way laser time-frequency transfer in common-view mode. (a) Stability corresponding to link residual; (b) residual of link correction
Table 1. Magnitude of link error corrections in the DRO laser time-frequency transfer (elevation>20°)
View tableTable 1. Magnitude of link error corrections in the DRO laser time-frequency transfer (elevation>20°)
Uncertainty source Correction magnitude Introduction Instantaneous Euclidean distance （one-way） 0.909 to 1.582 s Consider First-order light time correction （one-way） -1739.628 to 1557.462 ns Consider Second-order light time correction （one-way） -5.283 to 5.130 ps Consider Atmospheric refraction correction （one-way） 9.723 to 28.072 ns Consider First-order light time correction （two-way） -1.866875 to 1.870272 μs Consider Second-order light time correction （two-way） 26.420 to 210.472 ps Consider Asymmetry induced by atmospheric refraction （two-way） -13.825 to 13.835 ps Consider Light time corrections induced by atmospheric refraction （one-way） -4×10-2 to 3×10-2 ps Ignore Light time corrections induced by atmospheric refraction （two-way） -8×10-2 to 7×10-2 ps Ignore Shapiro time-delay of sun （one-way） 17.646 to 30.822 ns Consider Shapiro time-delay of moon （one-way） 0.494 to 2.668 ps Consider Shapiro time-delay of earth （one-way） 116.995 to 139.453 ps Consider Shapiro time-delay of sun （two-way） 10-21 s Ignore Shapiro time-delay of moon （two-way） 10-24 s Ignore Shapiro time-delay of earth （two-way） 10-22 s Ignore Redshift of earth （one-way and two-way） 32 μs （32.3 d） Consider Doppler shift （one-way and two-way） 15 μs （32.3 d） Consider Redshift of moon （one-way and two-way） 400 ns （32.3 d） Consider Redshift of sun （one-way and two-way） 20 ns （32.3 d） Consider LRA-detector correction （one-way and two-way） 0.634 to 10 ps Consider
Table 2. Parameter settings in simulation scenarios
View tableTable 2. Parameter settings in simulation scenarios
Scenario Parameter setting Scenario 1 Position error: 10 m in R direction, 100 m in T direction, 100 m in N direction
Velocity error: 5 mm/s in R direction, 2 cm/s in T direction, 2 cm/s in N direction
Calibration data (position relation): 5 mm
Attitude error: 180″, four times orbital frequency period
Tracking elevation: 20°‒65°
Meteorological parameter error: pressure error of 10 Pa, temperature error of 1 ℃, relative humidity of 5%
Scenario 2 Position error: 100 m in R direction, 1000 m in T direction, 1000 m in N direction
Velocity error: 1 cm/s in R direction, 4 cm/s in T direction, 4 cm/s in N direction
Calibration data (position relation): 1 cm
Attitude error: 360″, six times orbital frequency period
Tracking elevation: 20°‒65°
Meteorological parameter error: pressure error of 50 Pa, temperature error of 5 ℃, relative humidity of 8%
Table 3. Correction uncertainty of each error term of DRO two-way laser time-frequency transfer
View tableTable 3. Correction uncertainty of each error term of DRO two-way laser time-frequency transfer
Error term Uncertainty Scenario 1 Scenario 2 First-order light time correction -9×10-14 to 2×10-13 -9×10-13 to 2.3×10-12 Second-order light time correction -3×10-17 to 4×10-18 -2×10-16 to 4.5×10-17 Asymmetry induced by atmospheric refraction -3×10-14 to 3×10-14 -2×10-13 to 2×10-13 Redshift of earth -1×10-14 to 0 -1×10-13 to 0 Doppler shift -1.2×10-12 to 0 -2.5×10-12 to 0 Redshift of sun 0 to 2×10-16 0 to 2×10-15 Redshift of moon 0 to 2×10-16 0 to 2×10-15 LRA-detector correction -2.5×10-13 to -6×10-14 -5×10-13 to -1×10-13
Table 4. Correction uncertainty of each error term of DRO one-way laser time-frequency transfer
View tableTable 4. Correction uncertainty of each error term of DRO one-way laser time-frequency transfer
Error term Uncertainty Scenario 1 Scenario 2 Instantaneous Euclidean distance -3.7×10-8 to 3.4×10-8 -3.7×10-7 to 3.4×10-7 First-order light time correction 2.2×10-13 to 4.4×10-13 6.8×10-13 to 1.3×10-12 Second-order light time correction 4×10-17 to 4.5×10-17 8.7×10-17 to 8.9×10-17 Atmospheric refraction correction -1.6×10-10 to 8.5×10-11 -9.6×10-10 to -5×10-10 Shapiro time-delay of sun -7×10-16 to -6×10-16 -8×10-15 to -6×10-15 Shapiro time-delay of moon -6×10-20 to -4×10-20 -6.1×10-19 to -5.9×10-19 Shapiro time-delay of earth -5×10-18 to -1×10-18 -4×10-17 to -1×10-17 Redshift of earth -1×10-14 to 0 -1×10-13 to 0 Doppler shift -1.2×10-12 to 0 -2.5×10-12 to 0 Redshift of sun 0 to 2×10-16 0 to 2×10-15 Redshift of moon 0 to 2×10-16 0 to 2×10-15 LRA-detector correction -2.5×10-13 to -6×10-14 -5×10-13 to -1×10-13
Table 5. Correction uncertainty of each error term of DRO one-way laser time-frequency transfer in common-view mode
View tableTable 5. Correction uncertainty of each error term of DRO one-way laser time-frequency transfer in common-view mode
Error term Uncertainty Instantaneous Euclidean distance -1.6×10-9 to -9×10-10 First-order light time correction -2.5×10-13 to 2.5×10-13 Second-order light time correction 4×10-20 to 3×10-19 Atmospheric refraction correction -3×10-11 to 4×10-11 Shapiro time-delay of sun -3×10-17 to -2×10-17 Shapiro time-delay of moon -2×10-21 to -1×10-21 Shapiro time-delay of earth -2×10-18 to -5×10-19 Redshift of earth -5×10-16 to 4×10-16 Doppler shift -5×10-15 to -4.7×10-15 Redshift of sun 8×10-19 to 1×10-18 Redshift of moon 7×10-19 to 8×10-19 LRA-detector correction -3×10-14 to 4×10-14
Tools
Get Citation
Copy Citation Text
Renfang Geng, Zhibo Wu, Yong Huang, Wendong Meng, Kai Tang, Haifeng Zhang, Tong Liu, Wenbin Wang, Zhongping Zhang. Calculation Model and Error Analysis of Lunar Laser Time-Frequency Transfer Based on General Relativity[J]. Chinese Journal of Lasers, 2025, 52(2): 0204003
Paper Information
Category: Measurement and metrology
Received: May. 15, 2024
Accepted: Jul. 17, 2024
Published Online: Jan. 20, 2025
The Author Email: Zhibo Wu (wzb@shao.ac.cn), Yong Huang (yongh@shao.ac.cn)
CSTR:32183.14.CJL240878
© Copyright 2018-2021 | Chinese Laser Press.
All Rights Reserved 沪ICP备15018463号-20