BDS-3/Galileo Time and Frequency Transfer with Quad-Frequency Precise Point Positioning
Abstract
:1. Introduction
2. Methods
2.1. General Observations
2.2. Dual-Frequency IF PPP Model
2.3. Quad-Frequency IF PPP Models
2.4. Quad-Frequency Uncombined PPP Model
2.5. Characteristic of Quad-Frequency GNSS PPP Time Transfer Models
3. Results and Discussion
3.1. Data Acquisition and Processing Strategies
3.2. Quad-Frequency BDS-3 PPP Time Transfer Solutions
3.3. Quad-Frequency Galileo PPP Time Transfer Solutions
3.4. Observation Residuals
3.5. Positioning, Tropospheric Delay, and IFB Estimates
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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e1 | e2 | e3 | e4 | Noise Amplification | ||
---|---|---|---|---|---|---|
IF0 | B1I-B3I | 2.9437 | −1.9437 | 0 | 0 | 3.5275 |
IF1 | B1I-B3I | 2.9437 | −1.9437 | 0 | 0 | 3.5275 |
B1C-B2a | 0 | 0 | 2.2606 | −1.2606 | 2.5883 | |
IF2 | B1I-B3I-B1C | 1.3877 | −1.8908 | 1.5031 | 0 | 2.7857 |
B1I-B3I-B2a | 2.3433 | −0.0893 | 0 | −1.2543 | 2.6594 | |
UC | B1I | 1 | 0 | 0 | 0 | 1 |
B3I | 0 | 1 | 0 | 0 | 1 | |
B1C | 0 | 0 | 1 | 0 | 1 | |
B2a | 0 | 0 | 0 | 1 | 1 |
e1 | e2 | e3 | e4 | Noise Amplification | ||
---|---|---|---|---|---|---|
IF0 | E1-E5a | 2.2606 | −1.2606 | 0 | 0 | 2.5883 |
IF1 | E1-E5a | 2.2606 | −1.2606 | 0 | 0 | 2.5883 |
E1-E5b | 2.4220 | −1.4220 | 0 | 0 | 2.8086 | |
E1-E5 | 2.3380 | −1.3380 | 0 | 0 | 2.6938 | |
IF2 | E1-E5a-E5b | 2.3149 | −0.8363 | −0.4787 | 0 | 2.5075 |
E1-E5a-E5 | 2.2929 | −0.7340 | 0 | −0.5589 | 2.4715 | |
UC | E1 | 1 | 0 | 0 | 0 | 1 |
E5a | 0 | 1 | 0 | 0 | 1 | |
E5b | 0 | 0 | 1 | 0 | 1 | |
E5 | 0 | 0 | 0 | 1 | 1 |
Station Name | Timing Lab | Receiver | Antenna | External Clock | |
---|---|---|---|---|---|
BDS-3 | BRCH | PTB | CETC-54-GMR-4016 | GNSS-750 | UTC(PTB) |
XIA3 | NTSC | CETC-54-GMR-4016 | NOV750.R4 | UTC(NTSC) | |
Galileo | PTBB | PTB | SEPT POLARX4TR | LEIAR25.R4—LEIT | UTC(PTB) |
PT11 | PTB | SEPT POLARX5TR | LEIAR25.R4—LEIT | UTC(PTB) | |
BRUX | ROB | SEPT POLARX4TR | JAVRINGANT_DM—NONE | UTC(ROB) |
Item | Strategy |
---|---|
Observations | BDS-3: undifferenced and uncombined observations in B1I, B3I, B1C, and B2a frequency Galileo: undifferenced and uncombined observations in E1, E5a, E5b, and E5 frequency |
Weight of observation | Elevation-dependent |
Cutoff angle | 10° |
Sampling rate | 30 s |
PCO and PCV | Corrected |
Station displacement | Corrected [35] |
Wind up | Corrected [36] |
Relativistic effect | Corrected |
Estimator | Kalman filter |
Phase ambiguity | Estimated as constants at each arc (float values) |
IFB | Estimated as random walk (RW) noise [18] |
Receiver position | Estimated as constants in static model |
Receiver clock offset | Estimated as white noise |
Ionospheric delay | IF0, IF1, IF2 models: first-order effects removed with IF combination UC model: estimated as white noise |
Tropospheric delay | Wet delay: estimated as random walk noise Dry delay: corrected by Saastamoinen model Mapping function: GMF [37] |
DOY | IF0 | IF1 | IF2 | UC | ||||
---|---|---|---|---|---|---|---|---|
Mean | STD | Mean | STD | Mean | STD | Mean | STD | |
277 | −90.28 | 0.10 | −90.29 | 0.09 | −91.17 | 0.10 | −90.27 | 0.10 |
278 | −90.46 | 0.03 | −90.42 | 0.04 | −91.34 | 0.03 | −90.44 | 0.03 |
279 | −90.57 | 0.09 | −90.60 | 0.11 | −91.44 | 0.09 | −90.57 | 0.09 |
280 | −90.77 | 0.05 | −90.77 | 0.05 | −91.65 | 0.05 | −90.78 | 0.05 |
281 | −90.85 | 0.05 | −90.86 | 0.06 | −91.74 | 0.06 | −90.87 | 0.05 |
282 | −90.79 | 0.06 | −90.79 | 0.08 | −91.68 | 0.07 | −90.81 | 0.06 |
DOY | IF0 | IF1 | IF2 | UC | ||||
---|---|---|---|---|---|---|---|---|
Mean | STD | Mean | STD | Mean | STD | Mean | STD | |
277 | −146.60 | 0.03 | −146.67 | 0.05 | −144.60 | 0.04 | −146.60 | 0.03 |
278 | −146.61 | 0.03 | −146.66 | 0.04 | −144.62 | 0.04 | −146.61 | 0.03 |
279 | −146.60 | 0.03 | −146.65 | 0.06 | −144.59 | 0.05 | −146.59 | 0.04 |
280 | −146.66 | 0.03 | −146.69 | 0.04 | −144.63 | 0.04 | −146.65 | 0.03 |
281 | −146.66 | 0.03 | −146.72 | 0.05 | −144.70 | 0.05 | −146.64 | 0.03 |
282 | −146.63 | 0.04 | −146.68 | 0.06 | −144.65 | 0.05 | −146.61 | 0.04 |
DOY | E (cm) | N (cm) | U (cm) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
IF0 | IF1 | IF2 | UC | IF0 | IF1 | IF2 | UC | IF0 | IF1 | IF2 | UC | ||
BRCH | 15 | 2.03 | 0.71 | 0.65 | 1.03 | 0.51 | 0.29 | 0.59 | 0.59 | 2.76 | 2.25 | 2.72 | 2.13 |
16 | 1.84 | 0.56 | 0.41 | 0.56 | 0.77 | 0.31 | 0.69 | 0.48 | 2.87 | 2.46 | 2.67 | 2.79 | |
17 | 1.67 | 0.41 | 0.70 | 0.82 | 0.92 | 0.43 | 0.77 | 0.75 | 2.10 | 2.67 | 2.14 | 2.05 | |
18 | 1.64 | 0.30 | 0.64 | 0.90 | 0.84 | 0.31 | 0.61 | 0.67 | 2.54 | 2.52 | 2.34 | 2.50 | |
19 | 0.85 | 0.30 | 0.22 | 0.55 | 0.85 | 0.35 | 0.51 | 0.84 | 2.42 | 2.38 | 2.15 | 2.41 | |
XIA3 | 15 | 0.75 | 0.67 | 0.90 | 0.59 | 0.93 | 0.50 | 0.52 | 0.84 | 3.91 | 3.68 | 3.48 | 3.70 |
16 | 1.59 | 2.25 | 1.61 | 1.91 | 0.71 | 0.38 | 0.27 | 0.62 | 2.53 | 3.39 | 2.91 | 2.49 | |
17 | 2.79 | 2.75 | 2.62 | 2.03 | 0.45 | 0.19 | 0.22 | 0.41 | 3.35 | 3.53 | 3.00 | 3.20 | |
18 | 2.86 | 2.81 | 2.84 | 2.86 | 0.52 | 0.19 | 0.33 | 0.43 | 3.85 | 3.10 | 3.79 | 3.57 | |
19 | 2.63 | 2.60 | 2.75 | 2.25 | 0.45 | 0.18 | 0.35 | 0.43 | 3.61 | 3.60 | 3.57 | 3.57 |
DOY | E(cm) | N(cm) | U(cm) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
IF0 | IF1 | IF2 | UC | IF0 | IF1 | IF2 | UC | IF0 | IF1 | IF2 | UC | ||
BRUX | 277 | 0.42 | 0.14 | 0.15 | 0.36 | 0.15 | 0.17 | 0.12 | 0.08 | 0.96 | 1.17 | 1.51 | 0.95 |
278 | 0.35 | 0.09 | 0.11 | 0.35 | 0.19 | 0.20 | 0.15 | 0.08 | 0.99 | 1.16 | 1.18 | 0.91 | |
279 | 0.46 | 0.21 | 0.23 | 0.40 | 0.20 | 0.20 | 0.15 | 0.09 | 0.94 | 0.88 | 0.88 | 0.90 | |
280 | 0.39 | 0.16 | 0.17 | 0.35 | 0.23 | 0.22 | 0.18 | 0.13 | 0.86 | 0.86 | 0.87 | 0.81 | |
281 | 0.34 | 0.14 | 0.15 | 0.32 | 0.24 | 0.24 | 0.20 | 0.14 | 0.89 | 0.83 | 0.84 | 0.85 | |
282 | 0.35 | 0.16 | 0.18 | 0.31 | 0.24 | 0.25 | 0.20 | 0.14 | 0.88 | 0.85 | 0.87 | 0.85 | |
PT11 | 277 | 0.45 | 0.46 | 0.13 | 0.45 | 0.13 | 0.12 | 0.13 | 0.13 | 1.10 | 1.09 | 1.21 | 1.06 |
278 | 0.41 | 0.42 | 0.11 | 0.40 | 0.11 | 0.08 | 0.11 | 0.11 | 0.90 | 0.88 | 1.00 | 0.77 | |
279 | 0.39 | 0.39 | 0.10 | 0.33 | 0.10 | 0.07 | 0.10 | 0.10 | 0.78 | 0.76 | 0.81 | 0.79 | |
280 | 0.34 | 0.34 | 0.08 | 0.37 | 0.08 | 0.06 | 0.08 | 0.08 | 0.80 | 0.80 | 0.82 | 0.75 | |
281 | 0.34 | 0.33 | 0.08 | 0.31 | 0.08 | 0.06 | 0.08 | 0.08 | 0.77 | 0.79 | 0.77 | 0.77 | |
282 | 0.35 | 0.34 | 0.12 | 0.31 | 0.12 | 0.06 | 0.12 | 0.12 | 0.80 | 0.83 | 0.83 | 0.73 | |
PTBB | 277 | 0.10 | 0.39 | 0.11 | 0.10 | 0.31 | 0.58 | 0.47 | 0.49 | 0.85 | 0.80 | 0.90 | 0.51 |
278 | 0.36 | 0.80 | 0.34 | 0.26 | 0.13 | 0.21 | 0.12 | 0.11 | 1.12 | 0.82 | 0.92 | 0.73 | |
279 | 0.63 | 0.63 | 0.19 | 0.07 | 0.11 | 0.19 | 0.13 | 0.12 | 1.43 | 0.75 | 0.98 | 0.98 | |
280 | 0.20 | 0.52 | 0.20 | 0.18 | 0.15 | 0.18 | 0.13 | 0.09 | 1.28 | 0.99 | 0.89 | 0.82 | |
281 | 0.15 | 0.27 | 0.07 | 0.14 | 0.18 | 0.12 | 0.08 | 0.12 | 1.31 | 0.99 | 0.80 | 0.83 | |
282 | 0.10 | 0.08 | 0.11 | 0.07 | 0.19 | 0.09 | 0.08 | 0.09 | 1.33 | 0.89 | 0.78 | 0.82 |
DOY | IF0 | IF1 | IF2 | UC | |
---|---|---|---|---|---|
BRCH | 15 | 1.3 | 1.32 | 1.32 | 1.31 |
16 | 0.80 | 0.80 | 0.83 | 0.84 | |
17 | 1.20 | 1.40 | 1.40 | 1.21 | |
18 | 1.20 | 1.02 | 1.02 | 0.64 | |
19 | 1.00 | 0.88 | 0.88 | 0.74 | |
XIA3 | 15 | 1.76 | 1.82 | 1.82 | 1.81 |
16 | 2.06 | 2.11 | 2.11 | 2.01 | |
17 | 2.17 | 2.20 | 2.19 | 2.01 | |
18 | 1.66 | 1.93 | 1.94 | 1.95 | |
19 | 1.72 | 1.78 | 1.78 | 1.78 |
DOY | IF0 | IF1 | IF2 | UC | |
---|---|---|---|---|---|
BRUX | 277 | 0.98 | 1.00 | 1.04 | 0.88 |
278 | 0.61 | 0.76 | 0.70 | 0.57 | |
279 | 0.60 | 0.92 | 0.76 | 0.64 | |
280 | 0.52 | 0.63 | 0.63 | 0.52 | |
281 | 0.83 | 1.04 | 0.96 | 0.81 | |
282 | 0.77 | 0.80 | 0.86 | 0.71 | |
PT11 | 277 | 0.97 | 0.96 | 0.98 | 0.84 |
278 | 0.60 | 0.81 | 0.73 | 0.58 | |
279 | 0.59 | 0.72 | 0.58 | 0.54 | |
280 | 0.40 | 0.48 | 0.47 | 0.39 | |
281 | 0.65 | 0.74 | 0.69 | 0.64 | |
282 | 0.79 | 0.80 | 0.84 | 0.78 | |
PTBB | 277 | 0.86 | 0.90 | 0.91 | 0.72 |
278 | 0.53 | 0.63 | 0.62 | 0.50 | |
279 | 0.75 | 0.88 | 0.90 | 0.70 | |
280 | 0.53 | 0.68 | 0.57 | 0.51 | |
281 | 0.8 | 0.91 | 1.05 | 0.83 | |
282 | 0.60 | 0.90 | 0.87 | 0.56 |
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Ge, Y.; Cao, X.; Shen, F.; Yang, X.; Wang, S. BDS-3/Galileo Time and Frequency Transfer with Quad-Frequency Precise Point Positioning. Remote Sens. 2021, 13, 2704. https://doi.org/10.3390/rs13142704
Ge Y, Cao X, Shen F, Yang X, Wang S. BDS-3/Galileo Time and Frequency Transfer with Quad-Frequency Precise Point Positioning. Remote Sensing. 2021; 13(14):2704. https://doi.org/10.3390/rs13142704
Chicago/Turabian StyleGe, Yulong, Xinyun Cao, Fei Shen, Xuhai Yang, and Shengli Wang. 2021. "BDS-3/Galileo Time and Frequency Transfer with Quad-Frequency Precise Point Positioning" Remote Sensing 13, no. 14: 2704. https://doi.org/10.3390/rs13142704