Figure 1.
Stations used for precise orbit determination (POD) of BeiDou satellites. The green diamonds represent iGMAS stations and the black circles represent GA tracking stations. The blue and red lines indicate the trajectories of the BeiDou-2 and BeiDou-3e satellites, respectively.
Figure 1.
Stations used for precise orbit determination (POD) of BeiDou satellites. The green diamonds represent iGMAS stations and the black circles represent GA tracking stations. The blue and red lines indicate the trajectories of the BeiDou-2 and BeiDou-3e satellites, respectively.
Figure 2.
Multipath (MP) combinations for BeiDou-2 (C10, C14), BeiDou-3e (C31, C34), and GPS (G32) satellites with respect to elevation. For BeiDou satellites, MP1 and MP3 represent the B1 and B3 frequency MPs, respectively, whereas for global positioning satellites (GPS) (right column), MP1 and MP2 represent the L1 and L2 frequency MPs. Blue dots represent MP1 and red dots represent MP3/MP2.
Figure 2.
Multipath (MP) combinations for BeiDou-2 (C10, C14), BeiDou-3e (C31, C34), and GPS (G32) satellites with respect to elevation. For BeiDou satellites, MP1 and MP3 represent the B1 and B3 frequency MPs, respectively, whereas for global positioning satellites (GPS) (right column), MP1 and MP2 represent the L1 and L2 frequency MPs. Blue dots represent MP1 and red dots represent MP3/MP2.
Figure 3.
MP combinations for BeiDou-2 and BeiDou-3e satellites as a function of azimuth and elevation. The first and second columns represent BeiDou-2 inclined geosynchronous orbits (IGSOs) and medium Earth orbits (MEOs), respectively, the third column represents BeiDou-3e satellites, and the last column represents GPS satellites. The MP for the B1I and L1 signals is shown at the top and the MP for the B3I and L2 signals is shown at the bottom.
Figure 3.
MP combinations for BeiDou-2 and BeiDou-3e satellites as a function of azimuth and elevation. The first and second columns represent BeiDou-2 inclined geosynchronous orbits (IGSOs) and medium Earth orbits (MEOs), respectively, the third column represents BeiDou-3e satellites, and the last column represents GPS satellites. The MP for the B1I and L1 signals is shown at the top and the MP for the B3I and L2 signals is shown at the bottom.
Figure 4.
BeiDou-2 satellite attitude control modes: yaw-steering (YS) (a) and orbit-normal (ON) (b). In YS mode, the satellite rotates around the z axis, and the x axis remains yawing all the time, while during the ON period, the x axis stops yawing and is consistent with the velocity throughout.
Figure 4.
BeiDou-2 satellite attitude control modes: yaw-steering (YS) (a) and orbit-normal (ON) (b). In YS mode, the satellite rotates around the z axis, and the x axis remains yawing all the time, while during the ON period, the x axis stops yawing and is consistent with the velocity throughout.
Figure 5.
Comparison of RMS values of orbit overlap before and after ambiguity fixing. The dark yellow and red bars represent real-valued ambiguity (float) and ambiguity fixed (fixed) solutions, respectively.
Figure 5.
Comparison of RMS values of orbit overlap before and after ambiguity fixing. The dark yellow and red bars represent real-valued ambiguity (float) and ambiguity fixed (fixed) solutions, respectively.
Figure 6.
SLR residuals for BeiDou-2 satellites (top) and BeiDou-3e satellites (bottom).
Figure 6.
SLR residuals for BeiDou-2 satellites (top) and BeiDou-3e satellites (bottom).
Figure 7.
STD values for BeiDou clock products using one-day overlaps between two adjacent arcs with the middle day in the first arc as a reference.
Figure 7.
STD values for BeiDou clock products using one-day overlaps between two adjacent arcs with the middle day in the first arc as a reference.
Figure 8.
Stations used for static and kinematic PPP. Black points represent four stations, TOMP, ALBY, HOB2, and STR1, which are located in Australia.
Figure 8.
Stations used for static and kinematic PPP. Black points represent four stations, TOMP, ALBY, HOB2, and STR1, which are located in Australia.
Figure 9.
Variations in number of satellites used and position dilution of precision (PDOP) values of GPS, GB114, GB134, B114 and B134 solutions for station STR1 on DOY 057, 2017.
Figure 9.
Variations in number of satellites used and position dilution of precision (PDOP) values of GPS, GB114, GB134, B114 and B134 solutions for station STR1 on DOY 057, 2017.
Figure 10.
RMS values of precision for PPP in E, N, and U components at four stations (TOMP, ALBY, HOB2 and STR1) using five solutions compared with ground truth values.
Figure 10.
RMS values of precision for PPP in E, N, and U components at four stations (TOMP, ALBY, HOB2 and STR1) using five solutions compared with ground truth values.
Figure 11.
Average convergence times and RMS values for kinematic PPP at the TOMP, ALBY, HOB2 and STR1. The top panel shows the convergence times using five solutions, and the RMS values of the E, N, and U components are illustrated in the bottom panel.
Figure 11.
Average convergence times and RMS values for kinematic PPP at the TOMP, ALBY, HOB2 and STR1. The top panel shows the convergence times using five solutions, and the RMS values of the E, N, and U components are illustrated in the bottom panel.
Table 1.
Information on BeiDou-2- and BeiDou-3e- capable receivers. International GNSS Monitoring and Assessment Service (iGMAS).
Table 1.
Information on BeiDou-2- and BeiDou-3e- capable receivers. International GNSS Monitoring and Assessment Service (iGMAS).
Site | Location | Agency | Receiver Type | Antenna Type |
---|
ABJA | Nigeria, Abuja | iGMAS | gnss_ggr | RINT-8CH CETD |
GUA1 | China, Urumchi | iGMAS | gnss_ggr | RINT-8CH CETD |
HMNS | South Africa, Hermanus | iGMAS | gnss_ggr | RINT-8CH CETD |
BJF1 | China, Beijing | iGMAS | CETC-54-GMR-4016 | LEIAR25.R4 LEIT |
BRCH | Germany, Braunschweig | iGMAS | CETC-54-GMR-4011 | NOV750.R4 NOVS |
DWIN | Australia, Darwin | iGMAS | CETC-54-GMR-4011 | GNSS-750 NONE |
KNDY | Sri Lanka, Kandy | iGMAS | CETC-54-GMR-4016 | GNSS-750 NONE |
LHA1 | China, Lhasa | iGMAS | CETC-54-GMR-4016 | NOV750.R4 NOVS |
WUH1 | China, Wuhan | iGMAS | CETC-54-GMR-4016 | LEIAR25.R4 LEIT |
ZHON | Antarctica, Zhongshan Station | iGMAS | CETC-54-GMR-4011 | GNSS-750 NONE |
ALBY | Australia, Albany | GA | SEPT POLARX5 | JAVRINGANT_DM SCIS |
ARUB | Australia, Arubiddy | GA | SEPT POLARX5 | LEIAR25.R3 NONE |
CEDU | Australia, Ceduna | GA | SEPT POLARX5 | AOAD/M_T NONE |
DAV1 | Antarctica, Davis | GA | SEPT POLARX5 | LEIAR25.R3 LEIT |
HOB2 | Australia, Hobart | GA | SEPT POLARX5 | AOAD/M_T NONE |
KUNU | Australia, Kununurra | GA | SEPT POLARX5 | JAVRINGANT_DM SCIS |
MEDO | Australia, Meadow Station | GA | SEPT POLARX5 | LEIAR25.R3 LEIT |
NCLF | Australia, Northcliffe | GA | SEPT POLARX5 | JAVRINGANT_DM SCIS |
NORS | Australia, Norseman | GA | SEPT POLARX5 | JAVRINGANT_DM SCIS |
PTHL | Australia, Port Hedland | GA | SEPT POLARX5 | LEIAR25.R3 LEIT |
STR1 | Australia, Canberra | GA | SEPT POLARX5 | ASH701945C_M NONE |
THEV | Australia, Thevenard | GA | SEPT POLARX5 | LEIAR25.R3 LEIT |
TOMP | Australia, Tom Price | GA | SEPT POLARX5 | LEIAR25.R3 LEIT |
WILU | Australia, Wiluna | GA | SEPT POLARX5 | LEIAR25.R3 LEIT |
Table 2.
Mean and root mean square (RMS) values (cm) of MP combinations for BeiDou-2, BeiDou-3e, and GPS satellites.
Table 2.
Mean and root mean square (RMS) values (cm) of MP combinations for BeiDou-2, BeiDou-3e, and GPS satellites.
| BeiDou-2 IGSO | BeiDou-2 MEO | BeiDou-3e IGSO | BeiDou-3e MEO | GPS |
---|
B1 | B3 | B1 | B3 | B1 | B3 | B1 | B3 | L1 | L2 |
---|
Mean | 1.8 | 1.5 | 1.2 | 1.1 | 0.2 | 0.1 | −0.3 | 0.3 | −0.1 | −0.1 |
RMS | 40.7 | 23.8 | 52.5 | 30.3 | 33.1 | 21.9 | 29.9 | 26.0 | 34.1 | 34.3 |
Table 3.
Observational models and force models used in POD processing strategy. Phase center offset (PCO); phase center variation (PCV); zenith troposphere delays (ZTDs); Empirical CODE Orbit Model (ECOM).
Table 3.
Observational models and force models used in POD processing strategy. Phase center offset (PCO); phase center variation (PCV); zenith troposphere delays (ZTDs); Empirical CODE Orbit Model (ECOM).
Item | Model | Reference |
---|
Basic observations | Undifferenced ionosphere-free code and phase combination of B1I and B3I signals | |
Sampling interval | 300 s | |
Cutoff elevation | 10° | |
Arc length | 3 days | |
Weighting | Prior precision of phase and code observations is 2 cm and 2 m, respectively, and elevation-dependent data weighting | |
Satellite antenna phase center | C06-C14: PCO and PCV corrected with values estimated by Wuhan University (except C13); C31-C34: corrected with data supplied by BeiDou Operational Control Center (OCC) | [7] |
Tropospheric delay | Saastamoinen model, global mapping function, two-hourly ZTDs | [37,38] |
Relativity effect | Considered according to IERS Conventions 2010 | [39] |
Earth orientation parameters | Fixed according to IERS C04 | [40] |
Geopotential | EIGEN_GL04C up to degree 12 × 12 (European Improved Gravity model of the Earth by New techniques) | |
N-body gravitation | Sun, Moon, and other planets: JPL DE405 (Jet Propulsion Laboratory Development Ephemeris 405) ephemeris used | |
Solar radiation | ECOM five-parameter model with a constant acceleration bias in along-track direction | [28] |
Attitude model | Both YS and ON models for BeiDou-2; YS model only for BeiDou-3e | |
Table 4.
PCO values for BeiDou-3e satellites (cm).
Table 4.
PCO values for BeiDou-3e satellites (cm).
| PCO |
---|
X | Y | Z |
---|
C31 | −5 | 0 | 100 |
C32 | −4.5 | −30 | 250 |
C33 | −20 | 0 | 150 |
C34 | −20 | 0 | 150 |
Table 5.
Results of overlap comparison of real-valued ambiguity solution for BeiDou-2 and BeiDou-3e satellites in along-track, cross-track, radial and three-dimensional (3D) directions (cm). Pseudo random noise (PRN).
Table 5.
Results of overlap comparison of real-valued ambiguity solution for BeiDou-2 and BeiDou-3e satellites in along-track, cross-track, radial and three-dimensional (3D) directions (cm). Pseudo random noise (PRN).
Satellite Type | PRN | Along-Track | Cross-Track | Radial | 3D |
---|
BeiDou-2 GEO | C01 | 46.6 | 4.3 | 5.5 | 47.1 |
C02 | 51.8 | 4.7 | 6.0 | 52.4 |
C03 | 61.1 | 3.2 | 5.7 | 61.4 |
C04 | 71.7 | 6.7 | 5.8 | 72.2 |
C05 | 73.4 | 8.0 | 7.6 | 74.2 |
BeiDou-2 IGSO | C06 | 13.4 | 19.4 | 5.1 | 24.1 |
C07 | 14.0 | 13.2 | 4.8 | 19.9 |
C08 | 14.8 | 15.5 | 4.8 | 21.9 |
C09 | 15.5 | 18.7 | 5.4 | 24.9 |
C10 | 14.8 | 13.3 | 4.4 | 20.4 |
C13 | 14.9 | 16.9 | 4.8 | 23.0 |
BeiDou-2 MEO | C11 | 17.3 | 12.8 | 4.8 | 22.0 |
C12 | 15.5 | 11.5 | 4.3 | 19.7 |
C14 | 15.6 | 11.6 | 4.9 | 20.0 |
BeiDou-3e IGSO | C31 | 21.5 | 15.7 | 6.5 | 27.4 |
C32 | 16.9 | 15.1 | 5.5 | 23.3 |
BeiDou-3e MEO | C33 | 17.1 | 12.3 | 4.8 | 21.6 |
C34 | 20.2 | 15.1 | 5.5 | 25.8 |
Table 6.
Satellite laser ranging (SLR) offsets for BeiDou-2 and BeiDou-3e satellites (cm).
Table 6.
Satellite laser ranging (SLR) offsets for BeiDou-2 and BeiDou-3e satellites (cm).
| SLR Offsets |
---|
X | Y | Z |
---|
C01 | −54.38 | −57.04 | 109.30 |
C08 | −40.03 | −57.30 | 109.34 |
C10 | −40.23 | −57.30 | 110.00 |
C11 | −37.54 | −53.80 | 110.00 |
C13 | −40.23 | −57.30 | 110.00 |
C31 | −95.91 | 18.13 | 63.76 |
C32 | 18.51 | 68.54 | 196.02 |
C33 | 61.21 | −7.17 | 122.90 |
C34 | 61.01 | −7.12 | 124.48 |
Table 7.
SLR validation of BeiDou-2 and BeiDou-3e orbits. STD, MEAN, and RMS represent the standard deviation, mean value, and root mean square of the two-way SLR residual, NP# and NP(U) represent the number of tracking points and points from which the data were used, and % represents the data utilization percentage (units: cm vs. adimensional).
Table 7.
SLR validation of BeiDou-2 and BeiDou-3e orbits. STD, MEAN, and RMS represent the standard deviation, mean value, and root mean square of the two-way SLR residual, NP# and NP(U) represent the number of tracking points and points from which the data were used, and % represents the data utilization percentage (units: cm vs. adimensional).
PRN | STD | MEAN | RMS | NP# | NP(U) | % |
---|
C01 | 20.0 | −18.9 | 27.5 | 305 | 305 | 100 |
C08 | 9.8 | −0.3 | 9.8 | 345 | 331 | 96 |
C10 | 8.3 | 0.8 | 8.4 | 270 | 256 | 95 |
C11 | 6.8 | −0.6 | 6.8 | 499 | 484 | 97 |
C13 | 6.2 | 0.7 | 6.2 | 293 | 293 | 100 |
C32 | 9.6 | −9.5 | 13.9 | 85 | 85 | 100 |
C33 | 3.8 | 8.1 | 8.9 | 33 | 33 | 100 |
C34 | 4.2 | 8.6 | 9.5 | 58 | 58 | 100 |
Table 8.
Average STD values for BeiDou-2 and BeiDou-3e clock offset in overlapping arcs with the middle day in the first arc as a reference (units: ns).
Table 8.
Average STD values for BeiDou-2 and BeiDou-3e clock offset in overlapping arcs with the middle day in the first arc as a reference (units: ns).
| BeiDou-2 GEO | BeiDou-2 IGSO | BeiDou-2 MEO | BeiDou-3e IGSO | Beidou-3e MEO | ALL |
---|
STD | 0.22 | 0.17 | 0.15 | 0.18 | 0.17 | 0.18 |
Table 9.
GPS and BeiDou solutions utilized to achieve precise point positioning (PPP).
Table 9.
GPS and BeiDou solutions utilized to achieve precise point positioning (PPP).
Solution | Description |
---|
GPS | GPS only |
GB114 | GPS and BeiDou PRN 1-14 |
GB134 | GPS and BeiDou PRN 1-14, 31-34 |
B114 | BeiDou PRN 1-14 |
B134 | BeiDou PRN 1-14, 31-34 |
Table 10.
Precision of GPS and BeiDou solutions for static PPP of E, N, and U components at four stations (TOMP, ALBY, HOB2, and STR1) calculated during the period from DOY 052 to DOY 068, 2017 (RMS values in cm). East (E); North (N); Up (U).
Table 10.
Precision of GPS and BeiDou solutions for static PPP of E, N, and U components at four stations (TOMP, ALBY, HOB2, and STR1) calculated during the period from DOY 052 to DOY 068, 2017 (RMS values in cm). East (E); North (N); Up (U).
| Site | TOMP | ALBY | HOB2 | STR1 | Average |
---|
Sol. | | E | N | U | E | N | U | E | N | U | E | N | U | E | N | U |
---|
GPS | 0.55 | 0.52 | 1.26 | 0.49 | 0.34 | 0.79 | 0.38 | 0.36 | 0.39 | 0.40 | 0.30 | 0.43 | 0.46 | 0.38 | 0.72 |
GB114 | 0.37 | 0.46 | 1.06 | 0.62 | 0.37 | 0.90 | 0.37 | 0.30 | 0.48 | 0.41 | 0.20 | 0.59 | 0.44 | 0.33 | 0.76 |
GB134 | 0.40 | 0.30 | 1.34 | 0.54 | 0.44 | 0.86 | 0.36 | 0.32 | 0.49 | 0.38 | 0.20 | 0.64 | 0.42 | 0.32 | 0.83 |
B134 | 0.73 | 0.34 | 1.90 | 0.75 | 0.68 | 1.47 | 0.77 | 0.58 | 1.86 | 0.84 | 0.52 | 1.79 | 0.77 | 0.53 | 1.76 |
B114 | 0.71 | 0.53 | 1.41 | 0.91 | 0.59 | 1.76 | 1.25 | 0.49 | 1.84 | 0.87 | 0.47 | 1.61 | 0.94 | 0.52 | 1.66 |
Table 11.
RMS values of GPS, GB114, GB134, B134 and B114 solutions at the TOMP, ALBY, HOB2 and STR1 for kinematic PPP in the E, N, and U components (calculated above) and relative convergence times (Con. Time). The RMS values are in cm and the convergence times are in minutes.
Table 11.
RMS values of GPS, GB114, GB134, B134 and B114 solutions at the TOMP, ALBY, HOB2 and STR1 for kinematic PPP in the E, N, and U components (calculated above) and relative convergence times (Con. Time). The RMS values are in cm and the convergence times are in minutes.
| Site | TOMP | ALBY | HOB2 | STR1 | Average |
---|
Sol. | | E | N | U | E | N | U | E | N | U | E | N | U | E | N | U | Con. Time |
---|
GPS | 1.81 | 1.26 | 2.23 | 1.81 | 1.25 | 2.23 | 1.77 | 1.22 | 2.20 | 1.79 | 1.23 | 2.23 | 1.79 | 1.24 | 2.22 | 36 |
GB114 | 1.84 | 1.28 | 2.24 | 1.90 | 1.33 | 2.29 | 1.88 | 1.32 | 2.26 | 1.87 | 1.29 | 2.24 | 1.87 | 1.30 | 2.26 | 18.5 |
GB134 | 1.91 | 1.27 | 2.32 | 1.88 | 1.29 | 2.34 | 1.86 | 1.25 | 2.32 | 1.88 | 1.32 | 2.33 | 1.88 | 1.28 | 2.33 | 13.5 |
B134 | 2.42 | 1.75 | 3.68 | 2.48 | 1.83 | 3.61 | 2.50 | 1.83 | 3.78 | 2.48 | 1.81 | 3.94 | 2.47 | 1.80 | 3.75 | 43.5 |
B114 | 2.56 | 2.00 | 3.93 | 2.59 | 2.03 | 3.97 | 2.64 | 2.07 | 4.20 | 2.62 | 2.05 | 4.45 | 2.60 | 2.04 | 4.14 | 46 |