Article Figures & Data
Figures
- FIGURE 1
Conceptual illustration of time synchronization and clock determination for a LEO satellite constellation
The GMSs and master processing center (MPC) are given here only for a demonstration of the concept.
- FIGURE 2
Relative clock errors between GRACE C and D on December 1, 2019, determined using the CNES RT products
STD represents the STD of the relative clock errors.
- FIGURE 3
Satellite clock errors of GRACE C (left) and D (right) on December 1, 2019, determined using the CNES RT products
STD represents the STD of the satellite clock errors.
- FIGURE 4
Relative clock errors between GRACE C and D on December 1, 2019, determined using the CNES RT products (top left), the predicted part of the IGS UR products (top right), and the broadcast ephemeris (bottom)
STD represents the STD of the relative clock errors.
- FIGURE 5
MDEV of the relative clock errors between GRACE C and D on December 1, 2019, determined using the CNES RT products (left) and broadcast ephemeris (right)
- FIGURE 6
Average STDs of relative clock errors between GRACE C and D for December 1–7, 2019, determined using different real-time GNSS products
- FIGURE 7
Relative along-track orbital errors between GRACE C and D on December 1, 2019, determined using the CNES RT products (top left), the predicted part of the IGS UR products (top right), and the broadcast ephemeris (bottom)
- FIGURE 8
Average OURE of the relative orbital errors between GRACE C and D for December 1–7, 2019
- FIGURE 9
Errors of low- (left) and high-accuracy (right) reference satellite orbits for GRACE C on December 1, 2019
- FIGURE 10
Relative clock errors between GRACE C and D on December 1, 2019, with the introduction of different reference satellite orbits when the CNES RT products (left) and broadcast ephemeris (right) are used
The PCV SLS method was applied in the processing. Reference orbits A and B refer to the low-accuracy reference orbits in the left panel of Figure 9 and the high-accuracy reference orbits in the right panel of Figure 9, respectively.
Tables
Identifier Explanation Transmission Update Interval Orbits/Clocks Accuracy Orbits/Clocks CNES RT CNES real-time products Internet (real-time stream) 5 min / 5 s 3–5 cm / 0.05–0.15 ns IGS UR Predicted part of the IGS ultra-rapid products Internet (file transfer protocol) 15 min 5 cm / 1.5 ns BRDC Broadcast ephemeris from the GNSS navigation message Satellite link 2 h 1 m / 2.5 ns - TABLE 2
Average STDs and MDEVs of the Relative Clock Errors Between GRACE C and D for December 1–7, 2019
GNSS Product RD BLS KN BLS KN SLS PCV SLS Average STD (ns) CNES RT 0.033 0.076 0.198 0.158 IGS UR 0.294 0.398 0.645 0.159 BRDC 1.288 1.804 2.854 0.184 Average MDEV at 120 s CNES RT 3.4 × 10−14 3.6 × 10−13 4.9 × 10−12 1.3 × 10−12 IGS UR 1.8 × 10−12 1.5 × 10−12 2.4 × 10−12 1.3 × 10−12 BRDC 6.5 × 10−12 6.6 × 10−12 7.8 × 10−12 1.5 × 10−12 Average MDEV at 1200 s CNES RT 8.6 × 10−15 2.9 × 10−14 2.5 × 10−13 1.5 × 10−13 IGS UR 6.3 × 10−14 1.7 × 10−13 4.6 × 10−13 1.5 × 10−13 BRDC 2.9 × 10−13 8.6 × 10−13 1.9 × 10−12 1.9 × 10−13 Average MDEV at 12000 s CNES RT 2.8 × 10−15 6.4 × 10−15 1.3 × 10−14 8.0 × 10−15 IGS UR 3.3 × 10−14 3.8 × 10−14 5.7 × 10−14 8.1 × 10−15 BRDC 1.2 × 10−13 1.6 × 10−13 2.3 × 10−13 9.2 × 10−15 - TABLE 3
Average RMS of the Relative Orbital Errors Between GRACE C and D for December 1–7, 2019 σOURE,rv denotes the RMS of the relative OURE not considering the relative clock errors (see Equation (9)), and σSISRE,rv denotes the relative SISRE considering the relative clock errors (see Equation (10)).
Processing Strategy σR,rv (m) σS,rv (m) σW,rv (m) σOURE,rv (m) σSISRE,rv (m) CNES RT RD BLS 0.0078 0.0141 0.0058 0.0102 0.0145 KN BLS 0.0250 0.0220 0.0173 0.0210 0.0287 KN SLS 0.0391 0.0381 0.0355 0.0373 0.0655 PCV SLS 0.0430 0.0396 0.0411 0.0409 0.0568 IGS UR RD BLS 0.0231 0.0478 0.0311 0.0373 0.0988 KN BLS 0.1195 0.1018 0.0724 0.0956 0.1447 KN SLS 0.1982 0.1950 0.1547 0.1807 0.2516 PCV SLS 0.0430 0.0395 0.0407 0.0407 0.0569 BRDC RD BLS 0.1010 0.2077 0.1142 0.1560 0.4312 KN BLS 0.5511 0.4768 0.3263 0.4418 0.6567 KN SLS 0.8727 0.9293 0.6323 0.8111 1.1332 PCV SLS 0.0550 0.0520 0.0549 0.0537 0.0703 - TABLE 4
RMS of the Relative Orbital Errors Obtained Via the PCV SLS Method
The results for low- and high-accuracy reference satellite orbits are separated by “/”
GNSS products σR,rv (m) σS,rv (m) σW,rv (m) CNES RT products 0.0430 / 0.0453 0.0429 / 0.0439 0.0361 / 0.0409 IGP products 0.0511 / 0.0454 0.0449 / 0.0438 0.0380 / 0.0408 Broadcast products 0.0520 / 0.0552 0.0519 / 0.0531 0.0560 / 0.0600
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