Clustering Code Biases between BDS-2 and BDS-3 Satellites and Effects on Joint Solution
Abstract
:1. Introduction
2. Methodology
2.1. Observations
2.2. ISCB Estimation Algorithm
3. Characteristics of BDS, 2 and BDS, 3 ISCB
3.1. Data Preparation
3.2. Clustering Biases between BDS, 2 and BDS, 3
3.3. ISCB Time Variation Characteristics
4. Results and Discussion
4.1. Systematic Biases in the BDS, 2+3 Joint Solution
4.2. BDS, 2+3 Joint Model with Code Bias Self-Calibration
4.3. Residual Analysis
4.4. Improvements in BDS, 2+3 Joint PPP
5. Conclusions
- The ISCB real, time estimation algorithm for single stations presented in this paper accurately stripped off the receiver, dependent ISCB and clock offset biases from the pseudorange observations simultaneously.
- We analyzed the ISCB characteristics of BDS, 2 and BDS, 3 based on the B1I + B3I signal and found there to be an obvious clustering code bias phenomenon between the BDS, 2 and BDS, 3 satellites, leading to systematic biases existing in the BDS, 2+3 joint solution.
- We proposed the BDS, 2+3 joint solution with code bias self, calibration, which can accurately strip off clustering code biases between the BDS, 2 and BDS, 3 satellites and can greatly improve the PPP convergence speed and accuracy.
- The statistics showed that the residual biases and RMS of BDS, 2+3 joint PPP improved by 36% and 15%, respectively, and the convergence time improved by approximately 35%. In the convergence stage, the positioning accuracy improved by approximately 38% and 21% in the horizontal and vertical directions, respectively.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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PRN | SVN | NORAD ID | SVN | System | Manufacture | Notes(UTC) | Civil Signal |
---|---|---|---|---|---|---|---|
C01 | C020 | 44231 | GEO-8 | BDS-2 | CAST | 17 May, 2019 | B1I/B2I/B3I |
C02 | C016 | 38953 | GEO-6 | BDS-2 | CAST | 25 Oct, 2012 | B1I/B2I/B3I |
C03 | C018 | 41586 | GEO-7 | BDS-2 | CAST | 12 June, 2016 | B1I/B2I/B3I |
C04 | C006 | 37210 | GEO-4 | BDS-2 | CAST | 1 Nov, 2010 | B1I/B2I/B3I |
C05 | C011 | 38091 | GEO-5 | BDS-2 | CAST | 25, Feb, 2012 | B1I/B2I/B3I |
C06 | C005 | 36828 | IGSO, 1 | BDS, 2 | CAST | 1, Aug, 2010 | B1I/B2I/B3I |
C07 | C007 | 37256 | IGSO, 2 | BDS, 2 | CAST | 18, Dec, 2010 | B1I/B2I/B3I |
C08 | C008 | 37384 | IGSO, 3 | BDS, 2 | CAST | 10, Apr, 2011 | B1I/B2I/B3I |
C09 | C009 | 37763 | IGSO, 4 | BDS, 2 | CAST | 27, Jul, 2011 | B1I/B2I/B3I |
C10 | C010 | 37948 | IGSO, 5 | BDS, 2 | CAST | 2, Dec, 2011 | B1I/B2I/B3I |
C11 | C012 | 38250 | MEO, 3 | BDS, 2 | CAST | 30, Apr, 2012 | B1I/B2I/B3I |
C12 | C013 | 38251 | MEO, 4 | BDS, 2 | CAST | 30, Apr, 2012 | B1I/B2I/B3I |
C13 | C017 | 41434 | IGSO, 6 | BDS, 2 | CAST | 30, Mar, 2016 | B1I/B2I/B3I |
C14 | C015 | 38775 | MEO, 6 | BDS, 2 | CAST | 19, Sep, 2012 | B1I/B2I/B3I |
C16 | C019 | 43539 | IGSO, 7 | BDS, 2 | CAST | 10, Jul, 2018 | B1I/B2I/B3I |
C19 | C201 | 43001 | MEO, 1 | BDS, 3 | CAST | 5, Nov, 2017 | B1I/B3I/B1C/B2a/B2b |
C20 | C202 | 43002 | MEO, 2 | BDS, 3 | CAST | 5, Nov, 2017 | B1I/B3I/B1C/B2a/B2b |
C21 | C206 | 43208 | MEO, 3 | BDS, 3 | CAST | 12, Feb, 2018 | B1I/B3I/B1C/B2a/B2b |
C22 | C205 | 43207 | MEO, 4 | BDS, 3 | CAST | 12, Feb, 2018 | B1I/B3I/B1C/B2a/B2b |
C23 | C209 | 43581 | MEO, 5 | BDS, 3 | CAST | 29, Jul, 2018 | B1I/B3I/B1C/B2a/B2b |
C24 | C210 | 43582 | MEO, 6 | BDS, 3 | CAST | 29, Jul, 2018 | B1I/B3I/B1C/B2a/B2b |
C25 | C212 | 43603 | MEO, 11 | BDS, 3 | SECM | 24, Aug, 2018 | B1I/B3I/B1C/B2a/B2b |
C26 | C211 | 43602 | MEO, 12 | BDS, 3 | SECM | 24, Aug, 2018 | B1I/B3I/B1C/B2a/B2b |
C27 | C203 | 43107 | MEO, 7 | BDS, 3 | SECM | 12, Jan, 2018 | B1I/B3I/B1C/B2a/B2b |
C28 | C204 | 43108 | MEO, 8 | BDS, 3 | SECM | 12, Jan, 2018 | B1I/B3I/B1C/B2a/B2b |
C29 | C207 | 43245 | MEO, 9 | BDS, 3 | SECM | 29, Mar, 2018 | B1I/B3I/B1C/B2a/B2b |
C30 | C208 | 43246 | MEO, 10 | BDS, 3 | SECM | 29, Mar, 2018 | B1I/B3I/B1C/B2a/B2b |
C32 | C213 | 43622 | MEO, 13 | BDS, 3 | CAST | 19, Sep, 2018 | B1I/B3I/B1C/B2a/B2b |
C33 | C214 | 43623 | MEO, 14 | BDS, 3 | CAST | 19, Sep, 2018 | B1I/B3I/B1C/B2a/B2b |
C34 | C216 | 43648 | MEO, 15 | BDS, 3 | SECM | 15, Oct, 2018 | B1I/B3I/B1C/B2a/B2b |
C35 | C215 | 43647 | MEO, 16 | BDS, 3 | SECM | 15, Oct, 2018 | B1I/B3I/B1C/B2a/B2b |
C36 | C218 | 43706 | MEO, 17 | BDS, 3 | CAST | 18, Nov, 2018 | B1I/B3I/B1C/B2a/B2b |
C37 | C219 | 43707 | MEO, 18 | BDS, 3 | CAST | 18, Nov, 2018 | B1I/B3I/B1C/B2a/B2b |
C38 | C220 | 44204 | IGSO, 1 | BDS, 3 | CAST | 20, Apr, 2019 | B1I/B3I/B1C/B2a/B2b |
C39 | C221 | 44337 | IGSO, 2 | BDS, 3 | CAST | 24, Jun, 2019 | B1I/B3I/B1C/B2a/B2b |
C40 | C224 | 44709 | IGSO, 3 | BDS, 3 | CAST | 4, Nov, 2019 | B1I/B3I/B1C/B2a/B2b |
C41 | C227 | 44864 | MEO, 19 | BDS, 3 | CAST | 16, Dec, 2019 | B1I/B3I/B1C/B2a/B2b |
C42 | C228 | 44865 | MEO, 20 | BDS, 3 | CAST | 16, Dec, 2019 | B1I/B3I/B1C/B2a/B2b |
C43 | C226 | 44794 | MEO, 21 | BDS, 3 | SECM | 23, Nov, 2019 | B1I/B3I/B1C/B2a/B2b |
C44 | C225 | 44793 | MEO, 22 | BDS, 3 | SECM | 23, Nov, 2019 | B1I/B3I/B1C/B2a/B2b |
C45 | C223 | 44543 | MEO, 23 | BDS, 3 | CAST | 22, Sep, 2019 | B1I/B3I/B1C/B2a/B2b |
C46 | C222 | 44542 | MEO, 24 | BDS, 3 | CAST | 22, Sep, 2019 | B1I/B3I/B1C/B2a/B2b |
C59 | C217 | 43683 | GEO, 1 | BDS, 3 | CAST | 1, Nov, 2018 | B1I/B3I |
C60 | C229 | 45344 | GEO, 2 | BDS, 3 | CAST | 9, Mar, 2020 | B1I/B3I |
C61 | C230 | 45807 | GEO, 3 | BDS, 3 | CAST | 23, Jun, 2020 | B1I/B3I |
Manufacturer | Type | Firmware | Antenna | Site | BDS Signal |
---|---|---|---|---|---|
Septentrio | POLARX5TR | 5.3.0 | SEPCHOKE_B3E6 | CEBR | B1I/B2I/B3I |
POLARX5 | 5.3.0 | SEPCHOKE_B3E6 | KIRU, KOUR, REDU | ||
TRM59800.00 | NKLG | ||||
Trimble | ALLOY | 5.37 5.37 | TRM57971.00 | BRST | B1I/B2I/B3I |
TRM59800.00 | MCHL | ||||
5.42 | TRM57971.00 | UNB3 | |||
5.43 | LEIAR25.R3 | KIR8, MAR7 | |||
NETR9 | 5.42 | TRM59800.00 | METG | ||
TRM115000.00 | POAL, POVE, SALU, SAVO, TOPL, UFPR |
Parameters | Model | |
---|---|---|
Observations | UD IF pseudorange/carrier phase | |
Prior information | Pseudorange 1.0 m; carrier phase 0.02 cycles | |
Cut, off elevation | 7° | |
Observation weights | p = 1, elev. >30° p = 2sin(elev.), elev. ≤30° | |
Interval | 30s | |
PCO/PCV | Satellite | GPS, Galileo PCO: IGS14.atx [28]; BDS, 2 GEO PCO: IGS M, GEX; BDS, 2 IGSO/MEO PCO: ESA Mode [29]; BDS, 3 MEO: www.beidou.gov.cn GPS PCV: IGS14.atx; BDS, Galileo PCV: Uncorrected |
Receiver | GPS PCO: IGS14.atx; BDS, Galileo PCO: Same as GPS; GPS PCV: IGS14.atx; BDS, Galileo PCV: Same as GPS | |
Adjustment method | Square root information filtering [30] | |
Troposphere delay | Saastamoinen model + GMF mapping function random, walk process for each epoch | |
Receiver clock offset | Estimated as white noise | |
Ambiguity | Float | |
ISCB | Constant estimation with zero, mean condition every day [25] |
Manufacturer | Station | ISCB Average | ISB between BDS, 2 and BDS, 3 | ISCB STD | ||
---|---|---|---|---|---|---|
BDS, 2 | BDS, 3 | BDS, 2 | BDS, 3 | |||
Septentrio | CEBR | 0.906 | −0.476 | 1.382 | 0.477 | 0.191 |
KIRU | 0.853 | −0.534 | 1.387 | 0.210 | 0.153 | |
KOUR | 1.267 | −0.248 | 1.515 | 0.417 | 0.197 | |
REDU | 0.905 | −0.612 | 1.517 | 0.383 | 0.225 | |
NKLG | 1.105 | −0.515 | 1.620 | 0.523 | 0.191 | |
Average | 1.007 | −0.477 | 1.484 | 0.402 | 0.191 | |
Trimble | BRST | −1.664 | 1.484 | −3.148 | 0.217 | 0.340 |
MCHL | −2.979 | 3.276 | −6.255 | 0.232 | 0.202 | |
UNB3 | −0.766 | 0.142 | −0.907 | 0.325 | 0.163 | |
KIR8 | −0.168 | 0.091 | −0.259 | 0.208 | 0.135 | |
MAR7 | −0.106 | 0.069 | −0.176 | 0.245 | 0.166 | |
METG | 0.497 | −0.467 | 0.964 | 0.233 | 0.176 | |
POAL | −0.885 | 0.223 | −1.108 | 0.418 | 0.255 | |
POVE | −0.686 | 0.172 | −0.858 | 0.416 | 0.289 | |
SALU | −0.669 | 0.167 | −0.836 | 0.551 | 0.427 | |
SAVO | −0.339 | 0.085 | −0.424 | 0.478 | 0.244 | |
TOPL | −0.633 | 0.158 | −0.792 | 0.408 | 0.211 | |
UFPR | −0.683 | 0.171 | −0.854 | 0.429 | 0.225 | |
Average | −0.757 | 0.464 | −1.221 | 0.347 | 0.236 |
Model | Convergence Condition | Average | ||||
---|---|---|---|---|---|---|
40 cm | 30 cm | 20 cm | 10 cm | |||
Convergence time in the horizontal direction (min) | BDS | 52 | 68 | 91.5 | 133 | / |
BDS+ISCB | 18.5 | 38 | 58.5 | 99.5 | / | |
Improvement rate | 64% | 44% | 36% | 25% | 42% | |
Convergence time in the vertical direction (min) | BDS | 31.5 | 40 | 64 | / | / |
BDS+ISCB | 18.5 | 32.5 | 48.5 | / | / | |
Improvement rate | 41% | 19% | 24% | / | 28% |
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Chen, L.; Li, M.; Zhao, Y.; Zheng, F.; Zhang, X.; Shi, C. Clustering Code Biases between BDS-2 and BDS-3 Satellites and Effects on Joint Solution. Remote Sens. 2021, 13, 15. https://doi.org/10.3390/rs13010015
Chen L, Li M, Zhao Y, Zheng F, Zhang X, Shi C. Clustering Code Biases between BDS-2 and BDS-3 Satellites and Effects on Joint Solution. Remote Sensing. 2021; 13(1):15. https://doi.org/10.3390/rs13010015
Chicago/Turabian StyleChen, Liang, Min Li, Ying Zhao, Fu Zheng, Xuejun Zhang, and Chuang Shi. 2021. "Clustering Code Biases between BDS-2 and BDS-3 Satellites and Effects on Joint Solution" Remote Sensing 13, no. 1: 15. https://doi.org/10.3390/rs13010015