Abstract
This article first clearly figures out the relationship between parameters of timing group delay (TGD) and differential code bias (DCB) for BDS, and demonstrates the equivalence of TGD and DCB correction models combining theory with practice. The TGD/DCB correction models have been extended to various occasions for BDS positioning, and such models have been evaluated by real triple-frequency datasets. To test the effectiveness of broadcast TGDs in the navigation message and DCBs provided by the Multi-GNSS Experiment (MGEX), both standard point positioning (SPP) and precise point positioning (PPP) tests are carried out for BDS signals with different schemes. Furthermore, the influence of differential code biases on BDS positioning estimates such as coordinates, receiver clock biases, tropospheric delays and carrier phase ambiguities is investigated comprehensively. Comparative analysis show that the unmodeled differential code biases degrade the performance of BDS SPP by a factor of two or more, whereas the estimates of PPP are subject to varying degrees of influences. For SPP, the accuracy of dual-frequency combinations is slightly worse than that of single-frequency, and they are much more sensitive to the differential code biases, particularly for the B2B3 combination. For PPP, the uncorrected differential code biases are mostly absorbed into the receiver clock bias and carrier phase ambiguities and thus resulting in a much longer convergence time. Even though the influence of the differential code biases could be mitigated over time and comparable positioning accuracy could be achieved after convergence, it is suggested to properly handle with the differential code biases since it is vital for PPP convergence and integer ambiguity resolution.
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References
Abdel-salam M (2005) Precise point positioning using un-differenced code and carrier phase observations. Dissertation, University of Calgary, Canada. UCGE reports no. 20229
CSNO (2012) BeiDou navigation satellite system signal in space interface control document-open service signal B1I, version 1.0. China Satellite Navigation Office, Dec 2012
CSNO (2013) BeiDou navigation satellite system signal in space interface control document-open service signal, version 2.0. China Satellite Navigation Office, Dec 2013
Dach R, Montenbruck O, Prange L (2014) Status of the IGS-MGEX project. In: Proceedings of EUREF 2014 symposium, Vilnius, Lithuania, 3–7 June
Deng Z, Zhao Q, Springer T, Prange L, Uhlemann M (2014) Orbit and clock determination-BeiDou. In: Proceedings of IGS workshop, Pasadena, USA, 23–27 June
Dow JM, Neilan RE, Rizos C (2009) The International GNSS Service in a changing landscape of global navigation satellite systems. J Geod 83(7):191–198. doi:10.1007/s00190-008-0300-3
Feltens J, Schaer S (1998) IGS products for the ionosphere, IGS positioning paper. In: Proceedings of the IGS analysis centers workshop, Darmstadt, Germany, 9–11 Feb
Gao Y (2008) GNSS biases, their effect and calibration. In: Proceedings of IGS workshop, Miami Beach, USA, 2–6 June
He L, Ge M, Wang J, Wickert J, Schuh H (2013) Experimental study on the precise orbit determination of the BeiDou navigation satellite system. Sensors 13(3):2911–2928. doi:10.3390/s130302911
Hernández-Pajares M, Juan J, Sanz J, Orus R, Garcia-Rigo A, Feltens J, Komjathy A, Schaer S, Krankowski A (2009) The IGS VTEC maps: a reliable source of ionospheric information since 1998. J Geod 83(3):263–275. doi:10.1007/s00190-008-0266-1
Kouba J, Hérous P (2001) Precise point positioning using IGS orbit and clock products. GPS Solut 5(2):12–28. doi:10.1007/PL00012883
Li M, Qu L, Zhao Q, Guo J, Su X, Li X (2014) Precise point positioning with the BeiDou navigation satellite system. Sensors 14(1):927–943. doi:10.3390/s140100927
Li Z, Yuan Y, Li H, Ou J, Huo X (2012) Two-step method for the determination of the differential code biases of COMPASS satellites. J Geod 86(11):1059–1076. doi:10.1007/s00190-012-0565-4
Liu J, Bi S, Zheng J, Xie J (2014) Effect of separation of navigation satellite antenna inter-frequency phase centers on TGD parameter. In: China satellite navigation conference (CSNC) 2014 Proceedings. Lecture notes in electrical engineering, vols II, 304, pp 227–238. doi:10.1007/978-3-642-54743-0_20
Lou Y, Liu Y, Shi C, Yao X, Zheng F (2014) Precise orbit determination of BeiDou constellation based on BETS and MGEX network. Sci Rep 4:4692. doi:10.1038/srep04692
Montenbruck O, Steigenberger P (2013) The BeiDou navigation message. J Glob Position Syst 12(1):1–12. doi:10.5081/jgps.12.1.1
Montenbruck O, Hauschild A, Steigenberger P, Hugentobler U, Teunissen P, Nakamura S (2013) Initial assessment of the COMPASS/BeiDou-2 regional navigation satellite system. GPS Solut 17(2):211–222. doi:10.1007/s10291-012-0272-x
Montenbruck O, Steigenberger P, Hauschild A (2014) Differential code bias estimation using multi-gnss observations and global ionosphere maps. In: Proceedings of ION ITM 2014, San Diego, USA, 26–28 Jan
Petit G, Luzum B (2010) IERS Conventions 2010 (IERS Technical Note No. 36). Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, p 179. ISBN:3-89888-989-6.
Rao GS (2007) GPS satellite and receiver instrumental biases estimation using least squares method for accurate ionosphere modeling. J Earth Syst Sci 116:407–411. doi:10.1007/s12040-007-0039-x
Ray J (2001) Updated P1–C1 biases and cc2noncc. IGS Mail No. 3220, 5 March
Rizos C, Montenbruck O, Weber R, Neilan R, Hugentobler U (2013) The IGS MGEX Experiment as a milestone for a comprehensive multi-GNSS service. In: Proceedings of ION-PNT-2013, Honolulu, USA, 22–25 April
Schaer S (2003) IGS GLONASS tracking data. IGS Mail No. 4371, 8 May.
Schaer S (2008) Differential code biases (DCB) in GNSS analysis. In: Proceedings of IGS workshop, Miami Beach, USA, 2–6 June
Schaer S (2012) Overview of relevant GNSS biases. In: Proceedings of IGS workshop on GNSS biases. University of Bern, Switzerland, 18–19 Jan
Schaer S, Steigenberger P (2006) Determination and use of GPS differential code biases values. In: Proceedings of IGS workshop, Darmstadt, Germany, 8–11 May
Shi C, Zhao Q, Hu Z, Liu J (2013) Precise relative positioning using real tracking data from COMPASS GEO and IGSO satellites. GPS Solut 17(1):103–119. doi:10.1007/s10291-012-0264-x
Tetewsky A, Ross J, Soltz A, Vaughn N, Anzperger J, O’Brien C, Graham D, Craig D and Lozow J (2009) Making sense of inter-signal corrections-accounting for GPS satellite calibration parameters in legacy and modernized ionosphere correction algorithms. InsideGNSS:37–48, July/August
Wu JT, Wu SC, Hajj GA, Bertiger WI, Lichten SM (1993) Effects of antenna orientation on GPS carrier phases. Man Geod 18:91–98
Wu X, Hu X, Wang G, Zhong H, Tang C (2013) Evaluation of COMPASS ionospheric model in GNSS positioning. Adv Space Res 51(6):959–968. doi:10.1016/j.asr.2012.09.039
Yang YX, Li JL, Wang AB, Xu JY, He HB, Guo HR, Shen JF, Dai X (2014) Preliminary assessment of the navigation and positioning performance of BeiDou regional navigation satellite system. Sci China Earth Sci 57(1):144–152. doi:10.1007/s11430-013-4769-0
Zhang X, Liu J, Forsberg R (2006) Application of precise point positioning in airborne survey. Geomat Inform Sci Wuhan Univ 31(1):19–22 (in Chinese)
Zhao Q, Guo J, Li M, Qu L, Hu Z, Shi C, Liu J (2013) Initial results of precise orbit and clock determination for COMPASS navigation satellite system. J Geod 87(5):475–486. doi:10.1007/s00190-013-0622-7
Acknowledgments
The authors gratefully acknowledge IGS Multi-GNSS Experiment (MGEX) for providing GNSS data and products. We also appreciate the editor-in-chief, Roland Klees, the handling editor, Pascal Willis, and three anonymous reviewers for their valuable comments and improvements to this manuscript. This study was supported by the National Natural Science Foundation of China (No: 41474025, No: 41404006) and International Postdoctoral Exchange Fellowship Program 2013 by the Office of China Postdoctoral Council (No. 2013042).
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Guo, F., Zhang, X. & Wang, J. Timing group delay and differential code bias corrections for BeiDou positioning. J Geod 89, 427–445 (2015). https://doi.org/10.1007/s00190-015-0788-2
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DOI: https://doi.org/10.1007/s00190-015-0788-2