Abstract
Nowadays, GLONASS is providing CDMA signals on the third G3 frequency of two GLONASS-K1 and four GLONASS-M + satellites, making it possible for the joint use of GLONASS FDMA and CDMA signals for precise point positioning (PPP). However, there are two main obstacles to GLONASS triple-frequency PPP. First, a triple-frequency PPP model that simultaneously uses GLONASS CDMA and FDMA signals is currently available. Second, significant IFCB errors are noticed, defined as the difference between satellite clocks computed with different ionospheric-free carrier phase combinations. Therefore, this contribution presents a new GLONASS FDMA + CDMA PPP model considering IFCB errors. A total of 135 globally distributed MGEX stations with 150-day datasets are utilized to estimate GLONASS IFCBs, and another six stations are selected to validate GLONASS triple-frequency PPP. Results indicate that GLONASS IFCBs are satellite dependent and exhibit periodic signals. Peak-to-peak amplitudes of the 150-day IFCB series are in meters: (− 0.53, − 0.36, R04), (− 0.42, − 0.52, R05), (− 0.04, − 0.04, R09), (− 0.68, − 0.52, R12), (− 0.62, − 0.50, R21), and (− 1.68, − 1.16, R26). Unlike GLONASS-M + satellites, no obvious IFCB errors of GLONASS-K1 satellite R09 can be observed. This difference in IFCBs may originate from GLONASS satellite types. Besides, the average normalized cross-correlation values of satellite R05, R21, and R26 between IFCB series of two days with an interval of eight days are about 0.88, 0.96, and 0.93, respectively, which can be expected to be modeled even predicted future. With precise IFCB products, triple-frequency PPP can be performed. After employing IFCB corrections, the average positioning accuracy of GLONASS triple-frequency PPP is improved from (5.8, 11.4, 11.3, 16.9) mm to (3.6, 5.4, 7.7, 10.1) mm in the north, east, up and 3D components, respectively. However, the additional third CDMA frequency has only a marginal contribution to improving positioning accuracy compared with dual-frequency solutions.
Similar content being viewed by others
Data availability
GNSS observation data are provided by IGS Multi-GNSS Experiment (MGEX) project. Data from MGEX released by Institut Geographique National (IGN) can be accessed from ftp://igs.ign.fr/pub/igs/data/campaign/mgex/daily/rinex3 and released by Bundesamt für Kartographie und Geodäsie (BKG) can be accessed from ftp://igs.bkg.bund.de/IGS/obs.
References
Bona P (2000) Precision, cross correlation, and time correlation of GPS phase and code observations. GPS Solutions 4(2):3–13
Brack A, Männel B, Schuh H (2020) GLONASS FDMA data for RTK positioning: a five-system analysis. GPS Solutions 25(1):9
Elsobeiey M (2015) Precise point positioning using triple-frequency GPS measurements. J Navig 68(3):480–492
Fan L, Shi C, Li M, Wang C, Zheng F, Jing G, Zhang J (2019) GPS satellite inter-frequency clock bias estimation using triple-frequency raw observations. J Geodesy 93(12):2465–2479
Fan L, Wang C, Guo S, Fang X, Jing G, Shi C (2021) GNSS satellite inter-frequency clock bias estimation and correction based on IGS clock datum: a unified model and result validation using BDS-2 and BDS-3 multi-frequency data. J Geodesy 95(12):135
Hou P, Zhang B, Liu T (2020) Integer-estimable GLONASS FDMA model as applied to Kalman-filter-based short- to long-baseline RTK positioning. GPS Solutions 24(4):93
IAC (2021) GLONASS constellation status. Available from: https://www.glonass-iac.ru/glonass/sostavOG/, accessed 24 December 2021
Leick A, Rapoport L, Tatarnikov D (2015) GPS satellite surveying. Wiley, New York
Li H, Zhou X, Wu B, Wang J (2012) Estimation of the inter-frequency clock bias for the satellites of PRN25 and PRN01. Sci China Phys Mech Astron 55(11):2186–2193
Li H, Li B, Xiao G, Wang J, Xu T (2015) Improved method for estimating the inter-frequency satellite clock bias of triple-frequency GPS. GPS Solutions 20(4):751–760
Li X, Liu G, Li X, Zhou F, Feng G, Yuan Y, Zhang K (2019) Galileo PPP rapid ambiguity resolution with five-frequency observations. GPS Solutions 24(1):24
Li X, Li X, Liu G, Yuan Y, Freeshah M, Zhang K, Zhou F (2020) BDS multi-frequency PPP ambiguity resolution with new B2a/B2b/B2a + b signals and legacy B1I/B3I signals. J Geodesy 94(10):107
Montenbruck O, Hugentobler U, Dach R, Steigenberger P, Hauschild A (2012) Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite. GPS Solutions 16(3):303–313
Montenbruck O, Steigenberger P, Prange L, Deng Z, Zhao Q, Perosanz F, Schmid R (2017) The Multi-GNSS experiment (MGEX) of the international GNSS service (IGS)-achievements, prospects and challenges. Adv Space Res 59(7):1671–1697
Pan L, Zhang X, Li X, Liu J, Li X (2017a) Characteristics of inter-frequency clock bias for Block IIF satellites and its effect on triple-frequency GPS precise point positioning. GPS Solutions 21(2):811–822
Pan L, Li X, Zhang X, Li X, Lu C, Zhao Q, Liu J (2017b) Considering inter-frequency clock bias for bds triple-frequency precise point positioning. Remote Sensing 9(7):34–46
Pan L, Zhang X, Guo F, Liu J (2018) GPS inter-frequency clock bias estimation for both uncombined and ionospheric-free combined triple-frequency precise point positioning. J Geodesy 93(4):473–487
Pan L, Jiang X, Zhang X, Ge M, Schuh H (2020) GPS + Galileo + BeiDou precise point positioning with triple-frequency ambiguity resolution. GPS Solutions 24(3)
Sleewaegen J, Simsky A, Wilde W, Boon F, Willems T (2012) Demystifying GLONASS inter-frequency carrier phase biases. Inside GNSS 7(3):57–61
Steigenberger P, Hauschild A, Montenbruck O, Rodriguez-Solano C, Hugentobler U (2013) Orbit and Clock Determination of QZS-1 Based on the CONGO Network. Navigation 60(1):31–40
Teunissen PJG, Khodabandeh A (2019) GLONASS ambiguity resolution. GPS Solutions 23(4):101
Wang N, Yuan Y, Li Z, Montenbruck O, Tan B (2015) Determination of differential code biases with multi-GNSS observations. J Geodesy 90(3):209–228
Zaminpardaz S, Teunissen PJG, Nadarajah N (2017) GLONASS CDMA L3 ambiguity resolution and positioning. GPS Solutions 21(2):535–549
Zaminpardaz S, Teunissen PJG, Khodabandeh A (2021) GLONASS–only FDMA+CDMA RTK: Performance and outlook. GPS Solutions 25(3):1–12
Zhang B, Hou P, Zha J, Liu T (2021a) Integer-estimable FDMA model as an enabler of GLONASS PPP-RTK. J Geodesy 95(8):91
Zhang F, Chai H, Li L, Xiao G, Du Z (2021b) Estimation and analysis of GPS inter-fequency clock biases from long-term triple-frequency observations. GPS Solutions 25(4):126–136
Zhang F, Chai H, Li L, Wang M, Feng X, Du Z (2022) Understanding the characteristic of GLONASS inter-frequency clock bias using both FDMA and CDMA signals. GPS Solutions 26(2):1–7
Zhou F, Xu T (2021) Modeling and assessment of GPS/BDS/Galileo triple-frequency precise point positioning. Acta Geodaetica Et Cartographica Sinica 50(1):61–70
Zhou F, Dong D, Ge M, Li P, Wickert J, Schuh H (2017) Simultaneous estimation of GLONASS pseudorange inter-frequency biases in precise point positioning using undifferenced and uncombined observations. GPS Solutions 22(1):19
Acknowledgements
Thanks go to MGEX for offering observation data. This study was financially supported by the National Natural Science Foundation of China (42074014).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhang, F., Chai, H., Wang, M. et al. Considering inter-frequency clock bias for GLONASS FDMA + CDMA precise point positioning. GPS Solut 27, 10 (2023). https://doi.org/10.1007/s10291-022-01348-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10291-022-01348-7