Abstract
In recent years, single-frequency precise point positioning (SF-PPP) has taken increasing attention from the GNSS community owing to its operational simplicity and cost-effectiveness. Thanks to the real-time service (RTS) products of the International GNSS Service (IGS), it is possible to use SF-PPP solutions in real-time tropospheric delay retrieval. Moreover, the advent of newly-emerged satellite systems, such as Galileo and BeiDou, offers significant opportunities to enhance its performance in real-time tropospheric delay estimation. Still, to take advantage of the potential benefits of multi-GNSS combinations, it is required to consider the stochastic properties of observations from different navigation systems. Therefore, the main objective of this study is to improve the tropospheric delay estimation performance of the multi-GNSS SF-PPP solution, including GPS, GLONASS, Galileo, and BeiDou, with advanced stochastic approaches. For this purpose, this study proposes an advanced weighting strategy that employs the variance component estimation method to specify the weights of multi-GNSS observations in the real-time SF-PPP process. The experimental tests reveal that the employment of the advanced weighting strategy in the multi-GNSS solution provides an accuracy of 2.18 cm in tropospheric delay estimation, which means an improvement of 17.4% on average compared with the conventional weighting approach. Besides, separately analyzing the recent performance of each navigation system is another objective of this study. The results indicate that within single-system SF-PPP solutions, Galileo provides the highest accuracy for the zenith total delay (ZTD) estimation with an average RMS error of 3.22 cm which is better than that of GPS solution by 8.3%.
Similar content being viewed by others
References
AbdRabbou M, El-Shazly A, Ahmed K (2018) Comparative analysis of multi-constellation GNSS single-frequency precise point positioning. Sur Rev 50(361):373–382. https://doi.org/10.1080/00396265.2017.1296628
Amiri-Simkooei AR, Zangeneh-Nejad F, Asgari J (2013) Least-squares variance component estimation applied to GPS geometry-based observation model. J Surv Eng-ASCE 139(4):176–187. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000107
Bahadur B, Nohutcu M (2018) PPPH: a MATLAB-based software for multi-GNSS precise point positioning analysis. GPS Solut 22(4):1–10. https://doi.org/10.1007/s10291-018-0777-z
Bahadur B, Nohutcu M (2021) Integration of variance component estimation with robust Kalman filter for single-frequency multi-GNSS positioning. Measurement 173:108596. https://doi.org/10.1016/j.measurement.2020.108596
BDS (2021) BeiDou open service signal-in-space Interface Control Document (ICD), http://en.beidou.gov.cn/SYSTEMS/ICD/. Accessed 27 Jan 2022
Bevis M, Businger S, Chiswell S, Herring TA, Anthes RA, Rocken C, Ware RH (1994) GPS meteorology: mapping zenith wet delays onto precipitable water. J Appl Meteorol 33(3):379–386. https://doi.org/10.1175/1520-0450(1994)033%3C0379:GMMZWD%3E2.0.CO;2
BKG (2021) BKG NTRIP Client (BNC). https://igs.bkg.bund.de/ntrip/download. Accessed 27 Jan 2022
Cai C, Gao Y (2013) Modeling and assessment of combined GPS/GLONASS precise point positioning. GPS Solut 17(2):223–236. https://doi.org/10.1007/s10291-012-0273-9
Cai C, Pan L, Gao Y (2014) A precise weighting approach with application to combined L1/B1 GPS/BeiDou positioning. J Navig 67(5):911–925. https://doi.org/10.1017/S0373463314000320
Davis JL, Herring TA, Shapiro II, Rogers AEE, Elgered G (1985) Geodesy by radio interferometry: Effects of atmospheric modeling errors on estimates of baseline length. Radio Sci 20(6):1593–1607. https://doi.org/10.1029/RS020i006p01593
De Haan S (2013) Assimilation of GNSS ZTD and radar radial velocity for the benefit of very-short-range regional weather forecasts. Q J R Meteorol Soc 139(677):2097–2107. https://doi.org/10.1002/qj.2087
Deng J, Zhao X, Zhang A, Ke F (2017) A robust method for GPS/BDS pseudorange differential positioning based on the Helmert variance component estimation. J Sens 2017:8172342. https://doi.org/10.1155/2017/8172342
Dousa J, Vaclavovic P (2014) Real-time zenith tropospheric delays in support of numerical weather prediction applications. Adv Space Res 53(9):1347–1358. https://doi.org/10.1016/j.asr.2014.02.021
Fan C, Guan Q, Zhu Z, Peng F, Xiang W (2019) Fuzzy weighting approach for single point positioning with single-frequency pseudo-range observations. Adv Space Res 63(9):2982–2994. https://doi.org/10.1016/j.asr.2014.02.021
Gao Z, Shen W, Zhang H, Ge M, Niu X (2016) Application of Helmert variance component based adaptive Kalman filter in multi-GNSS PPP/INS tightly coupled integration. Remote Sens 8(7):553. https://doi.org/10.3390/rs8070553
Ge Y, Zhou F, Dai P, Qin W, Wang S, Yang X (2019) Precise point positioning time transfer with multi-GNSS single-frequency observations. Measurement 146:628–642. https://doi.org/10.1016/j.measurement.2019.07.009
Ge Y, Chen S, Wu T, Fan C, Qin W, Zhou F, Yang X (2021) An analysis of BDS-3 real-time PPP: Time transfer, positioning, and tropospheric delay retrieval. Measurement 172:108871. https://doi.org/10.1016/j.measurement.2020.108871
Gelb A (1974) Applied optimal estimation. MIT press, Cambridge
GSA (2019) GNSS market report, Issue 6, October 2019, European GNSS Agency. https://doi.org/10.2878/031762
Guo F, Li X, Zhang X, Wang J (2017) The contribution of Multi-GNSS Experiment (MGEX) to precise point positioning. Adv Space Res 59(11):2714–2725. https://doi.org/10.1016/j.measurement.2020.108871
Hadas T, Bosy J (2015) IGS RTS precise orbits and clocks verification and quality degradation over time. GPS Solut 19(1):93–105. https://doi.org/10.1007/s10291-014-0369-5
Hadas T, Hobiger T (2020) Benefits of Using Galileo for Real-Time GNSS Meteorology. IEEE Geosci Remote Sens Lett 18(10):1756–1760. https://doi.org/10.1109/LGRS.2020.3007138
Hadas T, Teferle FN, Kazmierski K, Hordyniec P, Bosy J (2017) Optimum stochastic modeling for GNSS tropospheric delay estimation in real-time. GPS Solut 21(3):1069–1081. https://doi.org/10.1007/s10291-016-0595-0
Hadas T, Kazmierski K, Sośnica K (2019) Performance of Galileo-only dual-frequency absolute positioning using the fully serviceable Galileo constellation. GPS Solut 23(4):1–12. https://doi.org/10.1007/s10291-019-0900-9
Hadas T, Hobiger T, Hordyniec P (2020) Considering different recent advancements in GNSS on real-time zenith troposphere estimates. GPS Solut 24(4):1–14. https://doi.org/10.1007/s10291-020-01014-w
Hopfield HS (1969) Two-quartic tropospheric refractivity profile for correcting satellite data. J Geophys Res 74(18):4487–4499. https://doi.org/10.1029/JC074i018p04487
Kazmierski K, Hadas T, Sośnica K (2018) Weighting of multi-GNSS observations in real-time precise point positioning. Remote Sens 10(1):84. https://doi.org/10.3390/rs10010084
Koch KR (1999) Parameter estimation and hypothesis testing in linear models. Springer Science & Business Media, Berlin
Kouba J, Héroux P (2001) Precise point positioning using IGS orbit and clock products. GPS Solut 5(2):12–28. https://doi.org/10.1007/PL00012883
Kouba J (2015) A guide to using International GNSS Service (IGS) products. https://kb.igs.org/hc/en-us/articles/201271873-A-Guide-to-Using-the-IGS-Products. Accessed 27 Jan 2022
Landskron D, Böhm J (2018) VMF3/GPT3: refined discrete and empirical troposphere mapping functions. J Geodesy 92(4):349–360. https://doi.org/10.1007/s00190-017-1066-2
Lee SW, Kouba J, Schutz B, Kim DH, Lee YJ (2013) Monitoring precipitable water vapor in real-time using global navigation satellite systems. J Geodesy 87(10):923–934. https://doi.org/10.1007/s00190-013-0655-y
Li X, Dick G, Lu C, Ge M, Nilsson T, Ning T, Wickert J, Schuh H (2015a) Multi-GNSS meteorology: real-time retrieving of atmospheric water vapor from BeiDou, Galileo, GLONASS, and GPS observations. IEEE Trans Geosci Remote Sens 53(12):6385–6393. https://doi.org/10.1109/TGRS.2015.2438395
Li X, Ge M, Dai X, Ren X, Fritsche M, Wickert J, Schuh H (2015b) Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo. J Geodesy 89(6):607–635. https://doi.org/10.1007/s00190-015-0802-8
Li L, Jia C, Zhao L, Cheng J, Liu J, Ding J (2016) Real-time single frequency precise point positioning using SBAS corrections. Sensors 16(8):1261. https://doi.org/10.3390/s16081261
Li Z, Wang N, Wang L, Liu A, Yuan H, Zhang K (2019) Regional ionospheric TEC modeling based on a two-layer spherical harmonic approximation for real-time single-frequency PPP. J Geodesy 93(9):1659–1671. https://doi.org/10.1007/s00190-019-01275-5
Li M, Nie W, Xu T, Rovira-Garcia A, Fang Z, Xu G (2020) Helmert variance component estimation for multi-GNSS relative positioning. Sensors 20(3):669. https://doi.org/10.3390/s20030669
Lu C, Chen X, Liu G, Dick G, Wickert J, Jiang X, Zheng K, Schuh H (2017) Real-time tropospheric delays retrieved from multi-GNSS observations and IGS real-time product streams. Remote Sens 9(12):1317. https://doi.org/10.3390/rs9121317
Ning Y, Han H, Zhang L (2018) Single-frequency precise point positioning enhanced with multi-GNSS observations and global ionosphere maps. Meas Sci Technol 30(1):015013. https://doi.org/10.1088/1361-6501/aaf0f6
Odolinski R, Teunissen PJG (2017) Low-cost, 4-system, precise GNSS positioning: a GPS, Galileo, BDS and QZSS ionosphere-weighted RTK analysis. Meas Sci Technol 28(12):125801. https://doi.org/10.1088/1361-6501/aa92eb
Pan L, Guo F (2018) Real-time tropospheric delay retrieval with GPS, GLONASS, Galileo and BDS data. Sci Rep 8(1):1–17. https://doi.org/10.1038/s41598-018-35155-3
Pan Z, Chai H, Kong Y (2017a) Integrating multi-GNSS to improve the performance of precise point positioning. Adv Space Res 60(12):2596–2606. https://doi.org/10.1016/j.asr.2017.01.014
Pan L, Zhang X, Liu J, Li X, Li X (2017b) Performance evaluation of single-frequency precise point positioning with GPS, GLONASS, BeiDou and Galileo. J Navig 70(3):465–482. https://doi.org/10.1017/S0373463316000771
Parvazi K, Farzaneh S, Safari A (2020) Role of the RLS-VCE-estimated stochastic model for improvement of accuracy and convergence time in multi-GNSS precise point positioning. Measurement 165:108073. https://doi.org/10.1016/j.measurement.2020.108073
Paziewski J, Sieradzki R, Wielgosz P (2018) On the applicability of Galileo FOC satellites with incorrect highly eccentric orbits: An evaluation of instantaneous medium-range positioning. Remote Sens 10(2):208. https://doi.org/10.3390/rs10020208
Petit G, Luzum B (2010) IERS Conventions 2010 IERS Technical Note 36, Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie,179 pp., ISBN 3–89888–989–6
Rao CR (1971) Estimation of variance and covariance components—MINQUE theory. J Multivar Anal 1(3):257–275. https://doi.org/10.1016/0047-259X(71)90001-7
Saastamoinen J (1972) Contributions to the theory of atmospheric refraction. Bull Géod 105(1):279–298. https://doi.org/10.1007/BF02521844
Steigenberger P, Hugentobler U, Loyer S, Perosanz F, Prange L, Dach R, Uhlemann M, Gendt G, Montenbruck O (2015) Galileo orbit and clock quality of the IGS multi-GNSS experiment. Adv Space Res 55(11):269–281. https://doi.org/10.1016/j.asr.2014.06.030
Sterle O, Stopar B, Prešeren PP (2015) Single-frequency precise point positioning: an analytical approach. J Geodesy 89(8):793–810. https://doi.org/10.1007/s00190-015-0816-2
Sun P, Zhang K, Wu S, Wang R, Wan M (2021) An investigation into real-time GPS/GLONASS single-frequency precise point positioning and its atmospheric mitigation strategies. Meas Sci Technol 32(11):115018. https://doi.org/10.1088/1361-6501/ac0a0e
Teunissen PJG, Amiri-Simkooei AR (2008) Least-squares variance component estimation. J Geodesy 82(2):65–82. https://doi.org/10.1007/s00190-007-0157-x
Teunissen PJG, Montenbruck O (2017) Springer handbook of global navigation satellite systems. Springer International Publishing, Cham
Wang K, Khodabandeh A, Teunissen PJG (2019a) Precision analysis of troposphere sensing using GPS single-frequency signals. Adv Space Res 63(1):148–159. https://doi.org/10.1016/j.asr.2018.09.006
Wang A, Chen J, Zhang Y, Meng L, Wang J (2019b) Performance of selected ionospheric models in multi-global navigation satellite system single-frequency positioning over China. Remote Sens 11(17):2070. https://doi.org/10.3390/rs11172070
Wang L, Li Z, Ge M, Neitzel F, Wang X, Yuan H (2019c) Investigation of the performance of real-time BDS-only precise point positioning using the IGS real-time service. GPS Solut 23(3):1–12. https://doi.org/10.1007/s10291-019-0856-9
Wanninger L (2012) Carrier-phase inter-frequency biases of GLONASS receivers. J Geodesy 86(2):139–148. https://doi.org/10.1007/s00190-011-0502-y
Wilgan K, Rohm W, Bosy J (2015) Multi-observation meteorological and GNSS data comparison with Numerical Weather Prediction model. Atmos Res 156:29–42. https://doi.org/10.1016/j.atmosres.2014.12.011
Wu J, Wu S, Hajj G, Bertiger W, Lichten S (1993) Effects of antenna orientation on GPS carrier phase. Manuscr Geod 18:91–98
Xia F, Ye S, Xia P, Zhao L, Jiang N, Chen D, Hu G (2019) Assessing the latest performance of Galileo-only PPP and the contribution of Galileo to Multi-GNSS PPP. Adv Space Res 63(9):2784–2795. https://doi.org/10.1016/j.asr.2018.06.008
Yu ZC (1996) A universal formula of maximum likelihood estimation of variance-covariance components. J Geodesy 70(4):233–240. https://doi.org/10.1007/BF00873704
Yunck TP (1993) Coping with the atmosphere and ionosphere in precise satellite and ground positioning. In: Valance-Jones A (ed) Environmental effects on spacecraft trajectories and positioning, AGU Monograph Series. 73:1–16. https://doi.org/10.1029/GM073p0001
Zhang Q, Zhao L, Zhao L, Zhou J (2018) An improved robust adaptive Kalman filter for GNSS precise point positioning. IEEE Sens J 18(10):4176–4186. https://doi.org/10.1109/JSEN.2018.2820097
Zhang Q, Zhao L, Zhou J (2019) A novel weighting approach for variance component estimation in GPS/BDS PPP. IEEE Sens J 19(10):3763–3771. https://doi.org/10.1109/JSEN.2019.2895041
Zhang X, Li P, Tu R, Lu X, Ge M, Schuh H (2020) Automatic calibration of process noise matrix and measurement noise covariance for multi-GNSS precise point positioning. Mathematics 8(4):502. https://doi.org/10.3390/math8040502
Zhao Q, Yao Y, Yao W, Li Z (2018) Real-time precise point positioning-based zenith tropospheric delay for precipitation forecasting. Sci Rep 8(1):1–12. https://doi.org/10.1038/s41598-018-26299-3
Zhao C, Zhang B, Li W, Yuan Y, Li M (2019) Simultaneous Retrieval of PWV and VTEC by Low-Cost Multi-GNSS Single-Frequency Receivers. Earth Space Sci 6(9):1694–1709. https://doi.org/10.1029/2019EA000650
Zheng F, Gu S, Gong X, Lou Y, Fan L, Shi C (2020) Real-time single-frequency pseudorange positioning in China based on regional satellite clock and ionospheric models. GPS Solut 24(1):1–13. https://doi.org/10.1007/s10291-019-0923-2
Zhou F, Dong D, Li W, Jiang X, Wickert J, Schuh H (2018) GAMP: An open-source software of multi-GNSS precise point positioning using undifferenced and uncombined observations. GPS Solut 22(2):1–10. https://doi.org/10.1007/s10291-018-0699-9
Zhou P, Wang J, Nie Z, Gao Y (2020) Estimation and representation of regional atmospheric corrections for augmenting real-time single-frequency PPP. GPS Solut 24(1):1–12. https://doi.org/10.1007/s10291-019-0920-5
Zhu S, Yue D, He L, Chen J, Liu Z (2021) Comparative analysis of four different single-frequency PPP models on positioning performance and atmosphere delay retrieval. Adv Space Res 67(12):3994–4010. https://doi.org/10.1016/j.asr.2021.02.026
Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res-Solid Earth 102(B3):5005–5017. https://doi.org/10.1029/96JB03860
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The author has no relevant financial or non-financial interests to disclose.
Additional information
Communicated by: H. Babaie
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bahadur, B. An improved weighting strategy for tropospheric delay estimation with real-time single-frequency precise positioning. Earth Sci Inform 15, 1267–1284 (2022). https://doi.org/10.1007/s12145-022-00814-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12145-022-00814-7