Abstract
The new generation of BDS-3 broadcasted open service signals B1C and B2a, which are compatible and interoperable with GPS and Galileo overlapping frequency signals, are suitable for multi-constellation global navigation satellite system (multi-GNSS) precise point positioning ambiguity resolution (PPP-AR). However, multipath errors caused by an actual complex environment can affect the ability of ambiguity resolution, thereby restricting the positioning performance of multi-GNSS. Due to different orbital repeat periods of GNSS systems, the implementation complexity of a multipath correction method based on time-domain repeatability is relatively high, while that based on spatial-domain repeatability are research hotspot at present, thanks to the advantages of simple algorithms, easy implementation, and real-time correction. Based on the original multipath hemispherical map (MHM) and trend-surface analysis MHM (TMHM) methods, four multipath processing schemes, namely, the independent modeling and correction (I-MHM, I-TMHM), together with the joint modeling and correction (C-MHM, C-TMHM) of different GNSS systems are proposed in this paper. We find that the residuals of GPS, BDS-3, and Galileo overlapping frequency show a strong correlation at the same spatial position after considering the GNSS inter-system biases in static PPP-AR modes, while the multipath joint modeling and correction method can improve the positioning performance more than the independent modeling and correction. This can be attributed to the ability of multi-GNSS to improve the space coverage within grids, making the modeling results more explanatory. Compared to C-MHM, the C-TMHM derived positioning accuracy and convergence time of combined GCE in 3D component can be improved by up to 29.3% and 40.7%, respectively. In addition, through using multi-GNSS data for multipath modeling, the modeling time can be shortened by more than half to obtain a correction effect similar to that of full orbit period modeling, specifically, 3-day data for GC modeling, while 4-day data for GE, CE, and GCE modeling. Finally, the performances of our improved multipath modeling method were verified and evaluated by using the observation data in environment with fewer blind areas. Compared with the uncorrected cases, the positioning accuracies of GC, GE, CE, and GCE in 3D component improve by 51.7, 63.8, 59.7, and 65.7%, after correcting the multipath error by the proposed C-TMHM method, while the convergence time can also be shortened by 55.3, 51.0, 52.2, and 64.2%, respectively. This research has significant applicability for mitigating multipath errors in various scenarios to improve positioning accuracy and reliability.
Similar content being viewed by others
Data availability
The data used in this manuscript are available from the corresponding author upon request. The availability of multi-GNSS and multi-frequency OSB products provided freely by CNES/NAV.
References
Atkins C, Ziebart M (2016) Effectiveness of observation-domain sidereal filtering for GPS precise point positioning. GPS Solut 20(1):111–122. https://doi.org/10.1007/s10291-015-0473-1
Banville S, Tang H (2010) Antenna rotation and its effects on kinematic precise point positioning. In: Proceedings ION GNSS 2010, Institute of Navigation, Portland, OR, September 21–24, pp 2545–2552
Boehm J, Niell A, Tregoning P, Schuh H (2006) Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys Res Lett 33:7
Cai M, Chen W, Dong D, Song L, Wang M, Wang Z, Zhou F, Zheng Z, Yu C (2016) Reduction of kinematic short baseline multipath efects based on multipath hemispherical map. Sens 16:1677. https://doi.org/10.3390/s16101677
Choi K, Bilich A, Larson KM, Axelrad P (2004) Modified sidereal filtering: implications for high-rate GPS positioning. Geophys Res Lett 31(22):178–198. https://doi.org/10.1029/2004gl021621
Collins P (2008) Isolating and estimating Undifferenced GPS integer ambiguities. In: Proceedings ION NTM 2008, Institute of Navigation, San Diego, CA, January 28–30, pp 720–732
de Bakker PF, Tiberius CCJM (2017) Real-time multi-GNSS single-frequency precise point positioning. GPS Solut 21(4):1791–1803. https://doi.org/10.1007/s10291-017-0653-2
Dierendonck AJV, Fenton P, Ford T (1992) Theory and performance of narrow correlator spacing in a GPS receiver. J Inst Navig 39(3):265–283. https://doi.org/10.1002/j.2161-4296.1992.tb02276.x
Dinius AM (1995) GPS antenna multipath rejection performance. Nasa Sti/recon Tech Rep N 96(58):16–21. https://doi.org/10.1002/wilm.10088
Dong D, Wang M, Chen W, Zeng Z, Song L, Zhang Q, Cai M, Cheng Y, Lv J (2016a) Mitigation of multipath effect in GNSS short baseline positioning by the multipath hemispherical map. J Geod 90(3):255–262. https://doi.org/10.1007/s00190-015-0870-9
Dong D, Chen W, Cai M, Zhou F, Wang M, Yu C, Zheng Z, Wang Y (2016b) Multi-antenna synchronized global navigation satellite system receiver and its advantages in high precision positioning applications. Front Earth Sci 10(4):772–783. https://doi.org/10.1007/s11707-016-0559-2
Geng J, Bock Y (2016) GLONASS fractional-cycle bias estimation across inhomogeneous receivers for PPP ambiguity resolution. J Geod 90(4):379–396. https://doi.org/10.1007/s00190-015-0879-0
Geng J, Chang H, Guo J, Li G, Wei N (2020) Three multi-frequency and multi-system GNSS high-precision point positioning methods and their performance in complex urban environment. Acta Geodaetica Et Cartographica Sinica 49(1):1–13
Genrich JF, Bock Y (1992) Rapid resolution of crustal motion at short ranges with the global positioning system. J Geophys Res Solid Earth 97(B3):3261–3269. https://doi.org/10.1029/91JB02997
Groves PD, Jiang Z (2013) Height aiding, C/N0 weighting and consistency checking for GNSS NLOS and multipath mitigation in urban areas. J Navig 66:653–669. https://doi.org/10.1017/S0373463313000350
Håkansson M, Jensen ABO, Horemuz M, Hedling G (2017) Review of code and phase biases in multi-GNSS positioning. GPS Solut 21(3):849–860. https://doi.org/10.1007/s10291-016-0572-7
Hsu LT (2018) Analysis and modeling GPS NLOS effect in highly urbanized area. GPS Solut 22:7. https://doi.org/10.1007/s10291-017-0667-9
Hung HK, Rau RJ (2013) Surface waves of the 2011 Tohoku earthquake: observations of Taiwan’s dense high-rate GPS network. J Geophys Res Solid Earth 118:332–345
Jin S, Su K (2019) Co-seismic displacement and waveforms of the 2018 Alaska earthquake from high-rate GPS PPP velocity estimation. J Geod 93(9):1559–1569. https://doi.org/10.1007/s00190-019-01269-3
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 15 Sept 2019
Laurichesse D, Privat A (2015) An open-source PPP client implementation for the CNES PPP-WIZARD demonstrator. In: Proceedings ION GNSS 2015, Institute of Navigation, Tampa, USA, September 14–18, pp 2780–2789
Li P, Zhang X (2014) Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning. GPS Solut 18(3):461–471. https://doi.org/10.1007/s10291-013-0345-5
Li X, Ge M, Lu C, Zhang Y, Wang R, Wickert J, Schuh H (2014) High-rate GPS seismology using real-time precise point positioning with ambiguity resolution. IEEE Trans Geosci Remote Sens 52(10):6165–6180. https://doi.org/10.1109/TGRS.2013.2295373
Li B, Zhang Z, Shen Y, Yang L (2018) A procedure for the significance testing of unmodeled errors in GNSS observations. J Geod 92:1171–1186. https://doi.org/10.1007/s00190-018-1111-9
Li X, Li X, Liu G, Feng G, Yuan Y, Zhang K, Ren X (2019) Triple-frequency PPP ambiguity resolution with multi-constellation GNSS: BDS and Galileo. J Geod 93(3):1105–1122. https://doi.org/10.1007/s00190-019-01229-x
Liu T, Yuan Y, Zhang B, Wang N, Chen Y (2017) Multi-GNSS precise point positioning (MGPPP) using raw observations. J Geod 91(3):253–268. https://doi.org/10.1007/s00190-016-0960-3
Liu X, Jiang W, Chen H, Zhao W, Huo L, Huang L, Chen Q (2019) An analysis of inter-system biases in BDS/GPS precise point positioning. GPS Solut 23:116. https://doi.org/10.1007/s10291-019-0906-3
Liu T, Jiang W, Laurichesse D, Chen H, Liu X, Wang J (2020) Assessing GPS/Galileo real-time precise point positioning with ambiguity resolution based on phase biases from CNES. Adv Space Res 66(4):810–825. https://doi.org/10.1016/j.asr.2020.04.054
Liu T, Chen H, Chen Q, Jiang W, Laurichesse D, An X, Geng T (2021) Characteristics of phase bias from CNES and its application in multi-frequency and multi-GNSS precise point positioning with ambiguity resolution. GPS Solut 25:58. https://doi.org/10.1007/s10291-021-01100-7
Lu M, Li W, Yao Z, Cui X (2019) Overview of BDS III new signals. Navigation 66(1):19–35. https://doi.org/10.1002/navi.296
Lu R, Chen W, Dong D, Wang Z, Zhang C, Peng Y, Yu C (2021) Multipath mitigation in GNSS precise point positioning based on trend-surface analysis and multipath hemispherical map. GPS Solut 25:119. https://doi.org/10.1007/s10291-021-01156-5
Lu R, Chen W, Zhang C, Li L, Peng Y, Zheng Z (2022) Characteristics of the BDS-3 multipath effect and mitigation methods using precise point positioning. GPS Solut 26:41. https://doi.org/10.1007/s10291-022-01227-1
Malys S, Jensen PA (1990) Geodetic point positioning with GPS carrier beat phase data from the CASA UNO experiment. Geophys Res Lett 17(5):651–654
Maqsood M, Gao S, Montenbruck O (2017) Antennas. In: Teunissen PJG, Montenbruck O (eds) Springer handbook of global navigation satellite systems. Springer, Cham, pp 505–534. https://doi.org/10.1007/978-3-319-42928-1_17
Pearson W (1966) Estimation of a correlation coefficient from an uncertainty measure. Psychometrika 31(3):421–433. https://doi.org/10.1007/BF02289473
Plag H, Pearlman M (2009) Global geodetic observing system. Meeting the requirements of a global society on a changing planet in 2020. Springer, Berlin
Saastamoinen J (1973) Contribution to the theory of atmospheric refraction: refraction corrections in satellite geodesy. Bull Geod 107(1):13–34
Schaer S (2016) Bias-SINEX format and implications for IGS bias products. IGS Workshop. Australia, February, Sydney, pp 8–12
Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70(1–2):65–82. https://doi.org/10.1007/BF00863419
Villiger A, Dach R, Schaer S, Prange L, Zimmermann F, Kuhlmann H, Wübbena G, Schmitz M, Beutler G, Jäggi A (2020) GNSS scale determination using calibrated receiver and Galileo satellite antenna patterns. J Geod 97:32. https://doi.org/10.1007/s00190-020-01417-0
Wang M, Wang J, Dong D, Chen W, Li H, Wang Z (2018) Advanced sidereal filtering for mitigating multipath effects in GNSS short baseline positioning. ISPRS Int J Geo Inf 7(6):228. https://doi.org/10.3390/ijgi7060228
Wang Z, Chen W, Dong D, Wang M, Cai M, Yu C, Zheng Z, Liu M (2019) Multipath mitigation based on trend-surface analysis applied to dual-antenna receiver with common clock. GPS Solut 23:104. https://doi.org/10.1007/s10291-019-0897-0
Wang Z, Chen W, Dong D, Zhang C, Peng Y, Zheng Z (2020) An advanced multipath mitigation method based on trend-surface analysis. Remote Sens 12:3601. https://doi.org/10.3390/rs12213601
Wu J, Wu S, Hajj G, Bertiger W, Lichten S (1993) Effects of antenna orientation on GPS carrier phase. Manuscr Geod 18:91–98
Yang Y, Gao W, Guo S, Mao Y, Yang Y (2019) Introduction to BeiDou-3 navigation satellite system. Navigation 66(1):7–18. https://doi.org/10.1002/navi.291
Zheng K, Zhang X, Li P, Li X, Ge M (2019) Multipath extraction and mitigation for high-rate multi-GNSS precise point positioning. J Geod 93(10):2037–2051. https://doi.org/10.1007/s00190-019-01300-7
Zheng K, Tan L, Liu K, Li P, Chen M, Zeng X (2022) Multipath mitigation for improving GPS narrow-lane uncalibrated phase delay estimation and speeding up PPP ambiguity resolution. Measurement 206:112243
Zhong P, Ding X, Zheng D, Chen W, Huang D (2008) Adaptive wavelet transform based on cross-validation method and its application to GPS multipath mitigation. GPS Solut 12(2):109–117. https://doi.org/10.1007/s10291-007-0071-y
Zhong P, Ding X, Yuan L, Xu Y, Kwok K, Chen Y (2009) Sidereal filtering based on single differences for mitigating GPS multipath effects on short baselines. J Geod 84:145–158. https://doi.org/10.1007/s00190-009-0352-z
Zhou F, Dong D, Li P, Li X, Schuh H (2019) Influence of stochastic modeling for inter-system biases on multi-GNSS undifferenced and uncombined precise point positioning. GPS Solut 23:59. https://doi.org/10.1007/s10291-019-0852-0
Zou X, Li Z, Wang Y, Deng C, Liu J (2021) Multipath error fusion modeling methods for multi-GNSS. Remote Sens 13(15):2925. https://doi.org/10.3390/rs13152925
Zumberge J, Heflin M, Jefferson D, Watkins M, Webb F (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res 102(B3):5005–5017. https://doi.org/10.1029/96JB03860
Acknowledgements
This work is sponsored by the National Natural Science Foundation of China (No. 41771475, 42174030), Social Development Project of Science and Technology Innovation Action Plan of Shanghai (No. 20dz1207107), the Special Fund of Hubei Luojia Laboratory (No. 220100020), the Hubei Provincial Science and Technology Innovation Talents (No. 2022EJD010), and the Research Funds of East China Normal University (No. 40500-20104-222460). We also acknowledge the CNES/NAV for providing the OSB products.
Author information
Authors and Affiliations
Contributions
RL and WC proposed the initial idea, designed the experiments, developed the software, and wrote the manuscript. ZL and DD extended the program, worked out technical details, and revised the manuscript. ZW, LH and XD helped with performing the experiments and analyzed the data. WJ supervised the study and modified the manuscript. All authors approved of the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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
Lu, R., Chen, W., Li, Z. et al. An improved joint modeling method for multipath mitigation of GPS, BDS-3, and Galileo overlapping frequency signals in typical environments. J Geod 97, 95 (2023). https://doi.org/10.1007/s00190-023-01788-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00190-023-01788-0