Abstract
Multipath effects caused by reflections in the near-field and far-field of a GNSS antenna represent a major error source in static and kinematic GNSS positioning applications. Since these effects are strongly site-specific, a generally valid and practicable analytical multipath model is still lacking. In contrast, using GNSS carrier phase observation residuals, the multipath stacking (MPS) methods are able to take site-specific conditions into account. We propose an advanced approach to performing residual-based MPS in the space domain. Being superior to most conventional attempts in which stacking cells have a fixed azimuthal resolution, our suggested method makes use of congruent cells and rigorous statistical assessments in terms of outlier detection and significance evaluation of the stacked values. The advanced stacking approach is applied to representative phase residuals from static precise point positioning. The results show that the use of congruent cells allows for MPS at high elevation angles and with a fine spatial resolution. Applying the resulting MPS maps at the residual level, both near-field and far-field effects at high and low elevation angles, respectively, can be significantly mitigated. In comparison with the conventional approach, the advanced one enables a larger reduction of about 20 % in the SD of residuals.
Similar content being viewed by others
References
Agnew DC, Larson KM (2007) Finding the repeat times of the GPS constellation. GPS Solut 11(1):71–76. doi:10.1007/s10291-006-0038-4
Alshawaf F, Fuhrmann T, Heck B, Hinz S, Knöpfler A, Luo X, Mayer M, Schenk A, Thiele A, Westerhaus M (2012) Integration of InSAR and GNSS observations for the determination of atmospheric water vapor. In: Krisp JM et al. (eds), Earth observation of global changes (EOGC), proceedings of EOGC2011, Munich, Germany, 13–15 April, 2011. Lecture Notes in Geoinformation and Cartography, Springer, Berlin, pp 147–162. doi:10.1007/978-3-642-32714-8_10
Bedford L, Brown N, Walford J (2009) New 3D four constellation high performance wideband choke ring antenna. In: Proceedings of ION GNSS 2009, Anaheim, CA, USA, 26–28 Jan 2009, pp 829–835
Bender M, Dick G, Wickert J, Schmidt T, Song S, Gendt G, Ge M, Rothacher M (2008) Validation of GPS slant delays using water vapour radiometers and weather models. Meteorol Z 17(6):807–812. doi:10.1127/0941-2948/2008/0341
Bilich A, Larson KM (2007) Mapping the GPS multipath environment using the signal-to-noise ratio (SNR). Radio Sci 42:RS6003. doi:10.1029/2007RS003652
Braasch MS (1996) Multipath effects. In: Parkinson BW et al. (eds) Global positioning system: theory and applications, vol 1, Am Inst of Aeronaut and Astronaut, Washington DC, Chap. 14
Dach R, Hugentobler U, Fridez P, Meindl M (2007) User manual of the Bernese GPS Software Version 5.0. Astronomical Institute, University of Bern, Stämpfli Publications AG, Bern, Switzerland
Dilßner F, Seeber G, Wübbena G, Schmitz M (2008) Impact of near-field effects on the GNSS position solution. In: Proceedings of ION GNSS 2008, Savannah, GA, USA, 16–19 September 2008, pp 612–624
Eissfeller B, Ameres G, Kropp V, Sanroma D (2007) Performance of GPS, GLONASS and Galileo. In: Fritsch D (ed) Photogrammetric Week 07, Stuttgart, Germany, 3–7 September, 2007, Wichmann, Berlin Offenbach, pp 185–199
Fan KK, Ding XL (2006) Estimation of GPS carrier phase multipath signals based on site environment. J Glob Position Syst 5(1–2):22–28
Fuhrmann T, Heck B, Knöpfler A, Masson F, Mayer M, Ulrich P, Westerhaus M, Zippelt, K (2012) Recent surface displacements in the Upper Rhine Graben—preliminary results from geodetic networks. Tectonophysics (online first). doi:10.1016/j.tecto.2012.10.012
Fuhrmann T, Knöpfler A, Luo X, Mayer M, Heck B (2010) Zur GNSS-basierten Bestimmung des atmosphärischen Wasserdampfgehalts mittels Precise Point Positioning. Karlsruhe Institute of Technology (KIT) Scientific Reports 7561, KIT Scientific Publishing, Karlsruhe, Germany
Hofmann-Wellenhof B, Lichtenegger H, Wasle E (2008) GNSS-Global Navigation Satellite Systems: GPS, GLONASS, Galileo & more. Springer, Wien
Iwabuchi T, Shoji Y, Shimada S, Nakamura H (2004) Tsukuba GPS Dense Net Campaign observation: improvement in GPS stacking maps of post-fit phase residuals estimated from three software packages. J Meteor Soc Jpn 82(1B):315–330
King MA, Watson CS (2010) Long GPS coordinate time series: multipath and geometry effects. J Geophys Res 115:B04403. doi:10.1029/2009JB006543
Knöpfler A, Masson F, Mayer M, Ulrich P, Heck B (2010) GURN (GNSS Upper Rhine Graben Network)—status and first results. In: Proceedings of FIG Congress 2010, Sydney, Australia, 11–16 April 2010
Lau L (2012) Comparison of measurement and position domain multipath filtering techniques with the repeatable GPS orbits for static antennas. Surv Rev 44(324):9–16. doi:10.1179/1752270611Y.0000000003
Lau L, Cross P (2006) A new signal-to-noise-ratio based stochastic model for GNSS high-precision carrier phase data processing algorithms in the presence of multipath errors. In: Proceedings of ION GNSS 2006, Fort Worth, TX, USA, 26–29 September 2006, pp 276–285
Lidberg M, Eksröm C, Johansson JM (2009) Site-dependent effects in high-accuracy applications of GNSS. EUREF Publication No. 17, Mitteilungen des Bundesamtes für Kartographie und Geodäsie, Band 42, pp 132–138
Liu H, Li X, Ge L, Rizos C, Wang F (2011) Variable length LMS adaptive filter for carrier phase multipath mitigation. GPS Solut 15(1):29–38. doi:10.1007/s10291-010-0165-9
Luo X (2013) GPS stochastic modelling—signal quality measures and ARMA processes. Springer theses: recognizing outstanding Ph.D. research, Springer, Berlin
Luo X, Mayer M, Heck B (2008) Improving the stochastic model of GNSS observations by means of SNR-based weighting. In: Sideris MG (ed) Observing our Changing Earth, Proceedings of the 2007 IAG General Assembly, Perugia, Italy, 2–13 July, 2007, IAG Symposia, vol. 133, Springer, Berlin, pp 725–734. doi:10.1007/978-3-540-85426-5_83
Mayer M, Knöpfler A, Heck B, Masson F, Ulrich P, Ferhat G (2012) GURN (GNSS Upper Rhine Graben Network)—Research Goals and First Results of a Transnational Geo-Scientific Network. In: Kenyon S et al. (eds) Geodesy for planet earth, Proceedings of the 2009 IAG Symposium, Buenos Aires, Argentina, 31 August–September 4, 2009, IAG Symposia, vol. 136, Springer, Berlin, pp 673–681. doi:10.1007/978-3-642-20338-1_83
Niell AE (1996) Global mapping functions for the atmosphere delay at radio wavelengths. J Geophys Res 101(B2):3227–3246. doi:10.1029/95JB03048
Ning T, Elgered G, Johansson JM (2011) The impact of microwave absorber and radome geometries on GNSS measurements of station coordinates and atmospheric water vapour. Adv Space Res 47(2):186–196. doi:10.1016/j.asr.2010.06.023
Park K-D, Elósegui P, Davis JL, Jarlemark POJ, Corey BE, Niell AE, Normandeau JE, Meertens CE, Andreatta VA (2004) Development of an antenna and multipath calibration system for Global Positioning System sites. Radio Sci 39:RS5002. doi:10.1029/2003RS002999
Ragheb AE, Clarke PJ, Edwards SJ (2007) GPS sidereal filtering: coordinate- and carrier-phase-level strategies. J Geod 81(5):325–335. doi:10.1007/s00190-006-0113-1
Ray JK (2006) What receiver technologies exist for mitigating GNSS pseudorange and carrier phase multipath? Inside GNSS 1(6):25–27
Rost C, Wanninger L (2009) Carrier phase multipath mitigation based on GNSS signal quality measurements. J Appl Geod 3(2):81–87. doi:10.1515/JAG.2009.009
Saastamoinen J (1973) Contribution to the theory of atmospheric refraction: Part II. Refraction corrections in satellite geodesy. Bull Geod 107(1):13–34. doi:10.1007/BF02522083
Schmid R, Steigenberger P, Gendt G, Ge M, Rothacher M (2007) Generation of a consistent absolute phase-center correction model for GPS receiver and satellite antennas. J Geod 81(12):781–798. doi:10.1007/s00190-007-0148-y
Seeber G (2003) Satellite geodesy, 2nd edn. Walter de Gruyter, Berlin
Snedecor GW, Cochran WG (1980) Statistical methods, 7th edn. Iowa State University Press, Ames
Wanninger L, May M (2000) Carrier phase multipath calibration of GPS reference stations. In: Proceedings of ION GPS 2000, Salt Lake City, UT, USA, 19–22 September, pp. 132–144
Wübbena G, Schmitz M, Matzke N (2011) On GNSS in situ station calibration of near-field multipath. In: Proceedings of the International Symposium on GNSS, Space-based and Ground-based Augmentation Systems and Applications, Brussels, Belgium, 29–30 November, 2010
Zhong P, Ding XL, Zheng DW, Chen W, Huang DF (2008) Adaptive wavelet transform based on cross-validation method and its application to GPS multipath mitigation. GPS Solut 12(2):109–117. doi:10.1007/s10291-007-0071-y
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 102(B3):5005–5017. doi:10.1029/96JB03860
Acknowledgments
We thank the data providers RENAG (France), RGP (France), Teria (France), Orpheon (France), SAPOS ® Baden-Württemberg (Germany), SAPOS ® Rheinland-Pfalz (Germany), swisstopo (Switzerland), European Permanent Network, IGS for supplying GNSS data for the GURN initiative. The authors are very grateful to anonymous reviewers for their constructive comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fuhrmann, T., Luo, X., Knöpfler, A. et al. Generating statistically robust multipath stacking maps using congruent cells. GPS Solut 19, 83–92 (2015). https://doi.org/10.1007/s10291-014-0367-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10291-014-0367-7