Skip to main content
SpringerLink
Log in

Combinations of Observations

  • Chapter
Springer Handbook of Global Navigation Satellite Systems

Part of the book series: Springer Handbooks ((SHB))

Zusammenfassung

This chapter introduces the concept of observation combinations, commonly used, for example, to compute positioning solutions with measurements from multiple frequencies or to study measurement noise, multipath, or ionospheric effects. Based on a generic parametrization for pseudorange and carrier-phase observations, a general expression for linear combinations is introduced. The impact of the coefficients on the properties and the noise of the combined observable is explained. The chapter covers combinations using measurements from a single satellite observed by one receiver. The discussion will then be extended to differential observations from two satellites, receivers and epochs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

AltBOC:

alternative BOC

CDMA:

code division multiple access

DCB:

differential code bias

FDMA:

frequency division multiple access

GLONASS:

Global’naya Navigatsionnaya Sputnikova Sistema (Russian Global Navigation Satellite System)

GNSS:

global navigation satellite system

GPS:

Global Positioning System

ISB:

intersystem bias

LAMBDA:

least-squares ambiguity decorrelation adjustment

QZSS:

Quasi-Zenith Satellite System

SD:

single-difference

TEC:

total electron content

References

  1. P. Enge, P. Misra: Global Positioning System: Signals, Measurements, and Performance, 2nd edn. (Ganga-Jamuna, Lincoln 2006)

    Google Scholar 

  2. P. Henkel, C. Günther: Reliable integer ambiguity resolution: Multi-frequency code carrier linear combinations and statistical a priori knowledge of attitude, Navigation 59(1), 61–75 (2012)

    Article  Google Scholar 

  3. M. Cocard, S. Bourgon, O. Kamali, P. Collins: A systematic investigation of optimal carrier-phase combinations for modernized triple-frequency GPS, J. Geod. 82(9), 555–564 (2008)

    Article  Google Scholar 

  4. X. Zhang, X. He: BDS triple-frequency carrier-phase linear combination models and their characteristics, Sci. China Earth Sci. 58(6), 896–905 (2015)

    Article  Google Scholar 

  5. M. Cocard, A. Geiger: Systematic search for all possible widelanes, Proc. 6th Int. Geod. Symp. Satell. Position., Columbus (1992) pp. 312–318

    Google Scholar 

  6. P. Collins: An overview of inter-frequency carrier phase combinations (1999) http://gauss.gge.unb.ca/papers.pdf/L1L2combinations.collins.pdf

  7. J. Jung: High integrity carrier phase navigation for future LAAS using multiple civilian GPS signals, Proc. ION GPS 1999, Nashville (ION, Virginia 1999) pp. 727–736

    Google Scholar 

  8. B. Forssell, M. Martin-Neira, R.A. Harris: Carrier phase ambiguity resolution in GNSS-2, Proc. ION GPS 1997, Kansas City (ION, Virginia 1997) pp. 1727–1736

    Google Scholar 

  9. U. Vollath, S. Birnbach, H. Landau: Analysis of three-carrier ambiguity resolution (TCAR) technique for precise relative positioning in GNSS-2, Proc. ION GPS 1998, Nashville (ION, Virginia 1998) pp. 417–426

    Google Scholar 

  10. R. Hatch, J. Jung, P. Enge, B. Pervan: Civilian GPS: The benefit of three frequencies, GPS Solutions 3(4), 1–9 (2000)

    Article  Google Scholar 

  11. J. Jung, P. Enge, B. Pervan: Optimization of cascade integer resolution with three civil GPS frequencies, Proc. ION GPS 2000, Salt Lake City (ION, Virginia 2000) pp. 2191–2200

    Google Scholar 

  12. P.J.G. Teunissen, P. Joosten, C. Tiberius: A comparison of TCAR, CIR and LAMBDA GNSS ambiguity resolution, Proc. ION GPS 2002, Portland (ION, Virginia 2002) pp. 2799–2808

    Google Scholar 

  13. S. Ji, W. Chen, C. Zhao, X. Ding, Y. Chen: Single epoch ambiguity resolution for Galileo with the CAR and LAMBDA methods, GPS Solutions 11(4), 259–268 (2007)

    Article  Google Scholar 

  14. K. O’Keefe, M. Petovello, W. Cao, G. Lachapelle, E. Guyader: Comparing multicarrier ambiguity resolution methods for geometry-based GPS and Galileo relative positioning and their application to low Earth orbiting satellite attitude determination, Int. J. Navig. Obs., 592073 (2009) doi:10.1155/2009/592073

    Google Scholar 

  15. W.G. Melbourne: The case for ranging in GPS based geodetic systems, Proc. 1st Int. Symp. Precise Position. Glob. Position. Syst., Rockville, ed. by C. Goad (NOAA, Washington DC 1985) pp. 373–386

    Google Scholar 

  16. G. Wübbena: Software developments for geodetic positioning with GPS using TI 4100 code and carrier measurements, Proc. 1st Int. Symp. Precise Position. Glob. Position. Syst., Rockville, ed. by C. Goad (NOAA, Washington DC 1985) pp. 403–412

    Google Scholar 

  17. G. Blewitt: An automatic editing algorithm for GPS data, Geophys. Res. Lett. 17(3), 199–202 (1990)

    Article  Google Scholar 

  18. S. Han, C. Rizos: The impact of two additional civilian GPS frequencies on ambiguity resolution strategies, Proc. ION Annu. Meet. 1999 (ION, Virginia 1999) pp. 315–321

    Google Scholar 

  19. P. Henkel, C. Günther: Three frequency linear combinations for Galileo, Proc. 4th Workshop Position., Navig. Commun., Hannover (2007) pp. 239–245

    Google Scholar 

  20. T.P. Yunck: Coping with the atmosphere and ionosphere in precise satellite and ground positioning. In: Environmental Effects on Spacecraft Positioning and Trajectories, ed. by A.V. Jones (AGU, Washington DC 1992) pp. 1–16

    Google Scholar 

  21. D. Odijk: Ionosphere-free phase combinations for modernized GPS, J. Surv. Eng. 129(4), 165–173 (2003)

    Article  Google Scholar 

  22. P.J.G. Teunissen, D. Odijk: Rank-defect integer estimation and phase-only modernized GPS ambiguity resolution, J. Geod. 76(9/10), 523–535 (2003)

    Article  Google Scholar 

  23. Z. Wang, Y. Wu, K. Zhang, Y. Meng: Triple-frequency method for high-order ionospheric refractive error modelling in GPS modernization, J. Glob. Position. Syst. 4(1/2), 291–295 (2005)

    Article  Google Scholar 

  24. M. Hernández-Pajares, Á. Aragón-Ángel, P. Defraigne, N. Bergeot, R. Prieto-Cerdeira, A. Garcea-Rigo: Distribution and mitigation of higher-order ionospheric effects on precise GNSS processing, J. Geophys. Res. Solid Earth 119(4), 3823–3837 (2014)

    Article  Google Scholar 

  25. T. Richert, N. El-Sheimy: Optimal linear combinations of triple frequency carrier phase data from future global navigation satellite systems, GPS Solutions 11(1), 11–19 (2007)

    Article  Google Scholar 

  26. Y. Feng: GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals, J. Geod. 82(12), 847–862 (2008)

    Article  Google Scholar 

  27. C. Kee, B. Parkinson: Calibration of multipath errors on GPS pseudorange measurements, Proc. ION GPS 1994, Salt Lake City (ION, Virginia 1994) pp. 353–362

    Google Scholar 

  28. P.D. Groves, Z. Jiang, M. Rudi, P. Strode: A portfolio approach to NLOS and multipath mitigation in dense urban areas, Proc. ION GNSS+ 2013, Nashville (ION, Virginia 2013) pp. 3231–3247

    Google Scholar 

  29. A. Simsky: Three’s the charm: Triple-frequency combinations in future GNSS, Inside GNSS 1(5), 38–41 (2006)

    Google Scholar 

  30. O. Montenbruck, A. Hauschild, P. Steigenberger, R.B. Langley: Three’s the challenge: A close look at GPS SVN62 triple-frequency signal combinations finds carrier-phase variations on the new L5, GPS World 21(8), 8–19 (2010)

    Google Scholar 

  31. O. Montenbruck, U. Hugentobler, R. Dach, P. Steigenberger, A. Hauschild: Apparent clock variations of the block IIF-1 (SVN62) GPS satellite, GPS Solutions 16(3), 303–313 (2012)

    Article  Google Scholar 

  32. J.T. Wu, S.C. Wu, G.A. Hajj, W.I. Bertiger, S.M. Lichten: Effects of antenna orientation on GPS carrier phase, Manuscr. Geod. 18(2), 91–98 (1993)

    Google Scholar 

  33. G. Blewitt: Basics of the GPS technique: Observation equations. In: Geodetic Applications of GPS, ed. by B. Jonsson (Swedish Land Survey, Gävle 1997)

    Google Scholar 

  34. D. Odijk, P.J.G. Teunissen: Characterization of between-receiver GPS-Galileo inter-system biases and their effect on mixed ambiguity resolution, GPS Solutions 17(4), 521–533 (2013)

    Article  Google Scholar 

  35. N. Nadarajah, P.J.G. Teunissen, J.-M. Sleewaegen, O. Montenbruck: The mixed-receiver BeiDou inter-satellite-type bias and its impact on RTK positioning, GPS Solutions 19(3), 357–368 (2015)

    Article  Google Scholar 

  36. P.J.G. Teunissen: The GPS phase-adjusted pseudorange, Proc. 2nd Int. Workshop High Precis. Navig., Stuttgart/Freudenstadt, ed. by K. Linkwitz, U. Hangleiter (Dümmler, Bonn 1991) pp. 115–125

    Google Scholar 

  37. L. Zhao, L. Li, X. Zhao: An adaptive Hatch filter to minimize the effects of ionosphere and multipath for GPS single point positioning, Proc. IEEE Int. Conf. Mechatron. Autom., Changchun (2009) pp. 4167–4172

    Google Scholar 

  38. B. Hoffmann-Wellenhof, H. Lichtenegger, E. Wasle: GNSS-Global Navigation Satellite Systems (Springer, Wien, New York 2008)

    Google Scholar 

  39. G.A. McGraw, R.S.Y. Young: Dual frequency smoothing DGPS performance evaluation studies, Proc. ION NTM 2005, San Diego (ION, Virginia 2005) pp. 170–181

    Google Scholar 

  40. P. Hwang, G. McGraw, J. Bader: Enhanced differential GPS carrier-smoothed code processing using dual-frequency measurements, Navigation 46(2), 127–137 (1999)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. German Space Operations Center, German Aerospace Center (DLR), Münchener Str. 20, 82234, Wessling, Germany

    André Hauschild

Authors
  1. André Hauschild
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to André Hauschild .

Editor information

Editors and Affiliations

  1. Dept. of Spatial Sciences, Curtin University, WA 6845, Perth, Australia

    Peter J.G. Teunissen

  2. Department of Geoscience and Remote Sensing, Delft University of Technology, 2600 GA, Delft, Netherlands

    Peter J.G. Teunissen

  3. German Aerospace Center (DLR), Münchener Str. 20, 82234, Wessling, Germany

    Oliver Montenbruck

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Hauschild, A. (2017). Combinations of Observations. In: Teunissen, P.J., Montenbruck, O. (eds) Springer Handbook of Global Navigation Satellite Systems. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-42928-1_20

Download citation

Publish with us

Policies and ethics

Search

Navigation