Skip to main content
SpringerLink
Log in

Positioning Model

  • Chapter
Springer Handbook of Global Navigation Satellite Systems

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

Zusammenfassung

The focus of this chapter is on the models for positioning. Since the global navigation satellite system (GNSS) observation equations are nonlinear in the position coordinates, the chapter is started with a section on the linearization of the observation equations for pseudorange (code) and carrier-phase. After that, absolute (point) positioning models are discussed, starting with the code-based single point positioning (SPP) model, followed by the model for precise point positioning (PPP), based on code and phase. The relative positioning models can be distinguished into code-dominated (differential GNSS or DGNSS) models and phase-dominated (real-time kinematic or RTK) models. For the latter type of models, a general multifrequency undifferenced model is presented, which may form the basis of both relative network model and the (absolute) model that enables PPP users to perform integer ambiguity resolution (PPP-RTK). After that the link is made between the undifferenced model and the single and double differenced versions of the positioning model and an overview is given of the various positioning concepts.

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

References

  1. C. Hegarty, E. Powers, B. Fonville: Accounting for timing biases between GPS, modernized GPS, and Galileo signals, Proc. 36th Annu. PTTI Meet., Washington DC (2004) pp. 307–317

    Google Scholar 

  2. R.E. Phelts, G.X. Gao, G. Wong, L. Heng, T. Walter, P. Enge, S. Erker, S. Thoelert, F. Meurer: New GPS signals – Aviation grade chips of the Block IIF, Inside GNSS 5(5), 36–45 (2010)

    Google Scholar 

  3. R. Piriz, M. Cueto, V. Fernandez, P. Tavella, I. Sesia, G. Cerretto, J. Hahn: GPS/Galileo interoperability: GGTO, timing biases and GIOVE-A experience, Proc. 38th Annu. Precise Time Time Interval (PTTI) Meet., Washington DC (2007) pp. 49–68

    Google Scholar 

  4. R. Dach, S. Schaer, S. Lutz, M. Meindl, G. Beutler: Combining the observations from different GNSS, Proc. EUREF 2010 Symp., Gävle (2010)

    Google Scholar 

  5. D. Odijk, P.J.G. Teunissen, L. Huisman: First results of mixed GPS+GIOVE single-frequency RTK in Australia, J. Spatial Sci. 57(1), 3–18 (2012)

    Article  Google Scholar 

  6. S. Schaer: Mapping and Predicting the Earth’s Ionosphere Using the Global Positioning System, Ph.D. Thesis (Astronomical Institute, Univ. Berne, Berne, Switzerland 1999)

    Google Scholar 

  7. O. Montenbruck, A. Hauschild: Code biases in multi-GNSS point positioning, Proc. ION ITM 2013, San Diego (ION, Virginia 2013) pp. 616–628

    Google Scholar 

  8. J. Hahn, E.D. Powers: Implementation of the GPS to Galileo time offset (GGTO), Proc. IEEE Int. FCS PTTI Syst. Appl. Meet., Vancouver (2005) pp. 33–37

    Google Scholar 

  9. P. Defraigne, W. Aerts, G. Cerretto, G. Signorile, E. Cantoni, I. Sesia, P. Tavella, A. Cernigliaro, A. Samperi, J.M. Sleewaegen: Advances on the use of Galileo signals in time metrology: Calibrated time transfer and estimation of UTC and GGTO using a combined commercial GPS-Galileo receiver, Proc. 45th Annu. PTTI Syst. Appl. Meet., Bellevue (2013) pp. 256–262

    Google Scholar 

  10. M. Aoki: QZSS: The Japanese quasi-zenith satellite system – Program updates and current status, Proc. 5th Meet. Int. Comm. GNSS (ICG), Torino (UNOOSA, Vienna 2010)

    Google Scholar 

  11. K.V.D. Rajarajan, S.C.N.T. Rathnakara, A.S. Ganeshan: Modeling of IRNSS system time-offset with respect to other GNSS, Contr. Theory Inf. 5(2), 10–17 (2015)

    Google Scholar 

  12. B. Hofmann-Wellenhof, H. Lichtenegger, E. Wasle: GNSS – Global Navigation Satellite Systems, GPS, GLONASS, Galileo and More (Springer, Wien 2008)

    Google Scholar 

  13. O. Montenbruck, P. Steigenberger: The BeiDou navigation message, J. Glob. Position. Syst. 12(1), 1–12 (2013)

    Article  Google Scholar 

  14. A.E. Zinoviev: Using GLONASS in combined GNSS receivers: Current status, Proc. ION GNSS 2005, Long Beach (ION, Virginia 2005) pp. 1046–1057

    Google Scholar 

  15. G. Gendt, Z. Altamimi, R. Dach, W. Söhne, T. Springer: GGSP: Realisation and maintenance of the Galileo terrestrial reference frame, Adv. Space Res. 47(2), 174–185 (2011)

    Article  Google Scholar 

  16. Indian Regional Navigation Satellite System – Signal in Space ICD for Standard Positioning Service, (Indian space research organization, Bangalore, 2014)

    Google Scholar 

  17. V. Vdovin: National reference systems of the Russian federation, used in GLONASS, including the user and fundamental segments, Proc. 8th Meet. Int. Comm. GNSS (ICG), Working Group D, Dubai (UNOOSA, Vienna 2013) pp. 1–11

    Google Scholar 

  18. P.J. de Jonge: A Processing Strategy for the Application of the GPS in Networks, Ph.D. Thesis (Netherlands Geodetic Commission, Delft 1998), Publications on Geodesy, 46

    Google Scholar 

  19. A. Leick, L. Rapoport, D. Tatarnikov: GPS Satellite Surveying, 4th edn. (John Wiley, Hoboken 2015)

    Google Scholar 

  20. P.J. Buist: Multi-Platform Integrated Positioning and Attitude Determination Using GNSS, Ph.D. Thesis (Delft University of Technology, Delft 2013)

    Google Scholar 

  21. T. Ebinuma: Precision Spacecraft Rendezvous Using Global Positioning System: An Integrated Hardware Approach, Ph.D. Thesis (University of Texas, Austin 2001)

    Google Scholar 

  22. Navstar GPS Space Segment/Navigation User Interfaces, Interface Specification IS-GPS-200H (Global Positioning Systems Directorate, Los Angeles Air Force Base, El Segundo 2013)

    Google Scholar 

  23. European Global Navigation Satellite Systems Agency: European GNSS (Galileo) Open Service Signal in Space Interface Control Document, OS SIS ICD, Iss. 1. (2010)

    Google Scholar 

  24. O. Montenbruck, P. Steigenberger, S. Riley: IRNSS orbit determination and broadcast ephemeris assessment, Proc. ION ITM 2015, Dana Point (2015) pp. 185–193

    Google Scholar 

  25. J. Ray, K. Senior: Geodetic techniques for time and frequency comparisons using GPS phase and code measurements, Metrologia 42(4), 215–232 (2005)

    Article  Google Scholar 

  26. A.Q. Le: Achieving decimetre accuracy with single frequency standalone GPS positioning, Proc. ION GNSS 2004, Long Beach (ION, Virginia 2004) pp. 1881–1892

    Google Scholar 

  27. E.D. Kaplan, C.J. Hegarty: Understanding GPS: Principles and Applications, 2nd edn. (Artech House, Boston, London 2006)

    Google Scholar 

  28. A. Tetewsky, J. Ross, A. Soltz, N. Vaughn, J. Anszperger, C. O’Brien, D. Graham, D. Craig, J. Lozow: Making sense of inter-signal corrections, Inside GNSS 4(4), 37–48a (2009)

    Google Scholar 

  29. BeiDou Navigation Satellite System Signal In Space Interface Control Document – Open Service Signal, v.2.0 (China Satellite Navigation Office, 2013)

    Google Scholar 

  30. Global Navigation Satellite System GLONASS-Interface Control Document, Vol. 5.1 (Russian Institute of Space Device Engineering, Moscow, 2008)

    Google Scholar 

  31. U. Rossbach: Positioning and Navigation Using the Russian Satellite System GLONASS, Ph.D. Thesis (Universität der Bundeswehr München, Munich 2000)

    Google Scholar 

  32. C.H. Yinger, W.A. Feess, R.D. Esposti, A. Chasko, B. Cosentino, D. Syse, B. Wilson, B. Wheaton: GPS satellite interfrequency biases, Proc. ION AM 1999, Cambridge (ION, Virginia 1999) pp. 347–354

    Google Scholar 

  33. O. Montenbruck, A. Hauschild, P. Steigenberger: Differential code bias estimation using multi-GNSS observations and global ionosphere maps, Navigation 61(3), 191–201 (2014)

    Article  Google Scholar 

  34. E. Sardón, A. Rius, N. Zarraoa: Estimation of the transmitter and receiver differential biases and the ionospheric total electron content from global positioning system observations, Radio Sci. 29(3), 577–586 (1994)

    Article  Google Scholar 

  35. M. Ge, G. Gendt, M. Rothacher, C. Shi, J. Liu: Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations, J. Geod. 82(7), 389–399 (2008)

    Article  Google Scholar 

  36. J. Kouba, P. Héroux: Precise point positioning using IGS orbit and clock products, GPS Solutions 5(2), 12–28 (2001)

    Article  Google Scholar 

  37. A.J. Mannucci, B.D. Wilson, C.D. Edwards: A new method for monitoring the Earth’s ionospheric total electron content using the GPS global network, Proc. ION GPS 1993, Salt Lake City (ION, Virginia 1993) pp. 1323–1332

    Google Scholar 

  38. J.A. Klobuchar: Ionospheric time-delay algorithm for single-frequency GPS users, IEEE Trans. Aerosp. Electron. Syst. 23(3), 325–331 (1987)

    Article  Google Scholar 

  39. A. Angrisano, S. Gaglione, C. Gioia, M. Massaro, U. Robustelli: Assessment of NeQuick ionospheric model for Galileo single-frequency users, Acta Geophysica 61(6), 1457–1476 (2013)

    Article  Google Scholar 

  40. J. Saastamoinen: Atmospheric correction for the troposphere and stratosphere in radio ranging of satellites. In: The Use of Artificial Satellites for Geodesy, AGU Geophys. Monogr., Vol. 15, ed. by H.W. Henriksen, A. Mancini, B.M. Chovitz (The American Geophysical Union, Washington 1972) pp. 247–251

    Google Scholar 

  41. S. Bancroft: An algebraic solution of the GPS equations, IEEE Trans. Aerosp. Electron. Syst. 21(7), 56–59 (1985)

    Article  Google Scholar 

  42. L.O. Krause: A direct solution to GPS-type navigation equations, IEEE Trans. Aerosp. Electron. Syst. 23(2), 225–232 (1987)

    Article  Google Scholar 

  43. A. Kleusberg: Analytical GPS navigation solution, Quo vadis geodesia…? In: Festschrift for Erik W. Grafarend on the Occasion of his 60th Birthday, ed. by F. Krumm, V.S. Schwarze (Univ. Stuttgart, Stuttgart 1999) pp. 247–251

    Google Scholar 

  44. 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 

  45. R.B. Langley: Dilution of precision, GPS World 10(5), 52–59 (1999)

    Google Scholar 

  46. P.J.G. Teunissen: A proof of Nielsen’s conjecture on the GPS dilution of precision, IEEE Trans. Aerosp. Electron. Syst. 34(2), 693–695 (1998)

    Article  Google Scholar 

  47. P.J.G. Teunissen: GPS op afstand bekeken (in Dutch). In: Een halve eeuw in de goede richting – Lustrumboek Snellius 1985-1990, (DUM, Delft 1990) pp. 215–233

    Google Scholar 

  48. P. Héroux, J. Kouba: GPS precise point positioning with a difference, Proc. Geomatics’95, Ottawa (1995) pp. 1–11

    Google Scholar 

  49. J.F. Zumberge, M.B. Heflin, D.C. Jefferson, M.M. Watkins, F.H. Webb: Precise point positioning for the efficient and robust analysis of GPS data from large networks, J. Geophys. Res. 102(B3), 5005–5017 (1997)

    Article  Google Scholar 

  50. A.E. Niell: Global mapping functions for the atmosphere delay at radio wavelengths, J. Geophys. Res. 101(B2), 3227–3246 (1996)

    Article  Google Scholar 

  51. L. Wanninger: Carrier-phase inter-frequency biases of GLONASS receivers, J. Geod. 86(2), 139–148 (2012)

    Article  Google Scholar 

  52. H. van der Marel, P.F. de Bakker: Single-vs. dual-frequency precise point positioning – What are the tradeoffs between using L1-only and L1+L2 for PPP?, GNSS Solutions 7(4), 30–35 (2012)

    Google Scholar 

  53. D. Odijk, P.J.G. Teunissen, A. Khodabandeh: Galileo IOV RTK positioning: Standalone and combined with GPS, Survey Rev. 46(337), 267–277 (2014)

    Article  Google Scholar 

  54. R. Odolinski, P.J.G. Teunissen, D. Odijk: Combined GPS and BeiDou instantaneous RTK positioning, Navigation 61(2), 135–148 (2014)

    Article  Google Scholar 

  55. T. Takasu, A. Yasuda: Kalman-filter-based integer ambiguity resolution strategy for long-baseline RTK with ionosphere and troposphere estimation, Proc. ION GNSS 2010, Portland (ION, Virginia 2010) pp. 161–171

    Google Scholar 

  56. R. Odolinski, P.J.G. Teunissen, D. Odijk: Combined GPS+BDS+Galileo+QZSS for long baseline RTK positioning, Proc. ION GNSS 2014, Tampa (ION, Virginia 2014) pp. 2326–2340

    Google Scholar 

  57. G. Wübbena, M. Schmitz, A. Bagge: PPP-RTK: Precise point positioning using state-space reprentation in RTK networks, Proc. ION GNSS 2005, Long Beach (ION, Virginia 2005) pp. 2584–2594

    Google Scholar 

  58. O. Montenbruck, P. Steigenberger, A. Hauschild: Broadcast versus precise ephemerides: A multi-GNSS perspective, GPS Solutions 19(2), 321–333 (2015)

    Article  Google Scholar 

  59. P.J.G. Teunissen, A. Kleusberg (Eds.): GPS for Geodesy, 2nd edn. (Springer, Berlin 1998)

    Google Scholar 

  60. P.J.G. Teunissen: The geometry-free GPS ambiguity search space with a weighted ionosphere, J. Geod. 71(6), 370–383 (1997)

    Article  Google Scholar 

  61. W. Lindlohr, D. Wells: GPS design using undifferenced carrier beat phase observations, Manuscripta Geodaetica 10(4), 255–295 (1985)

    Google Scholar 

  62. C.C. Goad: Precise relative position determination using global positioning system carrier phase measurments in a nondifference mode, Proc. 1st Int. Symp. Precise Position. Glob. Position. Syst., Rockville, ed. by C. Goad (U.S. Department of Commerce, Maryland 1985) pp. 347–356

    Google Scholar 

  63. G. Blewitt: Carrier phase ambiguity resolution for the global positioning system applied to geodetic baselines up to 2000 km, J. Geophys. Res. 94(B8), 10187–10203 (1989)

    Article  Google Scholar 

  64. P.J.G. Teunissen: The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation, J. Geod. 70(1/2), 65–82 (1995)

    Article  Google Scholar 

  65. P.J.G. Teunissen, D. Odijk, B. Zhang: PPP-RTK: Results of CORS network-based PPP with integer ambiguity resolution, J. Aeronaut., Astronaut. Aviat., Ser. A 42(4), 223–230 (2010)

    Google Scholar 

  66. B. Zhang, P.J.G. Teunissen, D. Odijk: A novel un-differenced PPP-RTK concept, RIN J. Navig. 64(Supplement S1), S180–S191 (2011)

    Article  Google Scholar 

  67. D. Odijk, P.J.G. Teunissen, B. Zhang: Single-frequency integer ambiguity resolution enabled GPS precise point positioning, J. Surv. Eng. 138(4), 193–202 (2012)

    Article  Google Scholar 

  68. C. Rocken, R. Ware, T. van Hove, F. Solheim, C. Alber, J. Johnson: Sensing atmospheric water vapor with the global positioning system, Geophys. Res. Lett. 20(23), 2631–2634 (1993)

    Article  Google Scholar 

  69. D. Odijk, B. Zhang, A. Khodabandeh, R. Odolinski, P.J.G. Teunissen: On the estimability of parameters in undifferenced GNSS network and PPP-RTK user models by means of S-system theory, J. Geod. 90(1), 15–44 (2016)

    Article  Google Scholar 

  70. P. Collins, S. Bisnath, F. Lahaye, P. Héroux: Undifferenced GPS ambiguity resolution using the decoupled clock model and ambiguity datum fixing, Navigation 57(2), 123–135 (2010)

    Article  Google Scholar 

  71. J. Geng, F.N. Teferle, X. Meng, A.H. Dodson: Towards PPP-RTK: Ambiguity resolution in real-time precise point positioning, Adv. Space Res. 47(10), 1664–1673 (2011)

    Article  Google Scholar 

  72. S. Loyer, F. Perosanz, F. Mercier, H. Capdeville, J.-C. Marty: Zero-difference GPS ambiguity resolution at CNES-CLS IGS Analysis Center, J. Geod. 86(11), 991–1003 (2012)

    Article  Google Scholar 

  73. P.J.G. Teunissen, A. Khodabandeh: Review and principles of PPP-RTK methods, J. Geod. 89(3), 217–240 (2015)

    Article  Google Scholar 

  74. R. Christensen: Linear Models for Multivariate, Time Series, and Spatial Data (Springer, Berlin 1991)

    Book  Google Scholar 

  75. H. Landau, X. Chen, S. Klose, R. Leandro, U. Vollath: Trimble’s RTK and DGPS solutions in comparison with precise point positioning, Observing our Changing Earth, Proc. Int. Assoc. Geod. Symp. 133, Perugia, ed. by M.G. Sideris (Springer, Berlin 2009) pp. 709–718

    Google Scholar 

  76. C. Kee, B.W. Parkinson: Wide area differential GPS (WADGPS): Future navigation system, IEEE Trans. Aerosp. Electron. Syst. 32(2), 795–808 (1996)

    Article  Google Scholar 

  77. R.J.P. van Bree, C.C.J.M. Tiberius: Real-time single-frequency precise point positioning: Accuracy assessment, GPS Solutions 16(2), 259–266 (2012)

    Article  Google Scholar 

  78. M.O. Kechine, C.C.J.M. Tiberius, H. van der Marel: Experimental verification of internet-based global differential GPS, Proc. ION GPS 2003, Portland (ION, Virginia 2003) pp. 28–37

    Google Scholar 

  79. D. Lapucha, K. de Jong, X. Liu, T. Melgard, O. Oerpen, E. Vigen: Recent advances in wide area real-time precise positioning, TransNav Int. J. Marine Navig. Safety Sea Transp. 5(1), 87–92 (2011)

    Google Scholar 

  80. J.D. Bossler, J.R. Jensen, R.B. McMaster, C. Rizos (Eds.): Manual of Geospatial Science and Technology (Taylor Francis, London 2002)

    Google Scholar 

  81. D. Laurichesse: Phase biases estimation for integer ambiguity resolution, Proc. PPP-RTK Open Stand. Symp., Frankfurt am Main (BKG, Frankfurt 2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fugro Intersite B.V., Dillenburgsingel 69, 2263 HW, Leidschendam, Netherlands

    Dennis Odijk

Authors
  1. Dennis Odijk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dennis Odijk .

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

Odijk, D. (2017). Positioning Model. 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_21

Download citation

Publish with us

Policies and ethics

Search

Navigation