Advertisement

GPS Solutions

, Volume 20, Issue 4, pp 687–701 | Cite as

Benefits of receiver clock modeling in code-based GNSS navigation

  • Thomas KrawinkelEmail author
  • Steffen Schön
Original Article

Abstract

Due to the limited frequency stability and poor accuracy of typical quartz oscillators built-in GNSS receivers, an additional receiver clock error has to be estimated in addition to the coordinates. This leads to several drawbacks especially in kinematic applications: At least four satellites in view are needed for navigation, high correlations between the clock estimates and the up-coordinates. This situation can be improved distinctly when connecting atomic clocks to GNSS receivers and modeling their behavior in a physically meaningful way (receiver clock modeling). Recent developments in miniaturizing atomic clocks result in so-called chip-scale atomic clocks and open up the possibility of using stable atomic clocks in GNSS navigation. We present two different methods of receiver clock modeling, namely in an extended Kalman filter and a sequential least-squares adjustment for code-based GNSS navigation using three different miniaturized atomic clocks. Using the data of several kinematic test drives, the benefits of clock modeling for GPS navigation solutions are assessed: decrease in the noise of the up-coordinates by up to 69 % to 20 cm level, decrease in minimal detectable biases by 16 %, and elimination of spikes and subsequently decrease in large position errors (35 %). Hence, a more robust position is obtained. Additionally, artificial partial satellite outages are generated to demonstrate position solutions with only three satellites in view.

Keywords

GNSS Receiver clock modeling Allan deviation Clock coasting 

Notes

Acknowledgments

The authors would like to thank Andreas Bauch and Thomas Polewka of PTB for their support and commitment during execution and analysis of the clock comparisons. We also acknowledge the very helpful comments of the two anonymous reviewers. Furthermore, we thank IGS, CODE, and ESOC for their free to use GNSS products which were a valuable contribution to our case study. This work was funded by the Federal Ministry of Economics and Technology of Germany, following a resolution of the German Bundestag (Project Number: 50NA1321).

References

  1. Allan D (1987) Time and frequency (the-domain) characterization, estimation, and prediction of precision clocks and oscillators. IEEE Trans Ultrason Ferroelectr Freq Control 34:647–654CrossRefGoogle Scholar
  2. Baarda W (1968) A testing procedure for use in geodetic networks. Netherlands Geodetic Commission, Publications on Geodesy, New Series 2(5), DelftGoogle Scholar
  3. Barnes J, Chi A, Cutler L, Healey D, Leeson D, McGunigal T, Mullen J, Smith W, Sydnor R, Vessot R, Winkler G (1971) Characterization of frequency stability. IEEE Trans Instrum Meas 20:105–120CrossRefGoogle Scholar
  4. Bednarz S, Misra P (2006) Receiver clock-based integrity monitoring for GPS precision approaches. IEEE Trans Aerosp Electron Syst 41(2):636–643CrossRefGoogle Scholar
  5. Dach R, Hugentobler U, Fridez P, Meindl M (2007) Bernese GPS software version 5.0. Astronomical Institute, University of Bern, BernGoogle Scholar
  6. Dow J, Neilan R, Rizos C (2009) The international GNSS service in a changing landscape of global navigation satellite systems. J Geodesy 83:191–198. doi: 10.1007/s00190-008-0300-3 CrossRefGoogle Scholar
  7. Jackson Labs, Inc. (2015) Product description. http://www.jackson-labs.com/index.php/products/ln_csac
  8. Kleusberg A (2003) Analytical GPS navigation solution. In: Grafarend EW, Krumm FW, Schwarze VS (eds) Geodesy—the challenges of the 3rd millennium. Springer, Berlin, pp 93–96CrossRefGoogle Scholar
  9. Knable N, Kalafus RM (1984) Clock coasting and altimeter error analysis for GPS. Navigation 31(4):289–302. doi: 10.1002/j.2161-4296.1984.tb00880.x CrossRefGoogle Scholar
  10. Krawinkel T, Schön S (2014a) Application of miniaturized atomic clocks in kinematic GNSS single point positioning. In: Proceedings of the 28th European frequency and time forum (EFTF), pp 97–100Google Scholar
  11. Krawinkel T, Schön S (2014b) Applying miniaturized atomic clocks for improved kinematic GNSS single point positioning. In: Proceedings of ION GNSS+ 2014, Institute of Navigation, Tampa, FL, pp 2431–2439Google Scholar
  12. Riley W (2008) Handbook of frequency stability analysis. NIST special publication 1065. Boulder, COGoogle Scholar
  13. Salzmann M (1993) Least squares filtering and testing for geodetic navigation applications. Netherlands Geodetic Commission, Publications on Geodesy, New Series 37. DelftGoogle Scholar
  14. Schön S (2013) Zum Potenzial von modernen Atomuhren für die kinematische absolute Positionierung mit GNSS. In: Mayer M (ed) GNSS 2013—Schneller. Genauer. Effizienter. Beiträge zum 124. DVW-Seminar am 14. und 15. März 2013 in Karlsruhe, Schriftenreihe des DVW, Band 70. Wißner, Augsburg, pp 227–243Google Scholar
  15. Stanford Research Systems (2015) Product description. http://www.thinksrs.com/products/PRS10.htm
  16. Sturza MA (1983) GPS navigation using three satellites and a precise clock. Navigation 30(2):146–156. doi: 10.1002/j.2161-4296.1983.tb00831.x CrossRefGoogle Scholar
  17. van Dierendonck A, McGraw J, Brown RG (1985) Relationship between Allan variances and Kalman filter parameters. In: Proceedings of the sixteenth annual precise time and time interval (PTTI) applications and planning meeting, pp 273–292Google Scholar
  18. van Diggelen F (2009) A-GPS: assisted GPS, GNSS, and SBAS. Artech House, BostonGoogle Scholar
  19. Weinbach U (2013) Feasibility and impact of receiver clock modeling in precise GPS data analysis. In: Dissertation, Leibniz Universität Hannover, GermanyGoogle Scholar
  20. Weinbach U, Schön S (2011) GNSS receiver clock modeling when using high-precision oscillators and its impact on PPP. Adv Space Res 47:229–238CrossRefGoogle Scholar
  21. 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 102:5005–5017. doi: 10.1029/96JB03860 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut für ErdmessungLeibniz Universität HannoverHannoverGermany

Personalised recommendations