Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-26T20:55:46.732Z Has data issue: false hasContentIssue false
  • English
  • Français

Lower Bounds on DOP

Published online by Cambridge University Press:  22 June 2017

Peter F. Swaszek ,
Richard J. Hartnett  and
Kelly C. Seals
Peter F. Swaszek*
Affiliation:
(Department of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, Kingston RI USA)
Richard J. Hartnett
Affiliation:
(Department of Engineering, U. S. Coast Guard Academy, New London CT USA)
Kelly C. Seals
Affiliation:
(Department of Engineering, U. S. Coast Guard Academy, New London CT USA)
*
(E-mail: swaszek@uri.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

Code phase Global Navigation Satellite System (GNSS) positioning performance is often described by the Geometric or Position Dilution of Precision (GDOP or PDOP), functions of the number of satellites employed in the solution and their geometry. This paper develops lower bounds to both metrics solely as functions of the number of satellites, effectively removing the added complexity caused by their locations in the sky, to allow users to assess how well their receivers are performing with respect to the best possible performance. Such bounds will be useful as receivers sub-select from the plethora of satellites available with multiple GNSS constellations. The bounds are initially developed for one constellation assuming that the satellites are at or above the horizon. Satellite constellations that essentially achieve the bounds are discussed, again with value toward the problem of satellite selection. The bounds are then extended to a non-zero mask angle and to multiple constellations.

Keywords

Dilution of PrecisionMulti-constellation GNSS Performance
Type
Research Article
Information
The Journal of Navigation , Volume 70 , Issue 5 , September 2017 , pp. 1041 - 1061
Copyright
Copyright © The Royal Institute of Navigation 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Conley, R., Cosentino, R., Hegarty, C., Kaplan, E., Leva, J., Uijt de Haag, M., and Van Dyke, K. (2006). Performance of stand-alone GPS. Understanding GPS: Principles and Applications, Artech House, 2nd Ed., 301–378.Google Scholar
Gerbeth, D., Felux, M., Circiu, M-S., and Caamano, M. (2016). Optimized selection of satellites subsets for a multi-constellation GBAS.” Proceedings of the 2016 ION International Technical Meeting, Jan. 25–28, 2016. Monterey CA.CrossRefGoogle Scholar
Han, S., Chen, P., Gui, Q., Li, J. and Wei, M. (2013). Minimum of GDOP of satellite navigation and its applications in ISL establishment of Walker-δ constellation. China Satellite Navigation Conference, Springer, 139–149.Google Scholar
Han, S., Gui, Q., Li, G. and Du, Y. (2014). Minimum of PDOP and its applications in inter-satellite links (ISL) establishment of Walker-(delta) constellation. Advances in Space Research, 54, 726–733.Google Scholar
Horn, R.A. and Johnson, C.R. (2013). Matrix Analysis, Cambridge Univ. Press, 2nd Ed. Google Scholar
Kihara, M. and Okada, T. (1984). A satellite selection method and accuracy for the Global Positioning System. Navigation, 31, 8–20.Google Scholar
Misra, P. and Enge, P. (2006). Global Positioning System: Signals, Measurements and Performance, Ganga-Jamuna Press, 2nd Ed. Google Scholar
Spilker, J.J. (1996). Satellite constellation and geometric dilution of precision. Global Positioning System: Theory and Applications Volume 1, 177–208.Google Scholar
Swaszek, P.F., Hartnett, R.J. and Seals, K.C. (2016). Multi-constellation GNSS: new bounds on GDOP and a related satellite selection process. Proceedings of the ION GNSS+2016, Sept. 12–16, 2016, Portland OR.CrossRefGoogle Scholar
Teng, Y. and Wang, J. (2014). “New characteristics of geometric dilution of precision (GDOP) for multi-GNSS constellations. The Journal of Navigation, 67, 1018–1028.CrossRefGoogle Scholar
Teng, Y., Wang, J., and Huang, Q. (2016). Mathematical minimum of geometric dilution of precision (GDOP) for dual-GNSS constellations. Advances in Space Research, 57, 183–188.Google Scholar
Walter, T., Blanch, J. and Kropp, V. (2016). Satellite selection for multi-constellation SBAS. Proceedings ION GNSS+2016, Sept. 12–16, 2016, Portland OR.CrossRefGoogle Scholar
Wei, M., Wang, J. and Li, J. (2012). A new satellite selection algorithm for real-time application. IEEE International Conference on Systems and Informatics, May 19–20, 2012, Yantai CHINA.Google Scholar
Zhang, M. and Zhang, J. (2009). A fast satellite selection algorithm: beyond four satellites. IEEE Journal of Selected Topics in Signal Processing, 3, 740–747.Google Scholar