Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T13:15:47.111Z Has data issue: false hasContentIssue false
  • English
  • Français

Consistency analysis of global positioning system position errors with typical statistical distributions

Published online by Cambridge University Press:  08 June 2021

Mariusz Specht Open the ORCID record for Mariusz Specht [Opens in a new window]
Mariusz Specht*
Affiliation:
Department of Transport and Logistics, Gdynia Maritime University, Morska, Gdynia, Poland
*
Corresponding author. E-mail: m.specht@wn.umg.edu.pl
Get access Rights & Permissions [Opens in a new window]

Abstract

Research into statistical distributions of φ, λ and two-dimensional (2D) position errors of the global positioning system (GPS) enables the evaluation of its accuracy. Based on this, the navigation applications in which the positioning system can be used are determined. However, studies of GPS accuracy indicate that the empirical φ and λ errors deviate from the typical normal distribution, significantly affecting the statistical distribution of 2D position errors. Therefore, determining the actual statistical distributions of position errors (1D and 2D) is decisive for the precision of calculating the actual accuracy of the GPS system. In this paper, based on two measurement sessions (900,000 and 237,000 fixes), the distributions of GPS position error statistics in both 1D and 2D space are analysed. Statistical distribution measures are determined using statistical tests, the hypothesis on the normal distribution of φ and λ errors is verified, and the consistency of GPS position errors with commonly used statistical distributions is assessed together with finding the best fit. Research has shown that φ and λ errors for the GPS system are normally distributed. It is proven that φ and λ errors are more concentrated around the central value than in a typical normal distribution (positive kurtosis) with a low value of asymmetry. Moreover, φ errors are clearly more concentrated than λ errors. This results in larger standard deviation values for φ errors than λ errors. The differences in both values were 25–39%. Regarding the 2D position error, it should be noted that the value of twice the distance root mean square (2DRMS) is about 10–14% greater than the value of R95. In addition, studies show that statistical distributions such as beta, gamma, lognormal and Weibull are the best fit for 2D position errors in the GPS system.

Keywords

statistical distributionnavigation positioning systemposition errorglobal positioning system (GPS)
Type
Research Article
Information
The Journal of Navigation , Volume 74 , Issue 6 , November 2021 , pp. 1201 - 1218
Check for updates
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Institute of Navigation

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

Bhatti, J. and Humphreys, T. E. (2017). Hostile control of ships via false GPS signals: Demonstration and detection. Navigation. Journal of the Institute of Navigation, 64(1), 51–66.Google Scholar
Bowditch, N. (1984). American Practical Navigator: An Epitome of Navigation. Washington, DC, USA: DMA.Google Scholar
Brodin, G., Cooper, J., Walsh, D. and Stevens, J. (2005). The effect of helicopter rotors on GPS signal reception. The Journal of Navigation, 58(3), 433–450.10.1017/S0373463305003371CrossRefGoogle Scholar
Chin, G. Y. (1987). Two-dimensional measures of accuracy in navigation systems. DOT-TSC-RSPA-87-1. Cambridge, MA, USA: TSC.Google Scholar
Cutler, T. J. (2003). Dutton's Nautical Navigation. 15th Edition. Annapolis, MD, USA: Naval Institute Press.Google Scholar
Deakin, R. E., Hunter, M. N. and Karney, C. F. F. (2010). The Gauss-Krüger Projection. Proceedings of the 23rd Victorian Regional Survey Conference, Warrnambool, Australia.Google Scholar
Elhajj, M. and Ochieng, W. (2020). Impact of new GPS signals on positioning accuracy for urban bus operations. The Journal of Navigation, 73(6), 1284–1305.CrossRefGoogle Scholar
Glomsvoll, O. and Bonenberg, L. K. (2017). GNSS jamming resilience for close to shore navigation in the northern sea. The Journal of Navigation, 70(1), 33–48.CrossRefGoogle Scholar
Grant, A., Williams, P., Ward, N. and Basker, S. (2009). GPS jamming and the impact on maritime navigation. The Journal of Navigation, 62(2), 173–187.CrossRefGoogle Scholar
Han, J., Park, J., Kim, J. and Son, N.-S. (2016). GPS-less coastal navigation using marine radar for USV operation. IFAC-PapersOnLine, 49(23), 598–603.CrossRefGoogle Scholar
Hofmann-Wellenhof, B., Legat, K. and Wieser, M. (2003). Navigation—Principles of Positioning and Guidance. Wien, Austria: Springer.Google Scholar
Kalafus, R. M. and Chin, G. Y. (1986). Measures of Accuracy in the Navstar/GPS: 2DRMS vs. CEP. Proceedings of the 1986 National Technical Meeting of The Institute of Navigation (NTM 1986), Long Beach, CA, USA.Google Scholar
Krasuski, K. and Savchuk, S. (2020). Accuracy assessment of aircraft positioning using the dual-frequency GPS code observations in aviation. Communications - Scientific Letters of the University of Zilina, 22(2), 23–30.CrossRefGoogle Scholar
Krasuski, K., Ciećko, A., Bakuła, M. and Wierzbicki, D. (2020). New strategy for improving the accuracy of aircraft positioning based on GPS SPP solution. Sensors, 20(17), 4921.CrossRefGoogle ScholarPubMed
Lachapelle, G., Cannon, M. E., Qiu, W. and Varner, C. (1996). Precise aircraft single-point positioning using GPS post-mission orbits and satellite clock corrections. Journal of Geodesy, 70, 562–571.CrossRefGoogle Scholar
MacLean, G. (2009). Weak GPS signal detection in animal tracking. The Journal of Navigation, 62(1), 1–21.CrossRefGoogle Scholar
Merry, K. and Bettinger, P. (2019). Smartphone GPS accuracy study in an urban environment. PLoS One, 14(7), e0219890.CrossRefGoogle Scholar
Naranjo, J. E., Jiménez, F., Aparicio, F. and Zato, J. (2009). GPS and inertial systems for high precision positioning on motorways. The Journal of Navigation, 62(2), 351–363.CrossRefGoogle Scholar
Ochieng, W. Y., Sauer, K., Walsh, D., Brodin, G., Griffin, S. and Denney, M. (2003). GPS integrity and potential impact on aviation safety. The Journal of Navigation, 56(1), 51–65.CrossRefGoogle Scholar
Ojeda, L. and Borenstein, J. (2007). Non-GPS navigation for security personnel and first responders. The Journal of Navigation, 60(3), 391–407.CrossRefGoogle Scholar
Ramesh, R., Jyothi, V. B. N., Vedachalam, N., Ramadass, G. A. and Atmanand, M. A. (2016). Development and performance validation of a navigation system for an underwater vehicle. The Journal of Navigation, 69(5), 1097–1113.CrossRefGoogle Scholar
Robustelli, U., Paziewski, J. and Pugliano, G. (2021). Observation quality assessment and performance of GNSS standalone positioning with code pseudoranges of dual-frequency Android smartphones. Sensors, 21(6), 2125.CrossRefGoogle ScholarPubMed
Rudnicki, J. and Specht, C. (2016). A method for the assessing of reliability characteristics relevant to an assumed position-fixing accuracy in navigational positioning systems. Polish Maritime Research, 23(3), 20–27.Google Scholar
Śniegocki, H., Specht, C. and Specht, M. (2014). Testing accuracy of maritime DGPS system based on long-term measurements campaigns over the years 2006–2014. International Journal of Civil Engineering and Technology, 5(10), 1–8.Google Scholar
Specht, C. (2010). Preliminary Accuracy Results of EGNOS After the Implementation of Operational Status. Proceedings of the 5th International Conference & Exhibition (MELAHA 2010), Cairo, Egypt.Google Scholar
Specht, M. (2015). The evaluation of the positioning accuracy of the EGNOS and DGPS systems based on the long-term measurements in the years 2006–2014. Polish Cartographical Review, 47(2), 99–108.10.1515/pcr-2015-0006CrossRefGoogle Scholar
Specht, M. (2019). Method of evaluating the positioning system capability for complying with the minimum accuracy requirements for the International Hydrographic Organization Orders. Sensors, 19(18), 3860.CrossRefGoogle ScholarPubMed
Specht, M. (2020). A statistical distribution analysis of navigation positioning system errors—issue of the empirical sample size. Sensors, 20(24), 7144.CrossRefGoogle ScholarPubMed
Specht, M. (2021). Consistency of the empirical distributions of navigation positioning system errors with theoretical distributions—comparative analysis of the DGPS and EGNOS systems in the years 2006 and 2014. Sensors, 21(1), 31.CrossRefGoogle Scholar
Sun, Q. C., Odolinski, R., Xia, J. C., Foster, J., Falkmer, T. and Lee, H. (2017). Validating the efficacy of GPS tracking vehicle movement for driving behaviour assessment. Travel Behaviour and Society, 6, 32–43.10.1016/j.tbs.2016.05.001CrossRefGoogle Scholar
U.S. DoD. (1993). Global Positioning System Standard Positioning Service Signal Specification. 1st Edition. Springfield, VA, USA: U.S. DoD.Google Scholar
van Diggelen, F. (1998). GPS accuracy: Lies, damn lies, and statistics. GPS World, 9, 1–6.Google Scholar
Zandbergen, P. A. and Barbeau, S. J. (2011). Positional accuracy of assisted GPS data from high-sensitivity GPS-enabled mobile phones. The Journal of Navigation, 64(3), 381–399.CrossRefGoogle Scholar