Journal of Geodesy

, Volume 92, Issue 1, pp 81–92 | Cite as

A resampling strategy based on bootstrap to reduce the effect of large blunders in GPS absolute positioning

  • Antonio Angrisano
  • Antonio Maratea
  • Salvatore Gaglione
Original Article


In the absence of obstacles, a GPS device is generally able to provide continuous and accurate estimates of position, while in urban scenarios buildings can generate multipath and echo-only phenomena that severely affect the continuity and the accuracy of the provided estimates. Receiver autonomous integrity monitoring (RAIM) techniques are able to reduce the negative consequences of large blunders in urban scenarios, but require both a good redundancy and a low contamination to be effective. In this paper a resampling strategy based on bootstrap is proposed as an alternative to RAIM, in order to estimate accurately position in case of low redundancy and multiple blunders: starting with the pseudorange measurement model, at each epoch the available measurements are bootstrapped—that is random sampled with replacement—and the generated a posteriori empirical distribution is exploited to derive the final position. Compared to standard bootstrap, in this paper the sampling probabilities are not uniform, but vary according to an indicator of the measurement quality. The proposed method has been compared with two different RAIM techniques on a data set collected in critical conditions, resulting in a clear improvement on all considered figures of merit.


GPS Blunder Bootstrap RAIM Absolute positioning 


  1. Alamgir S, Ali A (2013) Split sample bootstrap method. World Appl Sci J 21(7):983–993Google Scholar
  2. Alqurashi M, Wang J (2015) Performance analysis of fault detection and identification for multiple faults in GNSS and GNSS/INS integration. J Appl Geod 9(1):35–48. doi: 10.1515/jag-2014-0019 Google Scholar
  3. Amado C, Pires AM (2004) Robust bootstrap with non random weights based on the influence function. Commun Stat-Simul Comput 33(2):377–396CrossRefGoogle Scholar
  4. Amado C, Bianco AM, Boente G, Pires AM (2014) Robust bootstrap: an alternative to bootstrapping robust estimators. REVSTAT-Stat J 12(2):169–197Google Scholar
  5. Angrisano A, Gaglione S, Gioia C (2013a) Performance assessment of aided global navigation satellite system for land navigation. IET Radar Sonar Navig 7(6):671–680. doi: 10.1049/iet-rsn.2012.0224 CrossRefGoogle Scholar
  6. Angrisano A, Gioia C, Gaglione S, Del Core G (2013b) GNSS reliability testing in signal-degraded scenario. Int J Navig Obs. doi: 10.1155/2013/870365
  7. Athreya KB (1987) Bootstrap of the mean in the infinite variance case. Ann Stat 15(2):724–731CrossRefGoogle Scholar
  8. Baarda W (1968) A testing procedure for use in geodetic networks. Publications on Geodesy, New Series 2(5)Google Scholar
  9. Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, New YorkCrossRefGoogle Scholar
  10. Breiman L (1996a) Bagging predictors. Mach Learn 24(2):123–140. doi: 10.1023/A:1018054314350 Google Scholar
  11. Breiman L (1996b) Heuristics of instability and stabilization in model selection. Ann Stat 24(6):2350–2383. doi: 10.1214/aos/1032181158 CrossRefGoogle Scholar
  12. Breiman L (1998) Arcing classifier (with discussion and a rejoinder by the author). Ann Stat 26(3):801–849. doi: 10.1214/aos/1024691079 CrossRefGoogle Scholar
  13. Brown AK (1998) Receiver autonomous integrity monitoring using a 24-satellite GPS constellation. NAVIG J Inst Navig 5:21–33Google Scholar
  14. Brown R (1992) A baseline gps raim scheme and a note on the equivalence of three raim methods. Navigation 39(3):301–316. doi: 10.1002/j.2161-4296.1992.tb02278.x CrossRefGoogle Scholar
  15. Brown R (1993) Receiver autonomous integrity monitoring. Glob Positiom Syst Theory Appl 2:143–165Google Scholar
  16. Brown R, Chin G (1997) GPS raim calculation of threshold and protection radius using chi-square methods—a geometric approach. Glob Position Syst 5:155–179Google Scholar
  17. Castaldo G, Angrisano A, Gaglione S, Troisi S (2014) P-RANSAC: an integrity monitoring approach for GNSS signal degraded scenario. Int J Navig Obs 2014. doi: 10.1155/2014/173818
  18. Conley R, Cosentino R, Hegarty C, Kaplan E, Leva J, Uijt de Haag M, Van Dyke K (2006) Performance of stand-alone GPS. In: Understanding GPS: principles and applications. Artech House, NorwoodGoogle Scholar
  19. Dallah H (2012) A bootstrap approach to robust regression. Int J Appl Sci Technol 2(9) 114–118Google Scholar
  20. Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7(1):1–26. doi: 10.1214/aos/1176344552 CrossRefGoogle Scholar
  21. Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. No. 57 in monographs on statistics and applied probability. Chapman & Hall/CRC, Boca RatonCrossRefGoogle Scholar
  22. Godha S (2006) Performance evaluation of low cost MEMS-based IMU integrated with GPS for land vehicle navigation application. Ph.D thesis. University of Calgary, CanadaGoogle Scholar
  23. Hampel F, Ronchetti E, Rousseeuw PJ, Stahel W (2005) Robust statistics: the approach based on influence functions. Wiley, New YorkCrossRefGoogle Scholar
  24. Hewitson S, Wang J (2010) Extended receiver autonomous integrity monitoring (eraim) for GNSS/INS integration. J Surv Eng 136(1):13–22. doi: 10.1061/(ASCE)0733-9453(2010)136:1(13) CrossRefGoogle Scholar
  25. Hoffmann-Wellenhof B, Lichtenegger H, Collins J (1992) GPS theory and practice. Springer, Vienna. doi: 10.1007/978-3-7091-6199-9 Google Scholar
  26. Hu Z, Hu Y, Jin Y, Zheng S (2016) Measurement bootstrapping Kalman filter. Optik-Int J Light Electron Opt 127(4):2094–2101. doi: 10.1016/j.ijleo.2015.11.129 CrossRefGoogle Scholar
  27. Imon A, Ali MM (2005) Bootstrapping regression residuals. J Korean Data Inf Sci Soc 16(3):665–682Google Scholar
  28. Kaplan E, Hegarty C (2006) Understanding GPS: principles and applications. Artech house, NorwoodGoogle Scholar
  29. Kuusniemi H (2005) User-level reliability and quality monitoring in satellite-based personal navigation. PhD thesis, Institute of Digital and Computer Systems, Tampere University of Technology, FinlandGoogle Scholar
  30. Kuusniemi H, Lachapelle G (2004) GNSS signal reliability testing in urban and indoor environments. In: Proceedings of ION NTM 2004, ION NTM, San Diego, CA, 26–28 Jan 2004, pp 210–224Google Scholar
  31. Kuusniemi H, Lachapelle G, Takala J (2004) Position and velocity reliability testing in degraded GPS signal environments. GPS Solut 8(4):226–237. doi: 10.1007/s10291-004-0113-7 CrossRefGoogle Scholar
  32. Kuusniemi H, Wieser A, Lachapelle G, Takala J (2007) User-level reliability monitoring in urban personal satellite-navigation. IEEE Trans Aerosp Electron Syst 43(4):1305–1318. doi: 10.1109/TAES.2007.4441741 CrossRefGoogle Scholar
  33. Mohamad M, Ramli NM, Ghani NAM (2016) Weighted split sample bootstrap for regression models with high dimensional data. Indian J Sci Technol 9(28):1–6CrossRefGoogle Scholar
  34. Norazan M, Habshah M, Imon A, Chen S (2009a) Weighted bootstrap with probability in regression. In: WSEAS international conference. Proceedings. Mathematics and computers in science and engineering, World Scientific and Engineering Academy and Society, p 8Google Scholar
  35. Norazan MR, Midi H, Imon AHMR (2009b) Estimating regression coefficients using weighted bootstrap with probability. WSEAS Trans Math 8(7):362–371Google Scholar
  36. Parkinson B, Spilker J (1996) Global positioning system: theory and applications, vol 1-2. American Institute of Aeronautics and Astronautics, WashingtonCrossRefGoogle Scholar
  37. Peter J, Huber EMR (2009) Robust statistics. Wiley, New JerseyGoogle Scholar
  38. Raviv Y, Intrator N (1996) Bootstrapping with noise: an effective regularization technique. Connect Sci 8(3–4):355–372CrossRefGoogle Scholar
  39. Realini E (2009) goGPS–free and constrained relative kinematic positioning with low cost receivers. Ph.D thesis, Politecnico di Milano, ItalyGoogle Scholar
  40. Rodríguez A, Ruiz E (2012) Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters. Comput Stat Data Anal 56(1):62–74. doi: 10.1016/j.csda.2011.07.010 CrossRefGoogle Scholar
  41. Salibian-Barrera M, Zamar RH (2002) Bootstrapping robust estimates of regression. Ann Stat 30(2):556–582CrossRefGoogle Scholar
  42. Salibián-Barrera M, Van Aelst S, Willems G (2008) Fast and robust bootstrap. Stat Methods Appl 17(1):41–71CrossRefGoogle Scholar
  43. Shao J (1992) Bootstrap variance estimators with truncation. Stat Probab Lett 15(2):95–101CrossRefGoogle Scholar
  44. Shorack GR (1982) Bootstrapping robust regression. Commun Stat-Theory Methods 11(9):961–972CrossRefGoogle Scholar
  45. Singh K (1998) Breakdown theory for bootstrap quantiles. Ann Stat 26(5):1719–1732.
  46. Stoffer DS, Wall KD (1991) Bootstrapping state-space models: Gaussian maximum likelihood estimation and the Kalman filter. J Am Stat Assoc 86(416):1024–1033CrossRefGoogle Scholar
  47. Sturza M (1988) Navigation system integrity monitoring using redundant measurements. Navigation 35(4):483–501. doi: 10.1002/j.2161-4296.1988.tb00975.x CrossRefGoogle Scholar
  48. Walter T, Enge P (2004) Weighted raim for precision approach. In: Proceedings of ION GPS 1995, ION GPS, Palm Springs, CA, 12–15 Sep1995, pp 1995–2004Google Scholar
  49. Wang J, Satirapod C, Rizos C (2002) Stochastic assessment of GPS carrier phase measurements for precise static relative positioning. J Geod 76(2):95–104. doi: 10.1007/s00190-001-0225-6 CrossRefGoogle Scholar
  50. Willems G, Van Aelst S (2005) Fast and robust bootstrap for LTS. Computational Stat Data Anal 48(4):703–715CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.G. Fortunato UniversityBeneventoItaly
  2. 2.Department of Science and TechnologiesUniversity of Naples ParthenopeNaplesItaly

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