GPS Solutions

, Volume 14, Issue 4, pp 365–373 | Cite as

A windowing-recursive approach for GPS real-time kinematic positioning

Original article

Abstract

All conventional Kalman filtering methods depend to a great extent on dynamic models for describing the motion state of vehicle. However, low-cost GPS navigation systems do not provide velocity and acceleration measurements to construct dynamic models. Therefore, it is rather difficult to establish reasonable dynamic models. A windowing-recursive approach (WRA) which employs previous positions to predict the current position is proposed, and the transition matrix is modeled for transforming the previous positions to the current one. Two typical transition matrices are constructed by numerical polynomial fitting and extrapolation. A real vehicular GPS experiment is carried out to demonstrate the WRA performances in two relative positioning scenarios. The data are processed by the least squares approach and by WRA using the two developed transition matrices. The results show that the WRA performed excellently in a high sampling rate data. In case of a lower sampling rate, higher-order polynomial fitting and extrapolation models work better than lower-order models for a given window. In addition, the extrapolation models can alleviate the computation burdens significantly relative to the polynomial fitting models.

Keywords

GPS Transition matrix Windowing-recursive approach Kalman filter 

Notes

Acknowledgments

The work is partially sponsored by Natural Science Foundations of China (grant no. 40674003, 40874016), and partially supported by the fund from the Key Laboratory of Advanced Surveying Engineering of SBSM (grant no. TJES0809). The authors are very grateful to the anonymous reviewers for their constructive comments and suggestions.

References

  1. Bruton AM, Glennie CL, Schwarz KP (1999) Differentiation for high-precision GPS velocity and, acceleration determination. GPS Solutions 2(4):7–21CrossRefGoogle Scholar
  2. Chen W, Cross PA (1990) Integration of GPS and an inertial system for precise surveying applications. Surv Rev 30(238):375–395Google Scholar
  3. Cheng P (1999) Remarks on Doppler-aided smoothing of code ranges. J Geodesy 73:23–28CrossRefGoogle Scholar
  4. El-Diasty M, El-Rabbany A, Pagiatakis S (2006) New developments in state estimation for INS/GPS integrated systems. In: ION GNSS 19th international technical meeting of the satellite division, Fort Worth, TXGoogle Scholar
  5. Geng Y, Wang J (2008) Adaptive estimation of multiple fading factors in Kalman filter for navigation applications. GPS Solutions 12(4):273–279CrossRefGoogle Scholar
  6. Hatch R (1982) The synergism of GPS code and carrier measurements. In: Proceedings of the third international geodetic symposium on satellite Doppler positioning, Las Cruces, NM, vol 2, pp 1213–1231Google Scholar
  7. Hewitson S, Wang J (2007) GNSS receiver autonomous integrity monitoring (RAIM) with a dynamic model. J Navig 60(2):247–263CrossRefGoogle Scholar
  8. Huber PJ (1981) Robust statistics. John Wiley, New YorkCrossRefGoogle Scholar
  9. Koch KR, Yang YX (1998) Robust Kalman filter for rank deficient observation models. J Geodesy 72:436–441CrossRefGoogle Scholar
  10. Kuusniemi H, Lachapelle G, Takala JH (2004) Positioning and velocity reliability testing in degraded GPS signal environments. GPS Solutions 8:226–237. doi: 10.1007/s10291-004-0113-7 CrossRefGoogle Scholar
  11. Li BF, Shen YZ, Xu P (2008) Assessment of stochastic models for GPS measurements with different types of receivers. Chin Sci Bull 53(20):3219–3225CrossRefGoogle Scholar
  12. Logan SA, Leahy FJ, Kealy A (2003) Integration of GPS carrier phase and other measurements for kinematic mapping. J Geodesy 76:543–556CrossRefGoogle Scholar
  13. Mao XC, Wada M, Hashimoto H (2002) Nonlinear filtering algorithms for GPS using pseudorange and Doppler shift measurements. In: The IEEE 5th international conference on intelligent transportation systems, SingaporeGoogle Scholar
  14. Mohammed AQ, Robert BN, Washington YO (2006) A high accuracy fuzzy logic based map matching algorithm for road transport. J Intell Transp Syst 10(3):103–115Google Scholar
  15. Moore M, Wang J (2003) An extended dynamic model for kinematic positioning. J Navig 56(1):79–88CrossRefGoogle Scholar
  16. Schwarz KP, Cannon ME, Wong RVC (1989) A comparison of GPS kinematic models for determination of position and velocity along a trajectory. Manuscripta Geod 14:345–353Google Scholar
  17. Singer RA (1970) Estimating optimal tracking filter performance for manned maneuvering targets. IEEE Trans Aerosp Electron Syst 6(4):473–483CrossRefGoogle Scholar
  18. Umar IB, Washington YO, Shaojun F (2007) Integrity of an integrated GPS/INS system in the presence of slowly growing errors. Part I: a critical review. GPS Solut 11:173–181CrossRefGoogle Scholar
  19. Wang J (2000) Stochastic modelling for RTK GPS/Glonass positioning, Navigation. J US Inst Navig 46(4):297–305Google Scholar
  20. Yang Y (2002) Robust estimator for correlated observations based on bifactor equivalent weights. J Geodesy 76:353–358CrossRefGoogle Scholar
  21. Yang Y, Gao W (2005) Comparison of adaptive factors in Kalman filter on navigation results. J Navig 58(3):471–478CrossRefGoogle Scholar
  22. Yang Y, Xu T (2003) An adaptive Kalman filter based on sage windowing weights and variance components. J Navig 56(2):231–240CrossRefGoogle Scholar
  23. Yang Y, He H, Xu G (2001) A new adaptively robust filtering for kinematic geodetic positioning. J Geodesy 75(2):109–116CrossRefGoogle Scholar
  24. Zhang J, Zhang KF, Grenfell R, Deakin R (2006) Short note: on the relativistic Doppler effect for precise velocity determination using GPS. J Geodesy 80:104–110CrossRefGoogle Scholar
  25. Zhou HR, Kumar KSP (1984) A current statistical model and adaptive algorithm for estimating maneuvering targets [J]. AIAA J Guid 7(5):596–602CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Surveying and Geo-Informatics EngineeringTongji UniversityShanghaiPeople’s Republic of China
  2. 2.Key Laboratory of Advanced Surveying Engineering of State Bureau of Surveying and MappingShanghaiPeople’s Republic of China

Personalised recommendations