GPS Solutions

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

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

  • Zebo Zhou
  • Yunzhong ShenEmail author
  • Bofeng Li
Original article


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.


GPS Transition matrix Windowing-recursive approach Kalman filter 



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.


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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

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