GPS Solutions

, 22:39 | Cite as

Position-domain integrity risk-based ambiguity validation for the integer bootstrap estimator

  • Liang Li
  • Haodong Shi
  • Chun Jia
  • Jianhua Cheng
  • Hui Li
  • Lin Zhao
Original Article


Integrity monitoring for ambiguity resolution is of significance for utilizing the high-precision carrier phase differential positioning for safety–critical navigational applications. The integer bootstrap estimator can provide an analytical probability density function, which enables the precise evaluation of the integrity risk for ambiguity validation. In order to monitor the effect of unknown ambiguity bias on the integer bootstrap estimator, the position-domain integrity risk of the integer bootstrapped baseline is evaluated under the complete failure modes by using the worst-case protection principle. Furthermore, a partial ambiguity resolution method is developed in order to satisfy the predefined integrity risk requirement. Static and kinematic experiments are carried out to test the proposed method by comparing with the traditional ratio test method and the protection level-based method. The static experimental result has shown that the proposed method can achieve a significant global availability improvement by 51% at most. The kinematic result reveals that the proposed method obtains the best balance between the positioning accuracy and the continuity performance.


Integrity monitoring Bootstrapping Integrity risk Partial ambiguity resolution 



The authors thank Dr. Gang Liu from Naval Aeronautical and Astronautical University (China) for providing the kinematic GNSS data. This research was jointly funded by National Natural Science Foundation of China (Nos. 61773132, 61633008, 61374007, 61304235), the Fundamental Research Funds for Central Universities (No. HEUCFP201768), and the Post-Doctoral Scientific Research Foundation, Heilongjiang Province (No. LBH-Q15033).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Liang Li
    • 1
    • 2
  • Haodong Shi
    • 1
  • Chun Jia
    • 1
  • Jianhua Cheng
    • 1
  • Hui Li
    • 1
  • Lin Zhao
    • 1
  1. 1.College of AutomationHarbin Engineering UniversityHarbinChina
  2. 2.Academy of Opto-electronicsChinese Academy of SciencesBeijingChina

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