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GNSS integer ambiguity validation based on posterior probability

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Abstract

GNSS integer ambiguity validation is considered to be a challenge task for decades. Several kinds of validation tests are developed and widely used in these years, but theoretical basis is their weakness. Ambiguity validation theoretically is an issue of hypothesis test. In the frame of Bayesian hypothesis testing, posterior probability is the canonical standard that statistical decision should be based on. In this contribution, (i) we derive the posterior probability of the fixed ambiguity based on the Bayesian principle and modify it for practice ambiguity validation. (ii) The optimal property of the posterior probability test is proved based on an extended Neyman–Pearson lemma. Since validation failure rate is the issue users most concerned about, (iii) we derive the failure rate upper bound of the posterior probability test, so the user can use the posterior probability test either in the fixed posterior probability or in the fixed failure rate way. Simulated as well as real observed data are used for experimental validations. The results show that (i) the posterior probability test is the most effective within the R-ratio test, difference test, ellipsoidal integer aperture test and posterior probability test, (ii) the posterior probability test is computational efficient and (iii) the failure rate estimation for posterior probability test is useful.

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Acknowledgments

Some data in the experiment part are processed based on the “GPSTool” open source Matlab package. We appreciate Professor Takasu for providing this package. This work was financially supported by the National Key Basic Research and Development Program (NOs. 2012CB719902), National Natural Science Foundation of China (No. 41274013 and 41374082).

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Authors and Affiliations

  1. Beijing Satellite Navigation Center, Beijing, China

    Zemin Wu

  2. Department of Navigation, Naval University of Engineering, Wuhan, China

    Zemin Wu & Shaofeng Bian

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  1. Zemin Wu
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  2. Shaofeng Bian
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Correspondence to Zemin Wu.

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Wu, Z., Bian, S. GNSS integer ambiguity validation based on posterior probability. J Geod 89, 961–977 (2015). https://doi.org/10.1007/s00190-015-0826-0

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  • DOI: https://doi.org/10.1007/s00190-015-0826-0

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