Ambiguity Acceptance Testing : A Comparison of the Ratio Test and Difference Test

Wang, Lei, Verhagen, Sandra, & Feng, Yanming (2014) Ambiguity Acceptance Testing : A Comparison of the Ratio Test and Difference Test. In Sun, Jiadong, Jiao, Wenhai, Wu, Haitao, & Lu, Mingquan (Eds.) China Satellite Navigation Conference (CSNC) 2014 Proceedings: Volume II. Springer Berlin / Heidelberg, pp. 313-330.

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Integer ambiguity resolution is an indispensable procedure for all high precision GNSS applications. The correctness of the estimated integer ambiguities is the key to achieving highly reliable positioning, but the solution cannot be validated with classical hypothesis testing methods. The integer aperture estimation theory unifies all existing ambiguity validation tests and provides a new prospective to review existing methods, which enables us to have a better understanding on the ambiguity validation problem. This contribution analyses two simple but efficient ambiguity validation test methods, ratio test and difference test, from three aspects: acceptance region, probability basis and numerical results. The major contribution of this paper can be summarized as: (1) The ratio test acceptance region is overlap of ellipsoids while the difference test acceptance region is overlap of half-spaces. (2) The probability basis of these two popular tests is firstly analyzed. The difference test is an approximation to optimal integer aperture, while the ratio test follows an exponential relationship in probability. (3) The limitations of the two tests are firstly identified. The two tests may under-evaluate the failure risk if the model is not strong enough or the float ambiguities fall in particular region. (4) Extensive numerical results are used to compare the performance of these two tests. The simulation results show the ratio test outperforms the difference test in some models while difference test performs better in other models. Particularly in the medium baseline kinematic model, the difference tests outperforms the ratio test, the superiority is independent on frequency number, observation noise, satellite geometry, while it depends on success rate and failure rate tolerance. Smaller failure rate leads to larger performance discrepancy.

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ID Code: 72583
Item Type: Book Chapter
Keywords: Ratio test, Difference test, Ambiguity acceptance test, Ambiguity validation, Integer aperture estimation
DOI: 10.1007/978-3-642-54743-0_26
ISBN: 9783642547430
ISSN: 1876-1100
Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > DISTRIBUTED COMPUTING (080500)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > GEOMATIC ENGINEERING (090900) > Navigation and Position Fixing (090904)
Divisions: Current > Schools > School of Electrical Engineering & Computer Science
Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2014 Springer-Verlag Berlin Heidelberg
Copyright Statement: The final publication is available at Springer via
Deposited On: 04 Jun 2014 22:26
Last Modified: 14 Dec 2015 04:45

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