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

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China Satellite Navigation Conference (CSNC) 2014 Proceedings: Volume II

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 304))

Abstract

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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Acknowledgments

This work is financially supported by Australia cooperative research center for spatial information (CRC-SI) project 1.01 ‘New carrier phase processing strategies for achieving precise and reliable multi-satellite, multi-frequency GNSS/RNSS positioning in Australia’. Large scale simulation in this research is supported by QUT High performance computing facilities. This work is finalized during the first author staying at TU Delft with assistant professor Sandra Verhagen as his host. Valuable comments from Professor Peter J. G. Teunissen in Curtin University improve the quality of the manuscript significantly. All above support is gratefully acknowledged.

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Correspondence to Lei Wang .

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Wang, L., Verhagen, S., Feng, Y. (2014). Ambiguity Acceptance Testing: A Comparison of the Ratio Test and Difference Test. In: Sun, J., Jiao, W., Wu, H., Lu, M. (eds) China Satellite Navigation Conference (CSNC) 2014 Proceedings: Volume II. Lecture Notes in Electrical Engineering, vol 304. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54743-0_26

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  • DOI: https://doi.org/10.1007/978-3-642-54743-0_26

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