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GNSS best integer equivariant estimation using multivariant t-distribution: a case study for precise point positioning

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Abstract

A key prerequisite for fast and reliable solution convergence time in precise point positioning with ambiguity resolution is the successful determination of the initial integer ambiguity parameters. In this contribution, a reliable approach of partial ambiguity resolution based on the BIE using the t-distribution (BIE-td) is proposed and compared against existing algorithms, such as the partial ambiguity resolution-based LAMBDA method (PAR-Ps) and the iFlex method proposed by the Trimble Navigation company. A 31-day set of GNSS measurements, collected in 2018 from 17 globally distributed GNSS continuously operating reference stations (CORS), were processed to determine the best-fit distribution for the GNSS measurements. It is found that the t-distribution with three degrees of freedoms provides a better fit compared to the Gaussian distribution. The authors then propose a method for selecting the integer ambiguity candidates when using the BIE-td approach. This method is based on the differences of unknown parameters of interest (i.e. receiver’s coordinates) determined at two consecutive processing steps. Finally, another 30-day set of GNSS measurements, collected in 2019 from the same CORS, confirm that the iFlex method outperforms the PAR-Ps method in the sense of minimizing the position errors of a simulated kinematic test. In particular, compared to the PAR-Ps method for 99th percentile of errors, the iFlex method has an improved convergence time of about 10 min. In addition, the positioning performance using the BIE-td and iFlex methods is comparable, with a similar positioning accuracy for both horizontal and vertical coordinate components.

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Data availability

RINEX observation data from IGS stations and the precise satellite orbits and satellite clocks are real-time streamed using a modified version of the RTKLIB software, with a username and password obtained by Geoscience Australia. The satellite’s phase- and code-biases were obtained from the online archive of the Centre National d’Etudes Spatiales (CNES), http://www.ppp-wizard.net/products/. The open source software RTKLIB for GNSS measurement processing is available at http://www.rtklib.com/.

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Acknowledgements

Geoscience Australia and the IGS are acknowledged for providing the GNSS data as well as satellite orbit and clock corrections. The Raijin-NCI National Computational Infrastructure Australia is acknowledged for providing high-performance research computing resources for GNSS data processing. The authors thank Dr. Simon Banville for valuable discussions and encouragement in relation to this research. The contribution of Dr. Safoora Zaminpardaz for improving the theoretical part and reviewing the manuscript is greatly appreciated. The first author is supported by the Australia Award Scholarship Scheme to pursue a Ph.D. at the RMIT University, Melbourne, Australia.

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Authors and Affiliations

  1. School of Science, RMIT University, Melbourne, VIC, 3001, Australia

    Viet Duong, Ken Harima & Suelynn Choy

  2. School of Civil and Environmental Engineering, UNSW, Sydney, NSW, 2052, Australia

    Chris Rizos

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  1. Viet Duong
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  2. Ken Harima
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V. Duong designed the research, processed and analysed data and wrote the paper. K. Harima, S. Choy and C. Rizos advised the first author, and reviewed and improved the manuscript.

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Correspondence to Viet Duong.

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Duong, V., Harima, K., Choy, S. et al. GNSS best integer equivariant estimation using multivariant t-distribution: a case study for precise point positioning. J Geod 95, 10 (2021). https://doi.org/10.1007/s00190-020-01461-w

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