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Best integer equivariant position estimation for multi-GNSS RTK: a multivariate normal and t-distributed performance comparison

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Abstract

The best integer equivariant (BIE) estimator for the multivariate t-distribution was introduced in Teunissen (J Geod, 2020. https://doi.org/10.1007/s00190-020-01407-2), where it was shown that the BIE-weights will be different from that of the normal distribution. In this contribution, we analyze these BIE estimators while making use of multi global navigation satellite system (GNSS) data. The BIE-estimators are also compared to their least-squares (LS) and integer least-squares (ILS) contenders. Monte Carlo simulations are conducted so as to realize controlled performance comparisons of the different estimators for the purpose of multi-GNSS (GPS, Galileo, BDS and QZSS) single-frequency real-time kinematic positioning. The analyses are done in a qualitative sense by means of positioning scatter plots, and in a quantitative sense by means of numerical mean-squared-error (MSE) curves for the different estimators under different model strengths (receiver-satellite geometries and varying degrees of freedom). Particular attention is given to the difference in impact the multivariate t-distribution has when either only its cofactor matrix is in common with the normal distribution or its complete variance-covariance matrix. It will be shown that the BIE-estimators give better MSEs to both the LS- and ILS-estimator when the ILS success rate is different from zero and one, respectively. We also demonstrate that using the same BIE-estimator on different data distributions can give users an unrealistic sense of their solution quality, while the usage of two different BIE-estimators on the same data can have a marginal impact.

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Data Availability Statement

The broadcast ephemerides was used for satellite orbits and clocks. The simulated low-cost receiver observation data are stored at University of Otago, and the School of Surveying data facilities, and can be made available upon request by contacting the corresponding author R. Odolinski by email.

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Authors and Affiliations

  1. School of Surveying, University of Otago, Dunedin, New Zealand

    R. Odolinski

  2. Department of Geoscience and Remote Sensing, Delft University of Technology, Delft, The Netherlands

    P. J. G. Teunissen

  3. GNSS Research Centre, Curtin University of Technology, Perth, Australia

    P. J. G. Teunissen

  4. Department of Infrastructure Engineering, The University of Melbourne, Melbourne, Australia

    P. J. G. Teunissen

Authors
  1. R. Odolinski
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  2. P. J. G. Teunissen
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Contributions

The first author RO performed the research, wrote the manuscript and did the data analysis. PJGT gave feedback on the written manuscript, and wrote some of the theoretical parts, results and conclusions of the paper.

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Correspondence to R. Odolinski.

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Odolinski, R., Teunissen, P.J.G. Best integer equivariant position estimation for multi-GNSS RTK: a multivariate normal and t-distributed performance comparison. J Geod 96, 3 (2022). https://doi.org/10.1007/s00190-021-01591-9

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