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

Robert Odolinski*, P.J.G. Teunissen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
26 Downloads (Pure)


The best integer equivariant (BIE) estimator for the multivariate t-distribution was introduced in Teunissen (J Geod, 2020., 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.

Original languageEnglish
Article number3
Pages (from-to)1-14
Number of pages14
JournalJournal of Geodesy
Issue number1
Publication statusPublished - 2022

Bibliographical note

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  • Best integer equivariant (BIE) estimation
  • Mean squared error (MSE)
  • Multi-GNSS
  • Multivariate normal distribution
  • Multivariate t-distribution
  • Real-time kinematic (RTK) positioning


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