Print Email Facebook Twitter Best integer equivariant position estimation for multi-GNSS RTK Title Best integer equivariant position estimation for multi-GNSS RTK: A multivariate normal and t-distributed performance comparison Author Odolinski, Robert (University of Otago) Teunissen, P.J.G. (TU Delft Mathematical Geodesy and Positioning; Curtin University of Technology; University of Melbourne) Date 2022 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. Subject Best integer equivariant (BIE) estimationMean squared error (MSE)Multi-GNSSMultivariate normal distributionMultivariate t-distributionReal-time kinematic (RTK) positioning To reference this document use: http://resolver.tudelft.nl/uuid:bd116c48-0a9f-41ba-9925-a7df7f2ecdc4 DOI https://doi.org/10.1007/s00190-021-01591-9 Embargo date 2022-06-20 ISSN 0949-7714 Source Journal of Geodesy, 96 (1), 1-14 Bibliographical note Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type journal article Rights © 2022 Robert Odolinski, P.J.G. Teunissen Files PDF Odolinski_Teunissen2021_A ... sition.pdf 3.02 MB Close viewer /islandora/object/uuid:bd116c48-0a9f-41ba-9925-a7df7f2ecdc4/datastream/OBJ/view