Rigorous and fast constraints transformations at the solution level: case studies for regional and global GNSS networks

authored by: Dimitrios Ampatzidis, Lin Wang, Antonios Mouratidis, Kyriakos Balidakis
Abstract: The study introduces an efficient methodology to perform the transformations between station coordinate and velocity solutions where either minimum or redundant datum constraints have been imposed employing the estimated state vector and the covariance matrix thereof. The analytical methodology presented herein facilitates the datum alignment of large-network solutions, especially for the GNSS technique. The computational complexity reduction is achieved by avoiding the expensive normal equation system reconstruction and the subsequent inversion thereof, which is the current norm, in favor of an elegant approach involving the inversion of an up to 14-order matrix. All information parsed in our algorithm is readily available in the widely used space geodetic solution files following the Solution Independent Exchange (SINEX) format. Our transformation approach is evaluated in two globally distributed GNSS-derived solutions and one terrestrial reference frame with a spatial concentration in South America. The results prove the equivalence of the current and proposed algorithm and that our approach is at least an order of magnitude faster. In addition, we test the Fast Constraints Transformation (FCT) through simulated networks, with a size of up to 5000 stations. The FCT presented here accelerates the transformation by almost 140 times compared to the commonly used strategy.
Type: Article
Journal: GPS solutions
Volume: 26
ISSN: 1080-5370
Publication date: 01.04.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Earth and Planetary Sciences(all)
Electronic version(s): https://doi.org/10.1007/s10291-022-01225-3 (Access: Unknown)
https://link.springer.com/10.1007/s10291-022-01225-3 (Access: Unknown)

BibTeX

@article{763558b971334af985f5230fa6cce579,
title = "Rigorous and fast constraints transformations at the solution level: case studies for regional and global GNSS networks",
abstract = "The study introduces an efficient methodology to perform the transformations between station coordinate and velocity solutions where either minimum or redundant datum constraints have been imposed employing the estimated state vector and the covariance matrix thereof. The analytical methodology presented herein facilitates the datum alignment of large-network solutions, especially for the GNSS technique. The computational complexity reduction is achieved by avoiding the expensive normal equation system reconstruction and the subsequent inversion thereof, which is the current norm, in favor of an elegant approach involving the inversion of an up to 14-order matrix. All information parsed in our algorithm is readily available in the widely used space geodetic solution files following the Solution Independent Exchange (SINEX) format. Our transformation approach is evaluated in two globally distributed GNSS-derived solutions and one terrestrial reference frame with a spatial concentration in South America. The results prove the equivalence of the current and proposed algorithm and that our approach is at least an order of magnitude faster. In addition, we test the Fast Constraints Transformation (FCT) through simulated networks, with a size of up to 5000 stations. The FCT presented here accelerates the transformation by almost 140 times compared to the commonly used strategy.",
keywords = "Constraints, Fast constraint transformation, GNSS network, Least squares adjustment, SINEX, Terrestrial reference frames",
author = "Dimitrios Ampatzidis and Lin Wang and Antonios Mouratidis and Kyriakos Balidakis",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2022",
month = apr,
day = "1",
doi = "10.1007/s10291-022-01225-3",
language = "English",
volume = "26",
journal = "GPS solutions",
issn = "1080-5370",
publisher = "Springer Nature",
number = "2",
}