Solution-Level Fast Constraints Transformations with Case Studies for GNSS Networks
- 1Federal Agency for Cartography and Geodesy, Frankfurt am Main, Germany (lin.wang@bkg.bund.de)
- 2EO. Lab., Department of Physical & Environmental Geography, Aristotle University, Thessaloniki, Greece
- 3Earth System Modelling, GFZ German Research Centre for Geosciences, Potsdam, Germany
- 4Now at Department of Surveying and Geoinformatics Engineers, The International Hellenic University, Serres, Greece
The Hermert-like constrain condition is commonly used in various space geodetic reference frame alignment and reference frame definition, this often demands discussions on the proper constrain strength, selection of fiducial network, and more. Thus, the published and constrained reference frame products/solutions are often demanded the transformation to alternative constrain condition due to the area of interest change, reduction of the coverage, or other reasons.
We present an efficient methodology to transform reference reframe product to a posterior selection of the constrained condition from the product which either minimum or redundant datum constraints have been imposed. This analytical methodology significantly reduces the computation effort for datum alignment, especially for the large GNSS network. By avoiding the expensive normal equation system reconstruction and the subsequent inversion thereof, we achieved computational complexity reduction with an inversion of an auxiliary matrix of up to 14X14 dimension, while the computation is validated analytically as well as numerically to the truncation error level. This Fast Constraints Transformation (FCT) method can be conveniently applied to the widely used space geodetic solution files following the Solution Independent Exchange (SINEX) format, especially with our provided software package written in Matlab. We validate and evaluated FCT with two globally distributed GNSS-derived solutions and one South America terrestrial reference frame. The results confirm the numerical equivalence of the classical method and FCT. We also present the discussion on the computation efficiency with the above networks as well as numerical simulations. For the large network of up to 5000 stations, The FCT accelerates the transformation by more than 100 times compared to the classical strategy.
FCT method could serve as a beneficial procedure to many TRF-related applications, including but not limited to:
- Deploy Over Constain condition to an existing solution
- Transforming an Over Constrained solution to a Minimal Constrained solution
- Re-computation of a specified Minimal Constrained solution from an Over Constained or loosely-constrained solution.
- For global networks with a large number of stations the FCT significantly reduces the computation effort.
- For the cases of regional and local TRFs, the methodology shows significant advantages since the final product can be considered an Over Constrain solution.
- FCT could be applied for local and regional networks removing the imposed constraints and deriving the initial GNSS network.
How to cite: Wang, L., Ampatzidis, D., Mouratidis, A., and Balidakis, K.: Solution-Level Fast Constraints Transformations with Case Studies for GNSS Networks, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-10229, https://doi.org/10.5194/egusphere-egu22-10229, 2022.
