Abstract
Although centralized coordinates are applied in geodetic coordinate transformations implicitly or explicitly, the centering strategy has not been comprehensively investigated from the theoretical perspective. In this contribution, we replace the existing universal transformation model with a more compact formulation, where the singular cofactor matrix caused by the model structure is successfully evaded. Furthermore, the developed partition representation of the solution that avoids the numerical difficulty of the non-partition model is more general than any previous partition representation. According to the empirical pre-processing, we further establish two models: the shifting model and the translation elimination model. The former allowing arbitrary shifts in the coordinates of the same kind presents the translational invariance, i.e., the shift can be independent of the original coordinates and the structure of the stochastic model, whereas the latter removes the translation parameters in the pre-adjustment phase by the partial orthogonality of the coefficient matrices, which centralizes the coordinates and changes the stochastic model simultaneously. Test computations with different weight structures show the validity of these strategies.
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Acknowledgements
The authors thank Dr. A. Dermanis for his thoroughly constructive and valuable comments, which help clarify some of the subtle points for the reader's best interest, particularly in the conclusion section. We would also like to thank one additional anonymous reviewer for the many detailed comments. This work was supported by the National Natural Science Foundation of China (42274007; 42174049).
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Hu, Y., Fang, X. & Kutterer, H. Center strategies for universal transformations: modified iteration policy and two alternative models. GPS Solut 27, 92 (2023). https://doi.org/10.1007/s10291-023-01419-3
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DOI: https://doi.org/10.1007/s10291-023-01419-3