The use of the solution of the Geodetic Boundary Value Problem to the national linkage to an International Height Reference System: a conceptual review
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Abstract
The need to obtain heights with physical meaning is of great importance for engineering and, in a unique way, for Brazilian Army; this is because, historically, Brazilian Army acts in striking engineering interventions in the most varied corners of the national territory, which depend directly on the reliable determination of these heights. In this sense and for these purposes, there is a latent need to establish a vertical reference system in a national level with a strong physical base, fully linked to a global system with the same characteristics and according to current trends in the field. As recommended by the International Association of Geodesy (IAG), the state-of-art of altimetric determinations and vertical reference systems has, as its guideline, the search for the definition of an International Height Reference System (IHRS). This definition must be made by taking as reference an equipotential surface of Earth's gravity field with pre-defined geopotential value, and its primary vertical coordinates being defined based on a geopotential difference. In turn, the calculation of this geopotential is carried out, modernly, through the solution of the Geodetic Boundary Value Problem (GBVP) by different approaches, such as free and fixed scalar forms, each with advantages and recommendations. Thus, the present paper presents a conceptual review on these different techniques for the GBVP solution, evidencing variants and limitations, emphasizing also the benefits received for the Brazilian Army.
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