IAG 150 Years pp 305-311

Height System Unification Based on the Fixed GBVP Approach

Conference paper

DOI: 10.1007/1345_2015_104

Volume 143 of the book series International Association of Geodesy Symposia (IAG SYMPOSIA)
Cite this paper as:
Grombein T., Seitz K., Heck B. (2015) Height System Unification Based on the Fixed GBVP Approach. In: Rizos C., Willis P. (eds) IAG 150 Years. International Association of Geodesy Symposia, vol 143. Springer, Cham


In general, any national or regional height reference system is related to an individual vertical datum, defined by one or several tide gauges. The discrepancies of these local vertical datums cause height datum offsets in a range of about ±1–2 m at a global scale. For the purpose of height system unification, global geopotential models derived from homogeneous satellite data provide an important contribution. However, to achieve a unification of high precision, the use of local terrestrial gravity data in the framework of a Geodetic Boundary Value Problem (GBVP) is required. By solving the GBVP at GNSS/leveling benchmarks, the unknown height datum offsets can be estimated in a least squares adjustment. In contrast to previous studies, related to the scalar free GBVP based on gravity anomalies, this paper discusses the alternative use and benefit of the fixed GBVP. This modern formulation of the GBVP is related to gravity disturbances, using the surface of the Earth as boundary surface. In contrast to gravity anomalies, gravity disturbances are not affected by the discrepancies of the local height datum. Therefore, in comparison to a scalar free GBVP approach, the proposed method is not affected by indirect bias terms, which will simplify a height system unification. In this paper, the theory of the fixed GBVP approach is developed and formulas in spherical approximation are derived. Moreover, the method is validated using a closed loop simulation based on the global geopotential model EGM2008, showing mm-accuracy of the estimated height datum offsets.


Height system unification Geodetic boundary value problem (GBVP) Hotine’s integral formula 

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Geodetic Institute, Karlsruhe Institute of Technology (KIT)KarlsruheGermany