Extension of the DFHRS approach for gravity observations and computation design for a lcm fitted DFHRS of Europe

摘要

The Digital FEM Height Reference Surface - DFHRS - is modelled as a continuous surface in arbitrary large areas by bivariate polynomials p over a grid of Finite Element meshes (FEM). Up to now geoid heights N, deflections of the vertical (x,h) and identical points (h, H), were used as observation groups in a common a least squares computation of the DFHRS parameters p. Geoid models and sets of deflections of the vertical may be parted into different "patches" with individual datum-parameters to reduce the effect of existing medium- and long-waved systematic errors. The resulting DFHRS parameters p uniquely represent the Height Reference Surface HRS. The DFHRS database (DFHRS_DB) provides the separation DFHRS(p|B,L,h) =h-H, to transform ellipsoidal GNSS heights h into physical standard heights H directly. One part of this "DFHRS-correction" consists of the FEM representation of the HRS ("geoid-part") as function of the position (B, L), related to p. In case of significance, an additional "scale part" is introduced as a function of h. Introductionary the presentation gives a general overview about the state of the art of the concept of the Digital Finite Element Height Reference Surface (DFHRS), its standardization in GNSS services and industry, and DFHRS databases computed in different European states. The second part of the presentation is dealing with the further development of the DFHRS approach with respect to the rigorous mathematical approach of an introduction of gravity observations, based on spherical Cap Harmonics Analysis (SCHA). Computation results of the present evaluation of the l_cm gravity data based DFHRS of Saarland and Baden- Wiirttemberg are presented, as well as the present version of the DFHRS-software. Based on the computation results for Saarland and Baden-Wiirttemberg, and following the presentation of a one decimeter DFHRS for Europe on EUREF 2004, the last part of the presentation deals with the computation design for a one centimeter HRS-Europe based on the extended DFHRS approach.