Online and postprocessed GPS-heighting based on the concept of a Digital Height Reference Surface (DFHRS)

The DFHRS (Digital-Finite-Element-Height-Reference-Surface) project aims at the conversion of ellipsoidal GPS-heights h into heights H of a standard height system (e.g. orthometric or normal height system) in an online or postprocessed GPS-heighting. The DFHRS is modeled as a continuous surface called NFEM(p,x,y) in an arbitrary large area by bivariate polynomials over an irregular finite element mesh grid. With p we describe the total set of all polynomial coefficients in the meshes, and with x=x(B,L) and y=y(B,L) the metric plan position on the ellipsoid. The continuity of the DFHRS namely its Finite Element Model NFEM(p,x,y) along the borders of neighboring meshes is provided by condition equations C(p). In opposite to e.g. digital terrain models, the nodes of the finite element mesh of NFEM(p,x,y) may differ from the position of the observation data used for the determination of p. The parameters p of the DFHRS are computed in an adjustment procedure based on the observations of geoid heights N-G, deflections of the vertical (xi, eta), terrestrial heights H or height differences DeltaH, and ellipsoidal GPS heights h or height, differences Deltah. Geoid models are adapted by datum parameters d to the DFHRS ("geoid mapping") and above this they may be subdivided into different parts with individual datum parameters ("geoid patching"), in order to reduce their typical long-waved systematic errors. The computed DFHRS database is to be set up in a direct GPS-based online heighting in DGPS networks. No identical points or further transformations are needed. The DFHRS data base provides directly a correction Delta=Delta(B, L, h) to convert the GPS-height h into the standard height H. Examples for computation and use of DFHRS data-bases in DGPS-networks (e.g. SAPOS, Germany) are presented.