We present a local quasi-geoid (QG) model which combines a satellite-only global gravity model with local data sets using weighted least squares. The QG is computed for an area comprising the Netherlands, Belgium, and the southern North Sea. It uses a two-scale spherical radial basis function model complemented by bias parameters to account for systematic errors in the local gravity data sets. Variance factors are estimated for the noise covariance matrices of all involved data sets using variance component estimation. The standard deviation (SD) of the differences between the computed QG and GPS/leveling data is 0.95 and 1.52 cm for the Netherlands and Belgium, respectively. The fact that the SD of the control data is about 0.60 and 1.20 cm for the Netherlands and Belgium, respectively, points to a lower mean SD of the computed QG model of about 0.7 cm for the Netherlands and 1.0 cm for Belgium. The differences to a QG model computed with the remove-compute-restore technique range from −5.2 to 2.6 cm over the whole model domain and from −1.5 to 1.5 cm over the Netherlands and Belgium. A variogram analysis of the differences with respect to GPS/leveling data reveals a better performance of the computed QG model compared to a remove-compute-restore-based QG model for wavelengths >100 km for Belgium but not for the Netherlands. The latter is due to the fact that at the spatial scales resolved by the global gravity model, variance component estimation assigns significantly lower weights to the local data set in favor of the global gravity model.@en

Real-time orbit and clock corrections to GPS broadcast ephemeris, in short broadcast corrections (BCs), have become available as International GNSS Service (IGS) products through the IGS Real-time Service (RTS) in 2013. The BCs are distributed via the Network Transport of RTCMby Internet Protocol (NTRIP) according to RTCMState Space Representation standards. When applying the BCs in real-time Precise Point Positioning (PPP), user positions with sub-decimetre precision after convergence can be obtained. The IGS BCs refer to the International Terrestrial Reference Frame 2008 (ITRF2008). BCs in regional reference frames (RBCs) are available through regional NTRIP broadcasters in Europe, North-America, South-America and Australia. The IGS RTS website states that: Applying orbit and clock corrections from regional product streams in a real-time PPP solution automatically leads to regional coordinates. The PPP client would not need to transform coordinates because that is already done on the server side. However, in contrast to the PPP-approach that uses BCs in ITRF2008 followed by a transformation to the local datum, the approach based on RBCs causes a bias in the PPP solution due to the scale factor between regional and global reference frames. This scale induced bias is satellite geometry dependent when the conventional 14-parameter transformation from the global to the regional reference frame is applied to the satellite position vectors in ITRF2008, to derive the RBCs from the IGS BCs. The size of the scale induced bias is significant. The bias is up to 8 cm for the Australian GDA94 and up to 0.5 cm for the North American NAD83. Currently an additional satellite position dependent value is added to the satellite clock correction to deal with the scale induced biases of three RBCs, resulting in a transformed clock correction (Weber, BKG Ntrip Client (BNC) Version 2.9 – Manual, 2013). Applying these transformed clocks results in a remaining scale induced bias of less then 10mm for each RBC of ETRF2000, NAD83 and SIRGAS2000. For GDA94 the remaining scale induced bias is maximum 30 mm, this is caused by the large scale factor of GDA94 compared to other regional reference frames. This contribution will show that the remaining bias in the PPP solution is practically independent from satellite geometry and depends mainly on the user position; hence the remaining bias can be predicted and corrected for at any location.@en