4.6 The correction grid (GSB)

These datum transformation methods, discussed in the above points, however, provide enough accuracy for GIS applications, are not capable for high-precision geodetic-engineering purposes. Even the BW-method can transform between the modern triangulation based datums and the WGS84 only with a remaining error of half meter in a region like Hungary. The survey geodesy needs much higher accuracy: ten centimeters inside cities and villages and 20 centimeters outside the settlements. Therefore, the standard geodetic applications use higher order (in the Hungarian practice, e.g. fifth-order) polynomials for the calculations. Similar accuracy can be obtained using BW-transformations based on only the base points in the vicinity of our study area.

However these applications are accurate enough, they have a considerable hindrance. There is no way to define, therefore, apply them in GIS packages. These software items usually do not support these methods, we can not define them by parameter input. The BW-parameter grid (a seven-channel image, each channel containing the different BW-parameters, changing from place to place) can be used in some GIS packages, but its definition is quite difficult. There is, however, an application, whose definition is easier and is supported by many packages, including the open-source ones (e.g. the GDAL-based Quantum GIS). This is the correction grid, which is often referred to as, according to its standard file extension, Grid Shift Binary (GSB).

Similarly to the AM- and BW-methods, this does conversion between geodetic coordinates on different datums. The correction grid itself is a grid, which is equidistant along the meridians and parallels. The eastward and northward shift between the two datums should be given at their crossings, in arc seconds. We can give, if we know it, the errors of the shifts at all grid points. However, it is not compulsory, if the errors are unknown, we can simply give zeroes for these data fields. The real shift values are derived from horizontal base points, whose coordinates are known in both the source and the target datums. The eastward and northward (or, with negative sign: westward and southward) shifts are handled separately: we construct two (or, with the error grids: four) different grids. The shifts, read in the base points, are interpolated at the pre-set grid points, in both grids.

Fig. 19. The header of the GSB data. The first 11 rows is the general header, the next 10 rows refer to the subset extents, then follows the number of data points and the point shift and error data itself.

These grids, combined with their meta-data (e.g. resolution, extents; Fig. 19) should be converted into a binary file. The file can contain even more grids, with different resolution. Therefore we can define a correction dataset providing higher accuracy in some important regions, while we have a general transformation with unified accuracy for a larger area.

It shall be underlined again that the correction grid provides connection directly between the coordinates in the source and the target datums. Neither the AM-, nor the BW, nor any other conversions should be used; applying the grid makes all of them unnecessary. The GSB-method aims the accuracy of a few centimeters in case of transformation between modern networks. It can also provide surprising accuracy also at geo-referencing of historical maps, if the control point network is sufficiently dense and properly selected (Fig. 20).

Fig. 20. The GSB technology provides excellent fit of old maps to new ones (center of Budapest in a 18th century map; note that the east bank of the river was considerably far from the other bank int hat time).