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I have problem with CRS Bosnia and Herzegovina?

MGI 1901 / Balkans zone 6 EPSG:3908
MGI 31276 / Balkans zone 6 EPSG:31276

Which of these two is OK? When I open google sattelite image with openlayers plugin, MGI 1901 match an image, when I change to MGI 31276 vector layer mismatch about 300m. When I import my layers to Global Mapper, datum of vector is "MGI Austria" enter image description here

I need this projection:

enter image description here

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The MGI 1901 projection is ok. The Austrian surveying authority changed their MGI datum in the 1920ies, but the Yougoslav surveying authority did not follow, Hence they still surveyed in MGI 1901. The difference is in the +towgs84 parameters:

 MGI 1901 / Balkans zone 6
 +proj=tmerc +lat_0=0 +lon_0=18 +k=0.9999 +x_0=6500000 +y_0=0 +ellps=bessel +towgs84=682,-203,480,0,0,0,0 +units=m +no_defs

 MGI / Balkans zone 6
 +proj=tmerc +lat_0=0 +lon_0=18 +k=0.9999 +x_0=6500000 +y_0=0 +ellps=bessel +towgs84=577.326,90.129,463.919,5.137,1.474,5.297,2.4232 +units=m +no_defs

The MGI Austria ntv2 grid will be of little help for you, because it is calculated for Austria only. A detailed look into the Balkan CRS can be found here: http://spatial-analyst.net/wiki/index.php?title=MGI_/_Balkans_coordinate_systems

For use in Global Mapper, you find the included datums at http://www.globalmapper.com/helpv12/datum_list.htm. Apart from Hermannskogel, you might try one of the MGI entries.

See also Qgis OSM and layer projection problem

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