Description of Transformation - AT_MGI to ETRS89
AttributeEntry
Operation identifierAT_MGI to ETRS89
Operation identifier alias
CountryAustria
Country identifierAT
Operation valid area
Austria
Operation scopefor applications with an accuracy of about 1.5 m
Source coordinate reference system identifierAT_MGI (X, Y, Z)
Target coordinate reference system identifierETRS89 (X, Y, Z)
Operation version
1996, 84 identical points
Operation method name7 Parameter Helmert Transformation
Operation method name aliasPosition Vector Transformation
Operation method formula
7 Parameter Helmert Transformation,
 |X|   |X|    |Tx|   |  0  -Rz   Ry |   |X|       |X|
 |Y| = |Y| +  |Ty| + | Rz   0   -Rx | * |Y| + D * |Y|
 |Z|   |Z|    |Tz|   |-Ry   Rx    0 |   |Z|       |Z|
    T     S                                S         S

T          ... Target Datum 
S          ... Source Datum 
Tx, Ty, Tz ... geocentric X/Y/Z translations  [m]
Rx Ry, Rz  ... rotations around X/Y/Z axis    [radian]
D          ... correction of scale            [ppm]

see
Boucher, C., Altamimi, Z. (1992): The EUREF Terrestrial 
Reference System and its First Realizations. 
Veröffentlichungen der Bayerischen Kommission für die 
Internationale Erdmessung, Heft 52, München 1992, pages 
205-213 (1) 

REMARKS: in (1) correction of scale D is included in the 
rotation matrix 

******************* Attention *******************
In some transformation applications a different formula 
than the formula above could be in use. The signs and order 
of the rotation parameters are then define differently and 
rotation unit can be arcseconds. For test purposes you can 
find in this information system verification data to check 
your application to get correct results. 
 
Distinguish the following cases:
a) change of signs of rotation (Coordinate Frame Rotation)
   Rx = -Rx
   Ry = -Ry
   Rz = -Rz

b) change of signs and order of rotation 
   Rx = -Rz
   Ry = -Ry
   Rz = -Rx
******************* Attention *******************
Operation method parameters number7
Operation method remarks
The three-dimensional coordinates of (X,Y,Z) of AT_MGI 
were derived under using ellipsoidal heights, which are 
computed from levelling heights related to Molo Sartorio 
(Trieste) and a Geoid related to AT_MGI Datum Hermannskogel 
and Josefstadt in Bohemia 

REMARK: for transformation the (ellip) coord. must refer 
all to Prime Meridian Greenwich 
Operation parameter namegeocentric X translation
Operation parameter value+577.3 m
Operation parameter remarks
Operation parameter namegeocentric Y translation
Operation parameter value+90.1 m
Operation parameter remarks
Operation parameter namegeocentric Z translation
Operation parameter value+463.9 m
Operation parameter remarks
Operation parameter namerotation X-axis
Operation parameter value+5.137"
Operation parameter remarksto be in agreement with formulas the rotation parameter has to be converted to Radians
Operation parameter namerotation Y-axis
Operation parameter value+1.474"
Operation parameter remarksto be in agreement with formulas the rotation parameter has to be converted to Radians
Operation parameter namerotation Z-axis
Operation parameter value+5.297"
Operation parameter remarksto be in agreement with formulas the rotation parameter has to be converted to Radians
Operation parameter namecorrection of scale
Operation parameter value+2.42 ppm
Operation parameter remarks