Description of Transformation - HR_HDKS to ETRS89
AttributeEntry
Operation identifierHR_HDKS to ETRS89
Operation identifier alias
CountryCroatia
Country identifierHR
Operation valid area
Croatia
Operation scope
Source coordinate reference system identifierHR_HDKS (X, Y, Z)
Target coordinate reference system identifierETRS89 (X, Y, Z)
Operation version
2000, 120 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 coord. of HR_HDKS were derived under 
using ellip. heights (according to Bessel), wich are 
computed from levelling heights related to the tide gauge 
in Trieste and national geoid (Basic et al, 1999). 

Offical transformation parameters in Croatia refer to 
Coordinate Frame Rotation with different signs of 
rotations. 
Operation parameter namegeocentric X translation
Operation parameter value+551.7 m
Operation parameter remarks
Operation parameter namegeocentric Y translation
Operation parameter value+162.9 m
Operation parameter remarks
Operation parameter namegeocentric Z translation
Operation parameter value+467.9 m
Operation parameter remarks
Operation parameter namerotation X-axis
Operation parameter value+6.04"
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+1.96"
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-11.38"
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-4.82 ppm
Operation parameter remarks