5 Transformation parameters from HD-72 Datum to Global Ones

WARNING! Some of the signs on this page has changed after June 2002!!!

a) Parameters of transformation from HD-72 to WGS-72:

The transformation parameters have been derived in 1986 using the coordinates obtained in adjustment of the Hungarian Doppler Satellite Observation Campaign measurements carried out in 1985 (HDOC85) at 12 sites of the Hungarian Network (WGS-72 coordinates), from one hand, and the coordinates existing in HD-72 Datum, from the other hand.
They are as follows:

dX = -61.3 ± 8.5 m
dY = 82.0 ± 7.3 m
dZ = 16.3 ± 9.0 m
= -1.1 ± 0.8 ppm
EZ = -0.9 ± 0.2 arcsec
EY = -0.3 ± 0.4 arcsec
EX = -0.6 ± 0.2 arcsec

= 3.97 m2
= ± 0.37

Correlation matrix
C = 
|   1.0    0.4   -0.6   -0.4    0.0    0.9   -0.5 |
|   0.4    1.0   -0.5   -0.2    0.6    0.5   -0.8 |
|  -0.6   -0.5    1.0   -0.4   -0.1   -0.9    0.6 |
|  -0.4   -0.2   -0.4    1.0    0.0    0.0    0.0 |
|   0.0    0.6   -0.1    0.0    1.0    0.1   -0.2 |
|   0.9    0.5   -0.9    0.0    0.1    1.0   -0.5 |
|  -0.5   -0.8    0.6    0.0   -0.2   -0.5    1.0 |

b) Parameters of transformation from HD-72 to EUREF-89:
For extension of the EUREF-89 reference frame to Central Europe a EUREF-CS/H'91 (EUREF EAST'91) GPS observation campaign has been carried out. Hungary participated in it with observations at 5 terrestrial points of her Survey Control Network. Based on the coordinates of these 5 points adjusted in and referred to the EUREF-89 (as one of the realizations of WGS-84 global system), from one hand, and their HD-72 coordinates, from other hand, the following seven transformation parameters have been derived.

dX = 56.00 ± 5.58 m
dY = -75.77 ± 5.32 m
dZ = -15.31 ± 5.80 m
= 1.01 ± 5.58 0.62 ppm
EZ = 0.21 ± 0.14 arcsec
EY = 0.20 ± 0.22 arcsec
EX = 0.37 ± 0.17 arcsec
= ± 0.251
Degree of freedom: 8

Correlation matrix
C = 
  |  1.00    0.30   -0.51   -0.45   -0.06    0.87   -0.35 |
  |  0.30    1.00   -0.38   -0.17    0.70    0.38   -0.84 |
  | -0.51   -0.38    1.00   -0.49   -0.15   -0.85    0.54 |
  | -0.45   -0.17   -0.49    1.00    0.00    0.00    0.00 |
  | -0.06    0.70   -0.15    0.00    1.00    0.13   -0.24 |
  |  0.87    0.38   -0.85    0.00    0.13    1.00   -0.44 |
  | -0.35   -0.84    0.54    0.00   -0.24   -0.44    1.00 |
The transformation parameters obtained in a) and b) do not reflect the real difference between WGS-72 and EUREF-89 (which is a realization of WGS-84). The probable reason for that is that the height information of the points are of low accuracy.
Computation and confirmation of the final transformation parameters is under consideration.

Formula for transformation: 

|XGlobal|
|YGlobal|
|ZGlobal|
= 
|dX|
|dY|
|dZ|
 + (1 + ) x 
|  1     EZ    EY  |
| -EZ    1     EX  |
|  EY   -EX    1   |
x 
|XHD-72|
|YHD-72|
|ZHD-72|

where

XGlobal , YGlobal , ZGlobal - the coordinates in system WGS-72 or EUREF-89, alternatively,
dX , dY , dZ - origin difference between the two systems (translational parameters),
- scale difference between the two systems,
EX , EY , EZ - rotation around the X, Y, Z axis
XHD-72 , YHD-72 , ZHD-72 - coordinates in the HD-72 system

Source of information:
Joó, I. et al., 1985; Ádám, J., 1987; Official communications (Ádám, J. and Borza, T.); Gubler, E. et al. (eds), 1992; Gubler, E. et al. (eds), 1993; (see Chapter 8).
Signs on this page has been revised by:
Gábor Timár and Gábor Molnár (June, 2002.)
Back to the Description directory of the Hungarian Geodetic Reference
Jump to the Homepage of Department of Cartography and Geoinformatics, E ouml;tv ouml;s University, Budapest