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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B6. Istanbul 2004 
  
points also have to be changed after such an operation. 
Consistency is the goal, thus all old surveys must be converted 
to the new situation after an overall network adjustment. 
6.2 Transformation Parameters 
As private companies are in charge of cadastral surveying, they 
compute their own transformation parameters, in order to 
transform the coordinates of the parcels from WGS84 to local 
coordinate system. Those are computed based on common 
points in both systems (only in planimetry). This is acceptable 
within the project, but as the neighbouring project (North, 
south, West or East of the current project) is executed by 
different companies, there are some discrepancies between 
different sets of parameters computed by different companies. 
Example of different transformation parameters; 
Transformation parameters of company A, using Leica GPS 
receivers; 
Type of transformation: One step 2D Helmert transformation. 
Ellipsoid A WGS84, 
Ellipsoid B: unknown 
x 00371 
Yo -0.0422 
Shift dX = 60028.7678 m 
Shift dY ^ -3937.0827 m 
Rotation about Z = -647939.2824" 
Scale diff= -6.9260 ppm 
Transformation parameters of company B, applying Trimble 
GPS receivers; 
X, = -10336.893 
Yi. 7 :63263 405 
Translation East = -3.016 m 
Translation North- -1.236 m 
Rotation about Z = 0° 00 03.674219 " 
Scale factor = 0.99999236 
6.2.1 Solution: It is proposed that the mapping organization 
should take the responsibility of computing a unique set of 
parameters, to be published and applied by different companies, 
in this way, the coordinates would be homogenous after 
transformation to the local system. 
Basically there are 2 solutions for coordinate transformation; 
i- Geodetic rigorous transformation in 2 steps; 
Step 1- Change of ellipsoid 
As stated before the reference ellipsoid of Namibia is Bessel 
defined by; 
a = 6 377 397.155 
b = 6 356 078.963 
(1-e2) = 0.993 352 627 8 
e? = 0.006 674 372 231 
Vf — 1/299.152 8128 
There are 3 Bessel ellipsoids, with the following characteristics; 
Bessel 1841 
a7 6377397.155, 1/f= 299.1528128 
Bessel 1841 (Japan By Law) 
a = 6377397.155, 1/f= 299.152815351 
Bessel 1841 (Namibia) 
a = 6377483.865, 1/f = 299.1528128 
The difference is probably a matter of the units used: The 
flattening is the same for the European and the Namibian one, 
while the semi major axes have a ratio, which is identical to the 
ratio between the “Legal” meter and the International meter. 
Apparently the European Bessel is the same as Namibian 
Bessel, where the semi major axis is expressed in Legal meter 
It should be checked and a unique ellipsoid used by everyone. 
In Namibia there are only 3 shifts applied for transformation 
from WGS84 to Bessel 1841, namely; 
Shift X = -616 m 
Shift Y = -97 m 
Shift 2 = 251 m 
And for transformation from WGS84 to Bessel 1841 
(Namibia); 
Shift X = -615.64 m 
Shift Y = -102.08 m 
Shift Z = 255.81 m 
The Namibian mapping authorities should select the proper one 
to apply. Moreover they should compute also Rotation around 
X-axis, Rotation around Y-axis, Rotation around Z-axis, as 
well as scale factor, in order to have a unique set of parameters 
for the mapping organization, as well as all private companies. 
Step 2. 
The projection parameters should be defined per zone, 
according to the central meridian of the zone. 
ii- One step 3D transformation. 
The second solution consists of computing the transformation 
parameters (10 in case of Molodensky Badekas, and 7 in case 
of Bursa Wolf) per zone to transform directly from WGS84 to 
local projected coordinate system of the zone. 
Next the existing coordinate, surveyed previously, should be 
adjusted to new situation 
6.3 Cadastral surveying 
Cadastral surveying projects carried out by private companies 
are based on RTK. A copy of the report, including coordinate 
list is submitted to the organization. The cadastre authorities 
then check the coordinate of some checkpoints. If discrepancies 
are within the tolerance, then the project is accepted; otherwise 
in some cases they request repeating the surveying.