is difficult to assume that 7-parameter transformation correctly
describe the differences between the two coordinate systems.
Using a similarity transformation on a large network may not be
appropriate procedure, because it may distort local scale and
orientation in the net, originating mostly from the systemtic
errors in the measuring data reduction to the reference surface.
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Figure 4: Residuals in the astrogeodetic network of Slovenia
after the 7-parameter similarity transformation
The neglection of the impact of the deflection of the vertical to
the measured quantities and neglection of the geoidal heights
are the most common source of the systemtic errors in the
astrogeodetic network. However this type of transformation
gives an overall impresión about the relative point positions in
coordinate systems, and also serve as starting point for the
detailed assessment of the coordinate system.
The 7-parameter similarity transformation of the whole
astrogeodetic network shows the residuals of the transformed
point positions in the amount up to 1 m. The interesting fact is
that the largest residuals occur at the points located on lower
part of the country i.e. at the east and at the south-west.
Residuals of the transformed coordinates are given in Figure 4.
Interpolated displacements in the N-S and E-W directions, are
sketched in Figure 5.
With the 6-parameter coordinate transformation we compare
coordinate systems under the presumption of equal scale in both
systems. Such transformation is not very common procedure,
since coordinate system which should be transformed, results
from different measuring procedures or measuring techniques,
what is also the reason for the need of transformation. In general
it is much easier to accept that different measuring techniques
produce coordinate systems which are rotated, shifted to each
other and of different scale.
Figure 6: Residuals in the astrogeodetic network of Slovenia
after the 6-parameter similarity transformation
The residuals after the 6-parameter orthogonal transformation of
the ETRS 89 coordinate system to the national coordinate are in
the amount to the 2 m.' The residual vectors are now increasing
with the increased distance from the centre of the gravity ot the
network. The residual vectors of the border points at the eastern
and western part of the network exhibit large componets up to 2
m in the E-W direction. Concerning the opposite direction and
the almost parallel direction of the residual vectors at these
points, it is possible to say that the distance between eastern and
western part of the network are for about 4 meters too short. We
can even say that the territory of the Republic of Slovenia, as
presented in the official coordinate system, is for the same
amount i.e. for 4 meters too short in E-W direction, and for
about 2 m too short in N-S direction. Residuals of the 6-
parameter transformation are given in Figure 6.
The residuals in the Fig. 4 and in Fig 6. should be understood as
the discrepancies between official and the true point positions.
The same is valid also for the sketch in Fig. 5.
Figure 5: Interpolated displacements in the astrogeodetic network of Slovenia after the
7-parameter similarity transformation in N-S (left) and E-W (right) direction
with the contour interval 100 mm
At the end we tried to estimate the scale (the unit length) in the
local coordinate system as a function of a position in the
coordinate system. For the scale assessment we formed 37
triangles connecting 27 points in the net. In each triangle the
scale factor was estimated with the similarity 7-parameter
transformation. Scale factor as function of the position in the net