Positioning Accuracy Standards for Geodetic Control

Fig. 7: The 95 % point and relative ellipses and confidence
circles
Tab. 1: Positional and Local uncertainty of horizontal
coordinates (95 %)
Station Type To Station Horizontal uncertainties
(mm)
1 Positional 13.8
Local 2 0.7
Local 3 0.9
Local 4 1.2
Local average 0.93
2 Positional 12.9
Local 1 0.7
Local 3 0.9
Local 4 1.2
Local DT13 0.6
Local average 0.85
3 Positional 13.8
Local 1 0.9
Local 2 0.9
Local 4 1.2
Local DT55 0.7
Local average 0.93
4 Positional 16.4
Local 1 1.2
Local 2 1.2
Local 3 1.2
Local average 1.2
R. Paar, G. Novakovic, E. Zulijani – Positioning Accuracy Standards for Geodetic Control
made of steel. The bridge is designed for road and pedestrian
traffic. According to span dimension (100 – 300 m),
this is a big bridge. There are two traffic and two pedestrian
tracks, which are all together 10.5 m wide.
For the bridge reconstruction, the local geodetic network
was established. The network consists of six points
(fig. 6), monumented as shown on figure 5. For surveying
the network, Fast Static GPS method, in combination with
triangulation and trilateration, was used. The heights were
determined by precise differential levelling.
In this paper, calculation of Positional and Local uncertainty
of horizontal coordinates using only terrestrial
data is presented. The survey was connected to existing
control points DT13 and DT55 (fig. 7). During adjustment,
datum values are weighted using one-sigma their Positional
uncertainty. At first, results of a minimally constrained,
least squares adjustment of the survey measurements
are examined (using statistical tests) to ensure correct
weighting of the observations and freedom of outlying
observations (examination of the reliability). After
that, Positional and Local uncertainties of the new points
were determined (table 1).
Point error ellipses were used to compute error circle radii
for Positional uncertainty. Relative error ellipse values
were used to compute error circle radii for Local uncertainty.
The evaluation has been made from each point to
all adjacent points regardless of the direct connections in
the network.
The calculation of Positional and Local Uncertainty of
heights is identical to the method for calculation these values
for horizontal coordinates, except that in stead 95 %
confidence circles the 95 % confidence intervals are used.
From the results, we can conclude that high absolute and
relative precision of the established network were obtained.
4 Conclusion
The quality of geodetic control, which all works within
some project are based on, influences directly the successful
implementation of that project. The positioning precision,
as one of the most important component of geodetic
control quality, has been expressed in various ways depending
on the positioning method. The standards have
been referring to the precision of observations, and not
to the coordinates of geodetic control points. These standards
reflected the distance-dependant nature of terrestrial
surveying error: Triangulation and Traverse – directly
proportional to distance between points; differential levelling
– directly proportional to square root of the distance;
trigonometric levelling – directly proportional to distance
between points and GPS – horizontal: base error
þ directly proportional to distance between points
at 95 % confidence level, vertical: directly proportional
to distance between points.
Since the usage of multiple standards makes the comparison
of the accuracy of the points coordinates obtained
with various measuring methods very difficult, unique
standards have been established for expressing the spatial
data accuracy, and they are defined by international stan-
AVN 7/2009 285