Positioning Accuracy Standards for Geodetic Control

R. Paar, G. Novakovic,
E. Zulijani
In diesem Artikel wird ein kurzer Überblick der
Entwicklung internationaler Normen gegeben,
die zur Beurteilung geodätischer Referenzsysteme
dienlich sind. Heutzutage werden internationale
Normen verwendet, die auf dem Gebiet
raumbezogener Informationssysteme vorgeschrieben
sind (ISO 19113). Nach diesen Normen
werden zwei Typen raumbezogener Genauigkeiten
unterschieden: absolute und relative, beide
jeweils in zwei getrennten Komponenten: der
horizontalen und vertikalen.
Introduction
Modern rapid development of science and technology is
affecting the geodetic profession, both in the field of measuring
equipment as well as the methods of collecting,
processing, and managing the data. The expectations
and demands of users are also increasing, which leads
to the requested data, their quality, processing methodology
and other characteristics being clearly indicated. In
various fields of measuring technique, the uniqueness
has been tried to introduce in the manner of indicating
measuring information. The most important part of measuring
information is, beside the measurement result, the
quality of that result. The quality of data is the basic characteristic
according to which a user picks them up for his/
her needs. Since all geodetic works contained in some project
task lean on geodetic control points, their quality will
directly influence the quality of the works performed.
The main two elements of geodetic network quality are its
precision and reliability. In statistic, precision characterizes
the degree of mutual agreement among a series
of individual measurements, and only indicate spread
or dispersion of the random errors. The network reliability
refers to the ability to detect systematic errors (biases) and
blunders and to the effect that undetected blunders may
have on parameters – the coordinates of the points in
the network and their functions. This paper presents
only standards (not measures) for reporting the precision
of geodetic control positioning, prescribing by international
standards in the field of geospatial information that
have been accepted as European, i.e. Croatian standards.
Traditionally, the precision of positioning (horizontal and
vertical) of geodetic control has been expressed in various
ways. The standards have referred to the precision of measurements
and not to the position, i.e. the coordinates of
the points. In accordance with the development of mea-
Positioning Accuracy
Standards for Geodetic
Control
suring technology, these standards have been changing
as well. There have no unique standards that could be applied
regardless of the positioning method. Mostly, the old
standards have been using the expression dependant on
the distance between geodetic control points. However,
it has been revealed that the usage of multiple standards
makes it difficult to compare of the precision of coordinates
obtained by various measuring methods. Apart from
that, these standards are no longer appropriate in the age
of GNSS and GIS when it has become necessary to indicate
the positional accuracy of spatial data, which is required
in the process of establishing Spatial Data Infrastructure
(SDI) on national and global level. Hence, single
standards for reporting the positional accuracy (horizontal
and vertical) of individual points have been defined by
means of international standards. Since these standards
do not depend on the method of geodetic control positioning,
i.e. of the development of measuring technology, it is
reasonable to believe, that they will not be change so
quickly in the future. Although those standards are referring
primary on the points of the national reference geodetic
networks, they can be used for every positioning project
connected with the control points of known coordinates.
In this paper, current standards for reporting the positional
accuracy will be presented on the example of local
geodetic network established for the reconstruction of
Maslenica Bridge located near city Zadar in Croatia.
2 Development of the positioning accuracy
standards for geodetic control
The traditional method of establishing a horizontal geodetic
control (triangulation) was relatively straightforward.
It remained mostly unchanged (except small improvements
in instrumentation) from the end of 18 th century until
the development of electronic distance-measurement in
the 1950s. Triangulation networks were established in a
hierarchical manner, i.e. different levels of accuracy
were referred to as the „order“ of a point. The criteria referring
to individual network order have mostly defined
the allowed tolerance connected with measurement,
used instruments, the way of stabilisation etc. and not
to the position, i.e. coordinates of the points.
The first significant technological advance came with the
introduction of Electronic Distance Measurement (EDM)
in the 1950s, which increased speed and accuracy of surveying.
In some countries (e.g. USA) the accuracy standard of
classical triangulation network surveys has been described
by a proportional standard, which reflected the
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distance-dependant nature of terrestrial surveying error
(e.g. it has been prescribed that the First-order network
has got a minimum distance accuracy 1:100000. Distance
accuracy is the ratio of the relative positional error of a
pair of control points to the horizontal separation of those
points). The distance accuracy pertains to all pairs of
points. The worst distance accuracy (smallest denominator)
is taken as the accuracy for classification (FGCC
1984). Hence, the accuracy of coordinates of individual
points in the network has not been determined, but the order
of the entire network. The same concept was valid for
vertical networks. The accuracy standards have been referring
to the accuracy in determining height differences
(not to the bench mark heights) and they have been proportional
to distance: for differential levelling directly
proportional to square root of distance, and for trigonometric
levelling directly proportional to distance between
points.
The second, more significant technological advance has
been the development of Global Positioning System
(GPS) – an order of magnitude more precise (for horizontal
positioning) than the data obtained from earlier classical
methods. The accuracy of GPS surveys, being less
distance dependant requires different accuracy standards.
Since the previous survey standards were not adequate for
classifying high precision GPS survey, a new system of
classification has been adopted. In some countries, new
network orders are introduced and new standards set
that are valid only for GPS-positioning (e.g. USA, Australia).
Accuracy standards for GPS are expressed in terms of
maximum allowable base error and line-length error for
relative position (e.g. for B-order the allowed relative position
of a single points as related to some other is
8mm þ 1 ppm-minimum geometric accuracy standard
at the 95 % confidence level, FGCC 1988). The network
order has been determined, similarly as with triangulation,
according to the baseline in the network that has the smallest
relative accuracy. It must be emphasised that new, statistical
concept for reporting the results at defined confidence
level is applied here.
The use of multiple standards created difficulty in comparing
the accuracy of coordinate values obtained by different
survey methods. So, the new methodology for reporting
the accuracy of horizontal and vertical coordinate
values has been introduced, which is independent of positioning
methods. These criteria are contained in the standards
referring to the field of geospatial information.
2.1 Standardisation of geospatial data
There are various standard components for geodetic data
(NGS 2002). One of the components refers to the quality
standards. These are the accuracy standards and operational
standards for data collection. The criteria for positioning
accuracy reporting are prescribed by the standards
ISO 19113, ISO 19114 and ISO 19115, that have been accepted
as European, i.e. Croatian standards. ISO Standard
19113: Geographic Information – Quality principles defines
a data quality model and identifies Positional accuracy
as one of a spatial data quality element with two sub
elements: absolute or external accuracy and relative or
R. Paar, G. Novakovic, E. Zulijani – Positioning Accuracy Standards for Geodetic Control
internal accuracy. They express the quantitative information
about data quality. Positional accuracy (absolute and
relative) have to be reported for both horizontal and vertical
component of position.
Hence, when reporting the precision of geodetic control
positioning, two types of precision should be reported
in accordance with the mentioned standard: absolute
and relative, both for horizontal coordinates and for
height. These types of precision should be clearly defined
and their calculation explained.
Here is a comment referring to terminology. This standard
prescribes that absolute or relative accuracies are expressed
quantitatively (associate a number). This is not
in accordance with the definitions in Guide to the expression
of uncertainty in measurement (ISO 1995). In Appendix
D, article D.1.1.1 comment 2, is stated: Because „accuracy“
is a qualitative concept, one should not use it
quantitatively, that is, associate numbers with it; numbers
should be associated with measures of uncertainty instead.
Thus, one may write, „the standard uncertainty is 2 cm“
but not „the accuracy is 2 cm.“
Many countries, in their national accuracy standards for
geodetic control positioning, use different terms for reporting
absolute and relative accuracies, but they refer
to mentioned ISO standard. For example, in USA and Canada
these terms are Network accuracy (absolute accuracy)
and Local accuracy (relative accuracy). According
to definitions in GUM (ISO 1995), much more appropriate
are notation accepted in Australia: Positional uncertainty
(absolute) and Local uncertainty (relative). In Hungary,
the accepted terms are Positional accuracy (absolute)
and Positional precision (relative) (INSPIRE 2004). In
Croatia, these terms are not defined yet (Novaković
2006), so in our paper we will use the terms accepted
in Australia: Positional and Local uncertainty.
3 Geospatial positional accuracy standards
for geodetic control
Using various statistical methods, it can be created many
different position accuracy measures. The position is fundamentally
three dimensional, but not everyone is interested
in obtaining three-dimensional accuracy. One user
might care about horizontal accuracy, another might
want vertical. Thus, we must consider different 1-D, 2-
D or 3-D accuracy measures (statistics). Statistics can
have varying confidence levels and each of them has
its certain importance for particular applications. Each
of those measures provides an indication of the spread
or dispersion of the set of estimates about their mean
or expected value, reflecting the random error in the repeated
measurements, so, in fact, they provide an indication
of precision or repeatability.
The most commonly used linear measures (1-D) are 1-r
standard deviation (68.27 % probability) and 95 % Probability/Confidence
(95 % probability), typical used for expressing
the precision of vertical component of position.
In 2-D case (horizontal components of position), commonly
used measures are: 1-r Standard Error Circle
(39 % probability), Circular Error Probable (CEP)
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R. Paar, G. Novakovic, E. Zulijani – Positioning Accuracy Standards for Geodetic Control
(50 % probability), 95 % 2-D Positional Confidence Circle
(95 % probability), 2-Dev. Root Mean Square
(2DRMS) (95 – 98 % probability). In 3-D case, those measures
are: 1-r Spherical Standard Error (19.9 % probability),
Spherical Error Probable (SEP) (50 % probability),
95 % 3-D Confidence Spheroid (95 % probability) and
many others (EM 1110-1-1003, Diggelen 1998). GPS positional
accuracies are normally estimate and report using
root mean square (RMS) error statistic. The probability
associated with rms depends on whether one is using
rms in one, two, or three dimensions.
According to ISO standards, the geospatial positional uncertainty
shall be reported separately in two components:
horizontal and vertical. Reporting standards are a circle
for horizontal uncertainty and a linear value for vertical
uncertainty, both at specified confidence level (FGDC
1998, ICSM 2004) (fig. 1). It is accepted that the confidence
level for reporting the uncertainty of geodetic control
position is 95 %.
Horizontal: The reporting standard in the horizontal component
is the radius of a circle of uncertainty, such that
true or theoretical location of the point falls within that
circle, at the 95 % confidence level.
Vertical: The reporting standard in the vertical component
is a linear uncertainty value, such that true or theoretical
location of the point falls within the sum of the positive
and negative ranges of that linear uncertainty value, at the
95 % confidence level.
In Canada, instead of confidence circle, the uncertainty
region is confidence ellipse and reporting standard is
the values of the semi-major axes (GSD 1996).
Since the Positional accuracy consists of two sub-elements:
absolute and relative accuracy (ISO 19113), the
quantitative indication of the quality of coordinates (horizontal
and vertical) requires two criteria to be defined
and indicated. These are:
Positional Uncertainty of a control point is the value that
represents the uncertainty in the coordinates of the control
point with respect to the geodetic datum, at the 95 % confidence
level.
Geodetic datum is expressed by the geodetic value of
the control points that define national reference system.
For horizontal coordinates, the Positional uncertainty
of a point is the radius of the 95 % confidence circle.
For vertical coordinate, the Positional uncertainty of
Fig. 1: Standards for
positional uncertainty
a point is the 95 % confidence interval. Positional uncertainty
measures how well coordinates approach an
ideal, error-free datum. Positional Uncertainty can be
computed for any positioning project that is connected
to the national reference network.
Local uncertainty of a control point is a value that represents
the uncertainty in the coordinates of the control point
relative to the coordinates of other directly connected, adjacent
control points at the 95 % confidence level. The reported
Local Uncertainty is an approximate average of the
individual local uncertainty values between this control
point and other observed control points used to establish
the coordinate of the control point. Extremely high or low
individual local uncertainties are not considered in computing
the average Local uncertainty of a control point.
For horizontal coordinate, the Local uncertainty of a
point is computed using an average of the radius of
the 95 % relative confidence circle, between the point
and other adjacent points. For vertical coordinate,
the Local accuracy of a point is computed using an average
of the 95 % relative confidence intervals between
a point and other adjacent points.
Positional and local uncertainties are fundamentally similar
concepts. Local uncertainty describes positional uncertainty
between adjacent points, and Positional uncertainty
describes the positional uncertainty between a point and
the national reference network. Used together, it is possible
to estimate uncertainties between points not directly
measured, or compare positions determined from two separate
surveys (TxDOT 2005).
Additionally, the Positional and Local uncertainty may be
classified by comparing the radius of the 95 % confidence
circle for horizontal coordinate uncertainty, and the 95 %
confidence interval for vertical uncertainty, against a set
of standards (accuracy classes). Namely, in the process of
establishing the National Spatial Data Infrastructure
(NSDI), all spatial data (as well as geodetic control points)
are classified into individual precision classes. In some
countries, the organisations for standardisation or other
authorized institutions have officially prescribed the classification
into classes, as e.g.: USA – 13 classes (> 1mm
– 10 m) (FGDC 1998), Australia – same as USA, Canada
– 14 classes (1 cm–200 m) (GSD 1996), Mexico – 1 cm –
500 m (HANSEN ALBITES 2005).
3.1 Computation of the Positional and Local
uncertainty of the geodetic control points
The Positional and Local uncertainty (horizontal and vertical)
of each point in the network can be computed using
elements of a global variance-covariance matrix of the adjusted
parameters (coordinates), produced from a least
squares adjustment. This matrix contains the following information:
– standard deviations of the estimated parameters
– correlations between the parameters
– absolute or point error ellipses (or ellipsoids)
– line or relative error ellipses (or ellipsoids).
The global cofactor matrix of the coordinates can be partitioned
into block sub-matrices representing the cofactor
matrix for each station and the cofactor matrix between
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pairs of stations. The elements of absolute and relative
ellipses can be computed using elements of corresponding
sub-matrices (KUANG 1996, PELZER 1985).
3.1.1 Vertical coordinate uncertainty computation
The statistic used to represent the Positional and Local
uncertainty of the height of the point is the 95 % confidence
interval (fig. 1).
Positional uncertainty
The standard deviation, derived from the covariance matrix
of the estimated parameters, represents the one-sigma
Positional uncertainty of the adjusted height at the point.
The statistic used to represent the Positional uncertainty of
the vertical coordinate (height) of the point is the 95 %
confidence interval (fig. 1). To obtain the 95 % confidence
interval, the standard deviation is scaled by 1.96.
Local uncertainty
Local uncertainty at the point is based upon an average of
the individual local uncertainties (or relative uncertainties)
between that point and other adjacent points. The
standard deviation of the height difference between two
points can be derived from the covariance matrix of the
estimated parameters. To obtain the 95 % confidence interval,
the standard deviation of the height difference is
scaled by 1.96.
3.1.2 Horizontal coordinate uncertainty computation
The statistic used to represent the Positional and Local
uncertainty of the horizontal coordinates of the point is
the radius of the 95 % confidence circle (fig. 1). The radius
of the 95 % confidence circle can be computed using the
elements of standard error ellipse.
The „absolute“ or „point“ error ellipse gives the confidence
region of the coordinates of a single point with respect
to the constraining stations. The „relative“ or „line“
ellipses indicate the precision of any point in a network
relative to another point in that network. The equations
for computation the size and orientation of absolute
and relative ellipses are well known and published in
many textbooks and publications (e.g. PELZER 1985, CASP-
ARY 2000, KUANG 1996, WOLF, GHILANI 1997). Thus, the
Positional uncertainty of the point should be computed
using absolute or point error ellipse, and Local uncertainty
should be computed using line or relative error ellipses.
Fig. 2: The 95 % confidence ellipse and circle
R. Paar, G. Novakovic, E. Zulijani – Positioning Accuracy Standards for Geodetic Control
Positional uncertainty
Once the standard (point) error ellipse is available, the radius
r of the 95 % confidence circle (fig. 2) is approximated
by (LEENHOUTS 1985, GSD 1996, ICSM 2004):
r ¼ Kpa
where
Kp ¼ 1:960790 þ 0:004071 C þ 0:114276 C 2 þ 0:371625 C 3
C ¼ b=a
and
a semi-major axis of the standard error ellipse
b semi-minor axis of the standard error ellipse.
It must be noted that the coefficients in the above expression
are specific to the 95 % confidence level, so that the
radius of the 95 % confidence circle is obtained directly.
The radius of a 95 % circle of uncertainty is produced by
many least squares adjustment software (e.g. Trimble Total
Control).
In Canada, instead of the confidence circle, the statistics
for reporting the uncertainty of horizontal position is the
95 % confidence ellipse (fig. 2). The standard ellipse representing
the one-sigma Network accuracy (Positional
uncertainty) of the adjusted horizontal coordinates at a
point. To convert the standard ellipse to a 95 % confidence
ellipse the computed values of a and b must be multiplied
by the appropriate expansion factor (this factor is 2.45 for
adjustment with high degrees of freedom). The major
semi-axes of the 95 % confidence ellipse represent the
Network accuracy of a point (GSD 1996). It is not necessary
directly connect control point to a national reference
network to compute its Positional uncertainty. It is necessary
that the survey be connected to existing control points
with known Positional uncertainty values. Standard error
ellipse used to calculate Positional uncertainty might be
obtained by one of the following methods (ICSM 2004):
– Rigorous least squares adjustment of all observations
linking the point in question back to the national geodetic
datum. This would only be done as part of a national
adjustment, in which case the error ellipses for all
points in the adjustment would be available.
– A statistical combination of the chain of error ellipses
obtained from each level of the adjustment process,
down to the point in question.
– By constraining the control in the local least square adjustment
to the known error ellipse in terms of the national
geodetic datum.
Local uncertainty
The Local uncertainty at the point is based upon an average
of the individual local uncertainties (or relative uncertainties)
between that point and other adjacent points. The
calculation of Local Uncertainty is identical to the method
for calculation Positional Uncertainty, except that error
ellipse used is relative ellipse between the two points
in question, or the average of those from the point in question
to adjacent points in the network.
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R. Paar, G. Novakovic, E. Zulijani – Positioning Accuracy Standards for Geodetic Control
3.2 Example of calculating Positional and Local
uncertainty of geodetic control points
Although the illustrated standards for reporting the uncertainty
of coordinates are mostly founded for the points of
national reference geodetic networks, they can be used for
every positioning project connected with the reference
control points.
For many engineering applications, the precision of positioning
of two points relative to each other (local uncertainty)
is of much more importance that their precise positioning
in a coordinate system (Positional uncertainty).
The point ellipses may not indicate the relativity between
points if there is high correlation between them. In a minimally
constrained or constrained adjustment, there are different
point ellipses for each of the points, depending on
the choice of the fixed point(s), i.e. the absolute error
ellipses will vary with the choice of origin of a network.
However, in the minimally constrained adjustment, the
relative ellipses are practically fixed. The relative error
ellipses are unaffected by the choice of origin.
Computation of the Positional and Local uncertainty of
horizontal coordinates will be shown on the geodetic network
established for the reconstruction of old Maslenica
Bridge. The old Maslenica Bridge was demolished 1991,
during Croatian War of Independence (fig. 3), and its reconstruction
has been finished in 2006.
The new Maslenica Bridge (fig. 4) is 315.30 m long, according
to weight assignment, it is arch bridge, and it is
Fig. 3: Destroyed Maslenica Bridge
Fig. 4: Reconstructed Maslenica Bridge Fig. 5: Stabilization of the control points
Fig. 6: Configuration of the geodetic control of Maslenica
Bridge
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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-
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R. Paar, G. Novakovic, E. Zulijani – Positioning Accuracy Standards for Geodetic Control
dards. There is only one type of data used that the standards
refer to, i.e. the coordinates of geodetic control
points.
New standards present a significant change in expressing
the positioning accuracy of geodetic control points. They
describe general classification that is based on the accuracy
of spatial coordinates expressing at the defined confidence
level. Principal changes included requirements to
report numeric uncertainty values: a composite statistic
for horizontal uncertainty (radius of confidence circle
r) instead of individual component of uncertainty (sx,
sy), and standard deviation for vertical uncertainty.
Various data users have various demands with regard to
the quality of these data, and hence, two types of standards
have been defined for the geodetic control points: Positional
and Local uncertainty, which are compatible with
the quantities Absolute Positioning Accuracy and Relative
Positional Accuracy prescribed by ISO 19113. These
quantities might be applied to positions determined by
any means, but for geodetic surveying, they are computed
from the appropriate error ellipses (for horizontal position)
and standard deviations (for heights).
Positional and local uncertainties are simple indicators of
the quality of position. For horizontal coordinates of the
point, the uncertainty is the radius of a „circle of error“
derived using a 95 % confidence level. For height, the uncertainty
is a linear interval, using 95 % confidence level.
Positional uncertainty is global or absolute, computed
with respect to the reference frame or datum and Local
uncertainty is computed with respect to adjacent points
within the same data set or source.
Although the illustrated standards for reporting the uncertainty
of coordinates are mostly founded for the points of
national reference geodetic networks, they can be used for
every positioning project connected with the reference
control points. For engineering projects, it is more important
to obtain estimates of the precision of the relative positions
(local uncertainty) of two points, rather than of
their absolute positions (positional uncertainty).
Since the current standards do not refer to the quality of
surveying being constantly changed along with the development
of technology, this means of reporting the positioning
quality will not be changed so soon.
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Addresses of the autors:
Prof. Dr. sc. GORANA NOVAKOVIĆ, University of Zagreb,
Faculty of Geodesy, Kaciceva 26, 10000 Zagreb, Croatia,
Tel. þ 3 85-(1)-46 39-3 07, Fax þ 3 85-(1)-46 39-2 22.
gorana.novakovic@geof.hr
MSc. RINALDO PAAR, University of Zagreb, Faculty of
Geodesy, Kaciceva 26, 10000 Zagreb, Croatia, Tel.
þ 3 85-(1)-46 39-3 71, Fax þ 3 85-(1)-46 39-2 22.
rpaar@geof.hr
EMILI ZULIJANI, Univ.-Dipl. Ing., Geofoto d.o.o., Buzinski
prilaz 28, 10010 Zagreb, Croatia
286 AVN 7/2009

Abstract
Since the geodetic control points are the base (framework) for all surveying activities, the quality of these activities will
directly depend of the quality (accuracy) of geodetic control. Traditionally, the accuracy standards for geodetic control
positioning were related to the precision of observations, and not to the result, i.e. to the coordinates of geodetic control
points. In the application of various positioning methods there were different standards used, which often made the
comparison of measurement result quality impossible. Beside that, such standards are no longer adequate in the age of
GNSS and GIS. The establishment of highly precise spatial reference system at the global and at the national level, and also
great advance in achieving positioning precision referring to that system, have entailed new standards for reporting the
positional accuracy of geodetic control. Current standards are related to the spatial position (coordinates) of geodetic
control being independent of positioning methods or the survey instruments used. The paper presents these common
standards for reporting the precision of positioning geodetic control points (horizontal and vertical) prescribed by
international standards in the field of geospatial information that have been accepted as European, i.e. Croatian standards
(ISO 19113). In this paper, current standards for reporting the positional accuracy will be presented on the example of local
geodetic network established for the reconstruction of Maslenica Bridge located near city Zadar in Croatia.
Zusammenfassung
Festpunkte bilden den Rahmen aller Vermessungsarbeiten, so dass die Qualität (Genauigkeit) des Referenzsystems direkt
die Ergebnisse der Vermessungen beeinflusst. Die Qualität des Festpunktnetzes wird angegeben durch die Präzision
und durch die Zuverlässigkeit. In diesem Beitrag werden die Normen angesprochen, die für die Bestimmung der
Positionspräzision der Festpunkte relevant sind.
Die Genauigkeitsangaben für das geodätische Referenzsystem sind traditionell mit der Präzision der Beobachtungen
verbunden, und nicht mit dem Resultat, bzw. den Koordinaten der Festpunkte. Bei der Anwendung verschiedener
Messmethoden wurden unterschiedliche Normen benutzt, die den Vergleich der Qualität der Messresultate unmöglich
machen. Außerdem sind in der Zeit von GNSS und GIS derartige Normen nicht mehr relevant. Die Festlegung von
hochpräzisen Raumbezugssystemen auf globaler und nationaler Ebene, wie auch die Entwicklung von hochpräzisen
Verfahren der Positionsbestimmung erfordern die Bereitstellung neuer Normen. Jetzige Normen beziehen sich auf die
Raumposition (Koordinaten) des geodätischen Referenzsystems. Der Beitrag stellt die internationalen Normen für die
Bestimmung der Präzision der Festpunkte dar (horizontale und vertikale), die auf dem Gebiet der raumbezogenen
Informationssysteme vorgeschrieben sind und von europäischen bzw. kroatischen Normen übernommen worden sind
(ISO 19113). In diesem Beitrag werden die derzeitigen Normen für die Bestimmung der Positionsgenauigkeit dargestellt,
und zwar anhand eines Beispiels eines lokalen geodätischen Netzes, das für die Rekonstruktion der Maslenica-Brücke
neben der Stadt Zadar in Kroatien geschaffen worden ist.
Workshop „Basiswissen GDI“ vom 7. bis 11. September 2009
an der Fachhochschule Frankfurt am Main
Der fünftägige Workshop
Basiswissen GDI ist ein
Grundkurs für Personen, die
in ihrem Berufsumfeld mit
dem breiten Spektrum von
Geodateninfrastrukturen in
Berührung kommen. Das Angebot
richtet sich insbesondere
an Mitarbeiter der öffentlichen
Verwaltung sowie
Ingenieur- und Planungsbüros,
die unter anderem durch
die INSPIRE-Richtlinie animiert
sind, sich mit den Möglichkeiten
und Zielen einer
R. Paar, G. Novakovic, E. Zulijani – Positioning Accuracy Standards for Geodetic Control
Geodateninfrastruktur vertraut
zu machen.
Der Workshop setzt keinerlei
Vorwissen im Bereich der
Geodateninfrastrukturen voraus,
jedoch sollten die Teilnehmer
Grundkenntnisse in
der Anwendung von Geoinformationssystemen
sowie
der Behandlung von Geodaten
mitbringen. Der Workshop
findet an fünf aufeinander
folgenden Tagen statt,
wobei jeder Tag ein für sich
eigenes Themengebiet be-
handelt und getrennt gebucht
werden kann. In praxisnahen
Übungen werden Anwendungen
und Dienste einer GDI
selbständig erlernt und somit
die vorher gelegten theoretischen
Grundlagen vertieft.
Um dem Charakter eines
Workshops gerecht zu werden,
ist ausreichend Zeit vorgesehen
Fragen der Teilnehmer
zu Anwendungen und
Entwicklungen im Kontext
einer GDI zu beantworten
oder zu diskutieren. Wegen
ANKÜNDIGUNGEN
. . . . . . . . . . . . . .
des hohen Praxisanteils ist
die Teilnehmeranzahl auf
maximal 20 Personen pro
Tag begrenzt.
Dieser Workshop ist eine Gemeinschaftsveranstaltung
des Instituts für Kommunale
Geoinformationssysteme e.V.
(IKGIS) und der Fachhochschule
Frankfurt am Main.
Weitere Informationen:
www.gdi-testplattform.de
bzw. www.ikgis.de
AVN 7/2009 287