A GENERAL REVIEW OF THE DEFORMATION MONITORING TECHNIQUES AND A

CASE STUDY: ANALYSING DEFORMATIONS USING GPS/LEVELLING

S. Erol a, *, B. Erol a, T. Ayan a

a
ITU, Civil Engineering Faculty, Geodesy Division, 34469 Maslak Istanbul, Turkey - (erol, bihter, ayan)@itu.edu.tr

Commission VII, WG VII/5

KEY WORDS: Geodesy, Engineering, Structure, Disaster, Monitoring, Analysis

ABSTRACT:

Being sure is very important that the movements of an engineering structure, which serves the human life of today’s modern world,
are exhibiting safe behaviours. So, a lot of deformation monitoring studies for determining and analysing different kinds of
engineering structures such as high-rise buildings, dams, bridges, viaducts, industrial complexes etc., are implemented. During these
studies, the used measurement techniques and systems, which could be geodetic or non-geodetic, are determined considering the
type of the structure of which deformations will be monitored, its environmental conditions and expected accuracy from the
measurements. As related the used monitoring techniques, the deformation measurement equipments are varied. Also according to
professions who use the deformation monitoring techniques, these techniques and instrumentation have traditionally been
categorized in to two groups: geodetic surveys, which include conventional (terrestrial such as precise levelling measurements, angle
and distance measurements etc.), photogrammetric (terrestrial, aerial and digital photogrammetry), satellite (such as Global
Positioning System-GPS, InSAR), and some special techniques; geotechnical/structural measurements, using lasers, tiltmeters,
strainmeters, extensometers, joint-meters, plumb lines, micrometers etc. In this paper, some of these deformation measurement
techniques which are thought as more important and mostly used by the geodesy specialists will be reviewed. The importance and
need of carrying out the deformation measurements periodically in engineering structures will be emphasised.

Besides, a case study that is about implementing the deformation analysis of a large viaduct using GPS and Precise Levelling
measurements will be discussed here. As it is well known, engineering structures (such as in this viaduct) are subject of deformation
due to factors such as changes of ground water level, tidal phenomena, tectonic phenomena etc. In this study, the design, execution
and analysis of deformations in a high-way viaduct are going to be mentioned in detailed explanations as an example of
implementing the two geodetic techniques in deformation monitoring of large engineering structures. During the study, the control
network points were positioned with GPS measurement technique and height differences were supported with precise levelling
measurements. As the result of measurement campaigns, the X, Y, Z cartesian coordinates and height differences were determined
from the GPS measurements and precise levelling measurements respectively. Later on, deformation analysis using the height
differences according to provided data from the GPS and the data from the precise levelling were carried out separately. Then, the
3D deformation analysis using the GPS measurements data was carried out too. Founded results will be given in the paper.

1. INTRODUCTION measurements, are easier to adapt for automatic and continuous

monitoring than conventional instruments of geodetic
Engineering structures (such as dams, bridges, viaducts, high measurements. Geodetic techniques have traditionally been
rise buildings, etc.) are subject to deformation due to factors used mainly for determining the absolute displacements of
such as changes of ground water level, tidal phenomena, selected points on the surface of the object with respect to some
tectonic phenomena, etc. Monitoring and analyzing reference points that are assumed to be stable. Non-geodetic
deformations of these structures constitutes a special branch of techniques have mainly been used for relative deformation
Geodesy Science. There are several techniques for measuring measurements within the deformable object and its
the deformations. These can be grouped mainly into two as surroundings (Anonym, 2002).
geodetic and non-geodetic techniques.
The major motivation of this study is geodetic techniques in
Each main measurement technique has its own advantages and monitoring deformations of engineering structures and
drawbacks. Geodetic techniques, through a network of points analyzing. In determining deformations according to geodetic
interconnected by angle and/or distance measurements, usually techniques constitutes terrestrial measurement techniques or
supply a sufficient redundancy of observations for the statistical space based positioning techniques and/or combination of both
evaluation of their quality and for a detection of errors. They techniques. Until the very beginning of 1980’s, the
give global information on the behaviour of the deformable deformations in engineering structures had been determined just
structure while the non-geodetic techniques give localized and using conventional measurement techniques. After that, by
locally disturbed information without any check unless starting to use GPS measurement technique in geodetic and
compared with some other independent measurements. On the surveying applications, this very precise satellite based
other hand, the instruments, which are used in non-geodetic

* Corresponding author. This is useful to know for communication with the appropriate person in cases with more than one author.
positioning technique has become to use in deformation relative positions of any identifiable object points can be
measurements (Erol, 1999). determined from the geometrical relationship between the
intersecting optical rays which connect the image and object
GPS technique has benefits of high accuracy and simultaneous points. Aerial photogrammetry has been extensively used in
3-D positioning; however there are handicaps about vertical determining ground movements in ground subsidence studies in
positioning using this technique. Because, the height mining areas, and terrestrial photogrammetry has been used in
component is the least accurately determined GPS coordinate, monitoring of engineering structures. The main advantages of
predominantly due to inherent geometric weakness and using photogrammetry are the reduced time of field work;
atmospheric errors (Featherstone et al., 1998; Çelik et al., simultaneous three dimensional coordinates; and in principle an
2001). unlimited number of points can be monitored (Anonym, 2002).

Therefore, using GPS measurement technique in deformation Tilt and Inclination Measurements; The measurement of tilt is
measurements with millimeter level accuracy requires some usually understood as the determination of a deviation from the
special precautions that increase the measurement accuracy in horizontal plane, while inclination is interpreted as a deviation
GPS observables via eliminating or reducing some error sources from the vertical. The same instrument that measures tilt at a
such as using forced centering equipments, applying special point can be called either a tiltmeter or an inclinometer
measuring techniques like rapid static method for short depending on the interpretation of the results (Anonym, 2002).
baselines or designing special equipments for precise antenna
height readings (Erol and Ayan, 2003). The some of new techniques for deformation monitoring can be
listed as follows.
In some cases, even these special precautions might be
insufficient to reach the necessary accuracy level; at that time to Insar; Elevations can be determined from Synthetic Aperture
support GPS measurements with another measurement Radar (SAR) images by interferometric methods. This involves
technique would be very useful as an improving solution. the use of two antennas, displaced either vertically or
horizontally, installed on the same satellite or aircraft platform.
In this study, 1D and 3D deformation analysis of a large viaduct One of the antennas transmits the signal, but both receive it,
using GPS and Precise Levelling measurements are resulting in two images being created. The most accurate form
implemented. The control network points were positioned with of interferometric measurement is differential interferometry
GPS measurement technique and height differences were (InSAR), which involves the determination of elevation
supported with precise levelling measurements. As the result of differences between two epochs of terrain measurement. In this
measurement campaigns, the X, Y, Z cartesian coordinates and case, the variations in the radar signal phases are determined
height differences were determined from the GPS between the two epochs, which reveal terrain surface
measurements and precise levelling measurements respectively. deformations that may have occurred between the two
Later on, deformation analysis using the height differences occasions when the images were recorded. It is claimed that
according to provided data from the GPS and the data from the height differences as small as one centimeter can be detected by
precise levelling were carried out separately. Then, the 3D this method. Such a technique therefore has the potential of
deformation analysis using the GPS measurements data was being a cost effective, near-continuous, remote method of
carried out too. Explanation on used analysis methods and measuring terrain subsidence due to mining, and ground
founded results will be given in addition to general review of movement due to land subsidence, earthquake or volcanic
deformation analysis methods in the following sections. activity, etc.
(http://www.gmat.unsw.edu.au/snap/work/insar.htm, accessed
2. OVERVIEW OF DEFORMATION MEASUREMENT May 2004).
TECHNIQUES
Pseudolite; It is well known that for GPS-based deformation
As it is mentioned in the introduction part, measurement monitoring systems, the accuracy, availability, reliability and
techniques were divided mainly into two different groups as integrity of the positioning solutions is heavily dependent on
geodetic and non-geodetic techniques. These main techniques the number, and geometric distribution, of the satellites being
can also be divided sub-techniques. In the following, it can be tracked. However, in some situations, such as in urban
found short descriptions of the used techniques in deformation canyons, monitoring in valleys and in deep open-cut mines, the
measurements. number of visible satellites may not be sufficient to reliably
determine precise coordinates. Furthermore, it is impossible to
GPS; Global Positioning System offers advantages over use GPS for indoor applications and due to limitations of the
conventional terrestrial methods. Intervisibility between GPS satellite geometry; the accuracy of the height component is
stations is not strictly necessary, allowing greater flexibility in generally 2 or 3 times worse than the horizontal components.
the selection of station locations than for terrestrial geodetic These factors make it difficult to address GPS deformation
surveys. Measurements can be carried out during night or day, monitoring applications in areas where the number of visible
under varying weather conditions, which makes GPS satellites is limited or satellite geometry is poor, especially
measurements economical, especially when multiple receivers where real-time high accuracy height component monitoring is
can be deployed on the structure during the survey. With the needed, as in such applications as ground subsidence or
recent developed rapid static positioning techniques, the time deformation monitoring of man-made structures. Therefore, in
for the measurements at each station is reduced to a few order to improve the performance of GPS-only deformation
minutes (Anonym, 2002). monitoring systems, the integration of GPS with other
technologies needs to be investigated.
Photogrammetry; If an object is photographed from two or
more survey points of known relative positions (known Pseudolites (pseudo-satellites), which are ground-based
coordinates) with a known relative orientation of the camera(s), transmitters of GPS-like signals, can significantly enhance the
satellite geometry, and even replace the GPS satellite session plan. Also, precise levelling measurement technique
constellation in some circumstances (such as deformation was applied between network points.
monitoring indoors).
During GPS measurements, Trimble 4000 SSI and Leica
The geometry of the satellite constellation can be improved by System 300 dual frequencies receivers were used. Leveling
the careful selection of the pseudolite location(s). In the case of measurements were carried out using Koni 007 precise level.
GPS, the measurements with low elevation angles are usually
rejected in order to avoid serious multipath, tropospheric delay The network has 6 reference points, set around the viaduct and
and ionospheric bias. However, this is not necessary in the case 24 deformation points, set on the building of the viaduct and
of pseudolites. The quality of the measurements with less than they are established especially on the piers where expected to
half degree elevation angle (from the pseudolite transmitter to be most stabile places on the structures (see Figure 1).
the GPS receivers) is still very high. Therefore, high quality
Karasu Viaduct Network
pseudolite measurements with low elevation angles, when
4553750
included in data processing, can be expected to significantly
improve the ambiguity resolution performance and solution 4553500
3
111 2 1
121 112
accuracy, especially in the height component. The availability 131 122
a ck 141 132
Tr 151
142
rn 152
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Northing
161
is also increased because a pseudolite provides an additional 4553250 Marsh Area
No
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171
172
162

181 k
ranging source to augment the GPS constellation (Dai et al., 4553000
5
191
192
182

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6

ut Marsh Area

2001). 211
201
202 So Büyükçekmece Lake

212
4552750
221
222 Marsh Area
4

Laser Scanning; Existing techniques (e.g., surveying, GPS) 4552500

used to monitor large structures such as buildings, viaducts, 375250 375500 375750 376000 376250 376500 376750 377000 377250 377500 377750 378000 378250

Easting
dams and bridges, while very accurate, are greatly hindered by Figure 1: The configuration of geodetic network.
their low point density. Data acquisition time limits monitoring
to only a few samples located at strategic points on the 4. DEFORMATION ANALYSIS USING HEIGHT
structure. Ground-based laser scanning is a new technology DIFFERENCES
that allows rapid, remote measurement of millions of points,
thus providing an unprecedented amount of spatial information. With the aim of determining the deformations in engineering
This in turn permits more accurate prediction of the forces structures, landslide areas, crustal deformations etc., the
acting on a structure. As an emerging technology though, geodetic networks are built. The observations are carried out in
several issues concerning instrument calibration, sensitivity this geodetic network with certain intervals, and by this way
analysis, data processing and data filtering techniques require stabile network points and instable network points are verified.
investigation This provides to determine the changes on the observed
(http://www.cage.curtin.edu.au/~geogrp/projlaser.html, May structure or area (Demirel, 1987).
2004).
In general, the deformation analysis is evaluated in three steps
For any particular application of deformation measurements, in a geodetic network. In the first step, the measurements,
the most appropriate technique (or combination of techniques), which were carried out in t1 and t2 measurement epochs, are
which are going to be used, are determined as related to type of adjusted separately according to free adjustment method;
the structure, required accuracy and also economical aspects. outliers and systematic errors are detected and eliminated in this
step. In the second step, global test procedure is carried out and
3. NETWORK AND DATA by this test it is ensured that if the network point, which were
assumed as stabile, stayed really stabile in the ∆t = t 2 − t1 time
In this study, the deformations of the Karasu viaduct were
investigated using GPS and precise levelling data. Karasu interval or not. In the global test, after the free adjustment
viaduct is 2160 m in length. As the longest viaduct of the calculations of the networks separately, the combined free
Turkey, It is located in the west of Istanbul in one part of the adjustment is applied to both epoch measurements. (Ayan,
European Transit Motorway. The first 1000 meter of this 1982; Ayan et al., 1991).
viaduct crosses over the Büyükçekmece Lake and the piers of
the structure were constructed in to this lake (see Figure 1). After determining a group of stabile points as the result of
global test, following step of the analysis is the localizing of
The viaduct consists of two separate tracks as northern and height changes. For doing this, TH test values are calculated for
southern and was constructed on 110 piers (each track has 55 the every network points, except the stabile points, and they are
piers). There is 40-meter width between two piers and also one compared with F critical value that is given in the Fisher
deformation point is constructed with in every 5 piers sequence. distribution table (Erol and Ayan, 2003).

The deformation measurements of Karasu involved four v1T P1 v1 + v T2 P2 v 2

measurement campaigns. The first campaign was carried out in d = H 2 − H1 S 02 = f 0 = f1 + f 2
f1 + f 2
June 1996, the second in March 1997, the third in October 1997
−1
and the last one in April 1998. These four campaigns include d T Q dd d
GPS measurements and precise levelling measurements. With TH = Qdd = Q H1H1 + Q H 2 H 2 r = fG − f0
r S 02
the aim of investigating the deformations of this structure,
before carrying out the measurement campaigns, a well
designed local geodetic network had been established, and it If the TH > Fr , f 0 , 1−α , it is said that the height of the point
was measured using GPS technique according to designed changed significantly. Otherwise, it is resulted that d height
difference is not a displacement but it is caused by the random
measurement errors (Erol and Ayan, 2003).
Northern Track - Levelling+GPS
The conventional deformation analysis method was applied to
all three data sets (levelling derived height differences, GPS 80.0
60.0
derived height differences and the combination of both) as is 40.0

dh in mm
20.0
going to be mentioned below. And the results that obtained 0.0
-20.0
from evaluating these three data sets are shown in the graphics -40.0
-60.0
5 4 221 211 201 191 181 171 161 151 141 131 121 111 6 3 2 1

(see Figure 2, Figure 3 and Figure 4). -80.0

Points

Stochastic information involves the number of instrument setup dh 1-2 dh 2-3 dh 3-4
while evaluating levelling derived height differences in the
deformation analysis algorithm.
Figure 4: Combined derived height differences between
consecutive epochs for each point in the northern track
On the other hand, in the algorithm of the second evaluation,
the ellipsoidal height differences (dhij), which were derived
5. 3D DEFORMATION ANALYSIS WITH
from the GPS baseline solutions, are used as measurements,.
S-TRANSFORMATION USING GPS DATA
Also, the stochastic information of measurements comes from
the GPS baseline solutions. It can be accomplished the datum consistency between different
epochs by employing the S-Transformation. Also, the moving
In the third evaluation, height differences, derived from both points are determined by applying this transformation
measuring techniques, are used together and deformation consecutively. S-transformation is an operation that is used for
analysis is applied according to results of evaluation of transition from one datum to another datum without using a
combined data groups. A very important point that has to be new adjustment computation. With another word, S-
considered in the first step of this evaluation is that the both transformation is a transformation computation of the unknown
measurements groups derived from both techniques do not have parameters, which were determined in a datum, and their
the same accuracy naturally. And so, the stochastic information cofactor matrix, from the current datum to the new datum. The
between these measurement groups (relative to each other) has equations that imply the transition from the datum i to datum k
to be derived. In this study, for computing the weights of both are given below (Demirel, 1987; Başkaya, 1995).
measurement groups, Helmert Variance Component Estimation
(HVCE) Technique has been used.
x k = Sk x i
In here, only the graphics, which shows the height differences Q k = Sk Qi STk
of northern-track points, are given. Because of that the xx xx
deformations in both tracks points have the same character, so it −1
has been found sufficient to give results belongs to only one S k = I − G  G T E k G  GT Ek
 
track of the viaduct.
5.1 Global Test Using S-Transformation
Northern Track - Levelling
A control network is composed by the datum points and
deformation points. By the help of the datum points, the
80.0
60.0 control network, which were measured in ti and tj epochs, are
dh in mm

40.0
20.0 transformed to the same datum.
0.0
-20.0
-40.0
-60.0
4 221 211 201 191 181 171 161 151 141 131 121 111 3 2 1 While inspecting the significant movements of the points,
-80.0
continuous datum transformation is needed. Because of this,
Points
first of all, the networks, which are going to be compared each
dh 1-2 dh 2-3 dh 3-4 other, are adjusted in any datum such as using free adjustment.

Figure 2: Levelling derived height differences between In the result of free adjustment, the coordinates of the control
consecutive epochs for each point in the northern track network points, which were measured in any epoch, are divided
into two groups as f (datum points) and n (deformation points).

Northern Track - GPS Then, datum i and datum j were able to be transformed into the
same datum k by the help of the datum points. As the result,
80.0
60.0
the vectors of coordinate unknowns and also their cofactor
40.0
matrix are founded for the datum points in the same k datum.
dh in mm

20.0
0.0
-20.0
-40.0 5 4 221 211 201 191 181 171 161 151 141 131 121 111 6 3 2 1 By the global test, it is determined if there is any significant
-60.0
-80.0 movements in the datum points or not. In the result of global
Points test, if it is decided that there is deformation significantly in one
dh 1-2 dh 2-3 dh 3-4 part of the datum points, determining the significant point
movements using S-transformation (localization of the
Figure 3: GPS derived height differences between consecutive deformations) step is started. In this step, as is assumed that
epochs for each point in the northern track each of the datum points might change its position, for each
datum point, the group of datum points is divided in to two deformations, it has to be supported by precise levelling
parts: the first part includes the datum points, which are measurements in vertical positioning.
assumed as stable and the second part includes the datum point,
which is assumed as instable. And all the computation steps are In the first step of the process, the data, which were handled
repeated for each datum points. By this way, for all of the from both measurement methods, were processed for each
datum points, the probability of to be stabile or not has been epoch separately. By this way, the results, which had been
tested. At the end, the exact datum points are derived. derived from the independent solutions for each epoch, were
compared. This was done to obtain an impression of the quality
5.2 Determining the Deformation Values of the data, of possible inherent problems and to get first hints
on instable points, thus, allow applying a suitable deformation
After determining the significant point movements, the block of analysis strategy. This operation covers the only height
datum points, which don’t have any deformations, are to be component. In the result of this comparison, the benefits of the
determined. By the help of these datum points, both epochs are precise levelling measurements have been seen. The precise
shifted the same datum and deformation values are computed as levelling measurements have an effective role for checking the
explained below. heights derived from GPS measurements and also for clarifying
the antenna height problems, which could be occurred during
The deformation vector for point P: the GPS measurements and effect the height component
x j − x i  directly.
 k k d 
 j   x  After these processes, deformation analyses were carried out by
i
d = y − y k  = d  (21)
 k   y  using height differences from levelling measurements, from
z j − z i  d  GPS measurements and also by using combination of height
 k k   z  differences from both GPS and levelling measurements
respectively. In general meaning, the results were confirmed
and the magnitude of the vector:
each other. In the results, it was surprisingly found that the
d = dT d maximum height changes were in point 2 and point 4 (as it is
seen in the graphics), which were assumed as stabile at the
To determine the significance of these deformation vectors,
beginning of the project and even though that their
which are computed according to above equations, the H0 null
constructions are pillar. According to analysis of precise
hypothesis is carried out as given below.
levelling data, on the contrary of the situation in point 2 and
H0 : d = 0 point 4, there weren’t seen any changes in heights in the
And the test value: deformation points on the viaduct. On the other hand,
d T Q −1 d according to the second evaluation (using GPS derived height
T= dd differences) in some points on the viaduct, height changes were
2
3s0 reported.
While this test value is compared with critical value,
In the third evaluation, as a result of the Helmert Variance
F3, f;1 − α , and if T 〉 F3, f;1 − α , it is said that there is a Component Estimation it was computed that the weight of
significant 3D deformation in point P (Denli, 1998). height differences from levelling equals to 30 times of the
weight of GPS derived height differences. This result was
After GPS Data evaluation, 3D deformation analysis was reached in the third iteration step.
carried out as it is mentioned. After the analyses, the founded
horizontal displacements can be seen in Figure 5. In the graphics, height changes according to consecutive
measurement campaigns are seen. As the graphics of the first,
2_3 4552632.345
4_1
the second and the third evaluations are compared, it is not
4553464.390
reliable enough to use GPS measurements without special
precautions for the GPS error sources, such as multipath,
4552632.340
4_2

4553464.385
4552632.335
atmospheric effects, antenna height problems etc., in vertical
deformation analysis of engineering structures. According to
2_1
Northing
Northing

4552632.330
4_4
investigation of the result of the second evaluation, it was seen
changes in heights of some points on the viaduct. However,
4553464.380
4552632.325

2_4

4552632.320 while the first and third evaluations are considered, it is

4553464.375

4552632.315
understood that these changes, seemed to be deformations on
2_2
the object point of the viaduct according to results of the second
evaluation, were not significant and caused by the error sources
4_3
4553464.370 4552632.310
377775.445 377775.450 377775.455 377775.460 377775.465 375443.495 375443.500 375443.505 375443.510 375443.515

in GPS measurements especially antenna height problems.

Easting Easting

Figure 5: Horizontal displacements in points 2 and 4.

Thereafter, the 3D deformation analysis were carried out
6. RESULTS and CONCLUSION according to theoretical aspects that were explained in section 5
and the results of the priory adjustments and 1D deformation
As is very well known that, the weakest component of a analysis aid to the decision phase of 3D deformation analysis,
position obtained by GPS is the height component. This is while the network points are being grouped as stable or instable.
mainly because of the weakness of geometric structure of GPS. According to analyses results, horizontal displacements were
Because of this, GPS technology in determining vertical investigated in point 2 and point 4 in the outside of the viaduct
(see Figure 5).
However, at a first glance, it was surprising to found February 23-27 1987, Chamber of Surveying Engineers of
deformations in point 2 and point 4 that had been chosen as Turkey, Ankara, Turkey (in Turkish)
reference points, after geological and geophysical
investigations, the origin of these results was captured. Denli, H. H., 1998. GPS ile Marmara Bölgesindeki Yer
According to that the area is a marsh area that this characteristic Kabuğu Hareketlerinin Belirlenmesi, ITU Institute of Natural
might widen also underneath of these two reference points, 2 Sciences, PhD Thesis, February, 1998, Istanbul, Turkey (in
and 4. The uppermost soil layer in the region is not seemed to Turkish)
be stabile and the foundations of the constructions of the
reference points are not founded as deep as the piers of the Erol, S., 1999. Deformation Measurements and Analysis in
viaduct and so they are affected the environmental conditions Karasu Viaduct Using GPS Technique, MSc Thesis, June 1999,
easily. And these conditions supported the results of the Istanbul Technical University, Institute of Science and
analysis that in the object points on the viaduct, there were not Technology, Istanbul, Turkey (in Turkish)
exposed any significant movements. On the other hand, it is
Erol, S., Ayan, T., 2003. An Investigation on Deformation
possible to mention about the correlation between vertical
Measurements of Engineering Structures With GPS And
movements in two reference points, 2 and 4, and wet/ dry
Levelling Data Case Study, International Symposium on
seasons, because the uplift and sinking movements of these
Modern Technologies, Education and Professional Practice in
reference points seems very synchronic as related to seasonal
the Globalizing World, 6-7 November 2003, Sofia, Bulgaria
changes in amount of water (see Figures 2, 3 and 4).
Featherstone, W. E., Denith, M. C., Kirby, J. F. 1998.
The results of this study, experienced with measurements of Strategies for the Accurate Determination of Orthometric
Karasu viaduct, are thought to be very important remarks for Heights from GPS, Survey Review 34, 267 (January 1998),
deformation analysis studies using GPS measurements. As the pp.278-296
first remark, GPS measurement technique can be used for
determining deformations with some special precautions for
eliminating GPS error sources. These include using forced
centering mechanisms to avoid centering errors, using special
equipments for precision antenna height readings, using special
antenna types to avoid multipath effects etc. Also, during the
data processes it is necessary to clear the cycle slips from the
data, and to consider insufficiencies of the used tropospheric
and ionospheric models.

However, even though these precautions, to provide better

results in deformation analysis, GPS measurements have to be
supported with Precise Levelling measurements.

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Anonym, 2002. Structural Deformation Surveying (EM 1110-
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Ayan, T., 1982. General Review of Deformation Analysis in

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Başkaya, B., 1995. S-Transformasyonu ve Yatay Kontrol

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Çelik, R. N., Ayan, T., Denli, H., Özlüdemir, T., Erol, S.,
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Analizi, Türkiye I. Harita Bilimsel ve Teknik Kurultayı,