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Building and Environment 42 (2007) 393–399

www.elsevier.com/locate/buildenv

Assessing building displacement with GPS

Andres Seco�, Fermın Tirapu, Francisco Ramırez, Benat Garcıa, Jesus Cabrejas

Department of Projects and Rural Engineering, E.T.S.I.A. Public University of Navarre, Campus Arrosadıa S/N, Pamplona 31006, Spain

Received 31 May 2004; received in revised form 15 July 2005; accepted 19 July 2005

Abstract

In the frame of its researches concerning GPS positioning the Universidad Publica de Navarra has carried out in 2003 a study to

know the possibilities of this positioning technique for monitoring building’s displacements. A 30m concrete building was

monitored for several months by observations from a geodetic micronetwork placed around.

During the observation period the computed variations in position have standard deviations of 3.1mm in the XX -axis, 6.6mm in

the YY -axis and 9.1mm in the ZZ-axis. These values reveal that the building displacements are very small and that they are masked

by the characteristic errors of GPS observations. The correlation between the observed displacements and the weather variables was

analyzed and only temperature and direct radiation were significant, but the relationship was weak, with low values of the

correlation coefficients r. In the visual analysis of the coordinate variations we observed that the building suffers a negative

displacement with respect to the XX -axis in the morning up to noon, when the displacements become positive, with an observed

variation over the reference position of 72mm. With respect to the YY -axis, the building remains fairly stable until afternoon, in

which it moves north approximately 2mm in relation to the reference position. With respect to the ZZ-axis, we observed an increase

of the height of the building during the central hours of the day of around 1 cm. These displacements observed in the building agree

qualitatively with the a priori expected displacements as a function of the movement of the sun throughout the day.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Accurate dynamic positioning; GPS; Structure monitoring

1. Introduction and objectives

GPS is a positioning technique widely used fornavigation, in surveying and geodesic applications. Thistechnique allows determining point coordinates witheven sub-centimeter accuracy in real time, turning it intoa technology with wide applicability in many phases ofengineering projects, not only during construction, butalso during the operation phase.

Currently, there are several technologies availablethat allow monitoring structures, besides GPS, such asaccelerometry, laser interferometry, and digital tachy-metry [1]. All these techniques present a number ofdifficulties when it comes to the continuous monitoring

e front matter r 2005 Elsevier Ltd. All rights reserved.

ildenv.2005.07.027

ing author. Tel.: +34948 16 96 82;

91 48.

ess: andres.seco@unavarra.es (A. Seco).

of structures. Accelerometry is not suitable to detectstructure movements that happen slowly, while laserinterferometry and digital tachymetry are limited intheir application by weather conditions, cannot obtain3D displacements directly and cannot be automated [2].

GPS combines high accuracy of the results with thepossibility of surveying continuously in all weatherconditions and the ease of equipment installation, allowsa high degree of automation and can obtain results innearly real time, so systems based in RTK observationsare widely used in monitoring large structures, such asbuildings or bridges [3,4]. However, in this paper we aregoing to describe GPS monitoring of the small-scaledeformations that take place in a small building that,given their characteristics, normally would have beenmonitored using traditional techniques.

This work was carried out by the Geodesy team of theDepartment of Projects and Rural Engineering of the

ARTICLE IN PRESSA. Seco et al. / Building and Environment 42 (2007) 393–399394

Public University of Navarre (Spain). One researchfocus of this group is high-accuracy GPS applications,particularly in civil engineering.

2. GPS positioning

The GPS basic positioning is done by triangulation,calculating the distances between the receiver and aminimum of four satellites. These distances are calcu-lated by pseudorandom code correlation techniques.This mode, known as natural GPS, is the one generallyused in low-accuracy applications, with a precision ofthe order of a tenth of a meter.

In order to achieve precisions under a meter, onesingle GPS receiver is not enough. Two receivers,observing the same satellites, are required for what isknown as differential mode. This type of observation isbased on the consideration that the errors affecting bothreceivers are the same. This cancels out or reducesdramatically most of the error sources of GPS observa-tions, such as atmospheric delays, ephemeris errors, etc.allowing achieving even sub-centimetric accuracies whenthe distances between the receivers and the satellites areobtained through the carrier phase difference. Indifferential GPS the coordinates of the ‘‘roving’’ receiverare calculated as dX, dY, dZ in the GPS referencegeodetic system, in relation to the coordinates of theother receiver, called base station. Under these condi-tions, this 3D vector, dX, dY, dZ, between bothreceivers can be determined with an error smaller than1 part per million [5]. This is the measuring method usedin applications such as those of civil engineering, inwhich centimeter accuracies are required. This type ofpositioning requires the use of two GPS receivers,although only one is being used to survey. Theproliferation of this technology in civil engineering haslead to setting up permanent GPS reference stations.These stations, generally managed by the national orlocal administration, supply differential corrections tothe users in the surrounding area, that will then onlyneed one receiver working as rover, as the referencestation carries out the role of the base receiver. Thesestations are normally located on public buildings, inareas with enough population density where importantinfrastructures are constructed that justify the invest-ment. These kinds of locations have the advantages ofthe proximity to the demand areas, having restrictedaccess to the facility and having a supply of electricalpower and Internet access for the dissemination of thecorrections. The drawbacks are those of GPS systems inurban environments (multi-path effect and shadowingof the sky because of the close-by buildings and thepossible displacements of the structure on which thestation is placed. This last effect is generally the mostdifficult to obtain, as in most cases there is no relevant

data available. If the station suffers some displacementover time, the 3D vector that the users calculate from itwill also be displaced, so their differential positioningwill also be affected by this error.

3. Geodetic reference systems

3.1. The WGS84 geodetic system

WGS84 is the GPS reference system. This system isbased on replacing the geoid by the global ellipsoidWGS84 that gives name to the system, and is associatedto a set of Cartesian axes. GPS coordinates can beobtained as ellipsoidal or Cartesian coordinates, andtheir conversion is mathematically strict. This system ismaterialized in Europe by means of the ETRF89reference frame in the ETRS system.

In Spain, the densification of ETRF89 is calledREGENTE (in Spanish, Red GEodesica Nacional porTecnicas Espaciales or National Geodetic Networkthrough Spatial Techniques) and constitutes the SpanishNational GPS 3D Network.

3.2. The ED50 geodetic system

The system of coordinates of the Spanish geodesy isED50, that uses Hayford’s elipsoide with DatumPostdam as the planimetric origin. As the altimetricreference of the system is used, the vertical local oneorthonormal to the surface equipotential of gravity asthe origin of altitudes, is considered the average altitudeof the sea measured in Alicante.

If the planimetry and the altimetry of the system ED-50 are not in the same system, then we do not prune toconsider this one as an authentic 3D system but rather a2+1D. The coordinates UTM are Cartesian coordi-nated that are obtained from the system ED-50. Thesecoordinates are the habitually used one in the applica-tions of civil engineering for the comfort that supposesthe employment of Cartesian coordinates from thetopographic point of view.

This system is materialized in two different referenceframes. The first one is ROI (in Spanish, red de ordeninferior or lower-order network) for planimetry andNAP lines (in Spanish, nivelacion de alta precision orhigh-accuracy leveling) for altimetry. There is alsoaltimetry associated to the ROI, but it has low accuracy,since it was calculated from observations made fortrigonometrical triangulation, and not through leveling.

3.3. Coordinate transformation

According to Peyret et al. [8], in order to keep in thelocal system the accuracy achieved with the GPSobservations, it is necessary to have good coordinate

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transformation parameters. For low-accuracy applica-tions there are general parameters available thatguarantee sub-metric accuracies. For applications inwhich higher accuracy is needed, it is necessary todetermine the local transformation parameters.

Helmert 3D is a mathematically rigorous transforma-tion between two orthogonal coordinate systems.WGS84 is a 3D coordinate system but the local geodeticsystem does not meet this requirement, so the Helmerttransformation cannot be applied strictly when trans-forming coordinates from the WGS84 system to ED50.However, this transformation is valid in areas of up to afew square kilometers, where differences between theWGS84 and the geoid remain constant. This transfor-mation has the advantage of not introducing restrictionsor distortions in the GPS observations for their fitting tothe local network, so the accuracies are kept. Inaddition, the quality of the transformation can be setas a function of the residuals observed after computingthe transformation parameters.

Fig. 2. Points used for the WGS84 to ED50 coordinate transforma-

tion.

4. Study area

The goal of this experiment is to analyze thedisplacements of the Fuerte del Prıncipe building, nearthe center of Pamplona, shown in Fig. 1.

This building is held up by a reinforced concretestructure that has a total height of 30m, five of whichare under the street level. A noteworthy characteristic ofthis building is its full climatization system that keeps itat a temperature of 22 1C independently of externalweather conditions. This climatization system reduces togreat extent internal thermal fluctuations, and thereforebuilding deformations. On the roof of this building thereis a GPS reference station that provides differentialcorrections in real time and measurement files to theusers in the area. With these data, users can performdifferential GPS in their projects using as base receiverthe reference station. Due to its characteristics, thisbuilding does not comply with the International GPSservice (IGS) guidelines so it cannot be included in the

Fig. 1. (a) Location and (b)

international network of reference stations, as thepredictable displacements exceed the set tolerance [6].

5. Methodology

5.1. Preliminary works

The calculation of the local transformation para-meters was done using the Helmert method fromcoordinates in the ETRS89 and ED50 systems, from atotal of eight points distributed around Pamplona. Theresiduals obtained from this transformation were lessthan 1 cm on each axis for every point, thus validatingthe use of these parameters in the study area. (Fig. 2).

Once all the transformation parameters were com-puted, we established a geodetic micronetwork aroundthe Fuerte del Prıncipe building constituted by threepoints. We choose these locations based on theirsuitability as reference stations according to the IGScriteria, keeping in mind the difficulty to find adequatelocations in an urban setting. Basically it is necessary

view of the building.

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Table 1

GPS accuracy in standard deviation terms (mm)

Axis XX 2.95

Axis YY 4.13

Axis ZZ 8.11

A. Seco et al. / Building and Environment 42 (2007) 393–399396

that these locations are stable and their view of the sky isfree of obstacles. To these criteria we added the need foruninterrupted power supply and safety. Fig. 3 shows thelocations of the three points of the micronetwork andtheir distances to the building.

Two of the points chosen were located on lowconcrete buildings and the third on a metal stand atground level. A dual-frequency Leica 300GPS receiverwas placed in each location.

Once the points were set on the ground, we made a24-h-long observation using the GPS receiver as basereference at the reference station installed on thebuilding, and we calculated and compensated in blockthe positions of the three base receivers and the referencestation. We fixed the coordinates of the reference stationof the building for the calculation because its WGS84coordinates are well known and the errors of movementof the building in 24 h are averaged and removed. Thelocal coordinates in ED50+local vertical of this net-work were calculated from the ETRS89 coordinatesobtained in each point by applying the computed localtransformation parameters.

Before determining the deformations observed in thebuilding, we calculated the relative positions of the basereceivers every 10min for 1 week. The objective was toimprove our knowledge of the accuracy in terms ofstability, reliability and accuracy of the calculatedposition. We calculated a total of 1008 positions for

Fig. 3. Geodetic micronetwork.

all the combinations between two base receivers, withthe accuracies shown in Table 1.

This is a good indicator of the GPS accuracy withregard to the different error sources in our study area.Fig. 4 shows an example of the temporal distribution ofthe GPS errors of 17 March 2003 in the Larrabide–Cordovilla baseline. It is noticeable that the differencesin coordinates vary over time and these variations havean undulatory nature and occur with both high and lowfrequencies [4]. High frequencies, called noise, behave aswhite noise and do not provide information. Lowfrequencies, called bias, are caused by errors notmodeled by the GPS position calculation algorithm orby the non-modeled part of errors that can be modeled[7]. As we can observe, GPS errors are neither constantnor random, but a function of time. This bias repeatsitself every 24 h [8].

5.2. Observation campaign

The observation period was increased continuouslybetween 1 March and 3 July 2003 for 125 days. Wechose this time period because this is when the biggestdifferences in temperature over a 24-h period occur, sodeformations would be easier to observe. Measurementswere done in 10-min intervals, as observation epochs ofthis duration guarantee ambiguity resolution andmaximize the storage capacity of the receivers.

6. Results

During the observation period, a new position of theGPS at the reference station here considered as ‘‘rover’’,supposed to be moving along the day was registeredevery 10min, relative to each of the three base receivers.The final position in each moment was calculated as themean of the three positions available, in relation to thethree base receivers. In most cases, the coordinatedifferences computed in relation with each of the basereceivers were just a few millimeters, an indication of thequality of the coordinates obtained. In those cases inwhich an observation differed for more than 5mm fromthe mean of the other two, was discarded, as thisdifference was assumed to be a reading error. Thismethod allowed us to see the coordinates’ differencesindividually and to detect the calculation errors in the

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Fig. 4. Temporal distribution of the GPS errors of 17 March 2003 in

the Larrabide–Cordovilla baseline: (a) XX -axis, (b) YY -axis and (c)

ZZ-axis.

Table 2

Building’s GPS coordinate variation in terms of standard deviation

(mm)

Axis XX 3.10

Axis YY 6.60

Axis ZZ 9.14

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the reference coordinates on 15 May 2003.

A. Seco et al. / Building and Environment 42 (2007) 393–399 397

observed baselines better that in block calculatedcoordinates.

Table 2 summarizes the variation of the coordinatesobtained in the roving receiver throughout the observa-tion period.

As it can be noticed, the computed variations inposition have small standard deviations, being smaller inplanimetry than in altimetry. This demonstrates thatbuilding displacements are very small. The biggeraltimetric error can be due to higher displacements inheight as well as to the lower accuracy of altimetricobservations that are characteristic of GPS technology.We can point out that building displacements are verysmall, and the comparison of the accuracy valuesobserved with those in Table 1 reveals that the buildingdisplacements are masked by the characteristic errors ofGPS observations.

Fig. 5 shows a typical set of differences in positioncomputed every 10min with respect to the referencecoordinates of the roving receiver during a 24-h period.It can be noted that the magnitude of the variations of

the computed coordinates as well as its change over timeare very small.

In order to minimize the effect of bias and noise onthe observed displacements of the building, we pro-ceeded to recalculate all the coordinates every 2 h, andwe also show the results in Fig. 5. This resampling

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Fig. 6. Expected displacements of the building as a function of the position of the sun: (a) in the morning, (b) around noon and (c) in the evening.

Table 3

Correlation analysis of displacements vs. weather variables

Temperature Direct radiation Wind

Displacement on XX-axis Pearson’s correlation �0.054 �0.059 0.000

Bilateral significance 0.000 0.000 0.963

Displacement on YY-axis Pearson’s correlation 0.199 0.070 0.000

Bilateral significance 0.000 0.000 0.969

Displacement on ZZ-axis Pearson’s correlation 0.099 0.091 0.016

Bilateral significance 0.000 0.000 0.134

A. Seco et al. / Building and Environment 42 (2007) 393–399398

eliminates the noise of the observations as well as thebias to a great extent, without affecting the accuracy ofthe results, as the displacements of the building occurvery slowly. In the visual analysis of the coordinatevariations calculated every 2 h we observed that thebuilding suffers a negative displacement with respect tothe XX -axis in the morning up to noon, when thedisplacements become positive, with an observed varia-tion over the reference position of 72mm. With respectto the YY -axis, the building remains fairly stable untilthe afternoon, in which it moves north approximately2mm in relation to the reference position. With respectto the ZZ-axis, we observed an increase of the height ofthe building during the central hours of the day ofaround 1 cm. These displacements observed in thebuilding agree qualitatively with the a priori expecteddisplacements as a function of the movement of the sunthroughout the day, which is represented in Fig. 6.

In order to quantify statistically the relation betweenthe environmental conditions and the building move-ment, we analyzed the correlation between the observeddisplacements and the weather variables such astemperature, direct solar radiation and wind that couldhave an influence. Weather data are available on a 10-min basis from the meteorological station in theLarrabide location. The result of this correlationanalysis is shown in Table 3.

Pearson’s correlation reflects the degree of linearrelationship between two variables. It ranges from +1

to �1. A correlation of +1 means that there is a perfectpositive linear relationship between variables. Thebilateral significance stated the compatibility amongthe statistical population and the measured information.We can see in Table 3 that only temperature and directradiation are significant, although the relationship isweak, with low values of the correlation coefficients r,that prevent from building a prediction model ofdeformations based on weather variables.

7. Conclusions

This experiment was carried out to answer two mainquestions:

‘‘Is GPS an adequate tool to monitor deformations ina building?’’ and ‘‘Is the GPS reference stationlocated on the roof of the Fuerte del Prıncipe buildingstable?’’

We have reached the following conclusions:

1.

GPS allows for a high degree of automation during thedata acquisition process. We used 16MB cards thatcan register data every 10min over a 10-day period.

2.

During the 6 months that the installation, testingand data acquisition period lasted, there was noequipment failure or loss of data, proving thereliability of this technology operating in all weatherconditions.

ARTICLE IN PRESSA. Seco et al. / Building and Environment 42 (2007) 393–399 399

3.

If small displacements are expected, we recommendthe static method with carrier phase observation.

4.

We recommend a minimum observation time of10min, as with shorter times there is a risk of notresolving ambiguities, therefore not having anaccurate position.

5.

It is difficult to find good locations for GPSobservations in urban environments, due to thecloseness of the buildings.

6.

The Helmert 3D transformation has proven to bevalid for relatively small work areas.

7.

We have established the errors of GPS positioningin static mode every 10min in terms of standarddeviation as 2.95mm in the XX -axis, 4.13mm in theYY -axis and 8.11mm in the ZZ-axis.

8.

GPS errors are not random in nature. They followbiases that are repeated every 24 h, coinciding withthe repetition period of the constellation, so theconstellation geometry has proven to be the mainfactor to influence the bias.

9.

Differences of a few millimeters between thecoordinates obtained from the receiver on thebuilding in relation to each of the base receiversreveals the high precision of the measuring methodbeing used.

10.

The variations in the position of the receiver locatedon the building during the observation period havebeen established in terms of standard deviation as3.10mm in the XX -axis, 6.60mm in the YY -axis,and 9.14mm in the ZZ-axis. These variations arevery similar to the ones obtained during thecharacterization of the accuracy of the observations,concluding that building distortions are masked inthe results we obtained. In any case it is proven thatthe displacements suffered by this building are verysmall.

11.

It has been possible to visually establish displace-ments of 2mm in the XX -axis, 2mm in the YY -axis,and 10mm in the ZZ-axis, based on the observationof the daily charts of measured displacements. Givenhow small these displacements are compared to the

precision of the GPS observations, it was notpossible to statistically establish the correlationbetween the displacements and the weather vari-ables.

12.

Though the experiment carried out has allowed us toestablish the convenience of GPS observations forthe monitoring of structures, the small value of thedisplacements observed in the building studied limitsthe conclusions obtained. We recommend that, forfuture experiments, the buildings chosen have largeexpected displacements that would allow extendingthe conclusions.

Acknowledgments

The authors would like to acknowledge the Govern-ment of Navarre for sharing their data and theircollaboration throughout this experiment.

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