Case Study

Study of Reliable Rapid and Ultrarapid Static GNSS Surveyingfor Determination of the Coordinates of Control Points

in Obstructed ConditionsMieczysaw Bakua1

Abstract: This paper presents a method for the surveying and reliable processing of Global Navigation Satellite System (GNSS) observationsin rapid and ultrarapid static surveying for determination of control-point coordinates. The presented technique allows for reliable determinationof coordinates, even in the case of highly difcult observation conditions (e.g., for control points situated along forest edges or entirely in theforest, near buildings, or in the vicinity of power-transmission lines). The paper also analyzes different projects of the global positioning system(GPS/GLONASS) networks from the perspective of their credibility and reliability. The control-point coordinates are determined by threeGNSS receivers positioned in line on a special base, providing a credible control of GNSS baselines during rapid and ultrarapid static surveys.The GNSS receivers are separated by the distance of 0.5 m. Given the gross errors in baseline coordinates determined that happen in practice,simultaneous use of three receivers for position determination of a control point allows reliable determination of the coordinates even undersignicantly obstructed access to satellites. The practical surveys were conducted using Topcon and Trimble receivers using real and virtualreference stations. The presented survey andGNSSdata-processingmethodology allowobtaining centimeter-level accuracy in a fewminutes ofGPS/GLONASS observations for control points located in obstructed conditions. DOI: 10.1061/(ASCE)SU.1943-5428.0000109. 2013American Society of Civil Engineers.

CE Database subject headings: Global positioning; Geodetic surveys; Data processing; Reliability; Case studies.

Author keywords: Global positioning; Geodetic surveys; Data processing; Reliability; Accuracy.

Introduction

The concept of using a permanent reference-station network for globalpositioning system (GPS/GLONASS) positioning was investigatedby several research groups over 10 years ago (e.g., Wanninger 1995;Wbbena et al. 1996; Raquet 1997; Lachapelle et al. 2000; Euler et al.2001; Landau et al. 2002). Currently, commonly used permanentGlobal Navigation Satellite System (GNSS) reference stations im-proved the efciency of GNSS surveys, both for real-time kinematic(RTK) and static surveys. In Poland, the permanent reference-stationnetwork [the so-called Active Geodetic Network EUPOS in Poland(ASG-EUPOS)] for the entire country emerged in mid-2008 (Bosyet al. 2008). Establishment of the ASG-EUPOS system (and the RTKservices in particular) caused immense interest in satellite technologiesamong land surveyors and commonuse ofGNSS techniques.A seriouslimitation to the satellite techniques is the need to perform the surveys inopen terrainwith fewobstructions along the satellite-receiver line. In thecase of terrain obstructions, the survey is more challenging and fre-quently even impossible, particularly forRTKsurveys.The coordinatesof control points determined in that case suffer from gross errors foreither static (Bakua 2012) or RTK surveys (Bakua et al. 2009).Sometimes it is found that, despite redundant observations and

appropriate survey-network adjustment, the coordinates of points sit-uated around various terrain obstructions, such as buildings, power-transmission lines, or forests, contain errors in the decimeter level.

Usually, control points intended for a variety of survey-cartographicworks are designed in open terrain without any obstructions or dif-culties in access to the satellites. However, there are situations pro-viding absolutely no chance to place control points in the open terrain,though the coordinates of the points must be determined (this happens,for instance, during construction of roads and motorways). In theconstruction of highways, often running through forest areas in whichtrees are cut down, control points are positioned at the forest edge oreven a few meters within the forest or in the vicinity of power-transmission lines (Fig. 1).

Determination of the coordinates for such control points becomesproblematic because of the obstructions in the reception of satellitesignals. What is more, in the case of synchronic GNSS sessions, theobservation session length depends on the observation conditions atthe point with the most obstruction in access to satellites, whichresults in a signicant extension of the eld survey time. Generally,the accuracy of GNSS positioning is signicantly lower under aforest canopy and under an obstructed sky (e.g., El-Mowafy 2000;Hasegawa and Yoshimura 2003; Lee and Ge 2006; Pirti et al. 2010;Uradzinski et al. 2008).

In some countries, there are online processing services, but as littleas 15 min of GPS observations are required (Schwarz 2008). How-ever, automated processing systems need good-quality GPS data andtake no responsibility for their results (Bakua et al. 2011).

Baseline Layout in Rapid Static Surveying

In the case of rapid static surveys, at least two reference stationsare usually used. As a consequence, this survey technique (applied

1Associate Professor, Dept. of Satellite Geodesy and Navigation, 5Heweliusza St., Univ. of Warmia and Mazury, 10-724, Olsztyn, Poland.E-mail: mbakula@uwm.edu.pl

Note. Thismanuscript was submitted on June 8, 2012; approved on April1, 2013; published online on April 3, 2013. Discussion period open untilApril 1, 2014; separate discussions must be submitted for individualpapers. This paper is part of the Journal of Surveying Engineering,Vol. 139, No. 4, November 1, 2013. ASCE, ISSN 0733-9453/2013/4-188193/$25.00.

188 / JOURNAL OF SURVEYING ENGINEERING ASCE / NOVEMBER 2013

J. Surv. Eng. 2013.139:188-193.

Dow

nloa

ded

from

asc

elib

rary

.org

by

UN

IVER

SID

AD

E FE

DER

AL

DE

VIC

OSA

on

02/2

3/14

. Cop

yrig

ht A

SCE.

For

per

sona

l use

onl

y; a

ll rig

hts r

eser

ved.

since the early 1990s) requires a minimum of three GNSS receivers.When using three GNSS receivers, two of them would have to bepositioned on points with known coordinates, whereas the thirdwould move across the terrain and collect satellite observations onunknown points, the coordinates of which are to be determined.However, the application of three GNSS receivers results in too fewredundant observations. As a consequence, a survey was conductedusing a larger number of receivers, i.e., three reference stations. Inthe case of such solutions, the length of the observation sessiondepends not only on the conguration of satellites, but also on thelength of baselines from the reference stations. If a larger number ofreceivers are available, synchronic sessions can be applied (i.e.,neighboring points surveyed by different GNSS receivers over thesame timeperiod). Fig. 2 presents the example congurations for fourand six GNSS receivers. In the case of four GNSS receivers, two arelocated on the reference points with known coordinates, whereas theother two are located on points the coordinates of which are un-determined [Fig. 2(a)]. Similarly, in the case of six receivers, three arepositioned on the reference stations, whereas the other three partic-ipate in the synchronic sessions and are positioned on unknownpoints[Fig. 2(b)]. The advantage of such a solution is that the baselinesbetween neighboring points (e.g., baselines: 12, 23, 31) areavailable [Fig. 2(b)], which increases the reliability of coordinatedetermination. However, the survey session for the points situatedaround obstructions should be increased. The length of the obser-vation session is usually signicantly longer than that of the survey inan open area.

Baseline Layout in Ultrarapid Static Surveying

The permanent reference-station system allows a choice of virtualreference stations in any location around the survey area. Never-theless, it is found that the number of virtual reference stations inpractical postprocessing surveys does not increase the reliability ofthe survey at all (Bakua 2012), although, theoretically, it providesredundant observations. This is attributable to the fact that the virtualreference stations situated within a few kilometers are very highlycorrelated with one another. Consequently, although the design ofthe GNSS network may be very similar, in the case of two referencestations (real orvirtual) andone control point, each stations credibilityis different. Two real reference stations are two different GNSSreceivers that are subject to various noises related to the observationlocation. On the other hand, two virtual reference stations around thegiven point are calculated with the use of identical GNSS data. They

have exactly the same satellites during the individual observationepochs, but such consistency is not encountered in real surveys.Currently, in ultrarapid static surveys in which GPS/GLONASSobservations are used, determination of short baselines is possibleafter approximately 1min of observation (Bakua 2012) in the absenceof any terrain obstructions. The current advances in GNSS-receiverdesign (compactness) have provided a natural opportunity for a re-placement of the current surveying procedures with entirely new onesthat are faster and more reliable. As a consequence, the synchronicsessions in rapid static can be converted to radial sessions inwhich thesurveys are conducted by three GNSS receivers (Fig. 3) positioned ateach survey point. Although the virtual reference stations (VRS) inpostprocessing may also be the reference stations, in the case ofultrarapid static surveys in which the session length is just a fewminutes, the use of a local reference station is recommended (Fig. 4)because, as is known, the accuracy of the coordinates for the pointbeing determined depends on the accuracy of the reference station(Grejner-Brzezinska et al. 2009). Usually, the local reference station(BASE) gathers observations for a relatively long time (e.g., 12 h),which also allows accurate determination of its coordinates on thebasis of permanent reference stations (REF1, REF2, and REF3) ata distance of some tens of kilometers. On the other hand, the VRSobservations are dependent on ionosphere and troposphere activity,which have signicant importance in rapid static positioning(Wielgosz 2010). Therefore, when one is interested in subcentimeteraccuracy, a survey using ultrarapid static survey techniques will bemuch more reliable when conducted in relation to the local reference

Fig. 1. Examples of control points located in obstructed conditions (in construction of highway)

Fig. 2.Baselines for GNSS in rapid static surveys: (a) two rover GNSSreceivers; (b) three rover GNSS receivers

JOURNAL OF SURVEYING ENGINEERING ASCE / NOVEMBER 2013 / 189

J. Surv. Eng. 2013.139:188-193.

Dow

nloa

ded

from

asc

elib

rary

.org

by

UN

IVER

SID

AD

E FE

DER

AL

DE

VIC

OSA

on

02/2

3/14

. Cop

yrig

ht A

SCE.

For

per

sona

l use

onl

y; a

ll rig

hts r

eser

ved.

station. As in GNSS-relative positioning, the accuracy of thedetermined coordinates depends on the quality of the referenceobservations; use of ones own local reference stations is rec-ommended for determination of survey network coordinates byultrarapid survey techniques, whereas the virtual reference station(Fig. 4) or a station connecting the local reference stations (Base-1and Base-2) should be treated as the control station. Given that thelocal reference station provides a high accuracy of the coordinatesdetermined, the application of three receivers can guarantee thereliability of the accuracy for the coordinates determined. Appro-priate network design allows full reduction of ionosphere and tro-posphere errors in GNSS observations.

Reliability is the other important issue in the determination ofcoordinates and depends not only on the number and congurationof satellites but also on the survey methodology and, above all, theprocessing of GNSS data. Although there are different methods ofambiguity resolution, practice shows that errors caused by incorrectdetermination of ambiguities are still encountered. From a practicalpoint of view, the most dangerous situation is when the ambiguity-validation process performs successfully according to the statisticaltests but has gross errors in coordinates in reality. The ambiguitysearching criterion is just a statistical criterion and is not guaranteedin all applications (Xu 2002). Therefore, the ambiguity-validationprocess is still an open problem (Verhagen 2004). Recently, a methodof precise positioning without explicit ambiguity resolution has beendeveloped (Cellmer et al. 2010), although this method also does notresolve the validationproblem.Taking into account the considerationsdiscussed, the author applied in practice a solution with three roverGNSS receivers. The survey unit consists of one local referencestationandaunit of three roverGNSS receivers positionedon a special

base. The base is equipped with a sensitive compass thanks to whichthe base orientation in the north/south direction is possible. The centralGNSS receiver is always positioned on a vertical line from the pointbeing determined, and the other two receivers are set at a distance of0.5 m from it. As a consequence, in each control point is a smallsubnetwork consisting of three receivers: left, middle, and right(i.e., three baselines, the distances of which arexed and known: leftright5 1 m; leftmiddle5 rightmiddle5 0.5 m). After conductingthe adjustment process for many small subnetworks, the author ad-ditionally veries the height, length, and orientation consistencyconditions for all the three baselines in the given subnetwork. Thatstage can be achieved by computing the differences in horizontal(i.e., north and east;dN anddE) andvertical (dH) coordinates betweenthe outside receivers (left and right) and the central receiver (middle)

dN Nleft Nright

2

2Nmiddle

dE Eleft Eright

2

2Emiddle

dH Hleft Hright

2

2Hmiddle

(1)

If the horizontal and vertical values are lower than assumed (e.g., dNand dE# 0:01m; dH# 0:03m), then the coordinates of the controlpoint are computed as the arithmetic mean

N Nleft Nmiddle Nright

3

E Eleft Emiddle Eright

3

H Hleft Hmiddle Hright

3

(2)

This means that only after satisfying the subnetwork consistencyconditions are the computed baselines added to the local and virtualreference stations (BASE and VRS) and the permanent referencestations (REF1, REF2, REF3) (Fig. 4) to obtain the nal coordinatesof the control points [Eq. (2)].

The baseline length may be also a constraint in attitude de-termination (e.g., Kuylen et al. 2006; Wang et al. 2009; Teunissen2012) and can improve the ambiguity success rate for land, ship, andaircraft applications (Teunissen at al. 2011; Giorgi et al. 2012).

Practical Application of Reliable RapidStatic Surveying

Practical application of the previously described survey methodwas determined not only by the willingness to obtain the reliable

Fig. 3. Rapid and ultrarapid static survey GPS/GLONASS survey units

Fig. 4. Idea of redundant and reliable GNSS network in rapid andultrarapid static survey

190 / JOURNAL OF SURVEYING ENGINEERING ASCE / NOVEMBER 2013

J. Surv. Eng. 2013.139:188-193.

Dow

nloa

ded

from

asc

elib

rary

.org

by

UN

IVER

SID

AD

E FE

DER

AL

DE

VIC

OSA

on

02/2

3/14

. Cop

yrig

ht A

SCE.

For

per

sona

l use

onl

y; a

ll rig

hts r

eser

ved.

coordinates, but also by the terrain conditions. In the case of mo-torway construction, in which the works are conducted in areas thatare subject to continual transformations with lack of access roads tothe control network points, sessions of synchronic GNSS surveysare no longer economical compared with the new survey method-ology, referred to as the subnet approach. In the subnet approach, thesurvey is performed by a single personwho plays the role of both thedriver and the specialist for GNSS surveys and data processing. Forpoints particularly exposed to noise, immediately after conductingthe satellite observations, the data can be downloaded very quicklyfrom the GNSS receivers to a laptop, and the computations can beconducted using just three rover GNSS receivers. Such computa-tions only take a fewminutes and ensure that a repeated survey is notnecessary. If, however, a result is unsatisfactory, a natural extensionof the observation session is possible until achievement of correctresults. Additionally, for the purpose of increasing the reliability, eachreceiver can be congured differently (e.g., with different survey-interval settings or a different elevation angle for satellites received).This eld procedure allows the application of any compact GNSSreceiver and various software packages for processing the GNSSobservations. Such computations analyze not only whether thebaselines have the xed solution, but also verify the following: The heights of the receivers (left, middle, and right) match with

requirements; and The distances leftmiddle, middleright, and leftright are 0.5,

0.5, and 1 m, respectively.After conducting the computations of baselines (leftmiddle,

middleright, and leftright) for the given control point, the con-sistency of the described conditions is calculated with the rangesassumed by the operator. It should be noted that the previouslydescribed procedure for survey and initial processing of GNSS datacan be implemented without observations from the reference sta-tions. The nal adjustment of the entire network is obtained afterincluding the baselines from the reference stations. Fig. 5 isa sample sketch of the adjusted baselines (generated on the GNSSdata from the practical application) based on the local reference

stations (Base-1, Base-2, Base-3, and Base-4), the virtual station(VRS), and three permanent stations (REF1, REF2, and REF3).

In Fig. 5, the local reference stations are positioned on the controlpoints with full access to satellites; they are also linked with oneanother by observations from the virtual reference station. Fig. 6also presents the values of dN, dE, and dH (of the nal simulta-neous least-squares adjustment), i.e., the differences in coordinatesbetween the outside receivers and the middle receiver [Eq. (1)]. The

Fig. 5. Baselines for GNSS based on subnet approach and Topcon Tools software

Fig. 6.Differences in determined coordinates for left, right, andmiddlereceivers for horizontal coordinates (dN and dE) and vertical coordinate(dH)

JOURNAL OF SURVEYING ENGINEERING ASCE / NOVEMBER 2013 / 191

J. Surv. Eng. 2013.139:188-193.

Dow

nloa

ded

from

asc

elib

rary

.org

by

UN

IVER

SID

AD

E FE

DER

AL

DE

VIC

OSA

on

02/2

3/14

. Cop

yrig

ht A

SCE.

For

per

sona

l use

onl

y; a

ll rig

hts r

eser

ved.

differences were generally below 5 mm for the horizontal coor-dinates and less than 15 mm for the height. Additionally, Fig. 7presents the distribution of residual values of horizontal and heightcoordinates adjusted by means of the least-squares method for theentire network, as presented in Fig. 5, using Topcon Tools software(Topcon 2007). As shown, the residuals are less than 1 cm for thehorizontal coordinates,whereas they are slightly higher for the verticalcoordinate. Of course, the observation time for conducting effectivesurveys under difcult conditions using the proposed survey methoddepends on the GNSS receiver type and the software applied. Nev-ertheless, knowing the potential of the available hardware and soft-ware, the operator determines the observation time for each pointdepending on the terrain conditions. In the presented survey meth-odology, any GNSS receiver and different software can be used,which allows the wide application of the proposed survey method-ology in cases in which satellite access is difcult (Fig. 1).

In the presented new method of surveying, the coordinates ofevery control point are determined with the use of nine baselines,provided that all the baselines are determined correctly and are notexcluded from the adjustment (solution a1-b1-c1 in Fig. 8). Inpractice, however, there are situations in which some baselines areexcluded from the adjustment owing to large errors in relation toother baselines. The rejected baselines in the least-squares adjust-ment have large values of residuals. It is well known that in the naladjustment, the values of residuals should be close to zero. Thenumber of redundant baselines is also very important. If it is assumedthat one baseline between rover receivers may be excluded (solu-tions b2, b3, and b4 in Fig. 8) and one baseline between REF1 andREF2 station and three rover GNSS receivers (solutions a2, a3, anda4; and c2, c3, and c4 in Fig. 8), there are over 60 combinations ofdifferent network diagrams for every control point in rapid or ultra-rapid static surveying. In all 64 combinations, Eq. (1) can be used tocheck the reliability and calculate the nal coordinates [Eq. (2)] with atleast ve redundant observations, more than in traditional rapid staticsurveying (Fig. 2). The number of possible network designs dependson the number of rejected baselines that can be accepted in the naladjustment.

In the traditional rapid static surveying, in which two referencestations are available and one rover GNSS receiver is used, no base-line can be rejected because there are only two baselines (REF1Middle and REF2Middle). The new presented method of GNSSsurveying also uses two reference stations, but if, for instance, threebaselines are excluded, there are still six baselines to determinecoordinates of an unknown control point (e.g., solutions a2-b2-c2, a2-b2-c3, and a2-b2-c4) (Fig. 8).

Traditional reliability in geodetic network (inmeaning of a quality-control criteria) can be augmented with geometrical strength analysis(Vanicek et al. 2001) or with redundant observations (Seemkooei

2001). In the presented method of rapid and ultrarapid GNSS sur-veying, reliability of nal coordinates is checked by Eq. (1). If thedifferences of coordinates [Eq. (1)] are in the accepted range pre-dened by an operator, it means that the quality-control criteria arefullled. Note that coordinates of the three GNSS receivers (left,middle, and right) must be determined based on the local (Base-1 orBase-2) andVRSstations (Figs. 4 and5) toprovide solution reliability.

The described method offers the achievement of subcentimeteraccuracy of horizontal coordinates in the postprocessing mode.Additionally, this approach can be used in RTKmode (Bakua et al.2012).

Fig. 7. Histograms of residuals in components of nal least-squares adjustment: (a) north; (b) east; (c) height

Fig. 8. Designs of different GNSS baseline combinations in reliablerapid and ultrarapid static surveying

192 / JOURNAL OF SURVEYING ENGINEERING ASCE / NOVEMBER 2013

J. Surv. Eng. 2013.139:188-193.

Dow

nloa

ded

from

asc

elib

rary

.org

by

UN

IVER

SID

AD

E FE

DER

AL

DE

VIC

OSA

on

02/2

3/14

. Cop

yrig

ht A

SCE.

For

per

sona

l use

onl

y; a

ll rig

hts r

eser

ved.

Summary and Conclusions

Obtaining reliable, accurate coordinates in rapidGNSS surveys doesnot depend only on theGNSS receiver class or the software used; thecorrect eld surveyconducting procedure is just as important. It isnot possible to obtain reliable and accurate coordinates from a poorlyconducted eld survey. Although the manufacturers of GNSSreceivers and software usually do not indicate the exact surveyprocedures, they provide the accuracy of a baseline between twopoints that can be achieved (mainly to optimal conditionsi.e., fullaccess to satellites). Establishment of permanent reference stations hasresulted in a natural change of survey and GNSS observation pro-cessing methodology for rapid static surveys. According to themethodology proposed, during ultrarapid static survey the eldsurvey is conducted by one survey team that collects GNSS obser-vations from consecutive points using three rover GNSS receivers.The presented technique allows obtaining better accuracy from rapidstatic surveys than in the case of applying traditional survey meth-odologies.Reliable coordinates of control points can be obtained fromGPS/GLONASS sessions lasting for a fewminutes, even in the caseof terrain obstructions.

References

Bakua, M. (2012). An approach to reliable rapid static GNSS surveying.Surv. Rev., 44(327), 265271.

Bakua, M., Kazmierczak, R., and Grunwald, G. (2011). Analysis of thepossibilities for applying the ASG-EUPOS system services for estab-lishing the detailed control networks. Tech. Sci., 14(2), 217228.

Bakua, M., Oszczak, S., and Pelc-Mieczkowska, R. (2009). Performanceof RTK positioning in forest conditions: Case study. J. Surv. Eng.,135(3), 125130.

Bakua, M., Pelc-Mieczkowska, R., and Walawski, M. (2012). Reliableand redundant RTK positioning for applications in hard observationalconditions. Artif. Satell., 47(1), 2333.

Bosy, J., Oruba, A., Graszka, W., Leonczyk, M., and Ryczywolski, M.(2008). ASG-EUPOS densication of EUREF permanent network onthe territory of Poland. Rep. Geod., 2(85), 105112.

Cellmer, S., Wielgosz, P., and Rzepecka, Z. (2010). Modied ambiguityfunction approach for GPS carrier phase positioning. J. Geod., 84(4),267275.

El-Mowafy, A. (2000). Performance analysis of the RTK technique in anurban environment. Aust. Surv., 45(1), 4754.

Euler, H. J., Keenan, C. R., Zebhauser, B. E., and Wubbena, G. (2001).Study of simplied approach in utilizing information from permanentreference station arrays. Proc., 14th Int. Technical Meeting of theSatellite Division of the Institute of Navigation, Institute of Navigation,Manassas, VA, 379391.

Giorgi, G., Teunissen, P. J. G., Verhagen, S., and Buist, P. J. (2012).Instantaneous ambiguity resolution in global-navigation-satellite-system-based attitude determination applications: A multivariate constrained ap-proach. J. Guid. Control Dyn., 35(1), 5167.

Grejner-Brzezinska, D. A., Arlsan, N., Wielgosz, P., and Hong, C. K.(2009). Network calibration for unfavorable reference-rover geometryin network-based RTK: Ohio CORS case study. J. Surv. Eng., 135(3),90100.

Hasegawa, H., andYoshimura, T. (2003). Application of dual-frequencyGPSreceiver for static surveying under tree canopy. J. For. Res., 8(2), 103110.

Kuylen, L. V., Nemry, P., Boon, F., Simsky, A., and Lorga, J. F. M. (2006).Comparison of attitude performance for multi-antenna receivers. Eur.J. Navig., 4(2), 19.

Lachapelle, G., Alves, P., Fortes, L. P., Cannon, M. E., and Townsend, B.(2000). DGPSRTKpositioning using a reference network.Proc., 13thInt. Technical Meeting of the Satellite Division of the Institute ofNavigation, Institute of Navigation, Manassas, VA, 11651171.

Landau, H., Vollath, U., and Chen, X. (2002). Virtual reference stationsystems. J. Global Positioning Sys., 1(2), 137143.

Lee, I., and Ge, L. (2006). The performance of RTK-GPS for surveyingunder challenging environmental conditions. Earth, Planets Space,58(5), 515522.

Pirti, A., Gumus, K., Erkaya, H., and Gursel Hosbas, R. (2010). Evaluatingrepeatability of RTK GPS/GLONASS near/under forest environment.Croat. J. For. Eng., 31(1), 2333.

Raquet, J. (1997). A new approach to GPS carrier phase ambiguity res-olution using a reference receiver network. Proc., 1997 NationalTechnical Meeting of the Institute of Navigation, Institute of Navigation,Manassas, VA, 357366.

Schwarz, C. (2008). Heuristic weighting and data conditioning in theNational Geodetic Survey Rapid Static GPS software. J. Surv. Eng.,134(3), 7682.

Seemkooei, A. A. (2001). Comparison of reliability and geometricalstrength criteria in geodetic networks. J. Geod., 75(4), 227233.

Teunissen, P. J. G. (2012). The afne constrainedGNSS attitudemodel andits multivariate integer least-squares solution. J. Geod., 86(7), 547563.

Teunissen, P. J. G., Giorgi, G., and Buist, P. J. (2011). Testing of a newsingle-frequency GNSS carrier phase attitude determination method:Land, ship and aircraft experiments. GPS Solut., 15(1), 1528.

Topcon. (2007). Topcon tools post-processing software, reference manual,Topcon Positioning Systems, Inc., Livermore, CA.

Topcon Tools 6.11 [Computer software]. Livermore, CA, Topcon.Uradzinski, M., Kim, D., and Langley, R. B. (2008). The usefulness

of Internet-based (NTrip) RTK for navigation and intelligent trans-portation systems. Proc., 21th Int. Technical Meeting of the SatelliteDivision of the Institute of Navigation, Institute ofNavigation,Manassas,VA, 14371445.

Vanicek, P., Craymer, M. R., and Krakiwsky, E. J. (2001). Robustnessanalysis of geodetic horizontal networks. J. Geod., 75(4), 199209.

Verhagen, S. (2004). Integer ambiguity validation: An open problem?GPS Solut., 8(1), 3643.

Wang, B.,Miao, L.,Wang, S., and Shen, J. (2009). Aconstrained LAMBDAmethod for GPS attitude determination. GPS Solut., 13(2), 97107.

Wanninger, L. (1995). Improved ambiguity resolution by regional dif-ferential modeling of the ionosphere. Proc., 8th Int. Technical Meetingof the Satellite Division of the Institute of Navigation, Institute ofNavigation, Manassas, VA, 5562.

Wielgosz, P. (2010). Quality assessment of GPS rapid static positioningwithweighted ionospheric parameters in generalized least squares.GPSSolut., 15(2), 8999.

Wbbena, G., Bagge, A., Seeber, G., Bder, V., and Hankemeier, P. (1996).Reducing distance dependent errors for real-time precise DGPS appli-cations by establishing reference station networks. Proc., 9th Int.Technical Meeting of the Satellite Division of the Institute of Navigation,Institute of Navigation, Manassas, VA, 18451852.

Xu, G. (2002). A general criterion of integer ambiguity search. J. GlobalPositioning Sys., 1(2), 122131.

JOURNAL OF SURVEYING ENGINEERING ASCE / NOVEMBER 2013 / 193

J. Surv. Eng. 2013.139:188-193.

Dow

nloa

ded

from

asc

elib

rary

.org

by

UN

IVER

SID

AD

E FE

DER

AL

DE

VIC

OSA

on

02/2

3/14

. Cop

yrig

ht A

SCE.

For

per

sona

l use

onl

y; a

ll rig

hts r

eser

ved.