The use of global navigation satellite systems for deformation analysis of the Dargovských hrdinov housing estate

Transcription

1 Acta Montanstca Slovaca Ročník 16 (011), číslo 4, The use of global navgaton satellte systems for deformaton analyss of the Dargovských hrdnov housng estate Pavel Kukučka 1, Slavomír abant and Gabrel Wess In ths paper, the deformaton analyss of the Dargovských hrdnov housng estate usng global navgaton satellte systems s descrbed. Theoretcally, t deals wth the reasons of formaton of slope deformatons, the ways of ther measurement, and wth the recent development and avalablty of GNSS. Partcular attenton s pad to the descrpton of the deformaton analyss technque, begnnng wth workng out the project, locatng by the GNSS, up to processng and testng of the deformaton network. The practcal part s based on the theoretcal knowledge and descrbes the measurement procedure, the equpment used, workng methodology and testng of the bondng network. Based on the results obtaned by the deformaton analyss, the paper offers nformaton about the recent condton of the nvestgated area. Key words: deformatonal analyss, global navgaton satellte systems, GMM Introducton The global navgaton satellte systems (GNSS) are ncreasngly used to montor landslde areas for the needs of deformaton analyss. The advantage of these measurements s manly n ther hgh relablty and accuracy, as well as ther ndependence from the season and tme of measurements. The man advantage s n elmnaton of the necessty of drect vsblty between the ponts whch s,however, replaced by the necessty of satsfactory recepton of the sgnal from GNSS satelltes. The only condton s drect access of satellte sgnals at the measured ponts. The hghest accuracy of usng GNSS s acheved by relatve measurements of the phase of a carrer wave. Statc relatve-phase measurement s a basc and most often used method n geodesy. Over the last decade, GNSS have essentally ncreased ther accuracy that s a precondton for ther use also n the feld of engneerng geodesy for determnng shfts of buldng structures and slope deformatons. Slope deformatons are processes n whch, for dfferent reasons, the stablty of rock slopes s affected resultng n the sldng movement of rock masses. They pose a danger to all the planned and accomplshed structures whether we are talkng about people s dwellngs or buldngs whch make our lfe on ths planet easer. A slope s prone to slde due to ts geologcal structure, propertes of rocks, hydrogeologcal condtons, etc. The cause of slope movements s gravtaton. The most mportant passve force s the compactness of rock. At present 4 GNSS systems are n use or beng developed (www1): Global Postonng System (GPS NAVSTAR), Global navgaton Satellte System (GONASS), Galleo - a system beng bult by the EU wth global coverage by the year 014, Compass - an ndependent system beng developed by Chna wth global coverage by the year 017. In Slovaka, there are networks n operaton whch are used for spatal determnng of poston: SKPOS and eca SmartNet. SKPOS s a permanent servce consstng of the network of reference statons that processes and n real tme provdes geocentrc coordnates for precse locaton of objects and phenomena. The reference statons recevng GNSS sgnals are postoned n geodetc ponts. The ponts are manly placed on the roofs of the buldngs of and regstres whch are connected to the department vrtual prvate network (VPS) to provde hgh qualty electronc communcaton. In the year 010, other 3 reference statons SKVT (Vranov nad Topľou), BREZ (Brezno), JABO (Jaslovské Bohunce) became avalable, thus ncreasng the total number of reference statons to 6. (www, www3) eca SmartNet s an ntegrated software package that enables to centrally control and operate ndvdual reference statons or the whole networks of reference statons. Ths network s a modular system wth new advanced solutons for hgh-accuracy RTK networks wth extensve coverage, centralzed dstrbuton of data and admnstraton of data access. At present, the network ncludes 0 reference statons. In comparson wth SKPOS that uses the technology of Vrtual reference statons (VRS), the eca SmartNet network uses MAC 1 Ing. Pavel Kukučka, Ing. Slavomír abant, PhD., prof. Ing. Gabrel Wess, PhD., Techncal unverzty of Košce, Faculty of mnng, ecology, procces control, and geotechnology, Insttute of Geodesy, Cartography and Geographc Informaton Systems, Park Komenského 19, Košce, Slovak Republc, pavel.kukucka@tuke.sk, slavomr.labant@tuke.sk, gabrel.wess@tuke.sk. 319

2 Pavel Kukučka, Slavomír abant and Gabrel Wess: The use of global navgaton satellte systems for deformaton analyss of the Dargovských hrdnov housng estate (Master Auxlary Concept) whch s a newer technology. Moreover, MAC network soluton provdes homogenous accuracy ndependent from the dstance from the reference staton. (www4). ocaton of deformaton The Dargovských hrdnov housng estate, also known as Furča s part of the town of Košce located n the dstrct Košce III and s an ndependent cadastral area wth acreage of 1109 hectares. The housng estate stretches n the Košce basn on the top of a major morphologcal elevaton between the valley of the Rver Hornád n the west and the Torysa Rver n the east. The area n queston (Fg. 1) s demarcated by the roads Prešovská cesta, Sečovská cesta, the streets Treda armádneho generála. Svobodu and Herlanska. It s stuated n the Košce basn n the sub-unt of the Toryska hlly land and les m above the sea level. ocated n the area there can be found the Opátsky fault (of the Zemplnsko- Berehovsky system) that runs along the foothll of the western front slopes as well as of the Hornad system,.e. western Kosce fault and Kostoľanský fault. The area les n the warm clmatc zone T3 wth average annual temperatures varyng from to 8.9 C and wth on average 118 frost days per year, and average depth of sol freezng 111 cm. Accordng to SHMU measurements, the average long-term total amount of ranfall s mm. Fg. 1. Area map. Measurement of the network and evaluaton of sgnals Measurements were performed usng two types of doublefrequency recevers eca GPS900CS, eca GPS100 and a dgtal levellng devce Topcon D-101C. eca GPS100 (Fg. ) and eca GPS900CS (Fg. 3) are double-frequency geodetc RTK recevers that allow to use statc, fast statc, knematc and On the fly methods for measurements. Topcon D-101C allows to perform the levellng measurement usng the method of techncal, precse and very accurate levellng as well as layng-out. Pror to the measurement tself, thorough reconnassance of the terran was carred out n order to nvestgate the condton of the pont feld and select sutable observed ponts (herenafter OP) n the rsky areas. After the reconnassance, t was found out that n the area there were a lot of ponts servng for assessment of slope movements, however, some of these ponts were reconstructed and some of them were destroyed. All the ponts were stablzed as nterconnected geodetc ponts (lned drlled wells ftted wth a metal ppe and flled wth concrete). On the surface of each pllar there was cemented a metal plate wth a drlled hole 16 mm n dameter whch provded dependent centrng and the benchmark was ftted at the lower part of the pllars (Fg. 3). The choce of sutable OP n the rsky areas was dependent on the densty of the bult-up area and vegetaton cover. 5 OP marked B -6, B-10, C-0, P-III-1, P-IV-1 (Fg. 4) were selected for montorng slope deformatons stablzed wth the lned drlled wells where there was an ncreased antcpaton of movement. Selecton of these ponts was performed takng nto consderaton the opton of the best possble recepton of sgnals from the satelltes. Harngeš, Fg.. Measurng at the pont Harngeš. Fg. 3. Measurng at the pont P-IV-1. 30

3 Acta Montanstca Slovaca Ročník 16 (011), číslo 4, Varkapa and Šroká ponts were used for processng as reference ponts (herenafter marked as H, V, S) stablzed by naled sgns wth holes n stone prsms of the sze 0 x 0 x 70 cm protected by concrete rngs and protectve rods (Fg. ). (Sabova, 007, AMS) Before the expermental measurement, whch was performed on 13 June 009, a sutable method of measurement was selected to ensure the hghest accuracy of observaton. The selected method approprate for the ntended measurement was a statc method wth 3 peces of eca GPS100 equpment and 5 peces of eca GPS900CS equpment (+1 back- up) avalable to carry out the mea- these types of equpment, apart from ther techncal parameters, les manly n the fact that eca GPS100 receves only GPS sgnals and eca GPS900CS allows to recevee sgnals from the GPS satellte system as well as surement. The dfference between from GONASS (GNSS recever). That s because of ths very dfference that the posto- was nng of the equpment reassessed wth the concluson that GPS (eca GPS100) recevers should be nstalled on the reference ponts (here- was not blocked and a smaller number of observaton satelltes would be requred. GNSS (eca GPS900CS) recevers were pos- toned on the OP where a clear vew of the sky s sometmes lmted and t was necessary to ncrease the number of obser- vaton satelltes. In ths case these were GONASS satelltes that were used. nafter RP) H, V, S, where the sky Fg. 4. Stuaton of the deformaton networks. Before the measurement t was necessary to set the same mode of measurement for every pece of equpment to avod dstorton of the results of the measurements due to the wrong settng. eca GPS900CSS equpment was postoned on all of the OP usng a Zess pad and two types of fxng bolts. A clamp bolt was used for grppng of the Zess pad to the pllar thus provdng vertcal centrng; the second one was used for grppng of the antenna n the Zess pad. evellng was performed usng pre-rectfed optcal centrng devce mbedded nto the Zess pad. Recevers eca GPS100 were postoned on the RP on trpods wth three telescopc legs usng the Zess pad and a specal bolt. A rectfed optcal centrng devce was used for levellng the devces. Durng the observaton, the heght dfference of the recevers antennas and benchmarks of the ponts was determned by the levellng method usng a dgtal levellng devce Topcon D 101C. For each measurement the horzontal poston was adjusted so that the horzontal adjustment lne n the telescope of the levellng devce was the same as the heght determned on the antenna (Fg.5) and consequently the heght was electroncally read off several tmes for more precse adjustment on the code levellng lath placed on the benchmark of the pont. The resultng heght was calculated on the bass of the arthmetcal average. The control measurement of the slant dstance was performed by applyng an addtonal measurng tape to compare or eventually detectt gross errors. 4-hour observatons were recorded at all ponts Fg. 5. Feld of vew by the measured heght of wth the tme of measurement from 11:00-15:00. antenna. 31

4 Pavel Kukučka, Slavomír abant and Gabrel Wess: The use of global navgaton satellte systems for deformaton analyss of the Dargovských hrdnov housng estate Processng of the measured data was carred out usng the company software eca Geo Offce 5.0 (GO) where the fact was taken nto account that n the area of the town of Košce there were RP of two ndependent from each other permanent GNSS servces, namely KUKE reference staton of SKPOS servve placed on the buldng of the and regstry n Košce and KOSI reference staton of eca SmartNet network placed on Delluss pavlon on the campus of the Techncal Unversty. The data from the reference statons for the gven tme of measurement were receved from Ms Šalátová (data from KUKE) and from Mr E. Frohmanna, PhD (data from KOSI) upon wrtten requests n the exchange format RINEX. In order to compare the pont poston determned by SKPOS and eca SmartNet servce, n the software processng t was always only one pont was chosen as a RP from the par of KUKE and KOSI ponts and the other was not used so that two ndependent sets of the coordnates of the OP n the coordnate system Unfed Trgonometrc Cadastral Network 03 (UTCN 03) were obtaned. By comparson of the ndvdual sets of coordnates t was proved that the data provded by the state permanent servce of SKPOS observaton statons and the prvate eca SmartNet network were at the same accuracy level (Tab. 1). For the purposes of the deformaton analyss performed ndependent processng of the bondng network was performed whch corresponded to processng n the year 003 when the poston of the ponts was carred out usng the GNSS method and the heght was determned usng the hght precson levellng (HP) method. In the year 003 the ponts H, V, S were used as RP and because of that for the year 009 the KOS and KUKE ponts were excluded from processng. In the year 003, the HP method was used to determne the heghts of the ponts usng the levellng devce Zess N 007 wth an average klometer error 0,5 mm/km and n the year 009 determnaton of the heghts was carred out usng the GNSS statc method wth the vertcal poston determnaton 10 mm D ppm. As the yearly measurements dd not have the same precson level, and the ntal comparson of heghts by the GNSS method wth the year 003 showed consderable dfferences, processng of the 3D network was cancelled, n whch sgnfcant heght dfferences negatvely affected the overall results, and only postonng processng of the bondng network was carred out. Intal pre-processng of the observaton data was performed n GO 5.0 software envronment where, for the sake of updatng, transformaton of the coordnates of the OP and RP from the coordnate system ETRS 89 nto the local coordnate system UTCN 03 (Unfed Trgonometrc Cadastral Network 03) was carred out usng the transformaton parameters UTCN 03. Transformaton of the year 003 used for the deformaton analyss was performed usng smlar transformaton (Šütt, 1997), where on the bass on the respectve formulas the accuracy of the transformaton of ndvdual coordnates of the OP was determned wth an average value of the mean error of the transformaton mm. Gauss-Markov model wth full rank Postonng coordnates of 5 OP and 3 RP as well coordnate dfferences between them (Fg. 5) were used for D bondng processng of the estmates of unknown parameters usng Gauss-Markov model (GMM) gven by: v = AdCˆ d = A( Cˆ C ) ( ), Σ = s Q, 0 Tab. 1. Dfferences of coordnates of ponts. KUKE KOSI SKPOS SmartNet [m] [m] [mm] number of ponts - functonal part, - stochastc part, coordnate dfferences The structure of ndvdual values n ths network s defned by m = 5 GNSS vectors obtaned through observatons, n = m = 50 observaton components, b = 8 OP and k = b = 16 determned by parameters, wth k = 10 beng only for the OP. (Gašnec et al., 000; Pukanská et al., 007, Sabová et al., 007; Wess et al., 008): Vector of observatons (50,1) s created by poston coordnate dfferences between ndvdual network ponts whch are taken from the processng of vector n GO 5.0 software. The sequence of coordnate dfferences s gven n alphabetcal order of vector startng ponts based frstly on observed ponts and then on RP wth coordnate dfferences X, Y. Ths order s mantaned for the entre adjustment. B-6 B-10 C-0 P-III- 1 P-IV- 1 X Y Z X Y Z X Y Z X Y Z X Y Z (1) 3

5 Acta Montanstca Slovaca Ročník 16 (011), číslo 4, A vector of approxmate coordnates of OP C (10,1) s created by poston coordnates of OP, whch were taken from ntal processng n GO 5.0 software. A vector of approxmate observatons (50,1) s gven by relatve coordnate dfferences of approxmate coordnates of gven ponts = f ( C ). The order of ndvdual dfferences s the same as n vector of observatons. The vector of observaton addtves d (50,1) s gven by the dfference of the elements of the observaton vector and the vector of approxmate observatons : d = and s determned n mlmetres. Cofactor matrx Q (50,50) s a dagonal matrx wth cofactors on the man dagonal. Indvdual cofactors σ were calculated from the relatonshp Σ X, Y q =, where 0 = σ σ, σ = ( 5mm ppm) σ 0 n and the accuracy of the determnaton of the length of ndvdual vectors usng the statc method quoted by the manufacturer s 5 mm + 0,5 mm/km of the length. Confguraton matrx A (partal dervatons, desgn) characterses network geometry (confguraton) of the network. As there were 3 RP n the gven network, the matrx A (50,16) was dvded nto actve part A (50,10), whch was further processed and passve part A (50,6), whch belonged to 3 RP and was defned as: f ( C ) A =. If vectors and C are related to each other, the coeffcents wll have values { 1,1} C C = Cˆ and f not, they wll have value {} 0. Vector of estmates of auxlares of determned coordnates dc ˆ (10,1 n mm was determned usng a matrx multplcaton: dcˆ 1 1 = ( A Q A) A Q ( ) = N A Q d. () The vector of adjusted coordnates of the OP Ĉ (10,1) s determned by addton of the vector o of approxmate coordnates C and the vector of estmates of coordnate addtves for the calculated ponts dc ˆ : Cˆ = C + dcˆ. (3) Vector of correctons v (50,1) of observed values: v = AdCˆ d. (4) Vector of adjusted measured values ˆ (50,1): = + v (5) v Q v Estmated varance faktor s 0 (1,1) : s0 =. ( n k) (6) The covarance matrx Σ Ĉ (10,10) of adjusted coordnates X, Y Σ s Q Cˆ = 0 C ˆ (7) where on the man dagonal there are varances showng the accuracy of the estmates of the calculated coordnates. Covarance matrx of the adjusted values of the observed quanttes s Σ ) (50,50) : Σ ) = s Q) 0 (8) Redundancy matrx R (50,50) s the product of cofactor matrx 1 1 R Q Q = ( Q AN A ) Q. (9) = V Q and cofactor matrx of correctons Q : Tab. 3. Coordnates of OP and ther accuracy. V Table shows measured, approxmate and adjusted numercal data that relate to the measured values havng vector sze (50,1) gvng unts of quanttes. The total of the elements on the man dagonal of the redundancy matrx fulflls the equaton gven by the relatonshp to the redundances of the network: n tr( R) = r + r r = r = r = n k = = n = 1 1 Table 3 contans approxmate and adjusted numercal data that relate to the determned coordnates of the sze of vectors (10,1) gven wth the unts of ndvdual quanttes. Ponts coordnates o C (10,1) dc ˆ Ĉ σ (10,1) (10,1) (10,1) Ĉ [ m ] [ mm ] [ m ] [ mm ] X B Y B X B Y B X C Y C X P-III Y P-III X P-IV Y P-IV

6 Pavel Kukučka, Slavomír abant and Gabrel Wess: The use of global navgaton satellte systems for deformaton analyss of the Dargovských hrdnov housng estate After processng the measured quanttes t was necessary to verfy by statstcal testng f n the vector of the measured values there were any measurements contanng gross errors. Tab.. Measured data and ther accuracy. GNSS vector o (50,1) d man dag. v (50,1) (50,1) (50,1) ˆ σ (50,1) (50,1) ˆ man dag. Q (50,1) from pont to pont X/ Y [ m ] [ m ] [ mm ] [ mm ] [ m ] [ mm ] R (50,1) B-6 B-10 X Y B-6 C-0 X Y B-6 P-III-1 X Y B-6 P-IV-1 X Y B-6 H X Y B-6 S X Y B-6 V X Y B-10 C-0 X Y B-10 P-III-1 X Y B-10 P-IV-1 X Y B-10 S X Y B-10 V X Y C-0 P-III-1 X Y C-0 P-IV-1 X Y C-0 H X Y C-0 S X Y C-0 V X Y P-III-1 P-IV-1 X Y P-III-1 H X Y P-III-1 S X Y P-III-1 V X Y P-IV-1 H X Y P-IV-1 S X Y H V X Y S V X Y Testng of the network The adjusted network structure was tested usng varous methods. Sutablty of selecton of GMM used for adjustment was verfed by a global test of an estmatng model and the presence of remote measurements was tested by a Pope Tau method, Krűger's test and testng of dverged values. 34

7 Acta Montanstca Slovaca Ročník 16 (011), číslo 4, s0 In the global test, test statstcs T gven by the calculaton T = ( n k) = 0, 806 was compared wth σ 0 the crtcal value wth dvson χ (ch-square) at the level of sgnfcance α = 0, 05 and grades of freedom f = ( n k) : χ α ( n k) = 1, 484 where n = m = 50 represents the number of observaton components and k = b = 10 represents the number of determned parameters. As the crtcal value was hgher than the testng crteron χ α > T, the test dd not confrm any dfferences between the mathematcal model of processng and the observatons used, therefore t can be consdered as not dstorted and observatons as not contanng gross errors. (Caspary, 1987) Deformaton analyss Assessment of changes n the area n queston n the md perod t and t + 1 was carred out based on changes n the coordnates of the ponts n the gven area. Snce, as the result of carryng out bondng processng of the network the coordnates of the OP - B-6, B-10, C-0, P-III-1 and P-IV-1 n the UTCN system for the year 009 were adjusted, the deformaton analyss was performed. The stablty of the gven ponts n the perod between the years 003 and 009 was nvestgated. Through compa-rson of the adjusted coordnates of the OP n the years 003 and 009 the deformaton vector was determned gven by: Tab. 4. Testng of the networks wth local tests. testng of Pope Tau method Krűger's test from pont to pont dverged values TKRIT TX TY TKRIT TX TY TKRIT TX TY B-6 B B-6 C B-6 P-III B-6 P-IV B-6 H B-6 S B-6 V B-10 C B-10 P-III B-10 P-IV B-10 S B-10 V C-0 P-III C-0 P-IV C-0 H C-0 S C-0 V P-III-1 P-IV P-III-1 H P-III-1 S P-III-1 V P-IV-1 H P-IV-1 S H V S V t dcˆ = t t t dxˆ dyˆ ˆ dz = t003 t003 t003 ˆ t X ˆ t Y ˆ t Z Xˆ Yˆ Zˆ, = 1,,..,5. (10) Table 5 gves the dfferences of the coordnates for all the OP. The values of these dfferences were up to 6 mm only for the pont B-6 and P-VI-1 where the dfference of coordnates n the drecton of the y-axs was mm and n the drecton of the x-axs 1.9 mm. Postonal shft (Fg. 6) of these ponts was the bggest for the ponts B-6 and P-VI-1 whch was mm and mm whereas for other ponts t was up to 4.74 mm. Through subsequent testng by a global test and a local test t was nvestgated whether coordnate dfferences occured through movememts of ponts or arose based on the errors n the measurements and processng. Tab. 5. Coordnates of OP n the perod of 003 and 009. Epoch 009 Epoch 003 coordnate Postonal Bod dfferences shft [m] [m] [mm] [mm] B-6 X Y B-10 X Y C-0 X Y P-III-1 X Y P-IV-1 X

8 Pavel Kukučka, Slavomír abant and Gabrel Wess: The use of global navgaton satellte systems for deformaton analyss of the Dargovských hrdnov housng estate The stablty or nstablty of all the ponts was tested by the global test wth t003 o hypothess : ˆ t009 H ˆ 0 C C = 0. The testng statctcs T = 0, 419 was compared wth the crtcal value F - random varable T at the sgnfcance level α = 0,05 and degrees of freedom f = k 10, f = n k = : F ( α, f, f ),065. α 1 1 = 1 = It s gven that T < Fα, therefore the dfferences of coordnates can be consdered as a statstcally nsgnfcant stochastc change of the poston of a pont, and because of that all the OP can be consdered as stable. Though the global test dd not prove the self-movement of the ponts, localzaton testng was conducted to examne the stablty of ndvdual ponts. For each pont of the deformaton network the localzaton testng statstcs T was used gven by the relatonshp: ) ) dc Q ) dc dc T = F ( f = k1, f = n k), α s0 k1 where k 1 = s the number of the tested parameters of the partcular pont whch was compared wth the crtcal value T KRIT ( F α ) (Tab. 6) at the sgnfcance level α = 0, 05 and degrees of freedom f = k 1 =, f = n k = (Wess et al., 007). From Table 6 t s obvous that n the local testng of ponts n all the cases the crtcal value was bgger than the testng crteron, hence the OP - B-6, B-10, C-0, P-III-1 a P-IV-1 as well the area defned by these ponts could be consdered as stable. Graphc testng usng confdence ellpses (Sabová et al., 00) confrmed the conclu-sons drawn from global and local testng of the stablty of the OP located n the Dargovských hrdnov housng estate (Fg. 6). As the posto-nal vector of the pont shft n the perod of the years 003 and 009 was located nsde the confdence ellpse (Tab. 7), there was no shft and therefore t was about the accumulaton of the survey errors. = (1,,...,5) Tab. 6 ocal testng of ponts ponts T T KRIT B-6 B-10 C-0 P-III-1 P-IV-1 X Y X Y X Y X Y X Y (11) Tab.7. Parameters of the relatve confdence ellpses a [mm] b [mm] σ α [ g ] B B C P-III P-IV Fg. 6 Graphc testng wth confdence ellpses n the perod between 003 and 009. If a pont n the year 009 was outsde the ellpse, then we could state that there was a shft whch would be supported by the statstcal testng. From the conclusons of the deformaton analyss t appears that n the perod between the years 00 and 009 there occurred no shfts of ponts whatsoever and that coordnate dfferences that arose were only due to survey errors whch was proven by the dentfcaton test. 36

9 Acta Montanstca Slovaca Ročník 16 (011), číslo 4, Based on these conclusons, we can consder the area represented by the OP - B-6, B-10, C-0, P-III-1 and P-IV-1 as stable, however t s necessary to further montor ths area. Concluson Montorng of landslde areas s necessary to ensure safety and dentfy rsk factors. When montorng t s crucal to pay partcular attenton to developng the project and the choce of the method of work. It s always essental to consder economc, tme and accuracy crtera. The use of GNSS for the needs of deformaton nvestgaton appeared to be most useful both n terms of tme, relablty and precson. The advantage of ths choce was that determnaton of the vertcal poston of the ponts was less accurate what n case of processng the 3D deformaton network would affect the overall results. For that reason t s more advsable to determne the poston of the surveyed ponts usng the method of very precse levellng. As follows from the results of the deformaton analyss, coordnate dfferences of the surveyed ponts are statstcally sgnfcant whch s proved by the stablty of the area. References Caspary, W. F.: Concepts of network and deformaton analyss. 1 st edton. Kensngthon: School of surveyng The Unversty of New South Wales, p., ISBN Gašnec, J., Gašncová, S., Rajnak, M.: To the problem of the adjustment of D geodetc networks. In: Current ssues of land surveyng and engneerng geodesy : proceedngs from the nterenatonal scentfc semnar : Herľany, 9 10 October 000, FBERG, TU Košce, pp. 38-4, 000, ISBN Pukanská, K. and Wess, G.: The accuracy of locaton ponts usng GPS technology. Coal - Ores - Geologcal Survey, 14, 9, pp , 007, ISSN Sabová, J., Gašncová, S.: Graphc testng n deformaton montorng. Acta Montanstca Slovaca. Vol. 7, 00, no., pp , ISBN Sabová, J., Jakub, V.: Geodetc deformaton montorng. 1 st edton. Košce: Edtor centre and edtoral offce AMS, F BERG, Techncal Unversty of Košce, p., ISBN Sabová, J., Pukanská, K.: Projekt der Deformatonsuntersuchungen. Acta Montanstca Slovaca. Vol. 1, 007, Specal Issue no. 3, pp , ISBN Šütt, J.: Devatonless geodetc transformatons. Acta Montanstca Slovaca, Vol., 1997, no. 1, pp. 1-10, ISBN Tometz,.: Košce - Dargovských hrdnov housng estate, horzontal wells. Regstered n the Archeve of the geologcal survey, TUKE, 004. Wess, G., Gašnec, J., Engel, J., abant, S., Rákay, ml., Š.: Effect ncorrect ponts of the ocal Geodetc Network at results of the adjustment. Acta Montanstca Slovaca, Vol. 13, 008, 4, pp , ISBN Wess, G., Jakub, V.: The test verfcaton of 3D geodetc ponts and ther changes. Acta Montanstca Slovaca. 1, Specal Issue 3, 007, pp ISSN www1: Global navgaton satelte system [onlne]. [ct ]. Avalable at: www: Geodetc and Cartographc Insttute Bratslava [onlne]. [ct ]. Avalable at: www3: Web server SKPOS [onlne]. [ct ]. Avalable at: www4: SmartNet Slovaka [onlne]. [ct ]. Avalable at: 37