The results of the GPS network adjustment are the adjusted co-ordinate
components of vectors, the co-ordinates of network stations and accuracy
data. We have more options  to convert the co-ordinates into national
datum depending on whether the co-ordinates of the national initial station
are obtained from absolute point positioning (local datum) or the initial
station is included in the EUREF network having known co-ordinates. In the
latter case a quasi transformation can be performed with the known
transformation parameters. To reduce discrepancies we apply  2D Helmert,
affine  and 5th order polynomial transformations

Papp, Erik

Szűcs, László

Varga, József

English

Periodica Polytechnica (Budapest University of Technology and Economics)

PERIODICA POLYTECHNICA SER. CIV. ENG. VOL. 46, NO. 2, PP. 199–204 (2002)HUNGARIAN GPS NETWORK TRANSFORMATION INTODIFFERENT DATUMS AND PROJECTION SYSTEMSErik PAPP, László SZŰCS and József VARGADepartment of Geodesy and SurveyingBudapest University of Technology and EconomicsH–1521 Budapest, HungaryReceived: Jan. 25, 2002AbstractThe results of the GPS network adjustment are the adjusted co-ordinate components of vectors, theco-ordinates of network stations and accuracy data. We have more options to convert the co-ordinatesinto national datum depending on whether the co-ordinates of the national initial station are obtainedfrom absolute point positioning (local datum) or the initial station is included in the EUREF networkhaving known co-ordinates. In the latter case a quasi transformation can be performed with theknown transformation parameters. To reduce discrepancies we apply 2D Helmert, affine and 5thorder polynomial transformations.Keywords: GPS data processing, transformation.1. IntroductionThe application of GPS technology becomes more important nowadays. Every usercan choose from several manufacturers products including geodetic accuracy GPSreceivers and navigational receivers as well according to their demand and financialsituation. Most of the users apply such software systems for data processing whichbelong to receivers. Consequently the obtained results are very rarely suitable forimmediate practical aims. In most cases further computations needed for the ob-tained data can be applied to a user defined co-ordinate system. In the followingwe present kinds of computation methods and procedures which allow to convertGPS observable results processed by manufacturer’s software into the Hungarianunified national projection system (EOV), Gauss-Krüger and UTM projection sys-tems. The applied methods satisfy the accuracy requirements both for the geodeticand the geomatic fields. Using the national GPS network point with known EUREFco-ordinates, the adjusted co-ordinates will be in EUREF system as well. It is veryimportant to distinguish these two cases (EUREF and local datum) because one canobtain even 100 meter differences in co-ordinates for the same point applying theabove mentioned two methods (HOFMANN–WELLENHOF et al., 1994).200 E. PAPP et al.2. Transformation between GPS and National Geodetic DatumsIt could be seen that the derived co-ordinates refer either to local or to EUREFgeodetic datum (ÁDÁM–BORZA, 1995). Because none of them correspond withthe currently applied geodetic datum in Hungary, consequently, a transformationhas to be performed. Depending on source systems there are different options fortransformations. One can compute the transformation parameters in advance forlater use if the geodetic control network points have EUREF and unified nationalprojection system (EOV) co-ordinates as well. In contrast to the earlier case us-ing local datum we have to measure common points with GPS for determininglocal transformation parameters. In the following we present three transformationmethods. The first one can always be applied if at least three common points areavailable. The others have been established to perform transformation betweenEUREF and HD72 geodetic datums.2.1. The Seven Parameter 3D TransformationThe seven parameter spatial similarity transformation can be performed betweentwo 3D systems belonging to two different geodetic datums. The transformationparameters are the 3 rotation angles, the 3 translation parameters and the scale factor.For determination of seven parameters at least three common points are necessary3D co-ordinates of which are known in both systems. On the basis of three pointswe can set up nine equations for determining transformation parameters. As thenumber of equations (9) is greater than the number of unknown parameters (7) wecan use least-square adjustment technique for determination of the parameters. Thismethod can be applied between any arbitrary systems where the 3D co-ordinatesof common points are known. If the plain co-ordinates of the common points areavailable, we can compute the ellipsoidal latitudes and longitudes. The ellipsoidalheight can be obtained by adding orthometric height to the geoid undulation in agiven point. Using such ellipsoidal latitudes, longitudes and heights, it is possibleto compute the 3D co-ordinates. The step by step solution is described in (PAPP etal. 1997, 1999; VARGA 1986).3. Two Conversion Alternatives Using EUREF SystemWe used the Hungarian national GPS frame network consisting of 43 points withgiven EUREF and HD72 ellipsoidal co-ordinates and EOV plane co-ordinates aswell. The reference surface of EUREF geodetic datum is the GRS80 ellipsoidpractically with the identical parameters as WGS84 ellipsoid. The existing ref-erence system called Hungarian-Datum 1972 (HD72) was developed by applyingthe ellipsoid of the IUGG Geodetic Reference System-1967. In Hungary a doubleprojection is used, which means that first we project from IUGG67 ellipsoid to theHUNGARIAN GPS NETWORK TRANSFORMATION 201local Gaussian sphere, then from the sphere to the oblique conformal cylindricalprojection system (EOV) (VARGA, 1986).3.1. Co-ordinate Transformation Using Differences of Latitude and LongitudeFirst we computed geodetic latitudes and longitudes of the points at the GRS80 el-lipsoid, using the 3D Cartesian co-ordinates of the Hungarian national GPS framenetwork consisting of 43 points. Then we computed the geodetic latitudes and lon-gitudes of the same points at the IUGG67 ellipsoid from EOV 2D plain co-ordinates.The next step was the computation of the i , i co-ordinate differences at allpoints and the ,  arithmetical means determination. After this we changedthe GRS80 ellipsoidal co-ordinates of every newly observed point with d and dvalues and these approaching IUGG67 (), () co-ordinates were used for compu-tation of the approximate EOV co-ordinates. The obtained approximate EOV (Y ,X) co-ordinates are near to the real EOV Y , X co-ordinates which can be directlyused for geomatic purposes. In order to meet geodetic accuracy requirements andin geodetic applications we apply a 2D Helmert transformation, 2D affine trans-formation or fifth-order polynomial transformation to reduce transformation errors.Isolines had been constructed using remaining discrepancies (Fig.1–3).Fig. 1. Residuals after 2D Helmert transformation [m]3.2. IUGG67 Ellipsoid Centre FittingWe put the IUGG67 ellipsoid into the Earth’s centre of mass corresponding tothe WGS84 system. The approximate IUGG67 ellipsoidal co-ordinates computedfrom Cartesian GPS co-ordinates differ from the original IUGG67 ellipsoidal co-ordinates as a consequence of different parameters of IUGG67 and GRS80 ellip-202 E. PAPP et al.Fig. 2. Residuals after 2D affine transformation [m]Fig. 3. Residuals after fifth order polynomial transformation [m]soids. The magnitudes of differences are: d = +0.9430” and d = +4.0495”(PAPP et al., 1997; 1999). Changing the approximate IUGG67 ellipsoidal co-ordinates by these differences the obtained () and () values are close to the realIUGG67 ellipsoidal co-ordinates. The computation of the approximate EOV co-ordinates can be done according to the previous solution. For presenting remainingdiscrepancies isolines were constructed (Fig.4–6).4. Processing Software ProductsAdjusting, transformation and map projection conversation software products hadbeen developed based on the previously described principles by TU Budapest De-partment of Geodesy and Surveying which use Trimble 4000SE and 4600LS singleHUNGARIAN GPS NETWORK TRANSFORMATION 203Fig. 4. Residuals after 2D Helmert transformation [m]Fig. 5. Residuals after 2D affine transformation [m]frequency GPS receivers and Trimble GPSurvey Geomatics Office software for postprocessing observables. As a result of processing the obtained file consists of theendpoint co-ordinates, the co-ordinate components of the observed vectors and thereliabilities. This file contains the input data of the home-made post processingsoftware which can run under DOS and WINDOWS operation systems offering in-teractive computation. The network adjustment is the first step. Before the networkadjustment the datum points have to be fixed. After this the computation can bedone automatically. The next steps are transformations of adjusted network intodesired datums and national projection systems. The common points can be storedin a file but can also be entered by keyboard.A software system had been established on HEWLETT PACKARD 48SX sci-entific advanced calculator for quick and simple field computations. The available204 E. PAPP et al.Fig. 6. Residuals after fifth order polynomial transformation [m]software products include the Hungarian unified national projection system (EOV),2D Helmert transformation, 2D affine transformation and fifth order polynomialtransformation.References[1] ÁDÁM, J. – BORZA, T., The GPS Networks and their Comparison with the Traditional Networkof Hungary. Reports on Geodesy, Warsaw University of Technology, 1995, No. 3 (16).[2] HOFMANN-WELLENHOF, B. – KIENAST, G. – LICHTENEGGER, H., GPS in der Praxis.Springer-Verlag, Wien, New York, 1994.[3] PAPP, E. – SZŰCS, L. – VARGA, J., GPS Network Transformation into Different Datums andProjection Systems. Proceedings of the 4th International Seminar “GPS IN CENTRAL EU-ROPE” Penc, 7–9 May, Reports on Geodesy, Warsaw University of Technology, 1997, No. 4(27).[4] PAPP, E. – SZŰCS, L. – VARGA, J., GPS hálózatok transzformációja különböző geodéziaidátumokba és vetületi rendszerekbe. 12. Kozmikus Geodéziai Szeminárium Székesfehérvár, 1999.[5] VARGA, J., Alaphálózatok I. (Vetülettan) egyetemi jegyzet. (Map Projection. Lecture Notes inHungarian.) Tankönyvkiadó, Budapest, 1986.

HUNGARIAN GPS NETWORK TRANSFORMATION INTO DIFFERENT DATUMS AND PROJECTION SYSTEMS

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HUNGARIAN GPS NETWORK TRANSFORMATION INTO DIFFERENT DATUMS AND PROJECTION SYSTEMS

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Periodica Polytechnica (Budapest University of Technology and Economics)