Bir GPS ağı örneğinde 3 boyutlu dönüşüm modellerinin incelenmesi

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BİR GPS AĞI ÖRNEĞİNDE 3 BOYUTLU DÖNÜŞÜM MODELLERİNİN İNCELENMESİ ÖZET Yerel sistemlerde yapılan harita çalışmalarının temelini, yatay ve düşey olmak üzere iki kısımdan oluşan jeodezik kontrol ağlan teşkil etmektedir. Genellikle yatay kontrol ağlan için parametreleri belirlenmiş bir dönel elipsoit, düşey kontrol ağlan içinse jeoid ya da ortalama deniz seviyesi vb. gibi bir referans yüzeyi alınır. Ülkemizde de bu çalışmalar yapılırken, yatay kontrol ağlan için Uluslararası Elipsoit (a=6378388 m, f=V297) alınmıştır. Daha sonra yapılan birtakım hesaplar ile ülkemizin koordinatlan Avrupa Datumu 1950'ye (European Datum,1950=ED50) bağlanmıştır. Son yıllarda haritacılıkta yepyeni bir boyut oluşturan GPS (Global Positioning System) sistemi ile tüm jeodezik amaçlan gerçekleştirebilecek çalışmalar yapmak mümkündür. Ancak GPS ölçülerinin çözümü sonucu ulaşılan koordinat bilgileri, pratik olarak doğrudan doğruya kullanılamaz. Bunun nedeni GPS sistemi ile elde edilen koordinatlann (X, Y, Z ya da sin X (2) Z = hiN>+h sin ç (3) (1), (2) ve (3)'de N, eğrilik yançapıİV, a ?yj{a2 cos2

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THE STUDY OF THE 3-D TRANSFORMATION MODELS IN A GPS NETWORK SUMMARY The geodetic control networks that consist of horizontal and vertical parts constitute a base to geodetic applications in local systems. In general, for the horizontal networks an ellipsoid of defined parameters and for the vertical networks geoid or mean sea level is considered as reference surface. In Turkey the International Ellipsoid (a = 6378388 m, f = 1/297) is used as a reference surface for horizontal networks. Later with some more calculations, Turkey's coordinates tied to European Datum 1950 (ED50). In recent years with the development of GPS, which performed a new dimension to geodetic applications, it became possible to realize the applications of all geodetic aims. On the other hand, the coordinates determined by the process of GPS measurements can not be used directly in practical. The reason of this is, the coordinates determined by the GPS (X, Y, Zor + b2 sin 2 cp (4) As it can be seen from the above equations that the most important part of this procedure is to derive the ellipsoidal height value which is shown as h. The relation between the ellipsoidal height (h) and orthometrik height (//) is expressed by the; H =h-N (5) equation (Figure 1). Here N is the distance between the geoid and the ellipsoid or with a different expression, geoid undulation. TERRAIN Figure 1- The Relation Between Geoid and Ellipsoid To solve the problems faced in determining the 3D Cartesian coordinates in local systems, some approaches are used. In general, the following methods are used for this procedure;. Computation by producing ellipsoidal heights,. Computation by h=0 approach,. Computation by h=H approach (if the geoid undulations not known),. Including the geoid undulations to computation. xvIn this study the h=H+N and h^H approaches are used. According to both approaches;. Bursa-Wolf Model,. Molodensky-Badekas Model,. 9 Parameter Helmert Similarity Transformation Model,. 10 Parameter Afin Transformation Model, are used. Each of the 3D transformation models is applied to the discussed network separately for the h=H approach and the transformation is realized. For the calculation of (N) geoid undulations of common points necessary in k=H+N approach, the Turkish Astrogeodetic Network and a Digital Terrain Model given in Part 5 is used. The geoid undulations of common points determined by interpolating from 21 number of reference points belonging to Turkish Astrogeodetic Geoid and the effect of neglecting these geoid undulations is searched. The geoid undulations of common points are derived with 2 methods. As a result the arithmetical mean of these two methods is used in the calculations. Table 1. The Geoid Undulations of Common Points The geoid surface in the study area is shown in Figure 2. Figure 2. The Geoid Surface in the Study Area xviAfter the discussed calculations are done, the derived 3D Cartesian coordinates of common points are given in Table 2 and 3. Table 2- The X, Y, Z values of the Common Points in Local System Determined by the h=H Approach In 3D transformation, Bursa- Wolf and Molodensky-Badekas Models are used as 7 Parameter Similarity Transformation Models, 9 Parameter Helmert Similarity Transformation Model and 10 Parameter Afin Transformation Model is used as 3D Afin Transformation Models and the results of these models are compared. The local coordinates derived by the 3D transformation models are transformed to plane coordinates and 53 length information is produced. These lengths are compared with the length information previously measured with Total Station and have reduced to sea level. As a result of the transformations done with all of the models, if the coordinates derived with including the geoid undulations and the coordinates derived with neglecting the geoid undulations are compared in all points, the X and Z shifts are approximately same and the Y shift is different from X and Z but same in all points. xvnIf the effect of including the geoid undulations to transformation parameters is discussed, in Bursa-Wolf and 9 Parameter Helmert Similarity Transformation Models in all parameters random changes occurred; in Molodensky-Badekas and 10 Parameter Afin Transformation Model rotation and scale parameters had some changes but shift parameters did not have much effect. The length values have not been effected meaningfully by including the geoid undulations. The 10 Parameter Afin Transformation Model has given the best result in both h=H+N and h=H approaches. In transforming the GPS derived coordinates to local systems, 3D transformation models give better results than 2D transformation models whatever the shape of the network is. But in the calculation of 3D cartesian coordinates of local systems the position and size of the network should be considered for the decision of neglecting or including the geoid undulation. xvin

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Bir GPS ağı örneğinde 3 boyutlu dönüşüm modellerinin incelenmesi

The Study of the 3-D transformation models in a GPS network

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