Geri Dön

Jeodezi ve dönüşümler

Transformations in geodesy

  1. Tez No: 46628
  2. Yazar: ALİ KILIÇOĞLU
  3. Danışmanlar: PROF.DR. AHMET AKSOY
  4. Tez Türü: Yüksek Lisans
  5. Konular: Jeodezi ve Fotogrametri, Geodesy and Photogrammetry
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1995
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 109

Özet

ÖZET Jeodezi biliminin temel görevlerinden biri de fiziksel yeryüzünde doğal koordinat sistemlerinde yapılan jeodezik ölçülerle,kontrol noktalarının referans koordinat sistemlerinde koordinatlarının belirlenmesidir. Doğal koordinat sistemleri ile referans koordinat sistemleri arasındaki ve bu sistemlerin kendi aralarındaki fonksiyonel ilişkilerin belirlenmesi jeodezide koordinat dönüşümleri problemini oluşturur. Özellikle son yıllarda uydu jeodezisi teknikleriyle üç boyutlu global jeodezik ağların oluşturulması sağlanmış ve bugüne kadar yatay ve düşey olmak üzere ayrı ayrı oluşturulan jeodezik ağların birleştirilmesi ve global datumlara dönüştürülmesi problemleri açığa çıkmıştır. Bu çatışmada yukarıda sözü edilen dönüşüm problemleri genel olarak ele alınmakta ve sıklıkla karşılaşılabilecek durumlar için modeller ve çözüm yolları açıklanmaktadır. Elde mevcut veriler ve dönüştürülecek koordinat sistemleri gözönünde bulundurularak uygun dönüşüm modeli ve çözüm yolu bulunabilir.

Özet (Çeviri)

TRANSFORMATIONS IN GEODESY SUMMARY Appropriate and well defined reference coordinate systems are required for the description and modelling of the observations and the representation and interpretation of results. Especially, the accuracy of the satellite techniques depends on the accuracy of coordinate systems. Before the coordinate systems are explained, the terms system and frame, which have been used somewhat in a wrong way, are expressed. The distinction between a coordinate system and a reference frame, where the term system includes the description of the physical enviroment as well as the theories used in the definition of the coordinates. Once a set of theories and models is adopted, a coordinate system is implicitly established and the orbit determination and geodetic data reductions can be carried out. The second term frame means the practical realization of the coordinate system and is established by observations and a set of station coordinates of certain points on the earth. The distinction is indicated where necesarry. In this work, first, the mathematical meaning of the coordinate system is considered. A coordinate system S of a three-dimensional affine space A3 is a set consisting of a point O of the affine space (the origin of the coordinate system) and three linearly independent vectors (x,y,z) of the vector space V3 belonging to the affine space ( so that x,y,z form a basis of V3). A coordinate system is shown as E = { O, x, y_, z }. Any point of A3 can be expressed uniquely as a linear combination of three vectors, starting from O; P = 0 + (X1x + X2y + X3z) The numbers ^ are called the coordinates of P with respect to I : briefly, *2 = \Al 1^2. '^3 /S' A coordinate system of a plane or space is generally a reference system consisting of points, lines, rays, vectors, curves, or other elements of the plane or space with respect to this reference system which is uniquely vicharacterized by numbers. These numbers, written as an ordered 3-tuple, are called the coordinates of P with respect to Z ; P=PS = (0,x,y,z)2. A linear coordinate system I in space consists of a fixed point O of a space (the origin) and three non-coplanar lines intersecting at O, the coordinate axes (x-, y-, z-axes). A linear coordinate system in space is shown as l3={0,x,y,z}. Curvilinear coordinate systems in space are generalizations of the linear systems. They consist of three one parameter pencils of surfaces. Through each point P of space there passes one and only one surface of each pencil. The parameter values of these three surfaces are the curvilinear coordinates of P. Coordinate systems in geodesy generally are formed by physical and geometric parameters. For this reason, coordinate systems can be expressed in two parts; physical coordinates systems and reference coordinate systems. Measurements are made in physical coordinate systems and computations are made in reference coordinate systems. The more the relationship between physical and reference coordinate systems are developed, the better the results are. In addition, the coordinate systems may also be named as global or local systems as taking account of the method of establishing and using of the coordinate systems. Reference coordinate systems in satellite geodesy are global and geocentric by nature, because the satellite motion refers to earth's center of mass. In satellite geodesy two coordinate systems are required ; a space-fixed, inertial reference system (CIS) for the description of satellite motion and an earth- fixed, terrestrial reference system (CTS) for the position of the observation station and for the description of results from satellite geodesy. The transition from Conventional Inertial System (CIS) to the Conventional Terrestrial System (CTS) is realized through a sequence of rotations ; - Precession - Nutation - Earth rotation including polar motion. The coordinate systems used in conventional geodesy are generally established by terrestrial measurements so they are naturally local systems. Terrestrial measurements are by nature local in character and are usually described in local reference coordinate systems. The relationship between local and global datums must be known with sufficient accuracy. The establishment of precise transformation models between two different systems is one of the important tasks of geodesy. The transformations between any two coordinate systems are interpreted in three parts, such as; Vll- Three-dimensional (3-D) transformation - Two-dimensional (2-D) transformation - One-dimensional (1-D) transformation Three-Dimensional transformation; The Bursa-Wolf model relates two sets of coordinates which are treated as observations, with three translations, three rotations and a scale change. The latter seven quantities are unknown parameters to be estimated. For any collocated point, the model is ; X = T+(l+k)RU The Molodensky-Badekas model follows from Bursa-Wolf model by replacing the position vector (U) of an arbitrary point i, in one of the coordinate systems, by some of the position vector of the initial point (o) with respect to the origin, and the position of the arbitrary point, with respect to the initial point. The model is; X = T + U0 + (1+k) R (U-U0) The Veis model follows from Molodensky-Badekas model. In this model system U is not rotated around its axes, but rotated around local horizon system axes of the initial point. The position of the initial point and the scale change are the same with those of Molodensky-Badekas model. The model is; X = T + U0 + (1+k) M (U-U0) The Thomson-Krakiwsky model contains two sets of rotations. One set (e) for the geodetic coordinate system, and another (v|/) for the misoriented network in the same coordinate system. The model is ; X = T + (1+k) R, ( U0 + Ry (U-U0)N ) The symbols given above are briefly ; X : One of the coordinate system (e.g. satellite system) U : The second coordinate system (e.g. geodetic system, local datum) k : Scale change U0: The position of the initial point in geodetic system (U-U0)N : The position of an arbitrary point M, R : the rotation matrices VIllThe affine transformation is applied when the local horizontal datum is distorted and the scale of the horizontal control network and that of the vertical control network do not coincide eachother. For this reason a transformation model, which considers the distortion in horizontal network and the scale change between horizontal and the vertical control network, should be applied. The model is ; X = T + U0 + MTRSM (U-U0) where M and R are rotation matrices including the rotation parameters and S is the affinity matrix including scale changes and the azimuth of the direction of the maximum distortion. Two-dimensional transformations can easily be derived from three- dimensional transformation models. In geodesy, the three-dimensional transformation models are the most general forms. The basic two- dimensional models are similarity and affine transformations. Two-dimensional similarity transformation relates two orthonormal coordinate systems with two translations, one rotation and one scale change. For any collocated point, the model is; X = T + (l+k)RU Two-dimensional affine transformation is generally used in photogrammetry and cartography. Because, paper, film or other material used in these sciences are distorted that can be modeled in an affine transformation. Affine transformation model contains 6 transformation parameters. For any collocated point, the affine transformation model is; X = ax U + a2 V + a3 Y = a4U + a5V + a6 Some properties of the affine transformation are as follows; Any line is again a line after transformation Parallel lines are again parallel after transformation The ratio of two parts of a single line remains the same after transformation Distances change according to the directions, and scale remains the same in a certain direction Areas change a constant amount after transformation Two dimensional ellipsoidal transformation model can be applied in small regions. In this model, the formulas of the classical geodesy are used. ixIn geodesy, there are, generally, four kinds of height systems in use ; - Geopotential numbers and dynamic heights Geopotantiel numbers depend on earth's gravity potential and are shown as; C = -(W-W0) Since geopotential numbers have no metric meaning, they are reduced by a constant and dynamic heights are obtained. The reference surface for dynamic height is the geoid. - Orthometric heights The reference surface for orthometric height is the geoid. The orthometric height of a point on the physical surface of the earth is the distance measured along the plumb line of the point starting from the geoid. The relation between geopotential numbers and orthometric heights is as follows; H=C/g Some orthometric heights can be defined according to the definintion of the g in the formula above. - Normal heights Normal height is the orthometric height when the standard gravity field is assumed to be identical to the earth's gravity field. - Ellipsoidal heights The ellipsoidal height of a point on the physical surface of the earth is the distance measured along the ellipsoidal normal starting from the ellipsoid. The transition between any two of the heights systems can easily be done through simple transformation models. In this study, the transformation between orthometric and ellipsoidal height systems is examined. One of the transformation models depends on the determination of orthometric height differences from the known ellipsoidal and geoidal height differences. AH = Ah - ANThe second model is based on the regression equations, which are derived from differential transformation model, between two height systems at known points. Ah = ax cos(p cosX + a2 cos

Benzer Tezler

  1. Tez No

    83352

    1/1000 ölçekli paftaların sayısallaştırılmasında hassasiyet araştırması

    Examination of accuracy for dipitising 1/1000 scaled maps

    KEMAL YURT

    Yüksek Lisans

    Türkçe

    Türkçe

    1999

    Jeodezi ve FotogrametriKaradeniz Teknik Üniversitesi

    Jeodezi ve Fotogrametri Mühendisliği Ana Bilim Dalı

    DOÇ. DR. CEMAL BIYIK

  2. Tez No

    624178

    Yeni kentsel dönüşüm stratejisine esas uygulama örneği Üsküdar Ferah Mahallesi

    Üsküdar Ferah Mahallesi the case project based on new urban regeneration strategy

    ERTAN KELEŞ

    Yüksek Lisans

    Türkçe

    Türkçe

    2017

    Jeodezi ve FotogrametriOkan Üniversitesi

    Geomatik Mühendisliği Ana Bilim Dalı

    PROF. DR. NİHAT ENVER ÜLGER

  3. Tez No

    79184

    Uydu görüntülerinden-ulusal coğrafi bilgi sistemine temel oluşturacak nitelikte-topoğrafik harita üretimine veya güncelleştirmesine yönelik analiz ve öneriler

    Başlık çevirisi yok

    MUSTAFA ÖNDER

    Doktora

    Türkçe

    Türkçe

    1998

    Jeodezi ve FotogrametriYıldız Teknik Üniversitesi

    Jeodezi ve Fotogrametri Mühendisliği Ana Bilim Dalı

    PROF. DR. AYHAN ALKIŞ

  4. Tez No

    807243

    Analysis of safe roads and production of risk maps within the scope of integrated disaster management with geographical information systems

    Coğrafi bilgi sistemleri ile bütünleşik afet yönetimi kapsamında güvenli yolların analizi ve risk haritalarının üretilmesi

    OBAIDURRAHMAN SAFI

    Yüksek Lisans

    İngilizce

    İngilizce

    2023

    Jeodezi ve Fotogrametriİstanbul Teknik Üniversitesi

    Coğrafi Bilgi Teknolojileri Ana Bilim Dalı

    DR. ÖĞR. ÜYESİ MUHAMMED ENES ATİK

  5. Tez No

    139644

    Dönüşümler ve uygulamaları

    Conversions and their applications

    AHMET TANIK

    Yüksek Lisans

    Türkçe

    Türkçe

    2003

    Jeodezi ve FotogrametriYıldız Teknik Üniversitesi

    Jeodezi ve Fotogrametri Mühendisliği Ana Bilim Dalı

    PROF. DR. ABDULLAH PEKTEKİN

Geri Dön