 
Abbreviation: B24A02  Load: 30(L)
+ 0(P)
+ 0(FE)
+ 30(LE)
+ 0(S)
+ 0(PEE)
+ 0(E)
+ 0(DE)

Lecturers in charge:  prof. dr. sc. Tomislav Bašić
prof. dr. sc. Željko Hećimović 
Lecturers:  
Course description:
Adopting theoretical and practical knowledge in the field of geodetic reference systems and frames and their importance for the state survey and the basic geodetic works at the state level.
Learning outcomes at the level of the programme to which the course contributes
 Understand the role of geodesy, geoinformatics and spatial data in modern world, demonstrate competences in measuring systems, methods and technologies of measurement and spatial data collection.
 Understand mathematical methods and physical laws applied in geodesy and geoinformatics.
 Apply knowledge of mathematics and physics for the purpose of recognizing, formulating and solving of problems in the field of geodesy and geoinformatics.
 Establish geodetic networks needed in surveying and stakeout in order to provide the required quality of the works performed in certain space.
 Use information technology in solving geodetic and geoinformation tasks.
 Recognize problems and tasks in the application of geodetic and geoinformation principles and methods, and select proper procedures for their solution.
 Prepare official public documents, reports, graphic and cartographic presentations using the surveying results related to objects in space.
 Keep pace with and adopt new technological achievements in the field of surveying, geoinformation systems and services based on the position, and the changes in regulations, norms and standards.
Learning outcomes expected at the level of the course
 Define basic concepts related to the coordinate reference systems and frames,
 Analyze the physical and mathematical characteristics of reference system with respect to the fundamental parameters in respect to which it defines as well as the essential role of the reference frames in positioning, navigation and orientation of objects in space,
 Analyze measurement techniques and classify the differences between spatial, terrestrial and local (instrument fixed) reference frame,
 Analyze the old and the new official coordinate system, reference system and reference frame of Croatia, as well as old and new official height systems of Croatia, and adopt necessary knowledge about the relationship between HTRS96, ETRF89 and ITRFYY reference frames,
 Acquire knowledge and mathematical procedures to solve practical problems of numerical transformation and conversion of coordinates and time coordinate transformation.
Course content broken down in detail by weekly class schedule (syllabus)
Lectures (twohour lectures):
 The course organization: getting to know the teachers, subject content, literature, schedule and time of teaching, the use of elearning, obligations and rights of students, examination methods, rules of conduct of the class and experience from previous years.
 Introduction to Geodetic reference frames: concept, review and thematic scope of the course. Basic terms, acronyms and abbreviations. The fundamental role of the reference frames in the issue of positioning, navigation and orientation of the object in space.
 Mathematical foundations of coordinate systems: metric coordinate system, the metric tensor, Christoffel's symbols, orthonormal coordinate base, coordinate axes, coordinate surfaces, singularities and others. Differential field operations expressed in a particular coordinate system (gradient, divergence, turbulence fields, Laplace operator, etc.).
 he divisions of reference systems: physical principles of the coordinate system with respect to the Newtonian and relativistic theory. Cartesian coordinate system, ellipsoid coordinate system, a spherical coordinate system, the curved coordinate systems, natural (astronomical) coordinate system, the spacefixed reference systems, Earthfixed reference systems, instrument (sensor)  fixed (local) reference systems.
 Celestial Reference Systems (CRS): Horizontal coordinate system, Equatorial coordinate system, Ecliptic coordinate system, Galactic coordinate system, Supergalactic coordinate system. International Celestial Reference System (ICRS), the International Celestial Reference Framework (ICRF), time stability of ICRF's.
 Mathematicalphysical characteristics of the reference systems: with regard to the fundamental objects / parameters in respect of which it defines. Measurement techniques for defining reference systems (VLBI, SLR, LLR, DORIS, GNSS, FK, Hipparcos, etc.).
 Earth Orientation:Earth Orientation Parameters (EOP), precession and nutation of the Earth's axis of rotation, daily rotation of the Earth, the motion of the pole due to the Earth's crust, the International Earth Rotation Service (IERS), IERS EOP parameters.
 International Terrestrial Reference System (ITRS) and Frame (ITRF): The definition of the ITRS and ITRF, the measurement techniques to determine the ITRF, the Very Long Base Interferometry (VLBI) and HIPPARCOS satellite astrometric mission.
 ITRF  continuation: the Doppler effect, Doppler Orbitography by Radiopositioning Integrated on Satellite (DORIS), International DORIS Service, Satellite Laser Ranging (SLR), International Laser Ranging Service (ILRS), ITRF realizations (ITRFYY), use of ITRFs.
 European positional and height reference systems: the European positional and height datums, the European Terrestrial Reference System 1989 (ETRS89), ETRF's realizations (ETRFYY), European Vertical Reference Network (EUVN), the European internet portal of national coordinate reference systems.
 Instrument (sensor)  fixed (local) systems: Local astronomical reference systems, local ellipsoidal reference systems, examples of implementation of the local reference frames when measuring with terrestrial instruments / sensors (total stations, GNSS antenna, ...), sensors on floating platforms (car, boat, plane, ...), sensors on satellites and others.
 Height Systems: Ellipsoidal heights, geopotentialnumbers, othometric heights, dynamical heights, normal heights, normal orthometric heights, national height systems in Europe, height system datums, precise leveling (I and II. NVT) on Croatian territory, new height systems of the Republic of Croatia, United European Leveling Network (UELN).
 Reference systems in Croatia: Old and new coordinate reference systems and frame in Croatia, old and new geodetic datums (positional and height), the coordinate transformation from the old projection reference system (HDKS01/GK) into the new projection reference system (HTRS96/TM) and the reverse transformation, the accuracy of the transformation.
Exercises (to each proceeds auditoria exercise):
 1. Transformation and conversion of threedimensional Cartesian coordinates: Mastering the process of transformation of Cartesian rectangular 3D coordinates between the reference coordinate frames and the conversion of 3D Cartesian coordinates in the 3D ellipsoidal coordinates:
a) sevenparametric 3D Helmert's transformation: (X, Y, Z) > ITRF93 (X ', Y', Z ') ITRF89 b) conversion of coordinates: (X, Y, Z) > ITRF93 (fi, la, h) ITRF93
 2. Conversion and transformation of geodetic (ellipsoidal) coordinates:Mastering the conversion of 3D ellipsoidal coordinates in 3D Cartesian coordinates and transformation of ellipsoidal 3D coordinates in 3D ellipsoidal coordinates:
a) conversion of 3D ellipsoidal in 3D Cartesian coordinates: (fi, la, h) ETRF89 > (X, Y, Z) ETRF89, b) transformation of 3D ellipsoidal coordinates from the old to the new reference frame RH: (fi, la, h) HDKS (Bessel 1841) > (X, Y, Z) > HDKS (X ', Y', Z ') ETRF89 > (fi', la ', h') ETRF89 (GRS80)
 3. Determination of threedimensional Helmert's 7parameters transformation: Mastering the procedure of determining the parameters of the Helmert's 7parametric 3D transformations. Based on the coordinates of identical points in the two reference frames is determined: Tx, Ty, Tz (translations), dalfa, dbeta, dgama (rotations), dD (scale).
 4. Transformations of coordinates with respect to time changes: Application of Helmert 7parametric 3D transformation with the addition of temporal changes of coordinates between two geodetic reference frames. In the process of transformation are used: 7Helmert's transformation parameters (Tx, Ty, Tz, dD, dalfa, dbeta, dgama), velocities of movement points (vx, vy, vz) and rotation matrix of geotectonic plate R: (X, Y, Z) ITRF92 (94.6) > (X ', Y', Z ') ETRF89 (89.0)
Submit of all calculated task is through elearning systems (LMS).
Screening student work
 Class attendance  1.0
 Tests  2.0
 Oral exam  1.0
 Written exam  1.0

Compulsory literature: 
4.   Materijali objavljeni na eučenju
 Bašić, T, Ž.,Hećimović.: Geodetski referentni okviri, Geodetski fakultet, Zagreb. (skripta u pripremi)
 Neutsch, W. (1996): Coordinates. Walter de Gruyter
 HofmannWellenhof, B., Lichtenegger, H. Collins, J. (2000): GPS Theory and Practice, 5th Revised Edition, Springer, Wien  New York 
Recommended literature: 
3.   Jekeli, Ch. (2001): Inertial Navigation System with Geodetic Application. Walter de
Gruyter, Berlin.
 Moritz, H., HofmannWellenhof, B. (1993): Geometry, Relativity, Geodesy. Wichmann,
Karlsruhe.
 Torge, W. (2001): Geodesy, Walter de Gruyter (eng.); Torge, W. (2003): Geodäsie, Walter de Gruyter (njem.).
 International Earth Rotation and Reference Systems Service (IERS), http://www.iers.org.
 European Reference Frame (EUREF), http://www.eurefiag.net.
 Državna geodetska uprava: Izvješća o znanstvenostručnim projektima.
http://www.dgu.hr.
 Jean Souchay and Martine FeisselVernier (eds.) (2008): The International Celestial Reference System and Frame. IERS Technical Notes, No. 34, http://www.iers.org/.
 C. Boucher, Z. Altamimi, P. Sillard, and M. FeisselVernier (2004): The ITRF2000, IERS Technical Notes, No. 31, http://www.iers.org/. 
 