1. OPĆE INFORMACIJE

1.1. Nositelj predmeta

Tomislav Bašić,
Željko Hećimović

1.6. Godina studija

 II.

1.2. Naziv predmeta

Geodetski referentni okviri

1.7. Bodovna vrijednost (ECTS)

 5

1.3. Suradnici

Marko Pavasović

Marija Pejaković

Marijan Grgić

Matej Varga

1.8. Način izvođenja nastave (broj sati P+V+S+e-učenje)

 30 sati P

 30 sati V

1.4. Studijski program (preddiplomski, diplomski, integrirani)

 preddiplomski

1.9. Očekivani broj studenata na predmetu

 70

1.5. Status predmeta

 obvezni

1.10. Razina primjene e-učenja (1, 2, 3 razina), postotak izvođenja predmeta on line (maks. 20%)

 e-učenje razine 2

2. OPIS PREDMETA

2.1. Ciljevi predmeta

Usvajanje teorijskih i praktičnih znanja iz područjageodetskih referentnih sustava i okvira i njihovog značaja za državnu izmjeru odnosno osnovne geodetske radove na nivou države.

2.2. Uvjeti za upis predmeta i ulazne kompetencije potrebne za predmet

Položeni predmeti: Analitička geometrija i linearna algebra (I sem.), Fizika (I sem.), Vektorska analiza (II sem.),

Apsolvirani predmeti: Matematička analiza (I sem.), Osnove geoinformatike (I sem.), Analiza i obrada geodetskih mjerenja (III. sem.).

2.3. Ishodi učenja na razini programa kojima predmet pridonosi

Znanje i razumijevanje:

Razumjeti ulogu geodezije, geoinformatike i geoinformacija u suvremenom svijetu, poznavati mjerne sustave, metode i tehnologije mjerenja i prikupljanja prostornih podataka.

Razumjeti matematičke metode i fizikalne zakone koji se primjenjuju u geodeziji i geoinformatici.

 

Primjena znanja i razumijevanja:

Primijeniti znanja matematike i fizike u prepoznavanju, formuliranju i rješavanju inženjerskih zadataka.

Uspostavljati geodetske mreže za potrebe geodetskih izmjera i iskolčenja na način koji osigurava zahtjevanu kvalitetu provedenih radova u prostoru.

Upotrebljavati informatičku tehnologiju u rješavanju geodetskih i geoinformatičkih zadataka.

 

Donošenje zaključaka i sudova:

Prepoznati probleme i zadatke u primjeni geodetskih i geoinformacijskih načela i metoda, te odabrati ispravne postupke za njihovo rješavanje.

 

Prezentacije i rad u timu:

Izrađivati službene javne isprave, izvještaje, grafičke i kartografske prikaze s rezultatima izmjere prostornih objekata.

 

Vještine učenja i etike:

Pratiti i usvajati nova tehnološka dostignuća u području geodetske izmjere, geoinformacijskih sustava i usluga temeljenih na položaju te promjene propisa, normi i standarda.

 

2.4. Očekivani ishodi učenja na razini predmeta (4-10 ishoda učenja)

Studenti će:

-          definirati osnovne pojmove vezane za referentne koordinatne sustave i okvire,

-          analizirati fizikalno-matematičke karakteristike referentnih sustava s obzirom na fundamentalne parametre u odnosu na koje se definiraju kao i bitnu ulogu referentnih okvira u pozicioniranju, navigaciji i orijentaciji objekata u prostoru,

-          analizirati mjerne tehnike te klasificirati razlike između prostornih,terestričkihi lokalnih (za instrument fiksnih) referentnih okvira,

-          analizirati stari i novi službeni koordinatni sustav, referentni sustav i referentni okvir Hrvatske, kao i stari i novi službeni visinski sustav Hrvatske, te usvojiti nužna znanja o odnosu između HTRS96, ETRF89 i ITRFYY referentnih okvira,

-          ovladati znanjem i matematičkim postupcima rješavanja praktičnog numeričkog problema transformacija i konverzija koordinata kao i vremenskih transformacija koordinata.

2.5. Sadržaj predmeta detaljno razrađen prema satnici nastave

 

Sadržaj predavanja (dvosatna predavanja):

0. Organizacija predmeta – upoznavanje s nastavnicima, sadržajem predmeta, literaturom, rasporedom i vremenom izvođenja nastave, korištenja e-učenja, obvezama i pravima studenta, načinom provjere znanja, pravilima ponašanja na nastavi i iskustvima iz prethodnih godina.

1. Uvod u Geodetske referentne okvire – koncept, pregled i tematski obim predmeta. Osnovni pojmovi, akronimi i kratice. Fundamentalna uloga referentnih okvira u problematici pozicioniranja, navigacije i orijentacije objekta u prostoru.

2. Matematičke osnove koordinatnih sustava: metrika koordinatnog sustava, metrički tenzor, Christoffelovi simboli, ortonormirana koordinatna baza, koordinatne osi, koordinatne plohe, singulariteti i dr. Diferencijalne operacije polja izražene u pojedinom koordinatnom sustavu (gradijent, divergencija, vrtloženje polja, Laplace operator i dr.).

3. Podjele referentnih sustava: Fizikalne osnove koordinatnih sustava s obzirom na Newtonovu i relativističku teoriju. Kartezijev koordinatni sustav, elipsoidni koordinatni sustav, sferni koordinatni sustav, zakrivljeni koordinatni sustavi, prirodni (astronomski) koordinatni sustav, prostorno-fiksni referentni sustavi, Zemaljsko-fiksni referentni sustavi, instrument (senzor) - fiksni (lokalni) referentni sustavi.

4. Nebeski referentni sustavi (Celestial Reference System, CRS): Horizontski koordinatni sustav, ekvatorski koordinatni sustav, ekliptički koordinatni sustav, galaktički koordinatni sustav, supergalaktički koordinatni sustav.Međunarodni nebeski referentni sustav (International Celestial Reference System, ICRS), Međunarodni nebeski referentni okvir (International Celestial Reference Frame, ICRF), vremenska stabilnost ICRF-a.

5. Matematičko-fizikalne karakteristike referentnih sustava: s obzirom na fundamentalne objekte/parametre u odnosu na koje se definiraju. Tehnike mjerenja za definiranje referentnih sustava (VLBI, SLR, LLR, DORIS, GNSS, FK, HIPPARCOS i dr.).

6. Orijentacija Zemlje: Parametri orijentacije Zemlje (EarthOrientationParameters, EOP), precesija i nutacija osi rotacije Zemlje, dnevna rotacija Zemlje, gibanje pola s obzirom na Zemljinu koru, International EarthRotationService (IERS), IERS EOP parametri.

7. Međunarodni terestički referentni sustav i okvir (International Terrestrial Reference System (ITRS) andFrame (ITRF)): Definicija ITRS-a i ITRF-a, mjerne tehnike za određivanje ITRF-a, VeryLong Base Interferometry (VLBI), HIPPARCOS satelitska astrometrijska misija.

8. ITRF - nastavak: Doplerov utjecaj, Doppler OrbitographybyRadiopositioningIntegrated on Satellite (DORIS), International DORIS Service, Satelitska laserska mjerenja (Satellite Laser Ranging, SLR), Međunarodni servis laserskih mjerenja (International Laser Ranging System, ILRS), ITRF realizacije (ITRFYY), korištenje ITRF-a.

9. Europski položajni i visinski referntni sustavi: Europski položajni i visinski datumi, Europski terestički referentni sustav 1989 (European Terrestrial Reference System 1989, ETRS89), realizacije ETRF-a (ETRFYY), European Vertical Reference Network (EUVN), Europski internet portal nacionalnih koordinatnih referentnih sustava.

10. Instrument (senzor) - fiksni (lokalni) sustavi: Lokalni astronomski referentni sustavi, lokalni elipsoidni referentni sustavi, primjeri realizacije lokalnih referentnih okvira prilikom mjerenja terestričkim instrumentima/senzorima (totalna stanica, GNSS antena,...), senzorima na pomičnim platformama (auto, brod, avion,...), senzorima na satelitima i dr.

11. Visinski sustavi: Elipsoidne visine, geopotencijalne kote, rtometrijske visine, dinamičke visine, normalne visine, normalne ortometrijske visine, nacionalni visinski sustavi u Europi, datumi visinskih sustava, nivelmani visoke točnosti (I. i II. NVT) na teritoriju Hrvatske, novi visinski sustav Republike Hrvatske, United European Leveling Network (UELN).

12. Referentni sustavi u Hrvatskoj: Stari i novi referentni koordinatni sustavi i okviri u Hrvatskoj, stari i novi geodetski datumi (položajni i visinski), transformacija koordinata iz starog projekcijskog referentnog sustava (HDKS01/GK) u novi projekcijski referentni sustav (HTRS96/TM) i obrnuta transformacija, točnost transformacija.

 

Sadržaj vježbi (svakoj prethode auditorne vježbe):

1. Transformacija i konverzija kartezijevih trodimenzionalnih koordinata: Ovladavanje postupkom transformacije kartezijevih pravokutnih 3D koordinata između referentnih koordinatnih okvira te konverzija kartezijevih 3D koordinata u elipsoidne 3D koordinate:

a)        sedam-parametarska 3D Helmertova transformacija:

 (X,Y,Z) ITRF93 → (X',Y',Z') ITRF89

b)        konverzija koordinata:

 (X,Y,Z) ITRF93 → (φ,λ,h) ITRF93

 

2. Konverzija i transformacija geodetskih (elipsoidnih) koordinata:

Ovladavanje konverzijom 3D elipsoidnih koordinata u 3D kartezijeve koordinate te transformacija elipsoidnih 3D koordinata u elipsoidne 3D koordinate:

a)        konverzija 3D elipsoidnih u 3D kartezijeve koordinate:

(φ,λ,h) ETRF89 → (X,Y,Z) ETRF89

b)        transformacija 3D elipsoidnih koordinata iz starog u novi referentni okvir RH:

(φ,λ,h) HDKS (Bessel 1841) →

(X,Y,Z) HDKS → (X',Y',Z') ETRF89 → (φ',λ',h') ETRF89 (GRS80)

 

3. Određivanje parametara trodimenzionalne Helmertove 7-parametarske transformacije: Ovladavanje postupkom određivanja parametara Helmertove 7-parametarske 3D transformacije. Na osnovi koordinata identičnih točaka u dva referentna okvira određuje se: Tx, Ty, Tz (translacije), dα, dβ, dγ (rotacije), dD (mjerilo).

 

4. Transformacije koordinata s obzirom na vremenske promjene: Primjena Helmertove 7-parametarske 3D transformacije uz dodatak vremenske promjene koordinata između dvaju geodetskih referentnih okvira. U postupku transformacije se koriste: sedam Helmertovih transformacijskih parametara (Tx, Ty, Tz, dD, dα, dβ, dγ), brzine gibanja točaka (vx, vy, vz) i matrica rotacije geotektonskih ploča R:

 

 (X,Y,Z) ITRF92(94.6) → (X',Y',Z') ETRF89(89.0)

 

Predaja svih izračunatih zadatka je putem sustava e-učenja (LMS).

 

2.6. Vrste izvođenja nastave:

 predavanja

 seminari i radionice

 vježbe

 on line u cijelosti

 mješovito e-učenje

 terenska nastava

 samostalni zadaci

 multimedija i mreža

 laboratorij

 mentorski rad

       (ostalo upisati)

2.7. Komentari:

     

2.8. Obveze studenata

-        prisustvovanje na najmanje 70% sati predavanja i najmanje 70% sati vježbi (sukladno Pravilniku o studiranju),

-        uredna predaja svih zadataka vježbi (podrazumijeva predaju programa na vrijeme i kolokviranje istog kao dokaza samostalnog obavljanja računanja).

2.9. Praćenje rada studenata (upisati udio u ECTS bodovima za svaku aktivnost tako da ukupni broj ECTS bodova odgovara bodovnoj vrijednosti predmeta):

Pohađanje nastave

1,0

Istraživanje

 

Praktični rad

 

Eksperimentalni rad

 

Referat

 

 (Ostalo upisati)

 

Esej

 

Seminarski rad

 

 (Ostalo upisati)

 

Kolokviji

2,0

Usmeni ispit

1,0

 (Ostalo upisati)

 

Pismeni ispit

1,0

Projekt

 

 (Ostalo upisati)

 

2.10.    Ocjenjivanje i vrjednovanje rada studenata tijekom nastave i na završnom ispitu

Kolokviji tijekom semestra (2):

Kolokviji su provjere znanja koje obuhvaćaju sadržaj predavanja i vježbi. Bodovi prikupljeni na kolokvijima omogućuju oslobađanje od pisanog dijela ispita ili oslobađanje od cijelog ispita. Tijekom semestra održavaju se dva redovna kolokvija. Da bi student ostvario pravo pristupa 1. odnosno 2. kolokviju mora ispuniti slijedeće uvjete:

 

-            za pristup 1. kolokviju student mora „uredno“ predati 1. i 2. zadatak vježbi koji pokrivaju tematiku 1. kolokvija,

-            za pristup 2. kolokviju student mora ostvariti minimalno 30% (15) bodova iz 1. kolokvija te „uredno“ predati treći i četvrti zadatak vježbi koji pokrivaju tematiku 2. kolokvija.

 

Na svakom od dva kolokvija može se prikupiti najviše 50 bodova, tj. iz oba kolokvija najviše 100 bodova. Kolokviji se sastoje od 8 teorijskih pitanja koja donose maksimalno 64% od ukupno mogućih bodova i 2 numerička zadatka koja donose maksimalno 36% od ukupno mogućih bodova na svakom kolokviju. Ukupno prikupljeni bodovi na kolokvijima se vrednuju na sljedeći način:

 

-           ˂ 55 bodova - obaveza polaganja pisanog i usmenog dijela ispita,

-           55 – 64 bodova - ocjena dovoljan (2), obaveza polaganja usmenog dijela ispita,

-           65 – 75 bodova - ocjena dobar (3), oslobađanje od ispita,

-           76 – 87 bodova - ocjena vrlo dobar (4), oslobađanje od ispita,

-           88 – 100 bodova - ocjena izvrstan (5), oslobađanje od ispita.

 

Studenti koji prikupe dovoljan broj bodova za ocjene dobar (3) ili vrlo dobar (4), a nisu zadovoljni ocjenom, mogu pristupiti ispitu na redovnom ispitnom roku. U tom slučaju, ocjenjuje se znanje prikazano na tom ispitu. Prikupljeni bodovi na kolokvijima vrijede samo za jedan izlazak na ispit, što znači da u slučaju pada na ispitu student mora na slijedećem roku pristupiti pisanom i usmenom dijelu ispita kada se vrednuje samo znanje iskazano na tom ispitu. 

 

Ispiti (ljetni i jesenski rok):

Svaki ispit sastoji se od pismenog i usmenog dijela. Pismeni ispit se sastoji od 16 teorijskih pitanja na koja je potrebno odgovoriti cjelovitim (opsežnijim) odgovorom i tri računska zadatka. Svako teorijsko pitanje boduje se s 4 bod, a ispravno rješenje računskog zadatka s 12 boda, tako da je ukupan broj bodova koje student može ostvariti na pismenom ispitu 100.

Rješavanjem ispita student može ostvariti direktan upis ocjene iz kolegija sukladno sljedećem sustavu bodovanja:

61 - 70  bodova ® dovoljan (2)

71 - 80  bodova ® dobar (3)

81 - 90  bodova ® vrlo dobar (4)

91 - 100 bodova ® izvrstan (5)

 

Student koji želi odgovarati za veću ocjenu pristupa usmenom ispitu, na kojem u pravilu odgovara na 3-5 pitanja. Ocjena usmenog ispita određuje se na osnovi ispravnosti i cjelovitosti odgovora na postavljena pitanja. Ukupna ocjena je rezultat pismenog i usmenog dijela ispita s jednakim udjelom (težinom).

2.11.    Obvezna literatura (dostupna u knjižnici i putem ostalih medija)

Naslov

Broj primjeraka u knjižnici

Dostupnost putem ostalih medija

Bašić, T., Hećimović, Ž. (2014): Geodetski referentni okviri, ppt-predavanja u pdf formatu (ažuriraju se svake godine)

-

na Moodle-u

Altamimi, Z.; X. Collilieux; L. Métivier (2012): Analysisandresultsof ITRF2008. IERS Technical Note. No. 37, Frankfurt am Main. http://www.iers.org

-

web

Jekeli, Ch. (2012): Geometric Reference Systems inGeodesy, Ohio State University (pdf)

-

web

Fey, A.; D. Gordon; C.S. Jacobs (eds.) (2009): TheSecondRealizationofthe International Celestial Reference FramebyVeryLongBaselineInterferometry. IERS IVS Working Group. IERS Technical Note, No. 35. Frankfurt am Main.

-

web

     

     

     

2.12.Dopunska literatura (u trenutku prijave prijedloga studijskoga programa)

Moritz, H., Hofmann-Wellenhof, B. (1993): Geometry, Relativity, Geodesy. Wichmann, Karlsruhe,

Hofmann-Wellenhof, B., Lichtenegger, H. Collins, J. (2000): GPS TheoryandPractice, 5th RevisedEdition, Springer, Wien - New York.

Neutsch, W. (1996): Coordinates. Walter de Gruyter.

Soffel, M., Langhans, R. (2013): Space-Time Reference Systems. Springer, Wien - New York.

Jean Souchayand Martine Feissel-Vernier (eds.) (2008): The International Celestial Reference System andFrame. IERS Technical Notes, No. 34, http://www.iers.org/,

European Reference Frame (EUREF), http://www.euref-iag.net.

2.13.Načini praćenja kvalitete koji osiguravaju stjecanje izlaznih kompetencija

Studentice i studenti dužni su u četiri navrata (prilikom predaje zadataka vježbi) kolokvirati svaki zadatak i tako pokazati da su ga samostalno izradili.

Tijekom semestra studenti imaju priliku pristupiti na dva kolokvija kojima se provjerava njihovo praćenje odnosno usvajanje znanja s predavanja i izvršavanje obaveza na vježbama. Uspješno savladavanje obadva kolokvija omogućuje djelomično ili potpuno oslobođenje od ispita.

2.14.Ostalo (prema mišljenju

 predlagatelja)

Od studenata se očekuje poštivanje načela akademske čestitosti koja su uređena Etičkim kodeksom Sveučilišta (www.unizg.hr).

1. GENERAL INFORMATION

1.1.  Course teacher

Tomislav Bašić

ŽeljkoHećimović

1.6. Year of the study programme

II

1.2. Name of the course

Geodetic Reference Frame

1.7. Credits (ECTS)

5

1.3. Associate teachers

Marko Pavasović

Marija Pejaković

Marijan Grgić

Matej Varga

1.8. Type of instruction (number of hours L + S + E + e-learning)

 

30 L + 30 E

1.4. Study programme (undergraduate, graduate, integrated)

undergraduate

1.9. Expected enrolment in the course

70

1.5. Status of the course

obligatory

1.10. Level of application of e-learning (level 1, 2, 3), percentage of online instruction (max. 20%)

e-learning level 2

2. COUSE DESCRIPTION

2.1. Course objectives

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.

2.2. Course enrolment requirements and entry competences required for the course

Passed exams: Analytic geometry and linear algebra (I sem.), Physics (I. sem.), Vector analysis (II. sem.),

Absolved courses: Mathematical analysis (I sem.), Basics of geoinformatics (I sem.), Analysis and processing of geodetic measurements (III sem.).

2.3. Learning outcomes at the level of the programme to which the course contributes

Knowledge and understanding:

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.

 

Applying knowledge and understanding:

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.

 

Adoption of conclusions and judgments:

Recognize problems and tasks in the application of geodetic and geoinformation principles and methods, and select proper procedures for their solution.

 

Presentations and team work:

Prepare official public documents, reports, graphic and cartographic presentations using the surveying results related to objects in space.

 

Learning skills and ethics:

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.

2.4. Learning outcomes expected at the level of the course (4 to 10 learning outcomes)

Students will:

- 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.

2.5. Course content broken down in detail by weekly class schedule (syllabus)

Lectures (two-hour lectures):

0. The course organization: getting to know the teachers, subject content, literature, schedule and time of teaching, the use of e-learning, obligations and rights of students, examination methods, rules of conduct of the class and experience from previous years.

1. 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.

2. 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.).

3.The 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 space-fixed reference systems, Earth-fixed reference systems, instrument (sensor) - fixed (local) reference systems.

4. Celestial Reference Systems (CRS): Horizontal coordinate system, Equatorial coordinate system, Ecliptic coordinate system, Galactic coordinate system, Super-galactic coordinate system. International Celestial Reference System (ICRS), the International Celestial Reference Framework (ICRF), time stability of ICRF's.

5. Mathematical-physical 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.).

6.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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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).

12. 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 three-dimensional 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) seven-parametric 3D Helmert’s transformation:

 (X, Y, Z) → ITRF93 (X ', Y', Z ') ITRF89

b) conversion of coordinates:

 (X, Y, Z) → ITRF93 (φ, λ, 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:

 (φ, λ, h) ETRF89 → (X, Y, Z) ETRF89

b) transformation of 3D ellipsoidal coordinates from the old to the new reference frame RH:

 (φ, λ, h) HDKS (Bessel 1841) →

 (X, Y, Z) → HDKS (X ', Y', Z ') ETRF89 → (φ', λ ', h') ETRF89 (GRS80)

 

3. Determination of three-dimensional Helmert’s 7-parameters transformation: Mastering the procedure of determining the parameters of the Helmert’s 7-parametric 3D transformations. Based on the coordinates of identical points in the two reference frames is determined: Tx, Ty, Tz (translations), dα, dβ, dγ (rotations), dD (scale).

 

4. Transformations of coordinates with respect to time changes: Application of Helmert 7-parametric 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, dα, dβ, dγ), 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 e-learning systems (LMS).

2.6. Format of instruction:

 lectures

 seminars and workshops

 exercises

 on line in entirety

 partial e-learning

 field work

 independent assignments

 multimedia and the internet

 laboratory

 work with mentor

      (other)

2.7. Comments:

     

2.8. Studentresponsibilities

- Attendance at least 70% of lectures and at least 70% of the hours of training (in accordance with the Regulation of Studies),

- Orderly handover of all tasks exercises (implies submission and assessment of the program on time as evidence of individual performance computing).

2.9. Screening student work (name the proportion of ECTS credits for eachactivity so that the total number of ECTS credits is equal to the ECTS value of the course )

Class attendance

1.0

Research

     

Practical training

     

Experimental work

     

Report

     

      (other)

     

Essay

     

Seminar essay

     

      (other)

     

Tests

2.0

Oral exam

1.0

      (other)

     

Written exam

1.0

Project

     

      (other)

     

2.10. Grading and evaluating student work in class and at the final exam

Preliminary exams (colloquia) during the semester (2):

Colloquia are assessment covering the content of lectures and exercises. Points collected at colloquia allow the release of the written exam or the release of the examination. During the semester are held two regular colloquia. To qualify a student access to first or second colloquium must meet the following requirements:

 

- To access the first colloquium student must "regularly" hand over first and second assignment of exercises that cover the topic of the first tests,

- To access the second colloquium student must achieve a minimum of 34% (17) points from the first colloquium and "orderly" hand over the third and fourth task of exercises that cover the topic of the second colloquium.

 

On each of the two preliminary exams can collect a maximum of 50 points, i.e. from both colloquium maximum of 100 points. Preliminary exams consist of five theoretical issues which bring a maximum of 60% of the total possible points and two numerical tasks that deliver a maximum of 40% of the total possible points in each colloquium. Total collected points at colloquia are valued as follows:

 

- ˂ 55 points - the obligation of take the written and oral part of the exam,

- 55 - 64 points - score enough (2), the obligation to take the oral part of the exam,

- 65 - 75 points - good (3), the release of the exam,

- 76 - 87 points - very good (4), the release of the exam,

- 88 - 100 points - an excellent score (5), the release of the exam.

 

Students who collect enough points for a good (3) or very good (4), and are not satisfied with their grade, may take the examination at the regular examination period. In this case, evaluation is based on the knowledge shown in this test. The collected points at colloquia are only valid for one taking the exam, which means that in case of a fall on the exam the student has the following term access written and oral exam when evaluated only knowledge expressed in this exam.

 

Exams (summer and autumn period):

Each exam consists of a written and an oral part. Written exam consists of seven theoretical questions that need answering comprehensive (more extensive) response and one calculation task. Any theoretical question is scored with 1 point, a correct solution calculation task with 3 points, so the total number of points a student can achieve the final examination is 10. Solving the exam a student can earn a direct entry of grades in courses according to the following scoring system:

 

61 - 70 points - sufficient (2)

71 - 80 points - good (3)

81 - 90 points - very good (4)

91 - 100 points - excellent (5)

 

A student who wishes to respond to a higher grade access to the oral exam, which generally corresponds to 3-5 questions. Rating oral examination shall be determined on the basis of correctness and completeness of answers to the questions. Overall rating is result of the written and oral examination with equal share (weight).

2.11. Required literature (available in the library and via other media)

Title

Number of copies in the library

Availability via other media

Bašić, T., Hećimović Ž. (2014): Geodetic Reference Frames, ppt lectures in pdf format (updated yearly)

     

Moodle

Altamimi, Z.; X. Collilieux; L. Métivier (2012): Analysis and results of ITRF2008. IERS Technical Note. No. 37, Frankfurt am Main (http://www.iers.org)

     

web

Jekeli, Ch. (2012): Geometric Reference Systems in Geodesy, Ohio State University (pdf)

5 chair

     

Fey, A.; D. Gordon; C.S. Jacobs (eds.) (2009): The Second Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry. IERS IVS Working Group. IERS Technical Note, No. 35. Frankfurt am Main.

     

web

     

     

     

2.12.Optional literature (at the time of submission of study programme proposal)

Moritz, H., Hofmann-Wellenhof, B. (1993): Geometry, Relativity, Geodesy. Wichmann, Karlsruhe,

Hofmann-Wellenhof, B., Lichtenegger, H. Collins, J. (2000): GPS Theory and Practice, 5th Revised Edition, Springer, Wien - New York.

Neutsch, W. (1996): Coordinates. Walter de Gruyter.

Soffel, M.,Langhans, R. (2013): Space-Time Reference Systems. Springer, Wien - New York.

Jean Souchay and Martine Feissel-Vernier (eds.) (2008): The International Celestial Reference System and Frame. IERS Technical Notes, No. 34, http://www.iers.org/,

European Reference Frame (EUREF), http:www.euref-iag.net.

2.13.Quality assurance methods that ensure the acquisition of exit competences

The students are required on four occasions (when submitting assignments exercises) preliminary exam on each task in order to show that he was self-created.

During the semester, students have the opportunity to access the two colloquia that check their monitoring and learning from lectures and performing obligations during the exercises. Successfully mastering both colloquium allows partial or complete exemption from the exam.

2.14.Other (as the proposer wishes to add)

Students are expected to respect the principles of academic integrity which are regulated by the Code of Ethics of the University (www.unizg.hr).