Transformation coordinates from International Terrestrial Reference Frame 2000 to World Geodetic System 1984
Geodetic network is an essential frame of spatial data. Also it is an information system for geodetic and engineering surveys, land management, geodetic support of construction, monitoring of buildings and structures deformations, topographical mapping, development of geographical information systems, transport navigation. There are several coordinate systems to solve tasks as described above. Using Global Navigation Satellite Systems cause a problem of installing communication between coordinate systems. G.I.S. specialists should know how to work with various kinds of geospatial data, that are acquired from terrestrial surveying, Global Navigation Satellite System observations and online GNSS processing service. Besides coordinates can relate to global, regional and local reference systems (Bosy J., 2014). Geodesists should understand and be able to handle with reference frame conversions in order to get high-quality geospatial data: maps, digital models of the Earth. The aim of this research is to find better transformation model between ITRF2000 and WGS84 by comparison Bursa-Wolf and Molodensky-Badekas models.

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First of all, short definitions on two reference frames should be done. The ITRF is stands for International Terrestrial Reference Frame. It is earth-centered and earth-fixed datum. It was presented in 1988. Coordinates are based on the GRS80 ellipsoid, which was designed to suit the shape of the geoid. The geoid is an irregular surface, which coincides with the surface of the water in the seas and oceans. It is perpendicular to the direction of gravity at any point. ITRF is sustained by the International Earth Rotation and Reference Systems Service (Altamimi Z., 2011). Also it is a global network with points that have accurate coordinates. Coordinates are derived from geodetic measurements using GNSS and different laser rangings (Jannsen V., 2009). This network contains 800 stations that are distributed over the globe. The latest realization of the ITRF was done in 2008. The realization is a defining of stations’ coordinates and linear velocities (Altamimi Z., 2011).
In contrast, WGS84 is a regular Terrestrial Reference System. It is geocentric, right-handed, orthogonal coordinate system used in geodesy and navigation (NIMA, 2000). The WGS84 Coordinate System center is a geometric center of the WGS84 Ellipsoid. The National Geospatial Intelligence Agency operates this common Terrestrial Reference System. Due to National Imagery and Mapping Agency (1997) the last reference system is developed in order to match International Reference System. The X and Z axes are consonant with the Reference Meridian, Reference Pole consequently. Also Y axis is stationed on ninety degrees from X and Z axes (NIMA, 2000).
Furthermore, ITRF coordinates might differ from WGS84 coordinates in different regions at sub-metre level (Winter S., 2014). Consequently, two reference systems’ convention increases with time (Jannsen V., 2009). Aghamohammadi in his work stated that those varieties might be solved at the centimeter level by using seven-parameter conversion (Aghamohammadi A.).
Therefore, one datum can be transferred to another datum by the Helmert 7-parameter transformation (Knippers R., 1998). Those parameters are: three rotations (α, β, γ), origin shift of three coordinates (ΔX, ΔYandΔZ) and scale (s). The Helmert transformation model is a seven parameter transformation. It is either a position vector and coordinate frame conversion. In the coordinate frame transformation parameters are transformed for the whole reference system. The Bursa-Wolf transformation model is the position vector transformation (Deakin R., 2006). In contrast to the coordinate frame transformation it uses rotations that are refer to the point’s vector. These two models are almost the same. Yet their rotations have reversible signs.
Moreover, Aghamohammadi tested two transformation models – Bursa-Wolf and Molodensky-Badekas (Aghamohammadi A.). The first model’s formulas were done by Bursa in 1962. In 1963 Wolf had improved it. It is a seven-parameter model. It transfers three dimensional Cartesian coordinates between two datums. This model uses origin shifts of coordinates, rotation angles and scale change. Below its matrix-vector form:

The second model is Molodensky-Badekas model. It was introduced by Molodensky in 1962, then developed in 1969. It is also seven-parameter conformal conversion of Cartesian coordinates between different datums. The formula of transformation is:

Where ΔX, ΔY, ΔZ are the shifts between the barycenter and centroid of two networks. And rx, ry, rz are rotation of positions, ds – is a scale change.
Moreover, Aghamohammadi stated that Molodensky-Badekas model dissimilar from Bursa-Wolf model by the point about which axes are rotate and scale is changed (Aghamohammadi A.).The Molodensky-badekas model is often used for the conversion coordinates between terrestrial and satellite datums. Yet for that condition the central point should be the barycentre (Aghamohammadi A.).
In contrast the Bursa-Wolf transformation model does not need the centroid coordinates as in the Molodensky-Badekas model. Aghamohammadi described those two models in his work (Aghamohammadi A.). That author wrote that research was done in Iran region, where he compared transformation models to find appropriate model. The main issue of that work was that Iranian Permanent Network’s coordinates are estimated in ITRF. National GPS network coordinates are in WGS84 coordinate system. And differences from two reference systems can be more than ± meter. Due to results and some parameters concluded that Bursa-Wolf model is better that Molodensky-Badekas model (Aghamohammadi A.). The author wrote that the first model is simpler and easier to use than the second. Also it is better suits to the satellite datums.
Finally, there are many computer programs that allow us to transfer coordinates from one system to another. However, it is important to know which method you will choose in order to achieve expected result. I suppose that this work covered theoretical part of the issue. Besides the Bursa-Wolf model can be proposed as good model due to its simplicity. In the future work I can choose this model to transform coordinates from ITRF2000 to WGS84.
References

Aghamohammadi A., Nankali H. R., Djamour Y. Transformation from ITRF2000 to WGS84. [e-journal] Available though: National Cartographic Center of Iran website http://ncc.org.ir/_DouranPortal/Documents/a-aghamohammadi.pdf [Accessed 2 November 2014].
Altamimi Z., Boucher C., Sillard P. (2011) New Trends for the Realization of the International Terrestrial Reference System. [e-journal] Available through: University of Liege website http://www.ltas-vis.ulg.ac.be/cmsms/uploads/File/ITRS.pdf [Accessed 2 November 2014].
Bosy J., (2014) Global, Regional and National Geodetic Reference Frames for Geodesy and Geodynamics. [e-journal] Available through: scientific publisher Springer link.springer.com/article/10.1007%2Fs00024-013-0676-8#page-1 [Accessed 2 November 2014].
NIMA (2000) Its Definition and Relationships with Local Geodetic Systems. [e-journal] Available through National Geospatial-Intelligence Agency website http://earth-info.nga.mil/GandG/Publications/tr8350.2/wgs84fin.pdf [Accessed 2 November 2014].
Deakin R., (2006) A note on the Bursa-Wolf and Molodensky-Badekas transformations. [e-journal] Available through ResearchGate social networking website http://researchgate.net/publication/228757515_a_note_on_the_bursa-wolf_and_molodensky-badekas_transformations [Accessed 1 November 2014].
Knippers R., (1998) Coordinate systems and Map projections, ITC-notes. [e-journal] Available through: International Institute for Geo-Information Science and Earth Observation website http://kartoweb.itc.nl/geometrics/publications/kt20003coordtransuk.pdf [Accessed 1 November 2014].
Jannsen V.,(2009) Understanding Coordinate Systems, Datums and Transformations in Australia. [e-journal] Available through: University of Tasmania Library website http://eprints.utas.edu.au/9489/1/Janssen_2009_SSC2009_proceedings_version.pdf [Accessed 1 November 2014].
Winter S., Rizos C., (2014) Dynamic Datum Transformations in Australia and New Zealand. [e-journal] Available through: CEUR Workshop Proceedings publication service http://ceur-ws.org/Vol-1142/paper6.pdf [Accessed 2 November 2014].