Hamid Reza Nankali
National Cartographic Center of Iran
Manager of Surveying and Geodesy Dept
Email: [email protected]
This paper provides a practical solution to the transformation of International Terrestrial Reference Frame (ITRF2000) coordinates of Iranian permanent GPS Network(IPGN) into WGS84 system.
WGS84 is geocentric coordinate datum most fit to geoid in Iran (±30m) and is used as a reference ellipsoid. IPGN coordinates are in ITRF2000. ITRF coordinates will in general differ from WGS84coordinates, for two reasons, tectonic motions and reference frame difference.Differences between the ITRF2000 coordinate reference frame and the WGS84 are several cm in magnitude. A standard 7-parameter transformation can adequately model these differences at the cm level. Two model have been tested, Bursa-Wolf and Molodensky transformation models. Between these two, Bursa Wolf had the better result and can be used as a better long-term practical solution to these coordinate transformations. Iran is situated in a region of collision between two major tectonic plates: Eurasian and Arabian plates with the convergence rate 2.5±2mm (Vernant etal.2004). National Cartographic Center of Iran started to build a GPS permanent network (IPGN) for crustal deformation monitoring and estimating geo hazards in Iran. The data of this network stations are in ITRF and closed to IGS stations, but all GPS stations in local and national networks have coordinates in WGS84. NCC as a center, which is GPS data provider in the country, has to support all users with precise and accurate GPS data. According to the difference between these two systems, estimating the transformation parameters seems to be inevitable.
IPGN (Iranian Permanent GPS Network)
IPGN is a dense and wide permanent GPS station network which established in Iran (Tabriz-Tehran-Mashhad) and other active part of the country by National Cartographic Center of Iran. Since first 2005 this network has been designed both for crustal deformation monitoring and to serve as a highly precise geodetic network in Iran. This network is consists of 106 permanent stations in first phase. Average distance between dense parts is about 25 to 30km. GPS receivers are dual frequency from Ashtech uz12 and scheduled to receive dual band carrier phase data and code data every 30 second in daily mode (24h). Master data center for controlling the network and data analysis is settled in Tehran at National Cartographic Center of Iran. The data are processed by precise analysis software called Gamit_Globk which is developed by MIT and SIO. The results obtained by analysis are time series, group of coordinates, and time series of relative position of two site, and also velocity filed (Nankali et al., 2006)
Figure 1: IPGN stations distribution
IGS (International GNSS Service)
A proof of concept for the International Global Positioning System (GPS) Service for Geodynamics (IGS) was conducted with a three-month campaign during June through September 1992, and continued until December 1993 as a Pilot-Service until the establishment of the IGS as a service of the International Association of Geodesy (IAG). The IGS formally began on 1 January 1994. IGS is a member of the Federation of Astronomical and Geophysical Data Analysis Services (FAGS) and it operates in close cooperation with the International Earth Rotation and Reference Systems Service (IERS). Due to the expansion of IGS objectives, the name of the service was changed to International GPS Service (IGS) on 1 January 1999. Following further expansion of IGS, integrating data from the Russian GLONASS system and planning for the deployment of the European Galileo system, the name was changed to “International Global Navigation Satellite System (GNSS) Service” on 14 March 2005. The organization retains the acronym “IGS”.
The International GNSS Service is committed to providing the highest quality data and products as the standard for Global Navigation Satellite Systems (GNSS) in support of Earth science research, multidisciplinary applications, and education. These activities endeavor to advance scientific understanding of the Earth system components and their interactions, as well as to facilitate other applications benefiting society. The Service also develops the necessary standards and specifications and encourages international adherence to its conventions (https://igscb.jpl.nasa.gov).
Figure 2: IGS stations distribution
ITRF (International Terrestrial Reference Frame)
A Terrestrial Reference System (TRS) is a spatial reference system co-rotating with the Earth in its diurnal motion in space. In such a system, positions of points anchored on the Earth solid surface have coordinates which undergo only small variations with time, due to geophysical point with precisely determined coordinates in specific coordinate system (Cartesian, geographic, mapping..) attached to Terrestrial Reference System ). ITRF International Terrestrial Reference Frame is a set of physical points with precisely determined coordinates attached to Terrestrial Reference System. In another word, TFR is a physical materialization of TRS, making use of observations derived from Space Geodesy techniques (Altamimi 2000).
ITRF2000combines unconstrained Space Geodesy solutions that are free from any tectonic plate motion model. The ITRF2000 origin is define bye the Earth center of mass sensed by Satellite Laser Ranging (SLR) and its scale by SLR and Very Long Baseline Interferometry (VLBI). Its orientation is aligned to the ITRF97 at epoch 1997.0 and its orientation time evolution follows, conventionally, that of the NNR-NUVEL-1A model. This frame containing about 800 stations located at about 500 sites, with better distribution over the globe compared to past versions. About 50% of stations positions are determined to better than 1 cm and about 100 sites have their velocity estimated to at 1 mm/y level (Altamimi 2000).
Figure 3: ITRF2000 map
WGS84 (World Geodetic System 1984)
The World Geodetic System defines a fixed global reference frame for the Earth, for use in geodesy and navigation. The latest revision is WGS 84 dating from 1984 (last revised in 2004), which will be valid up to about 2010. Earlier schemes included WGS 72, WGS 64 and WGS 60. Efforts to supplement the various national surveying systems began in the 19th century with F.R. Helmert’s famous books Mathematische und Physikalische Theorien der Physikalischen Geodäsie. Austria and Germany initiated the foundation of a Central Bureau of “Internationale Erdmessung”, and a series of global ellipsoids of the Earth were derived (e.g. Helmert 1906, Hayford 1910/ 1924). In the late 1950s the United States DOD, together with scientists of other institutions and countries, began to develop the needed world system to which geodetic datums could be referred and compatibility established between the coordinates of widely separated sites of interest. Efforts of the U.S. Army, Navy and Air Force were combined leading to the DoD World Geodetic System 1960 (WGS 60).
In the early 1980s the need for a new world geodetic system was generally recognized by the geodetic community, also within the Department of Defense. WGS 72 no longer provided sufficient data, information, geographic coverage, or product accuracy for all then current and anticipated applications. The means for producing a new WGS were available in the form of improved data, increased data coverage, new data types and improved techniques. GRS 80 parameters together with available Doppler, satellite laser ranging and VLBI observations constituted significant new information. Also, an outstanding new source of data had become available from satellite radar altimetry. Also available was an advanced least squares method called collocation which allowed for a consistent combination solution from different types of measurements all relative to the Earth’s gravity field, i.e. geoid, gravity anomalies, deflections, dynamic Doppler, etc.
The new World Geodetic System was called WGS 84. It is currently the reference system being used by the Global Positioning System. It is geocentric and globally consistent within ±1 m. Current geodetic realizations of the geocentric reference system family ITRS (International Terrestrial Reference System) maintained by the IERS are geocentric, and internally consistent, at the few-cm level, while still being meter-level consistent with WGS 84 (WGS- Wikipedia).
Figure 4: Gravimetric datum orientation
As it has been mentioned before, IPGN station coordinates are estimated in ITRF whereas all the National GPS network coordinates are in WGS84. National Cartographic Center of Iran as the main center of providing GPS data for users all over the country has to support them with precise data. ITRF coordinates are in general differ from WGS84coordinates, this difference is not more than ±1 m in magnitude in Iran region. Due to this difference, transferring the IPGN coordinates, by means of transformation models, to the WGS84, for making them usable for different purposes in the country seemed to be inevitable.
In this case, two transformation models were chosen and tested in order to find best solution for this problem. The Molodensky-Badekas model and The Bursa-Wolf transformation model which both are explained below.
The Bursa-Wolf transformation model:
The Bursa-Wolf (Bursa, 1962; Wolf, 1963) seven-parameter conformal model for transforming three dimensional Cartesian co-ordinates between datums is especially suited to satellite datums on a global scale (Krakiwsky and Thomson, 1974). This comprises an origin shift from the geocenter in three-dimensional space (X0, Y0, Z0), rotation of the vector position (rx, ry, rz), and a scale change (ds). These are applied in matrix-vector form via
Where the subscripts W and I refer to the WGS84 and ITRF geodetic datums, respectively. The single three by-three rotation matrix is simplified from three separate rotation matrices by assuming that each axial rotation is differentially small (typically less than five arc seconds for most geodetic networks), thus permitting binomial series expansions of the sine and cosine terms for radian measure. The Molodensky-Badekas model:
The Molodensky-Badekas model (Molodensky et al., 1962; Badekas, 1969) is also a seven-parameter conformal transformation of three-dimensional Cartesian co-ordinates between datums, but is more suited to the transformation between terrestrial and satellite datums (Krakiwsky and Thomson, 1974). The Molodensky-Badekas model, as given by Krakiwsky and Thomson (1974), Burford (1985) and Harvey (1986), is to the Bursa-Wolf model. Therefore, the only conceptual difference between the Molodensky-Badekas and Bursa-Wolf models is the choice of the point about which the axial rotations and scale change are applied. As this point is the barycentre for the Molodensky-Badekas model, this model offers a more appropriate option for the transformation between terrestrial and satellite datums. Theoretically, the Bursa-Wolf and Molodensky-Badekas models should give the same results when the same data are used to determine the respective sets of transformation parameters (Harvey, 1986).
However, due to better results, in this region, the Bursa-Wolf was used for determination the transformation parameters.
First step in this process was selecting some stations if IPGN of which WGS coordinates were available and also have suitable distribution in Iran(fig5).These stations should have been stable enough to trust. The two transformation models were tested on these stations in order to find best transformation parameters. According to the results, Bursa-Wolf was better.
Figure 5: Selected stations in the first step
Figure 6: Residuals of selected stations in the first step
Last part of the first step was calculating the whole IPGN network coordinates in WGS84 by the estimated parameters. Second step in this problem was selecting some other stations to control the estimated parameters, so we select 9 stations in different part of the country according to table 1and then transfer these coordinates with estimated parameters. See the result in fig7 and table one.
Figure 7: Residuals of selected stations in second step
Table 1: Selected stations in second step
Figure 8: Residuals of all stations in X component
Figure 9: Residuals of all stations in Y component
Figure10: Residuals of all stations in Z component
As it is obvious in these charts the obtained parameters have acceptable results in three dimensions with residuals better than ±0.05 m in most stations in X and Y direction. As far as can be seen in the Z direction chart, the magnitude of residuals are extremely small and can say that it is ignorable. The last step done, was to compare 6 parameters with 7 parameters model in order to see whether by omitting scale from 7-parameter, the whole results will change or not. But no considerable difference was seen so in order to keep standard form of parameters, 7 parameters presented as final transformation parameters between ITRF2000 and WGS84 in Iran region.