ISO 900:2008 Certified Volue 2, Issue 0, April 203 Modified and Corrected Transforation of WGS72 (The Transit, Doppler) and WGS84 (GPS Datu) Stations To Adindan Datu Based On Clarke880 Ellipsoid ABSTRACT: - Seventeen control points given on the World Geodetic Syste 984 (WGS84) and Adindan datu are used to deterine transforation paraeters between WGS84 and Adindan datu. Using Doppler stations on Adindan datu,and the transforation paraeters of Doppler satellite datu (WGS72) and Adindan, differences in paraeters between the datu of GPS(WGS84) and Doppler (WGS72) were coputed. These differences are not properly equal to that adopted by USA Defense Mapping Agency (DMA). This is due to erroneous reductions of easured distances to the Clark 880 ellipsoid, and to the fact that geoid heights were not known perfectly. Keywords: Adindan-Sudan, Transit-Doppler and GPS datus (WGS72, WGS84). I. INTRODUCTION As the rapidly eerging industrial technology develops, ore precise geodetic inforation can be achieved. For soe areas of the world there still are little or no observational aterials. For these areas, additional or new surveys are required to relate ajor datus of the world ore precisely and develop standard world syste which will satisfy future needs. The geodetic satellite has provided useful techniques for such surveys. There are several iportant advantages in the satellite ethod of collecting geodetic inforation which can be suarized as:- Geocentric positions can be deterined directly; world wide coverage is possible; longer geodetic ties can be accoplished; inforation regarding iportant paraeters of the gravitational field can be obtained; and the geoid-ellipsoid suppuration at places of known heights above geoid can be obtained. The ai of this paper is to develop techniques which adapt different satellite positioning systes with Adindan datu. II. THE TRANSIT SATELLITE (DOPPLER) POSITIONING SSTEM The transit satellite syste was originally developed by the US Navy in cooperation with the Applied Physical Laboratory of Johns Hopkin University. It was called the US Navy Navigation Satellite Syste, or Transit. The technical approach grew fro experients to deterine the orbit of the first artificial satellite, Sputnik, by easuring the Doppler shift of its radio signal. The Transit Syste becae operational in 964 Abd Elrahi Elgizouli Mohaed Ahaed and was used at first for the navigation of the Navy s polarize subarine fleets. In 968 its use widened to include off-shore oil exploration, and geodetic and geophysical surveys. There are currently 6 Transit Satellites orbiting the earth; each satellite has a polar orbit with a period of about hour, 47in, at an altitude of about 00 k above the earth s surface. As a satellite travels around the earth, it continuously broad casts a serial strea of digital data that is phaseodulated on highly stable carrier frequencies of approxiately 400 and 50 MH. In geodetic and land surveying application data fro ultiple satellite passes are collected at fixed locations to be easured and are processed in two possible ways, point positioning and translocation. In point positioning data fro a single receiver are used to obtain the location coponents, latitude, longitude, and height. Horizontal positioning accuracy of about 5 can be achieved with the use of 25 satellite passes [8]. The point positioning used only in cases where approxiate locations are needed. Where the survey task requires accuracies better than, the sei-short arc translocation, or shortly translocation ethod, is applied. This ethod involves two or ore satellite receivers are located at the reote sites whose positions are to be deterined. III. THE GLOBAL POSITIONING SSTEM (GPS) The Transit Satellite Syste is unable to provide the accuracy for surveying at the parcel and traverse Level. Transit gives subetre accuracy only by observing ore than one day. There are only six Transit satellites available for global coverage. A consequence is that there are waiting ties between satellites of to one and half hours. The Transit satellites are only 00 k above the earth and thus are being affected ore by local gravity field variations than are the uch higher orbiting GPS satellites. Transit satellite transission at 50 MH and 400 MH are ore susceptible to ionospheric delay and disturbances than are the higher frequency GPS transissions. Finally, clock technology has iproved considerably over recent years to insure stable satellite transissions. The Navigation Syste with Tie and Ranging (NAVSTAR) Global Positioning syste (GPS) is all- weather, space-based navigation syste, which has been designed priarily for the United States Departent of Defense to satisfy the requireents of the 2
ISO 900:2008 Certified ilitary forces [2]. It has been developed since 973, and becae fully operational in 994, allowing the world wide and instantaneous deterination of a vehicle s position and velocity (i.e., navigation) as well as the precise coordination of tie. Actually, by GPS techniques, baseline vectors are easured and relative positions of points are accurately deterined. This is equivalent to easuring slope distance, aziuth, horizontal angle and vertical angle between the stations. Therefore, GPS surveys yield; distances, horizontal coordinates and heights. GPS uses pseudo ranges derived fro the broadcast satellite signal. The pseudo range is derived either fro easuring the travel tie of the (coded) signal and ultiplying it by its velocity or by easuring the phase of the signal. In both cases, the clocks of the receiver and the satellite are eployed. Since these clocks are never perfectly synchronized, instead of true ranges pseudo ranges are obtained where the synchronization error (denoted as clock error) is taken into account [6]. The key to the syste s accuracy is the fact that all signal coponents are precisely controlled by atoic clocks. The GPS satellites have four on board tie standards- two rubidiu and two cesiu clocks. These highly accurate frequency standards being the heart of GPS satellites, produce the fundaental L-band frequency of 0.23 MHz. Coherently derived fro this fundaental frequency are two signals, the L and the L2 carrier waves generated by ultiplying the fundaental frequency by 54 and 20, respectively, thus yielding L = 575.42 MHz, L2 = 227.60 MHz. Thus L-signal has a wave length of about 0.9 and L2 has a wave length 0.244. These dual frequencies are essential for the eliination of the ajor source of error i.e. ionospheric refraction. The pseudo ranges that are derived fro easured travel tie of the signal fro each satellite to the receiver use two pseudo-rando noise (PRN) codes that are odulated (superiposed) into the two base carrier waves. The first code is the C/A- code with an effective wave length of 293. is odulated only on L and is purposely oitted fro L2. The second code is the P- code (precision-code) also designated as the precise positioning services (PPS ), which has been reserved for use by the U.S. ilitary and other authorized users. The P-code with an effective wave length of 29.3 is odulated on both carriers L and L2 are also continuously odulated with the navigation data (satellite essage) bit strea at 50 egabits per second, i.e. 50 MHz about the health, clock inforation and position of the satellite. Receivers which only easure L carrier and C/A-code are known as single frequency receivers and receivers easuring both L and L2 carriers and C/A-code (soeties P-code as well) are called dual frequency receivers. To be able to easure carrier(s), receivers ust be able to either decode incoing odulated signals (coded receivers) or square Volue 2, Issue 0, April 203 the to get L and/or L2 carrier phases. The foration of C/A code is not classified, thus, available to users worldwide, but, the P-code is generally classified There are two iportant types of GPS observations (observable): pseudo range and carrier phase. Carrier phases are soeties also referred to as-carrier beat phases. Pseudo range techniques are generally used for navigation. In high precision surveying the carrier phase is used. Although the (undifferenced) phases can be used directly, it has becoe coon practice at least in surveying applications, to process certain linear cobination of the original carrier phase observation (double differences and triple differences) [9].The relation between the Cartesian (,, ) and Ellipsoid (, ) coordinates The relation between the Cartesian and ellipsoidal are given as = (N + h) cos cos = (N+h) cos sin..() = ( N(-e2 ) + h )sin Where, N = a / (-e2 sin2 )/2 and e2 = (a2-b2)/a2 = 2f-f2 a is the sei-ajor axis, b is the sei inor axis, e is the first eccentricity and f is the flattening of the ellipsoid. Fro eq. (), it is possible to define ellipsoidal coordinates in ters of the Cartesian coordinates as, tan = (N + h)/{ (2 + 2)/2 (N(- e2)+h)}.ay be solved iteratively..(2) tan = / h = (2 + 2)/2 sec - N Since ellipsoidal coordinates of the receivers k and are known, it can directly be transferred to projection coordinates (plane coordinate of N = Northing, E = Easting plus H = Elevation ) using the associated projection equations such as Universal Transverse Mercator (UTM) projection. Hence, aong other quantities for slope distance s/ and horizontal distance S, we have, S/ k = ( k2 + k2 + k2)/ 2 (3) (4) S k = ( Nk2 + Ek2)/2.. IV. DATUM TRANSFORMATIONS Transforation between co-ordinate systes are routinely carried out in surveying. If the co-ordinates are given for a nuber of stations coon to both coordinate systes, the transforation paraeters can be estiated fro a least-squares solution. When easuring with GPS there is usually a need for a transforation because GPS easures co-ordinates on a different syste to that used in any one particular country. Therefore the results obtained fro GPS need to be transfored into the local co-ordinate syste. 3
ISO 900:2008 Certified A TRANSFORMATION MODELS The transforation of three-diensional coordinate systes for the purpose of transforing geodetic datus has been given uch attention, in particular since geodetic satellite techniques ade it possible to relate local geodetic datus to a geocentric datu. Soe of the pertinent works are Veis(960), Molodenskii et al,(962), Bursa(962)-Wolf(963), Badekas(969), Vanicek and Wells(974), Leick and Van Gelder(975),and Soler and Van Gelder(987). Threediensional transforations are ore suitable for use with satellite positioning for a nuber of reasons. They are typically global in concept, they enable solution for height as well as horizontal position, and they are atheatically rigorous. The coplete threediensional transforation involves seven paraeters that relate Cartesian co-ordinates in the two systes. There are three-translation paraeters to relate the origins of the two systes (,, ),three rotation paraeters, one around each of the co-ordinate axis (,, ) to relate the orientation of the two systes and one scale paraeter (L) to account for any difference in scale between the two systes. We can consider a geodetic syste defining a rectangular co-ordinate syste (,, ) where the origin is at the centre of the reference ellipsoid. The paraeters of this ellipsoid will be the equatorial radius a and the flattening f. Knowing,, and a and f we can copute the geodetic coordinates (,, h ) of points in the "old" syste. We next ay consider a new rectangular co-ordinate syste,, whose origin ay be (for exaple) at the centre of ass of the earth. Given the paraeters a and f of a new reference ellipsoid we can copute the geodetic co-ordinates (,, h ) of points in the new syste. In the past few years there has been a growing interest in the relationship between geodetic datus and the geocentric coordinate systes. This has been due to a variety of reasons, the ost iportant of which is a need to cobine the results of satellite geodesy with terrestrial networks. Coordinates derived fro satellite observations ay be related to a geocentric syste, while geodetic coordinates derived fro terrestrial observations are defined with respect to a particular non geocentric reference ellipsoid. The purpose of this investigation is to describe a ethod for deterining the relation ship between the local datu in Sudan (Adindan) and satellite datus (WGS72 and WGS84). Each of Bursa-Wolf and Molodensky-Badekas odels were tested and the result of the test is stated in [0] and it was concluded that Bursa-Wolf odel is not suitable for datu transforation between local and satellite datus because it was seen that Bursa-Wolf odel has big standard deviation of the values of the translation paraeters. Accordingly it is suitable to choose the Molodensky-Badekas odel for the coputation of the datu transforation considered in Volue 2, Issue 0, April 203 this paper. THE MOLODENSK-BADEKAS MODEL: The Molodesky-Badekas odel [4] reoves the high correlations that ay exist between the odel paraeters by relating the to the centroid of the network or soe other convenient point M, with in the network. This odel gives the sae answers for the baseline length and angles of the survey network, and for the scale and rotation paraeters, as the Bursa-Wolf odel [7]. However, the translation paraeters are different and have higher a posterior precision. Where (,, ) is the average local position of the coon points (fig.). Fig.: Molodensky-Badekas Model Rearranging: 2 2 O2 T O The seven paraeters for either the Bursa-Wolf or the Molodensky odels can be solved for in a least-squares adjustent. The adjustent uses points with coordinates in both the satellite and local datu a long with their estiated variances and derives least squares Estiates of the seven transforation paraeters to fit the differences between the two sets of co-ordinates. The reliability of these derived paraeters is usually expressed in ters of standard deviation or variances. V. PREVIOUS INVESTIGATIONS The datu transforation between Adindan and WGS- 72 and WGS-84 have been obtained by [] fro stations distributed all over the Sudan. The estiated transforation paraeters and their corresponding standard errors are given in Table (). The datu transforations WGS72 and WGS84 as they are stated in [3], (transforation between WGS-72and WGS-84 (Molodensky, DMA Recoendation): = = 0, = 4.5, a = 2.0, f = 0.32057 0-7 ). Gi M 2 5 6 4
ISO 900:2008 Certified Table: The Datu Transforation Paraeters and Their Associated Errors between Adindan, WGS-72 and WGS-84 (R=, R=, R=) Paraeters WGS-84 WGS-72 () -46.00.89-47.2 0.89 () -33.50.89-34.2.0.89 () 205.30.89 200.4.0.89 L(pp) -.34.35 -.57.35 Rx 03 sec.64.87.64.87 Ry 03 sec 2.8.87 2.8.87 Rz 03 sec -4.82.6-4.82.6 VI. PROCEDURES For the purpose of the translation paraeters deterination between satellite and local datu a FORTRAN coputer progra was written to handle Molodensky-Badekas odel. The progra follows the cobined least squares adjustent technique. The input data consist of the ellipsoid coordinates of the two systes coon to satellite (Transit or GPS) and the Adindan datu. The output is the Cartesian (,,) coordinates and the transforation paraeters between the two systes with their standard deviation and residuals. The translation paraeters between Adindan and WGS72 were estiated using 4 stations distributed all over the Sudan. The estiated translation paraeters and their corresponding standard errors are given in Table 2. The results see to be consistent with sall variation fro the results obtained by [] (Table ). Table 2: Transforation Paraeters between WGS72 and WGS-84 to Adindan Atu (R=, R=, R=) Paraeters WGS72 WGS-84 () -50.3.97-56.6 2.64 () -28.7.97-6.5 2.64 () 20..97 207.9 2.64 L (pp) 0.82 2.86-0.98 4.3 R 02 sec -03.6. - 5.0.59 R 02 sec 4.4.43 2.5.84 R 02 sec -5.4.53-2.4 3.50 In this study, also well distributed GPS observation stations covering the whole country (Sudan) have been selected so as to be utilized in the deterination of datu transforation paraeters between Adindan and WGS-84 datus. Therefore these points have to be coon on the two systes, this is why the GPS points are choosed to be in the local network (Adindan datu). They were observed with geodetic GPS receivers, in static ode, and processed as a single point averaged to ore than one hour observation tie, relative to WGS 84 ellipsoid, using different receivers (where the points located at the Red Sea State and Khartou State were observed by SOKKIA, GSSA receivers and points at West Kordofan State were observed by integrated receivers of Trible and Ashtech, belong to British copany naed RACL. They are dual frequency Volue 2, Issue 0, April 203 receivers used to observe the three points in West Kordofan relative to base line in the sae area established with dual frequency carrier phase GPS relative to International Geodetic Service (IGS) stations. The reaining 9 points were observed by IGN (French, International copany) with air ports positioning project in Sudan using the Civil Aviation Authority (Sudan) Trible dual frequency receivers. The translation paraeters between Adindan and WGS84 were estiated using the coon 7 stations. The estiated translation paraeters and their corresponding standard errors are given in table 2. The results see to be different fro the previous investigation shown in table. VII. CONCLUSION Concluding that the Molodensky-Badekas odel (with its sall standard deviation) is suitable for the local and satellite datu transforation. Referring to the results shown above, it could be concluded that: Neither the satellite reference syste or the terrestrial datu is perfect. Both contain systeatic errors which affect the transforation odel, thereby producing distortions in the data analysis The estiated translation paraeters and their corresponding standard errors given in Table 2, showed variations in the solutions when copared with the investigations shown in Table. These variations ay be due to use of different station coordinates, the nuber and geoetric distribution of the stations used and also the variations are due to that the first investigations (Table ) were not done using the actual observed GPS values but they used to deterine the theoretical values of the translation paraeters between transit syste datu (NWL-9D, WGS-72 and WGS-84) by adding the theoretical shift values between the two systes, where this study is using the direct and actual observation values collected by the Geodetic GPS receivers since 995 up to the tie of preparing this study and accordingly it is well known that the GPS observed values are affected by the errors of GPS syste,also the error is due to that they are processed using the broadcast epheeris and there are no relative connection between these stations where each of the was a control point of different project which coputed by broadcast epheeris. VIII. FUTURE RECOMMENDATIONS For the GPS points to fit in the existing local syste after transforation, it is very iportant to ake sure of the accuracy of the local coordinates especially the orthoetric height. In order to obtain accurate ellipsoidal heights, the geoid separation at the easured points ust be known. This ay be deterined fro geoidal odel, here in Sudan the geoid separation of the Clarke 880 ellipsoid is neglected and it is approxiated to zero, but it is known that there are discrepancies between the orthoetric height and the height related to the surface of the geoid, so the neglection of the geoid 5
ISO 900:2008 Certified height is not the optial case. Also it is better to establish the origin of the local datu at the center of the network by establishing the datu by the astronoical geodetic orientation using a nuber of Laplace stations, distributed all over the country. The datu transforation basically works by taking the Cartesian coordinates of the GPS easured points (WGS-84 ellipsoid) and coparing the with the Cartesian coordinates of the local coordinates, fro this, shifts, rotations and a scale factor are calculated in order to transfer fro one ellipsoid to another, this syste of transforation will be used over virtually any area as long as the local coordinates (including height) are accurate, and also for this ethod it is always recoended that the surveyor have at least three points for which the coordinates are known in the local syste and in WGS-84, it is possible to copute transforation paraeters using only three coon points but using four allows for residuals to be calculated. For any precise GPS survey the absolute coordinates of one site in the network have to be known in WGS-84 to the possible accuracy. This can be accoplished by setting a geodetic GPS receiver at the station, in the static ode having a good GDOP values and utilizing the single point processing software to get the absolute coordinates of the station. The iniu observation for the coputation of a reliable single point position is probably about one hour with four or ore satellites and good GDOP. The longer the observation tie, the better the single point position will be. Referring to the practical aspects it is not recoended to use the published values of the transforation paraeters which installed in the software of the geodetic GPS (each GPS receiver software has its own paraeters) because they are approxiated to the whole region not to the area under consideration, and always they have a variation fro the actual paraeters of the considered area. It is recoended for the surveyor to deterine his own transforation paraeters using control points distributed over the area under consideration. REFERENCES [] Abd Alla K.and Fashir H. H., Space Geodesy for Monitoring Deforation and Datu Transforation In Sudan: In Sudan Engineering Society Journal, Journal. June 997 vol. 44 No. 35. 997. [2] Anderle, R. J., Transforation of terrestrial Survey data To Doppler Satellite Datus. IAG Syposiu on Coputational Method in Geoetrical Geodesy, Oxford 973. [3] Ashkenazi, V., Coordinate systes and reference datu, Astronoical and geodetic coordinates, Terrestrial and satellite datu. Nottingha University, 988 [4] Badekas, J., Investigations Related to the establishent of a World Geodetic Syste: In Rept. No. 24, Dep. Of Geodetic science, The Ohio State University, Colubus, 969. Volue 2, Issue 0, April 203 [5] Fashir, H. H., Salih, A. B. and Abdalla, K. A., The transforation between the Doppler Coordinate Syste and the geodetic coordinates Syste in Sudan. Aust. Journal, Geodesy, Photograetry and Surveying, Vol. 5, 989. [6] Hofann- Wellenhof. B., Lichtenegger, H., Collins, J., Global Positioning Syste, Theory and Practice, Second Edition, Springer-Verlog Wien New ork, 993. [7] King, R. W., Masters, E. G., Rizos, C. Stolz, A.. Collins, J., Surveying with Global Positioning Syste-GPS. Australia, 985. [8] Laurila, H. S., Electronic Surveying in Practice. University of Hawaiiat Manoa, 983. [9] Leick, A., GPS Satellite Surveying. Wiley, New ork Chichester Brisbane. In: Departent of Surveying Engineering, University of Maine, Orono, Maine, 990. [0] Mohaed, A. E., The Datu Transforation Paraeters between Sudanese datu and WGS-84 and its iplications on the local datu. A thesis subitted for the Degree of Maser of Science in Surveying Engineering. April, 995. [] Salih, A. Astrogeodetic and Dynaic geoid in Sudan. Int. Syposiu on Geodetic Measureents and coputations, A. B. u, aria, 987. [2] Wooden, WH., Navstar Global Positioning Syste. In: Proceedings of the First International Syposiu on Precise Positioning with the Global Positioning Syste, Rockville, Maryland, April 5-9, vol :23-32,985. 6