50-POINTS DATA FOR DERIVING TRANSFORMATION PARAMETERS OF GEODETIC DATA IN NIGERIA

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1 Ind. J. Sci. Res. and Tech ():97-0/Orupabo et al ISSN: (Online) 50-POINTS DATA FOR DERIVING TRANSFORMATION PARAMETERS OF GEODETIC DATA IN NIGERIA * S. Orupabo, T. A. Opuaji and I. A. Adekunle 2 Department of Surveying and Geomatics, Rivers State University of Science and Technology, Nkpolu, PortHarcourt, Nigeria Department of Surveying and Geoinformatics, Rivers State Polytechnic, Bori, Rivers State, Nigeria *Author for Correspondence ABSTRACT The need for continuous interchange of geodetic data between Minna datum and the World Geodetic System of 984 has brought about the need to derive datum transformation parameters based on Molodensky 7 parameter model. Geodetic coordinates used are subjected to a filtering process where an outlier was discovered. 3-Shift, 3- rotation and scale parameters derived in sequence are X = , Y= , = , r x = E-05, r y = E-06, r z = E-06 and k = E-06 respectively. Key Words: Minna datum, WGS 84 and 7-parameter Model INTRODUCTION Geodetic data involving primary control stations in Nigeria were initially based on the Minna datum established using the modified Clarke 880 ellipsoid as reference surface. The origin of this system, L40, is defined through = N = E = 279.6m (above geoid) (Uzodinma & Ezenwere, 993). Over the years the world geodetic community has updated the parameters of the unified world geodetic system (WGS) with the adoption of a new set of parameters for the best fitting ellipsoid. Currently, most globally applicable geodetic system including the global positioning system (GPS) have adopted WGS84 as the reference system with the following defining parameters for the ellipsoid (Rapp, 993). Semi major axis (a) = m Flattening f given by ( f ) = These ellipsoidal defining parameters can be viewed vis-a vis the modified Clarke 880 system (the old system) referred to earlier in this section with defining parameters given by a = m = f A geodetic problem arises when the requirement is to reconcile point co-ordinate values obtained with the old system and corresponding values based on the WGS84 (the new system). Most efforts at reconciling the two sets of coordinate values have used the methodology of rigorous co-ordinate transformation models where datum transformation parameters are obtained using classical techniques e.g. least squares techniques (Fajemirokun & Orupabo, 986). OBJECTIVES OF PRESENT METHODOLOGY The methodology here is to initially carry out a filtering process so that geodetic co-ordinates values that fall out of the norm in the simple numerical investigation procedure can be re-investigated, re-observed or re-assessed in one form or the other. The numerical procedure discussed here is expected to provide an insight into data quality and is recommended as an initial step before any form of rigorous datum transformation methodology is applied to geodetic data based on different datums. It can be argued that while the theory of datum transformation parameter derivation as has been applied by various researchers in this field appear to be similar in several respects, the problems arising from different parameter values for different datum transformation parameter programs has largely been in the data quality, type and location(orupabo,202). 97

2 Ind. J. Sci. Res. and Tech ():97-0/Orupabo et al ISSN: (Online) CLASSICAL METHODOLOGY In the classical methodology, a 7-parameter model is usually employed for datum transformations of the form X X X Y Y R Y ( L)... () X Y X X Y Figure : Relationship between geodetic datums In figure, X - Shift along X- axis from an old system X to the new system X Y - Shift along Y axis from an old system Y to the new system Y - Shift along - axis from an old system and to the new system L - Errors associated with scale parameter between the old system and the new system. R is a rotational matrix of the form R = w w v v... (2) The angles v, w and are small angular rotations about the co-ordinate axes (Vanicek et al., 983; Heikanen & Moritz, 967). The works of Fajemirokun and Orupabo, Ezeigbo and Fubara and several others have largely depended on this technique in their various attempts at datum transformation for Nigeria with varying values obtained for the parameters. As noted earlier, such methodologies and techniques of transformation have only been available and can be carried out as research programs and for specific programs. Again, an insight into parameter values obtained by various groups show considerable variability and sometimes is so localised as to render the derived transformation parameters inapplicable for large areas. Again the origin of the data used for the various programs may be conflicting. This may then lead to derived parameter values that are location sensitive. APPLICATION OF DATA SENSITIVE METHODOLOGY It is interesting that OSGOF has provided data that we can start with and then improve upon as more data of improved quality becomes available. OSGOF has now provided data for 50 points covering the country for latitudes ( ), longitude ( ) and heights (based on H or h for whatever height datum) given in table. The data is based on geodetic co-ordinate values observed for the Minna datum and the WGS 84 datum. The data points are plotted and shown in figure 2. In this work, we have concentrated on the treatment of this data individually in the, and h sense. 98

3 Ind. J. Sci. Res. and Tech ():97-0/Orupabo et al ISSN: (Online) Table : National Coordinates of Common Points in WGS 84 and Clark 880 Datum with Additional Points MINNA DATUM COORDINATES WGS 84(ITRF 2008) COORDINATES STATION NAME/ID LATITUDE LONGITUDE ORTHOMETRIC HEIGHT (M) LATITUDE LONGITUDE ELLIPSOIDAL HEIGHT (M) A N 9 9' '' E 2 3' '' m A N 0 36' '' E 20' '' m A N 0 07' '' E 2 22' '' m A N 7' '' E 0 25' '' m C C N 6 08' '' E 9 0' '' m C N 7 45' '' E 0 07' '' m CFL CFH CFA 33A N6 37' " E3 9' " D N 23' '' E 5 3' '' m D N 0 45' '' E 4 33' '' 350.2m H N7 27' " E8 36'.53445" H N7 30' " E8 58' " H N 8 4' '' E 8 48'.4687'' m L N7 2' " E3 20' " L L N 7 54' '' E 4 24' '' m MW N5 07'9.3452" E8 20' " N N 8 59' '' E 8 05' '' m N N N R N 3 34' '' E 5 23' '' R N 3 08' '' E 6 3' '' m R R N 2 0' '' E 5 53' '' m U N7 48' " E6 42' " U N 7 50' '' E 5 52' '' m U U N 6 46' '' E 7 5' '' m VS E4 50' " E7 02' " CBL L N L U D L D K N C N23A L N A U C A

4 Ind. J. Sci. Res. and Tech ():97-0/Orupabo et al ISSN: (Online) Figure 2: Plot of 50 Data Points from OSGoF NUMERICAL INVESTIGATIONS Using the OSGOF values of table, we arranged the value in order of magnitude and obtained as...2 i i ( i 50 ) In the same manner, we arranged values in order of magnitude to obtain...3 i i ( i 50 ) given by values given Figure 3: Plot of, l versus 00

5 Ind. J. Sci. Res. and Tech ():97-0/Orupabo et al ISSN: (Online) Figure 4: Plot of, l versus l This initial filtering process indicates that point with serial number 3 (fig. 3 & 4) on the new OSGoF data which is point U78 with coordinates (on the Minna datum) = 06 o = 7o h = m does not pass through this simple process. It is therefore not used in the coordinate transformation process. CONCLUSION The methodology used for the 7- parameter datum transformation technique is based on classical theory. One expects to get fairly the same results for different data sets and for various groups that carry out work in this area. For this work, having made these simplifying assumptions, we obtained the following values based on the Molodensky Badekas (Rapp, 993; Kiusalaas, 2005) to obtain rotational elements, translation and scale parameters of the following values: r x = E-05 ± E-06 r y = E-06 ± E-06 r z = E-06 ± E-06 The corresponding translational elements and scale are: X = ± Y = ± = ± Scale = E-06 ± E-06 We will here suggest the creation and adoption of an algorithm that can update these data values with increase in data in terms of quality and quantity. REFERENCES Fajemirokun FA & Orupabo S (986). Some Theoretical Considerations in the Transformation of Geodetic Data from one Datum to another. Proceedings of the 3 rd International Symposium on Geodesy in Africa, Ivory Coast 986. Heiskanen WA & Moritz H (967). Physical Geodesy, WH Foreman and Company, San Francisco. Kiusalaas J (2005). Numerical methods in Engineering with MATLAB. Cambridge University press. Orupabo S (202). Filtering and reconciliation of Minna and WGS 84 Datums for Geodetic Transformations Data in Nigeria. Workshop on the Adoption of Suitable Transformation Parameters for Nigeria. Rapp RH (993). Geometric Geodesy Part II. The Ohio State University Department of Science and Surveying. Uzodinma NV & Ezenwere OC (993). Map Projections. Practical Computations on the Traverse Mercator Projection. EL Demark company 294. Vanicek P & Krakawski E (983). Geodesy the Concepts. North Holland Publishing Company, Amsterdam 69. 0