Comparison of the Positions Computed from DGPS/GNSS Observations Using the New/Unified and Various Old Transformation Parameters in Nigeria

The accurate computation of positions of points from DGPS/GNSS observations acquired on the WGS84 ellipsoid in each country requires the application of transformation parameters. This is because, positions are determined with respect to the local datum/ellipsoid adopted for geodetic computation in each country. Prior to the derivation of the new/unified transformation parameters which were recently published by the Office of the Surveyor-General of the Federation, OSGOF, various sets of transformation parameters were determined by different multinational oil companies for use in Nigeria. Since the positions of reasonable number of points had been computed using these old sets of transformation parameters before the new/unified ones were derived and promulgated, there is need to verify which of the positions computed with the old sets of transformation parameters agree with the positions computed with the new/unified ones. Consequently, this paper compares the positions computed from DGPS/GNSS observations using the various, old sets and the unified transformation parameters. GNSS observations of four different points were processed with Compass post processing software using the various, old sets and the unified transformation parameters to obtain the positions of the points. The coordinates of each point obtained from the processing of the observations using the old sets of transformation parameters were compared with those obtained using the unified ones. The comparison results show that the positions computed using three different (SPDC, AGIP and DMA) sets of transformation parameters agree with those computed using the unified ones.


INTRODUCTION
The Navigation Satellite Timing and Ranging (NAVSTAR) Global Positioning System (GPS) is a worldwide radionavigation system created by the U. S. Department of Defense (DOD) to provide navigation, location, and timing information for military operations (Vail et al, 2015). The system consists of 24 satellites in space. These satellites are equipped with four atomic clocks each to provide accurate timing. They transmit two radio frequencies on two separate L-bands (L1 = 1575.42 MHz and L2=1227.60 MHz). The L1 signal consists of a Coarse/Acquisition (C/A) and a Precision (P) code. The L2 signal contains only the P-code. Only the C/A code of the L1 signal, known as the Standard Positioning Service (SPS), is available for civilian use. The L1 and L2 signals are available for military and other authorized users and provide a Precise Positioning Service (PPS) ). The GPS system consists of three basic elements: the space segment, control segment, and user segment. The space segment consists of the constellation of up to 24 active NAVSTAR satellites in six orbital tracks. The satellites are not in geo-synchronous orbit and are in constant motion relative to a ground user. The control segment consists of several ground stations that serve as uplinks to the satellites and that make adjustments to satellite orbits and clocks when necessary. The user segment consists of the GPS receiver which will typically consist of an antenna, multi-channel receiver, and processing unit (Vail et al, 2015 and. The DGPS/GNSS acquires observations on the WGS84 ellipsoid. But the acquired observations are processed to determined positions on the local datum as well as the local ellipsoid adopted for geodetic computations in various countries. In the determination of positions on the local datum from DGPS/GNSS observations obtained on the WGS84 datum/ellipsoid, the seven datum transformation parameters are applied.
Prior to the determination of the new set of transformation parameters recently published by the Office of the Surveyor-General of the Federation, OSGOF, various transformation parameters had been derived and used by various multinational oil companies including academic scholars for the processing of DGPS/GNSS observations in Nigeria. These transformation parameters were determined by various groups as well as scholars for these companies. The use of various sets of transformation parameters in the country was as a result of no unified set of transformation parameters. Uzodinma  Today, a new set of transformation parameters have been derived by academic scholars and signed into use as well published by the Office of the Surveyor-General of the Federation, OSGOF. Using the positions determined with the new as well as the unified set of transformation parameters as baselines for comparison of the same positions determined using these old sets of transformation parameters, those positions which were previously computed using the old sets of transformation parameters that agree with the positions computed with the new as well as the unified transformation parameters can be determined.
This paper presents the comparison of the positions previously computed from DGPS/GNSS observations using the various, old sets of transformation parameters with the coordinates computed using the new transformation parameters with a view of determining which of these computed positions using the old sets of transformation parameters agree with the ones computed using the new transformation parameters.

The Nigeria Geodetic Datum
The Nigeria Minna datum is a geodetic datum that is suitable for use in Nigeria-onshore and offshore. Minna datum references the Clarke 1880 (RGS) ellipsoid (Semi-major axis, a = 6378249.145m; Flattening, f = 1/293.465) and the Greenwich prime meridian. The datum origin is fundamental point: Minna base station L40. Latitude: 9°38'08.87"N, longitude: 6°30'58.76"E (of Greenwich). It is a geodetic datum for topographic mapping. It was defined by information from NIMA

Conversion between Geodetic and Cartesian Rectangular Coordinates
Geodetic coordinates can be converted to rectangular Cartesian coordinates by (Heiskanen andMoritz, 1967, andZiggah et al, 2017): Where, h and ,  are respectively the geodetic latitude, geodetic longitude and ellipsoidal height while X, Y, Z are the Cartesian coordinates to be estimated. h is ellipsoidal height (orthometric height, H + geoidal height, N). N in equation (1) is the radius of curvature in the prime vertical given by Ono (2009) as: Where, a is the semi-major axis while f is flattening given as : On the other hand, rectangular Cartesian coordinates can be converted to geographic coordinates using the following (Janssen, 2009): Where, 2 e = eccentricity squared = , 2 2 f f  N = radius of curvature as given in equation (2).

Transformation between WGS84 and Minna Datums
The processing of DGPS/GNSS observations which are always acquired on the WGS84 ellipsoid to obtain positions on the Minna datum/Clarke1880 ellipsoid requires datum transformation. This is because GPS/GNSS uses the WGS84 ellipsoid while the end datum is a local one with different ellipsoid which best fit the region of application, for instance, Minna datum. The accurate transformation of positions on the WGS84 ellipsoid to Minna Datum, Clarke 1880 ellipsoid requires the application of the seven datum transformation parameters. The application of the seven datum transformation parameters, requires their combination with the Cartesian coordinates, X, Y and Z (Eteje et al, 2018). These parameters consist of an origin shift in three dimension, ( ) and a change in scale ( S  ) (Ono, 2009 Electronic copy available at: https://ssrn.com/abstract=3308482 http://ijesc.org/

METHODOLOGY
The methodology adopted in this study is divided into data acquisition, data processing, and results presentation and analysis. Figure 1 shows the flow chart of the adopted methodology.

Data Acquisition
The data used in this study were GNSS observation data acquired using CHC900 GNSS dual frequency receivers. A total of four new stations (GPSESO1, GPSESO2, GPSESO3 and GPSESO4) were observed with respect to a control station (ASPXW42A). The observations were carried out with three GNSS receivers, two rover receivers and a base receiver. The observations were carried out in two different loops. In the first loop, the base receiver was set at the control station while the two rover receivers were occupying the two new points, GPSESO1 and GPSESO2 simultaneously (see Figure 2).

Fig. 2: GNSS observation Loop 1
In the second loop, while the base receiver still at the control station acquiring observations, the two rover receivers were moved to simultaneously occupy stations GPSESO3 and GPSESO4 (see Figure 3). Each of the four new points was occupied by the rover receiver for not less than 60 minutes during the observation.

Data Processing
The GNSS observations were processed using Compass post processing software. At first, the observations were processed using the new/unified set of transformation parameters as baseline positions of the points (see Figure 4). During the processing of the observations using the new transformation parameters, the scale factor was subtracted from 1 before use. This was because the processing output using the published scale factor, 0.99999393 was outrageous. Subsequently the various, old sets of transformation parameters were used one after the other to process the observations. The processing of the observations using the old sets of transformation parameters enabled the positions of the points to be determined using the old sets of transformation parameters. The positions of the points were computed in the NTM using the Nigeria west belt parameters.

Results Presentation and Analysis
Tables 3 presents the coordinates and heights of the points computed using the new/unified and the various, old sets of transformation parameters. This was done to enable the comparison between the positions obtained using the new/unified transformation parameters with those computed using the old sets of transformation parameters. From table 3, it can be seen that the positions processed with the transformation parameters derived by NORTEC were not presented. This was because the post processing software was unable to process the observations using the transformation parameters derived by NORTEC as the scale factor (-21.2688) was too large. Consequently, the entire processing was regarded as outlier and rejected. Electronic copy available at: https://ssrn.com/abstract=3308482 http://ijesc.org/ Tables 4 and figures 5 and 6 also present the coordinate and height differences between the positions obtained using the new/unified transformation parameters and those computed using the old sets of transformation parameters. This was done to enable the differences in northings, eastings and ellipsoidal heights of the observed points using the new and the old sets of transformation parameters be determined. It can be seen from    Prior to the derivation of these new transformation parameters, the previously derived ones had been used for the computation of positions of various points in the country. In order to know those positions which were previously computed using the old sets of transformation parameters that agree with the positions computed with the new/unified transformation parameters, this paper has presented the comparison between the positions computed from DGPS/GNSS observations using the various, old sets and the unified transformation parameters. GNSS observations of four different points were processed with Compass post processing software using the various, old sets and the unified transformation parameters to obtain the positions of the points. The coordinates of each point obtained from the processing of the observations using the old sets of transformation parameters were compared with those obtained using the unified ones. The comparison results show that the positions computed using three different (SPDC, AGIP and DMA) old sets of transformation parameters are in agreement with those computed using the unified transformation parameters.