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A STUDY OF SOME TRANSFORMATION PROCEDURES FOR NIGERIAN GEODETIC NETWORK
P.C. Nwilo, F.A. Fajemirokun, C.U. Ezeigbo, A. M. Oyewusi & E.G. AyodeleDepartment of Surveying & GeoinformaticsFaculty of EngineeringUniversity of Lagos, Akoka-Lagos, Nigeria. [email protected], [email protected], [email protected],[email protected] & [email protected]
ABSTRACT
The connection between global and local datums is usually established by transformation parameters. In
this study, two sets of transformation parameters relating the Nigerian geodetic datum (Clarke 1880) and
the global datum (WGS84) were investigated using the coordinates of fourteen common points on both
datums. The first set of transformation parameters (model1) are given in terms of variation in the
coordinates of the center (shift parameters) of the ellipsoid, semi-major axis and
flattening of the ellipsoid, while the second set (model 2) are given in terms of the changes in the
geodetic curvilinear coordinates of the initial point, semi-major axis and flattening .
Each set of transformation parameters was used to transform the coordinates referred to WGS84 ellipsoid
into the coordinates referred to Clarke 1880 ellipsoid. The effects of the different configurations of the
data on the estimated transformation parameters were investigated. From this study, it was found that,
using model 2, configuration 5, which consists of points centrally located in the geodetic network, gave
the best set of transformation parameters. The best set of transformation parameters are
, , .
Keywords: Datum, transformation parameters, geodetic coordinates.
1 INTRODUCTION
The Clarke 1880 ellipsoid was adopted as the reference ellipsoid for the Nigerian
Geodetic Datum to meet the requirements for mapping and engineering projects.
With the advent of the Navy Navigational Satellite System (NNSS) (Doppler), and
later Global Positioning System (GPS) as tools for geodetic positioning, there is
often the need to transform coordinates on the geocentric systems to coordinates
on the local systems, and vice versa.
1
Efforts have been made by both Nigerian and Foreign agencies to determine
transformation parameters for the Nigerian Geodetic Datum (Fubara, 1995).
There are various methods by which the transformations can be executed. No
conclusion has been reached as to which of them is the preferred approach and
no doubt this is an area where discussions will continue for some time to come
(Smith, 1997).
In this paper, efforts were made to investigate two types of transformation
procedures relating the Nigerian Geodetic Datum (Minna Datum) and the global
datum, the World Geodetic system (WGS 84), on which the GPS is based.
1.1 BASIC CONCEPT OF GEODETIC DATUM
A geodetic datum is a set of parameters that defines the size and shape of a
given reference ellipsoid, as well as its position and orientation with respect to
the real earth (geoid). A geodetic datum is often defined by a set of five
parameters, namely (Seeber, 2003):
Semi major axis of the reference ellipsoid
Flattening of the ellipsoid and
Change in the coordinates of the origin of the coordinate
system of the reference ellipsoid.
A geodetic datum can also be defined in terms of (Fubara,
1995):
Where,
and are as defined above
are changes in the latitude and longitude of the initial point of
the geodetic network
is the change in ellipsoidal height at the initial point of the
geodetic network
2
Two types of unrelated datums were in the past considered in geodesy: A
horizontal Datum, which forms the basis for the computation of horizontal
coordiates and a vertical datum, to which heights refer. The horizontal and
vertical datums were kept strictly separate, but today, because of satellite
techniques, a unified global datum is often adopted for the realization of
integrated geodetic procedures.
In the Nigerian geodetic network, the Clarke 1880 ellipsoid was adopted as the
horizontal geodetic datum, while the Lagos datum (physical location unknown),
close to the East mole, was adopted as the vertical datum. With the evolution of
space technology, a geocentric datum, which is used all over the world, is also in
use in Nigerian geodetic network.
The connection between global and local datums is established by
transformation parameters. To determine these transformation parameters,
points whose coordinates are known on both datums are chosen.
1.2 THE NIGERIAN GEODETIC DATUM
Several attempts have been made to determine transformation parameters for
the Nigerian Geodetic Datum, using either Doppler or WGS 84 coordinates and
Clarke 1880 coordinates (Oyeneye, 1985; Fajemirokun & Orupabo, 1986;
Ezeigbo, 1990a, b).
Some work was done by Campagine Generalie de Geophysique (Nigeria)
Limited (Fubara, 1995). The report provided coordinates of data points without
relevant background information for the assessment of the data quality. The
values of the datum shifts were also published without any indication on how they
were derived (Fubara, 1995).
Geodetic Positioning Service, in collaboration with oil producing companies in
Nigeria, has also determined transformation parameters for the Nigerian National
Petroleum Corporation (NNPC) using the combination of GPS and the Transit
Satellite System (Doppler) data (Fubara, 1995).
3
Geodetic Surveys Nigeria also determined seven transformation parameters for
Shell Petroleum Development Company (SDPC), for use in the Southern Nigeria
(Fubara, 1995).
In most of these investigations, it was observed that the transformation
parameters were determined using either Molodensky-Badekas or Bursa-Wolf
Model.
In this study, two transformation procedures (models) are investigated. In the
first model, the set of transformation parameters are the shift in the origin of the
coordinate axes , changes in semi-major axis and flattening of
the ellipsoid . In the second model, the set of transformation parameters
are the changes in geodetic coordinates at the network origin,
change in semi-major axis and flattening . The basic transformation
equations used are presented in the next section.
1.3 DATA USED FOR THE INVESTIGATIONS
The data used for this investigation were obtained from the Office of the Surveyor
General of the Federation (OSGOF). They consist of the geodetic (curvilinear)
coordinates of sixteen coincident points on both Minna datum and WGS84. Only
fourteen out of the sixteen data points were actually used for the investigation.
At an average of approximately one data point per 64,000 square km, the
available data are far from being adequate. The data points are equally poorly
distributed over the geodetic network. Furthermore, only scanty information on
the accuracy and the reliability of those data is available.
4
2.0 MATHEMATICAL FORMULATIONS
The relevant transformation equations in terms of are given
by (Heiskanen & Moritz, 1967, equation (5.55)):
(2.1a)
(2.1b)
(2.1c)
where are as defined in section 1.2.
Similarly, the transformation equations in terms of variations
are given by (Heiskanen & Moritz, 1967, equation (5.57)):
(2.2a)
(2.2b)
(2.2c)
where
changes in the geodetic coordinates of an initial point
parallel displacement or shift component of the origin of the
coordinate system of the reference ellipsoid
changes in the geodetic coordinates at an arbitrary point
5
changes in the parameters of the reference ellipsoid
Equations (2.2a, b & c) express the at an arbitrary point in terms of
at the initial point of the network and .
There are some similarities between equations (2.1a, b & c) and (2.2a, b & c).
They are infinitesimal transformations of geodetic coordinates. However, they
differ in the parameters used for the transformation (Heiskanen & Moritz, 1967).
Equations (2.2a, b & c) can also be expressed in terms of variations of deflection
components and and of geoidal undulation at the initial point of the
network using Vening Meinesz formulae (Heiskanen & Moritz, 1967, equation
(5.58); Torge, 1980; Musa, 2003):
(2.3)
Substituting equation (2.3) is into equations (2.2a, b & c), we obtain:
(2.4a)
(2.4b)
(2.4c)
6
where
refer to a local geodetic datum
refer to a world geodetic datum
Equations (2.1a, b & c) (Model 1) and equation (2.2a, b & c) (Model 2) are the
basic mathematical formulations used for estimating the transformation
parameters in this study, since the available data for the estimation are the
geodetic coordinates as opposed to the geoidal undulations and the
deflection components .
3. PARAMETER ESTIMATION
The linearized models of equations (2.1a, b & c) and (2.2a, b & c) can be
expressed as:
(3.1)
where,
is the vector of the correction to the transformation parameters
is the design matrix
is the vector of the misclosures, and
is the vector of the residuals of the observations
The least squares solution of equation (3.1), which is an estimate of the
parameter vector is given by (Mikhail, et al, 1981, equation (4.38); Ezeigbo,
1990a):
(3.2)
The error covariance matrix, which is a measure of accuracy of the estimated
vector of the parameters , is given by (Ibid, 1990a):
7
(3.3)
where,
is a posteriori variance of unit weight
is the weight matrix of the observations
4. NUMERICAL INVESTIGATIONS
Corrections to the approximate parameters were determined by equation (3.2).
By adding them to the approximate parameters, the required parameters were
obtained. The estimates derived from equation (3.2) for each set of
transformation parameters were used to transform geodetic coordinates referred
to WGS84 ellipsoid into geodetic coordinates referred to Clarke 1880 ellipsoid,
and the results were compared with the corresponding coordinates on Minna
datum.
4.1 CONFIGURATION OF STATIONS
The effects of the different configurations of the common points on the estimated
parameters were investigated. Five different configurations of the fourteen
common points, consisting of different numbers of common points were
considered (see table 4.1 and fig. 4.1).
Table 4.1: Configuration of Stations
Config. Distribution No. of
Obsn
Stations
1 All data Used 14 A10, U81, N127, CFL56, C21, R16, CFL9, CFL62, CFM45, CFM58,
CFL17, CFL20, CFL25, CFM10
2 North 11 N127, CFL56, R16, CFL9, CFL62, CFM45, CFM58, CFL17, CFL20,
CFL25, CFM10
3 East 8 A10, CFL56, C21, CFL62, CFM45, CFM58, CFL25, CFM10
4 West 6 U81, N127, R16, CFL9, CFL17, CFL20
5 Central 7 U81, N127, C21, CFL17, CFL20, CFL25, CFM10
8
4.2 CONVERGENCE OF ITERATED SOLUTIONS
A number of iterative steps were taken to arrive at a particular solution. The
iterated solutions investigated using either 5-parameter transformation or 3-
parameter transformation did not converge to specific values because of the
instability of the procedure. The instability of the 3-parameter transformation is
however less than that of 5-parameter transformation. Therefore, the values of
the transformation parameters from the first iteration for 3-parameter
transformation were adopted in this study.
4.3 ADOPTION OF THREE-PARAMETER TRANSFORMATION MODEL
The estimation of five datum transformation parameters in both models were
investigated but produced very unreliable results (not published in this paper).
This could be due to the possible correlation between the parameters. It may
also be due to the fact that the coordinate axes of Minna datum are not parallel to
those of WGS 84 datum. Therefore, because of the very high degree of 9
Figure 4.1: Network ConfigurationFigure 4.1: Network Configuration
Map of Nigeria Showing the Distribibution of Observation Points
$
$
$
$$
$
$
$
$
$
$
$$
$ $
$
N10
A10
U81
N127CFL56
C21
R16
N102
CFL9
CFL62
CFM45
CFM58CFL17 CFL20
CFL25
CFM10
300 0 300 600 KilometersN
$ Control Points
2
2
4
4
6
6
8
8
10
10
12
12
14
144 4
6 6
8 8
10 10
12 12
instability of 5-parameter model, 3-parameter model was adopted for further
investigations in this study.
4.4 SAMPLE COMPUTATION
The set of transformation parameters obtained using both models (equations
(2.1) and (2.2)) were used to transform a number of WGS84 coordinates into
Minna datum coordinates. The transformed coordinates were then compared
with the original coordinates in Minna datum to determine which of the models
gives the optimum result.
4.5 COMPUTATION OF THE DISPLACEMENTS OF THE TRANSFORMED POINTS
In order that the discrepancies between the transformed coordinates and the
corresponding coordinates in Minna Datum could be plotted in a graph, the
latitude and longitude components of these discrepancies were converted to
displacements . The formula used for the conversion is as given below:
(4.1)
where
Value in metres
Value in seconds of the discrepancy in latitude or longitude
Radius of the earth in metres
From the computed displacements in latitude and longitude and in
height directions, the displacement of the transformed point is given by:
(4.2)
By analyzing the values of for the different transformed points, the effect of the
different configurations on the transformation procedure is ascertained.
10
5 RESULTS AND ANALYSIS OF RESULTS
5.1 RESULTS
The results of some of the various investigations carried out in section 4 are
presented in this section. The results obtained using 5-parameter model and
those from the investigations in which N10 and N102 were incorporated were not
presented. This is because of the large residuals, which they produced when the
parameters from them were used to transform coordinates from WGS84 to Minna
datum. N102 is the origin of the Nigerian geodetic network while N10 is a point
whose orthometric height is very large compared with other points. It has a
height of 1396m, as against the closest height of 755m from the remaining
points. Consequently, further investigations, which were based on 3-parameter
model excluded these two points.
In table 5.1, we present the results of the three-parameter transformation
procedure, which were obtained using models 1 and 2. The three configurations
A, B and C show the results using the data sets with both N10 and N102
included; only N102 included; and N10 and N102 excluded, respectively.
Table 5.1: Effect of the Inclusion of Some Points (N10 & N102)
In tables 5.2a & b, the estimated parameters and their accuracies for different
configurations are presented. Only fourteen points (excluding N10 and N102)
are used in the investigations. Table 5.2a presents the results for model 1, while
table 5.2b presents the results for model 2.
3 TRANSFORMATION PARAMETERS
Conf.
Parameters
Conf. A
16 obs
Conf. B
15 obs
Conf. C
14 obs
MODELS
dx0 (m) 43.55±2.69 58.98±2.82 83.19±2.89
MODEL 1
dy0 (m) 43.15±8.39 13.23±8.55 11.70±8.55
dz0 (m) 184.86±12.53 142.55±12.73 47.30±12.98
195.16 184.84 89.39
dLat (sec) -9.36±0.41 -7.95±0.42 -4.78±0.43
MODEL 2
dLON (sec) -1.24±0.28 -0.21±0.28 -0.07±0.28
dh (m) 23.89±0.64 19.23±0.69 11.64±0.71
195.16 184.84 89.39
REMARK Inclusion of N10 & N102 Exclusion of N102 Exclusion of N10 & N102
11
Table 5.2a: Values of Estimated Parameters Using Model1
Table 5.2b: Values of Estimated Parameters Using Model 2
Table 5.3 presents the minimum and maximum residuals (in metres) in latitude,
longitude and geodetic height, for both models 1 and 2.
3- PARAMETER TRANSFORMATION
Conf.
Parameters
CONFIGURATIONS
Conf.1
14 obs
(All Data)
Conf.2
11 obs
(North)
Conf.3
8 obs
(East)
Conf.4
6 obs
(West)
Conf.5
7 obs
(Central)
dx0 (m) 83.19±2.89 52.06±16.78 70.13±4.24 158.40±7.29 99.92±5.73
dy0 (m) 11.70±8.55 -13.37±9.19 268.62±17.30 -733.83±47.01 -47.68±34.93
dz0 (m) 47.30±12.98 203.36±76.45 -153.41±18.81 86.82±19.65 -47.64±15.50
89.39 109.73 33.47 73.73 20.59
3- PARAMETER TRANSFORMATION
Conf.
Parameters
CONFIGURATIONS
Conf.1
14 obs
(All Data)
Conf.2
11 obs
(North)
Conf.3
8 obs
(East)
Conf.4
6 obs
(West)
Conf.5
7 obs
(Central)
dLAT (sec) -4.78±0.43 -9.94±2.53 1.71±0.62 -6.10±0.65 -1.70±0.51
dLON (sec) -0.07±0.28 0.63±0.30 -8.49±0.57 24.51±1.56 1.93±1.16
dh (m) 11.64±0.71 18.82±3.79 29.10±1.54 15.32±0.94 17.83±1.00
89.39 109.73 33.47 73.73 20.59
12
Table 5.3: Minimum and Maximum Residuals (metre)
Tables 5.4a & b show the linear displacement of each of the fourteen points used
for these investigations, when the five different configurations are used. Table
5.4a shows the results for model 1, while table 5.4b shows the results for model 2.
Figures 5.1a & b are the corresponding graphs for the two models.
Table 5.4a: Linear Displacements of Points after the Transformation
MODEL 1 MODEL2CONF. MINIMUM
(metre)MAXIMUM
(metre)MINIMUM
(metre)MAXIMUM
(metre)LAT LONG GEOD.
HGTLAT LONG GEOD.
HGTLAT LONG GEOD.
HGTLAT LONG GEOD.
HGT
CONF1 70.83 1.78 -40.19 180.07 88.09 30.93 70.78 1.80 -39.98 180.01 88.10 31.32
CONF2 229.79 -19.90 -55.28 339.64 66.31 32.94 229.78 -19.88 -54.92 339.63 66.34 33.60
CONF3 -130.38 264.32 -52.45 -18.12 350.72 10.63 -130.49 264.29 -51.46 -18.24 350.69 11.60
CONF4 111.19 -764.89 -111.87 236.43 -676.36 44.60 111.25 -764.97 -111.36 236.48 -676.45 45.13
CONF5 -24.62 -60.56 -42.41 85.02 25.75 20.75 -24.67 -60.62 -42.07 84.98 25.70 21.38
(MODEL 1)
Station Name
Conf.1 Conf.2 Conf.3 Conf.4 Conf.5
1 A10 131.0668 277.9388 334.6955 715.2656 31.4309
2 U81 112.8971 243.0356 364.2875 686.9151 51.171
3 N127 172.3023 332.5734 267.3068 793.9575 99.3208
4 CFL56 179.3320 331.4029 322.4634 738.1162 75.6037
5 C21 106.3164 246.3850 344.7656 706.682 45.8373
6 R16 177.5017 337.4354 271.6685 792.409 100.3815
7 CFL9 182.7361 341.7684 267.6353 796.4569 105.4186
8 CFL62 187.1176 339.1097 324.2925 738.7597 83.4569
9 CFM45 191.8262 341.7769 333.7793 738.086 92.4607
10 CFM58 181.3399 332.1821 327.8458 738.204 82.8495
11 CFL17 198.1843 342.7576 355.4482 712.8594 92.4682
12 CFL20 191.1687 335.8909 352.7893 713.1283 86.1813
13 CFL25 187.9011 333.3734 349.3668 715.9988 83.7006
14 CFM10 194.8850 342.3145 344.6298 724.3664 90.9899
13
Table 5.4b: Linear Displacements of Points after the Transformation
(MODEL 2)
Station Name
Conf.1 Conf.2 Conf.3 Conf.4 Conf.5
1 A10 130.9983 277.8926 334.6888 715.307 31.0366
2 U81 112.7982 242.9518 364.2301 686.9845 50.8972
3 N127 172.2424 332.5556 267.1865 794.0449 99.2354
4 CFL56 179.2999 331.4024 322.4767 738.1565 75.4828
5 C21 106.2082 246.3010 344.7251 706.7378 45.5323
6 R16 177.4524 337.4314 271.5175 792.5183 100.3259
7 CFL9 182.7509 341.8219 267.6068 796.5801 105.5379
8 CFL62 187.0812 339.1060 324.306 738.7916 83.3191
9 CFM45 191.7401 341.7318 333.6841 738.1081 92.1511
10 CFM58 181.2589 332.1382 327.7902 738.2196 82.547
11 CFL17 198.0942 342.7044 355.2831 712.932 92.1728
12 CFL20 191.0776 335.8357 352.6377 713.1953 85.8721
13 CFL25 187.8105 333.3187 349.2272 716.0594 83.3867
14 CFM10 194.8015 342.2692 344.5016 724.4199 90.7056
14
15
Figure 5.1a: Linear Displacement of the Transformed WGS84 (Model 1)Figure 5.1a: Linear Displacement of the Transformed WGS84 (Model 1)
Conf.1
Conf.2
Conf.3
Conf.4
Conf.5
0
100
200
300
400
500
600
700
800
900A
10
U81
N12
7
CFL
56 C21
R16
CFL
9
CFL
62
CFM
45
CFM
58
CFL
17
CFL
20
CFL
25
CFM
10
Stations
Line
ar D
ispl
acem
ent (
m)
(Mod
el 1
)
Conf.1
Conf.2
Conf.3
Conf.4
Conf.5
In table 5.5, we present the minimum and maximum linear displacements for the
five different configurations. In figure 5.2, we present the graphs of these linear
displacements for the different configurations and models.
16
Figure 5.1b: Linear Displacement of the Transformed WGS84 (Model 2)Figure 5.1b: Linear Displacement of the Transformed WGS84 (Model 2)
Conf.1
Conf.2
Conf.3
Conf.4
Conf.5
0
100
200
300
400
500
600
700
800
900
A10
U81
N12
7
CFL
56 C21
R16
CFL
9
CFL
62
CFM
45
CFM
58
CFL
17
CFL
20
CFL
25
CFM
10
Stations
Line
ar D
ispl
acem
ent
(m)
(Mod
el 2
)
Conf.1
Conf.2
Conf.3
Conf.4
Conf.5
Table 5.5: Minimum & Maximum Linear Displacement of the Transformed Coordinates
MODEL 1 MODEL2
CONF. MINIMUM (metre)
MAXIMUM(metre)
MINIMUM(metre)
MAXIMUM(metre)
CONF1 106.3164 198.1843 106.2082 198.0942
CONF2 243.0356 342.7576 242.9518 342.7044
CONF3 267.3068 364.2875 267.1865 364.2301
CONF4 686.9151 796.4569 686.9845 796.5801
CONF5 31.4309 105.4186 31.0366 105.5379
5.2 ANALYSIS OF RESULTS
From table 5.1, we observe that the inclusion of N102, the initial point of the
geodetic network, and N10, the point with extreme height value, has significant
effect on the 3-parameter transformation results. The residuals (not shown
here), when the two points were included were very large. This can be easily
explained for the case of N102, because of the singularity occasioned by the
inclusion of N102, twice during the estimation, first for deriving the approximate
parameters and second as observation point. However, the effect of N10 cannot
be readily explained.
17
Figure 5.2: Minimum and Maximum Linear Displacement for Models 1 & 2Figure 5.2: Minimum and Maximum Linear Displacement for Models 1 & 2
0
100
200
300
400
500
600
700
800
conf.1 conf.2 conf.3 conf.4 conf.5
Configurations
Min
& M
ax L
inea
r Dis
plac
emen
t (M
odel
1 &
Mod
el 2
)
Min_mod1
Max_mod1
Min_mod2
Max_mod2
Similarly, the large distortion present in the 5-parameter estimation can be attributed
to possible non-parallelism between the axes of the coordinate systems of WGS84
and Minna datum. Hence, as a result of the correlation between the shift and
orientation parameters in such situations, large distortions are bound to occur.
From tables 5.2a & b, we observe that the variations in the configurations of the data
points affect the estimated parameters. We also observe that the configuration 5
(with 7 observation points), which is considered centrally located, gave the variance
of unit weight, which is closest to unity in both models, as well as smallest absolute
values of the components of the shift parameter. The use of these values to
compute the residuals in table 5.3 clearly shows that configuration 5 gave the best
parameter estimation. Since it gave better results than configuration 1 which
consists of all the points, it shows that configuration more than the number of
observation points determines the accuracy of a transformation procedure.
In tables 5.4a & b, we see that U81 and C21 which are at the southernmost part of
the Nigerian geodetic network suffered the least linear displacement for most of the
configurations and models. These points are also among the points with least
Orthometric and geodetic heights. This seems to confirm our earlier observation on
the effect of height on the estimated parameters. Figures 5.1a & b give more
graphic picture of these results. Here, we observe a fairly uniform residuals along
the CFL-traverse.
Equally significant is the large residuals associated with configuration 4 in both
models 1 and 2. They are points located to the west of the geodetic network. There
is no special feature of this configuration that can easily account for the large
residuals.
Finally, figure 5.2 summarizes the effects of the configurations on the computed
residuals. We find that configuration 5 followed by configuration 1 gives the best
results. Configurations 3 and 2 follow with configuration 4 giving the worst results.
However, the graphs of models 1 and 2 coincide, showing that the difference
between the two models is not significant.
18
6 CONCLUSIONS AND RECOMMENDATIONS
6.1 CONCLUSIONS
In this study, the results of our investigations based on the limited data used have shown
that:
a. The model (model 2) consisting of initial point of the geodetic network gave slightly
better transformation procedure compared to the model (model 1) consisting of the
shift in the origin of the coordinates system.
b. The accuracies of the estimates of transformation parameters depend more on the
configuration of the network than on the number of observation points.
c. The configuration (conf. 5) which consists of the points centrally located in the
network gives the best result.
d. The inclusion of coordinates of initial point of the network in the estimation process
distorts the results and should not be used in the derivation of the transformation
parameters.
e. The coordinates of points with extreme high orthometric heights or ellipsoidal heights
should be avoided in deriving transformation parameters.
f. The best set of transformation parameters obtained from this study are:
, ,
6.2 RECOMMENDATIONS
a. There is a need for sufficient GPS observations to be carried out, at least on all the
existing Minna datum control points to ensure a reasonable coverage of the geodetic
network with coincident points. It is important to note that the office of the Surveyor
General of the Federation (OSGOF), is currently collaborating with the Centre for
Geodesy and Geodynamics (CGG), a centre under the National Space Research
and Development Agency (NASRDA), to improve on the existing number and
distribution of the required data points.
b. Points on fairly level ground should be preferred when selecting common points.
c. Further studies on the configurations will be needed to determine appropriate sets of
parameters for various portions of the geodetic network, when sufficient data are
available.
Acknowledgement
The data used for this study were obtained from OSGOF, Abuja. This is highly appreciated.
19
REFERENCE
[1] Ezeigbo C.U. (1990a): “A Doppler Satellite Derived Datum for Nigeria”. Acta Geodaetica
Geoph. Mont. Hung., Journal of Hungarian Academy of Science, Akadémiai Kiadó,
Budapest. Vol. 25 (3 – 4), pp. 399 – 413 (1990).
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