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SN Applied Sciences

, 1:713 | Cite as

Realization of time-dependent geocentric datum transformation parameters for Nigeria

  • Swafiyudeen BawaEmail author
  • Lazarus Mustapha Ojigi
  • Joseph Danasabe Dodo
  • Kola M. Lawal
Research Article
  • 72 Downloads
Part of the following topical collections:
  1. Earth and Environmental Sciences: Geoinformatics for Sustainable Development

Abstract

Geodetic reference frames were established decades ago by classical surveying techniques; however, due to biases caused by poor observation techniques and effects of plate tectonic, the origins are poorly defined and adopted. Due to plate tectonics, the relative position of points changes with time and therefore, datum such as MINNA requires redefinition at regular intervals to be in consonant with geodetic reference frame in use. Therefore, with the Continuously Operating Reference Stations (CORS) network in Nigeria, these biases can be mitigated and a more accurate datum transformation parameter between MINNA datum and ITRF can be developed and adopted. Therefore, this study presents the results of time-dependent datum transformation parameters proposed for Nigeria using 5-years GNSS data (from 2011 to 2015) obtained from the NigNet CORS. GAMIT GNSS scientific processing software was deployed in processing, while GLOBK was used for frame definition and datum transformation parameters development. Statistical assessments show the validity of the transformation parameters. The correlation value was found to be 1, root mean square error 0.00411, normalized mean absolute error 1.267E−10 and reliability index 1.0.

Keywords

Datum Geocentric Nigeria Transformation parameters 

1 Introduction

In recent years, the positional accuracy attainable from GNSS technology is at a millimetre level [10]. With this accuracy, coordinates change in a high pace over time due to plate tectonic motion and other geophysical phenomenon. Current and previous International Terrestrial Reference Frame (ITRF) realizations take into account tectonic plate motion and other deformation such as earthquakes. Therefore, coordinates of points with every new realization of ITRF change even at a later epoch of same realization.

The coordinates of geodetic datum are the fundamentals for positioning. However, GIS and surveying software as well as spatial data do not consider continuous changes in coordinates, meaning that national datum and coordinates are assumed fixed with time. Similarly, geodetic networks are known to form the basis of investigating the shape, dimension and in many cases the gravity field of the earth [10, 26]. Therefore, positioning is a major stakeholder in modern day society in that it is of interest in navigation and guidance, datum realization, crustal deformation, plate tectonic studies, amongst others.

Geodetic datums are curved reference surfaces used to express position with adopted ellipsoid of revolution, size and shape [10, 29]. Generally, local geodetic datums whose ellipsoid does not coincide with the earth’s centre of mass and geocentric datum whose ellipsoid coincides with the earth’s centre of mass are the two fundamental categories of geodetic datum [10]. Geodetic datum can be static, dynamic and semi-dynamic [9, 25, 27]. Traditional geodetic datums are assumed static in nature. This is because they consider the constantly changing earth to be static which is very untrue because they are affected by geological and tectonic activities.

Dynamic datum, on the other hand, is a function of time. This means that coordinates vary with time. Example of a dynamic datum is the ITRF [2, 3]. Therefore, to take into account the changing earth, the ITRF is updated after every 5 years to accommodate advances in processing and data improvement. Implementation of a dynamic datum is a very difficult task at national a level. This has to be done monthly or weekly, thereby making the choice of the correct epoch for referencing observation extremely complex [13].

Semi-dynamic datum considers the constantly changing earth’s motion, but coordinates are referred to a single reference epoch [9, 25, 27]. Coordinates in a semi-dynamic datum can be propagated from the pre-defined reference epoch to an epoch of interest. What needs update is the deformation model.

Rapid advances in space-geodetic technique such as GNSS, very-long-baseline interferometry (VLBI), Global Navigation Satellite System (GNSS), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) and their found application in geodesy and geomatics have led to a significant improvement in modern positioning and allied applications. The tectonic motion of the NUBIA plate which might result in volcanism, earthquakes and earth tremors and other deformation sources such as subsidence and soil creep [10] and un-modelled measurement biases [6] affect geodetic infrastructure (e.g. NigNet), and therefore, decrease the accuracy of reference station coordinates, thereby leading to inconsistencies in legal traceability of coordinates of NigNet coordinates over time [11].

Since the MINNA datum for Nigeria was realized based on classical methods of surveying, it is known to be subjected to biases as a result of poor observations and techniques [8]. Also, Nigerian MINNA datum is faced with biases such as inaccuracies of the scale factor by compression of the Clarke 1880, poor definition of origin, geoidal height model absence and difficulty in datum parameters determination [30]. Therefore, with these inherent errors, there is the need to move away from the still-in-use MINNA datum and adopt a new datum that is geocentric in nature as done in countries like Australia (GDA2020), China (CTRF2000), Indonesia (DGN1995), Malaysia (GDM2000), New Zealand (NZGD2000), USA (NAD83), amongst others [7, 20]. Studies of [5, 8, 12, 18, 25] further justify the need for this study, in that coordinates of points anywhere in the world will change with time. Therefore, by integrating velocity, epoch and episodic deformation information, locations of points can be kept on track. Therefore, this study presents and proposes a new time-dependent geocentric datum transformation parameters for Nigeria by processing 5 years (2011–2015) of the 14 NigNet tracking stations (Fig. 1) [19] and 9 IGS stations (Fig. 2) [22] using GAMIT for producing loose constrain estimate of position and covariance matrix and GLOBK for reference frame definition.
Fig. 1

Spatial distribution of NiGNet tracking stations with the station at KANO excluded

Fig. 2

Spatial distribution of IGS stations adopted for the study

2 Need for transformation parameters and coordinate update in Nigeria

With series of earth tremor occurrences in Nigeria, epoch-by-epoch realization of ITRF is essential so that spatial data of global, local, national and regional origin can be integrated with ease. Over the years, the development of transformation parameters for Nigeria particularly, the classical transformation which involves 7-parameter similarity (Helmert) transformation, has been met with several technical challenges such as inaccuracies of the scale factor by compression of the Clarke 1880, poor definition of origin, geoidal height model absence and difficulty in datum parameters determination as highlighted earlier. However, with the evolution of ITRF, the 7-parameter transformation has extended to 14-parameter transformation. The additional 7 parameters describe the transition of the initial 7 parameters with time [20]. Furthermore, depending on the need, surveys in Nigeria are reported in various coordinates that include Nigeria Transverse Mercator Projection (NTM), MINNA, World Geodetic System 1984 (WGS84) and ITRF. Ensuring the compatibility and uniformity of coordinates, [7] reported that the use of different coordinate system poses danger and a difficult task to achieve.

Therefore, the optimum way to achieve centimetre-level accuracy is to relate GNSS measurements to ITRF. Therefore, ITRF-based transformation parameters will go a long way towards realization of centimetre accuracy since deformation of the earth is taken into cognisance.

Most importantly, with modern space-geodetic techniques, such as the GNSS CORS network in Nigeria, the biases due to classical observational techniques and the phenomenon of plate tectonic motion can be mitigated and a more accurate geocentric datum transformation parameters between MINNA DATUM and the known ITRF can be developed and adopted. This study therefore aims at proposing time-dependent geocentric datum transformation parameters for Nigeria using 5-year (2011–2015) NigNet GNSS CORS data.

3 Materials and method

3.1 Test site description

In Nigeria, an initiative to establish a Continuously Operating Reference Stations (CORS) called NIGerian Reference GNSS NETwork (NIGNET) (see Fig. 1) which is a network of Continuous GNSS stations kicked off in 2008 by Office of the Surveyor General of the Federation (OSGoF). The initiative was aimed at contributing to the African Reference Frame (AFREF) and serve as a primary fiducial network that will define and materialize a new reference frame based on space-geodetic technique [19]. The study area is Nigeria located on the western part of Africa Plate between latitude 4° and 14°N and longitude 2° and 15°E. The details of the dataset used for this study are presented in Table 1. The spatial distribution of the NigNet and IGS stations used for the study is presented in Figs. 1 and 2, respectively.
Table 1

Summary of dataset and sources adopted for the study

S/N

Dataset(s)

Source(s)

Purpose(s)

1

RINEX files associated with 14 selected NigNet tracking stations from 1 January 2011 to 31 December 2015 (1826 days)

www.nignet.net

Time series analysis, position and velocity estimate and strain computation

2

Nine international GNSS services (IGS) stations from 1 January 2011 to 31 December 2015 (1826 days)

ftp://cddis.gsfc.nasa.gov

Position, velocity and frame realization

3

SP3 precise ephemeris orbits

http://cddis.nasa.gov

For GAMIT/GLOBK processing

4

Ocean tide loading model (FES2004)

ftp://everest.mit.edu/pub/GRIDS

Correction for ocean tide loading

5

Dry and wet Mmpping function (VMF1)

ftp://everest.mit.edu/pub/GRIDS

Incorporate and estimate tropospheric delay for both dry and wet mapping function

6

Atmospheric tidal loading (ATL) and non-tidal atmospheric loading (ATML)

ftp://everest.mit.edu/pub/GRIDS/

Correction for tidal and non-tidal atmospheric loading

3.2 GNSS data processing

GAMIT/GLOBK software release 10.6 was used for processing [14, 15, 16]. GAMIT/GLOBK is a comprehensive GNSS analysis package developed at Massachusetts Institute of Technology (MIT), the Harvard Smithsonian Center for Astrophysics (CFA) and the Scripps Institute of Oceanography (SIO) for estimating station coordinate and velocities, stochastic or functional representation of post-seismic deformations, atmospheric delays, satellite orbits and Earth orientation parameters [15, 32].

Depending on the task at hand, processing in GAMIT can be in single session or automatic batch processing (invoked when there is considerable large amount of data or multiple session of data and time is needed to be saved) using scripts for example sh_gamit in GAMIT or sh_glred in GLOBK. In the automatic batch processing, which was adopted in this study, the only preparation is assembling and preparation of control files like sestbl, sittbl, station.info, session.info, etc. Models applied to account for dynamic factors include Vienna Mapping Function (VMF1) for tropospheric mapping of dry and wet mapping function, FES2004 ocean tide loading model and IERS03 solid earth tide model.

The results obtained in automatic batch processing of GAMIT are generally loose constrain estimate of position and covariance matrix associated with a survey station. Table 2 depicts the processing parameters adopted for this study. The ASCII h-files containing loose-constrained weighted least squares estimate of sites coordinates and variance–covariance produced by GAMIT are converted to binary H-files readable by GLOBK to produce time series, velocity and reference frame definition.
Table 2

Basic processing parameters [4]

Parameter(s)

Description

RINEX data

30 s sampling rate

Orbital data

IGS final/precise orbit

Ocean tide loading

FES2004

Ionospheric model

Double-difference ionospheric-free (IF) linear combination

Adjustment

Kalman filter

Tropospheric delay model

Saastamoinen model

Elevation cut-off

10°

Antenna model

ELEV

Earth tide model

IERS03

Choice of experiment

Baseline

Dry and wet mapping function

New Vienna Mapping Function (VMF1)

Atmospheric tidal loading (ATL) and non-tidal atmospheric loading (ATML)

Yes

Observations

30-s sampling interval

Satellite orbits/earth orientation parameters

IGS final orbits (SP3) and IGS final EOP products

Meteorological observation source

VMF1

3.3 Reference frame definition

Frame realization was carried out in GLOBK by adopting the International Terrestrial Reference Frame (ITRF) as global constraints. In this study, solutions from GAMIT were constrained to ITRF2008 [2] and ITRF2014 [3] while estimating seven Helmert parameters (3 translation, 3 rotation and 1 scale) and their respective rates for each solution from GAMIT analysis. The study constrained NigNet tracking stations to global stations consisting of 9 selected IGS (see, for example, Fig. 2) sites in ITRF2008 and ITRF2014 using GLOBK. The solutions from GLOBK include velocity solution, reference frame and Euler plate motion parameters, amongst others.

3.4 Coordinates transformation method

Transformation of GNSS coordinate time series from one reference frame to another can be realized with Helmert 14-parameter or 7-parameter transformation. The Helmert 14-parameter was adopted for this study. These include 3 translations (which affects position of coordinate origin), 3 rotations (which affects orientation of coordinate axes) and 1 scale (affects length of coordinate axes), and their rates (achievable with a velocity model). The Euclidian similarity 14-parameter datum transformation model (Eqs. 1a1c) which includes three rotations, \(T_{x} (t)\), \(T_{y} (t)\), \(T_{z} (t)\), three translation (\(R_{x} (t)R_{y} (t)R_{z} (t)\)) and a scale factor \(S_{c} (t)\) [6, 10, 31], was adopted and tested to transform station coordinates and respective velocities at epoch 2015.9685 (2015/12/20) from ITRF08 and ITRF14 to a proposed Geocentric Datum of Nigeria (GDN). Though, Euler plate motion parameters can also be used [26].
$$\begin{aligned} X(t)_{\text{GDN}} & = T_{x} (t) + [1 + s(t)]X(t)_{{{\text{ITRF}}_{yy} }} \\ & \quad + R_{z} (t)Y(t)_{{{\text{ITRF}}_{yy} }} - R_{y} (t)Z_{{{\text{ITRF}}_{yy} }} \\ \end{aligned}$$
(1a)
$$\begin{aligned} Y(t)_{\text{GDN}} & = T_{y} (t) - R_{z} (t)X(t)_{{{\text{ITRF}}_{yy} }} \\ & \quad + [1 + s(t)]Y(t)_{{{\text{ITRF}}_{yy} }} + R_{x} (t)Z(t)_{{{\text{ITRF}}_{yy} }} \\ \end{aligned}$$
(1b)
$$\begin{aligned} Z(t)_{\text{GDN}} & = T_{z} (t) + R_{y} (t)X(t)_{{{\text{ITRF}}_{yy} }} \\ & \quad + [1 + s(t)]Z(t)_{{{\text{ITRF}}_{yy} }} - R_{x} (t)Y(t)_{{{\text{ITRF}}_{yy} }} \\ \end{aligned}$$
(1c)
The time-related variations are assumed to be linear; therefore, the quantities can be expressed by Eq. (2) [23, 24]. Equation (2) is inputted into Eq. (1) to finally get a 7-parameter transformation model.
$$\begin{aligned} & T_{x} = t_{x} (t_{0} ) + \dot{t}_{x} (t - t_{0} ) \\ & T_{y} = t_{y} (t_{0} ) + \dot{t}_{y} (t - t_{0} ) \\ & T_{z} = t_{z} (t_{0} ) + \dot{t}_{z} (t - t_{0} ) \\ & S_{c} = s_{c} (t_{0} ) + \dot{s}_{c} (t - t_{0} ) \\ & R_{x} = r_{x} (t_{0} ) + \dot{r}_{x} (t - t_{0} ) \\ & R_{y} = r_{y} (t_{0} ) + \dot{r}_{y} (t - t_{0} ) \\ & R_{z} = r_{z} (t_{0} ) + \dot{r}_{z} (t - t_{0} ) \\ \end{aligned}$$
(2)
where the 7 Helmert parameters \(r_{x} (t_{0} )\), \(r_{y} (t_{0} )\), \(r_{z} (t_{0} )\) (\(t_{x} (t_{0} )\), \(t_{y} (t_{0} )\), \(t_{z} (t_{0} )\) and \(s_{c} (t_{0} )\)) are rotations, translation and scale parameters in the position domain, respectively, at a reference epoch, which are constant. Their respective first time derivations in the rate domain are \(\dot{t}_{x}\), \(\dot{t}_{y}\), \(\dot{t}_{z}\), \(\dot{r}_{x}\), \(\dot{r}_{y}\),\(\dot{r}_{z}\) and \(\dot{s}_{c}\). The Helmert parameters and their first time derivatives are obtained by invoking a generalized constraint in glorg module of GLOBK.

3.5 Test statistics for validating transformation parameters

The accuracy, precision and reliability of the newly obtained transformation parameters were evaluated using standard model performance indicators. The normalized mean absolute error (NMEA) [28], root mean square error (RMSE), reliability index (RI) [21] and correlation coefficient (r) are given in Eqs. (3)–(6) [17].
$${\text{NMAE}} = \frac{{\sum\nolimits_{i = 1}^{n} {\left( {\left| {{\text{residuals}}_{i} |} \right.} \right)} }}{{n\bar{o}}}$$
(3)
$${\text{RMSE}} = \sqrt {\frac{{\sum\nolimits_{i = 1}^{n} {\left( {{\text{residuals}}_{i} } \right)^{2} } }}{n}}$$
(4)
$${\text{RI}} = \sqrt[{\exp }]{{\frac{{\sum\nolimits_{i = n}^{n} {\left( {\log \frac{{o_{i} }}{{p_{i} }}} \right)^{2} } }}{n}}}$$
(5)
$$r = \frac{{\sum\nolimits_{i = 1}^{n} {\left( {p_{i} - \bar{p}} \right)\left( {o_{i} - \bar{o}} \right)} }}{{\left[ {\sum\nolimits_{i = n}^{n} {\left( {p_{i} - \bar{p}} \right)^{2} } \sum\nolimits_{i = 1}^{n} {\left( {o_{i} - \bar{o}} \right)^{2} } } \right]^{1/2} }}$$
(6)
where \(n\) is the number of NigNet tracking stations used, \({\text{residuals}} = p_{i} - o_{i}\) and \(o_{i}\) and \(p_{i}\) are the ith computed and model estimated. Similarly, \(\bar{o}\) and \(\bar{p}\) are the mean computed and model estimates.

4 Results and analysis

4.1 Results

While estimating translation, rotation and scale (Helmert parameters) in GLOBK, a rigorous approach of frame definition was realized through a generalized constraints, where the study minimized the adjustments of coordinates of the frame-defining sites [15] as discussed earlier in Sect. 3.4. By minimizing the adjustment of coordinates of the frame-defining sites, all of the reference sites are free to adjust, thereby revealing bad data or coordinates solutions. Table 3 shows the summary of the time-dependent geocentric transformation parameters for Nigeria.
Table 3

Summary of ITRF08 and ITRF14 to geocentric datum of Nigeria 2015 (GDN15) transformation parameters and their uncertainties at reference epoch 2015.9685

ITRFyy

tx (mm)

ty (mm)

tz (mm)

sc (ppb)

rx (mas)

ry (mas)

rz (mas)

Rates

\(\dot{t}_{x}\) (mm/year)

\(\dot{t}_{y}\) (mm/year)

\(\dot{t}_{z}\) (mm/year)

\(\dot{s}_{c}\) (ppb/year)

\(\dot{r}_{x}\)( mas/year)

\(\dot{r}_{y}\) (mas/year)

\(\dot{r}_{z}\) (mas/year)

ITRF08

2.10 ± 0.00

− 4.96 ± 0.00

3.71 ± 0.00

− 0.862 ± 0.302

6.3947 ± 0.1110

42.7931 ± 0.0410

− 7.5334 ± 0.1910

Rates

− 7.0 ± 0.0004

3.4 ± 0.0013

− 0.89 ± 0.0009

0.528 ± 0.0863

− 0.3467 ± 0.0301

0.1222 ± 0.0116

0.3385 ± 0.0507

ITRF14

1.23 ± 0.00

− 2.02 ± 0.00

6.66 ± 0.00

− 0.141 ± 0.157

6.5439 ± 0.0558

47.2092 ± 0.0211

− 7.8789 ± 0.0979

Rates

− 7.0 ± 0.00027

3.4 ± 0.00080

− 0.89 ± 0.00056

0.322 ± 0.05184

− 0.0304 ± 0.01786

− 0.0944 ± 0.00701

− 0.0844 ± 0.03023

mas milli-arc seconds, ppb parts per billion

Similarly, Tables 4 and 5 are the coordinate solutions of the adopted NigNet stations in earth-centred earth-fixed (ECEF) and geodetic coordinate system, respectively. The residuals plots of the two coordinates systems in both reference frames are presented in Fig. 3a, b, with station RUST having the highest residual. The reason for this high residual is unknown in the present study. Probably, bad stabilization might be the cause, but the post-root mean square error (post-RMS) in ITRF14 for velocity and position system stabilization yielded 0.029 mm/year and 0.087 mm, respectively. In ITRF08, the post-root mean square error (post-RMS) for velocity and position system stabilization yielded 0.049 mm/year and 0.016 mm, respectively. [15] recommended value of 1–5 mm for position system stabilization. Therefore, bad stabilization is written off as the cause.
Table 4

Geocentric (ECEF) coordinates of NigNet in ITRF08 and ITRF14 at epoch 2015.9685

ITRF08 at epoch 2015.9685

ITRF14 at epoch 2015.9685

Station

X(m)

Y(m)

Z(m)

X(m)

Y(m)

Z(m)

MDGR

6,080,449.24413

1,418,433.59502

1,299,949.51341

6,080,449.24930

1,418,433.59434

1,299,949.51197

FUTY

6,145,058.44928

1,362,078.97999

1,029,390.00286

6,145,058.45130

1,362,078.97935

1,029,390.00254

GEMB

6,213,520.30484

1,228,500.48,824

763,261.05312

6,213,520.30668

1,228,500.48737

763,261.05293

CGGT

6,201,032.23378

995,277.36236

1,113,815.58849

6,201,032.23677

995,277.36246

1,113,815.58791

CLBR

6,287,174.18547

922,979.55290

546,713.85390

6,287,174.18627

922,979.55197

546,713.85325

ABUZ

6,203,493.78641

833,088.80383

1,225,614.72227

6,203,493.78850

833,088.80337

1,225,614.72216

HUKP

6,163,727.05738

821,421.99098

1,417,029.88278

6,163,727.05973

821,421.99077

1,417,029.88284

UNEC

6,284,298.27701

827,900.62128

708,988.67915

6,284,298.27866

827,900.62052

708,988.67908

OSGF

6,246,471.22824

820,848.83991

994,268.02177

6,246,471.22987

820,848.83931

994,268.02167

FPNO

6,301,965.77800

777,495.46754

600,049.71461

6,301,965.77942

777,495.46716

600,049.71555

RUST

6,308,859.02071

772,230.02159

530,354.55584

6,308,859.04088

772,230.02224

530,354.54541

FUTA

6,301,798.91397

566,460.90180

804,956.62950

6,301,798.91615

566,460.90087

804,956.62955

BKFP

6,211,960.31340

459,365.58393

1,368,115.13291

6,211,960.31551

459,365.58363

1,368,115.13312

ULAG

6,326,097.27163

375,576.21698

719,131.77913

6,326,097.27336

375,576.21624

719,131.77930

Table 5

Geodetic coordinates of NigNet in ITRF08 and ITRF14 at epoch 2015.9685

ITRF08 at epoch 2015.9685

ITRF14 at epoch 2015.9685

Station

Lat(°)

Lon(°)

h(m)

Lat(°)

Lon(°)

h(m)

MDGR

11.8380913021

13.1310026973

348.23460

11.8380912803

13.1310026805

348.23613

FUTY

9.3497435023

12.4977988278

247.39244

9.3497434968

12.4977988182

247.39420

GEMB

6.9172002414

11.1839415016

1795.64560

6.9172002378

11.1839414906

1795.64719

CGGT

10.1230954562

9.1183128390

916.43041

10.1230954464

9.1183128355

916.43324

CLBR

4.9503019072

8.3515696770

57.17408

4.9503019008

8.3515696676

57.17468

ABUZ

11.1517407664

7.6486883103

705.06138

11.1517407619

7.6486883036

705.06334

HUKP

12.9211546183

7.5909143745

559.61850

12.9211546142

7.5909143697

559.62076

UNEC

6.4248068753

7.5049922697

254.39541

6.4248068731

7.5049922610

254.39693

OSGF

9.0276667059

7.4863427013

532.64337

9.0276667028

7.4863426940

532.64487

FPNO

5.4345731482

7.0332392250

88.31087

5.4345731555

7.0332392200

88.31232

RUST

4.8018369060

6.9785222775

45.57414

4.8018367969

6.9785222612

45.59330

FUTA

7.2986402623

5.1364422289

410.58464

7.2986402604

5.1364422188

410.58673

BKFP

12.4685775715

4.2292431369

250.00403

12.4685775694

4.2292431328

250.00611

ULAG

6.5173274203

3.3976244443

44.55984

6.5173274201

3.3976244367

44.56153

Fig. 3

Residual plot of coordinate of a (in ECEF, Table 4) solutions in ITRF08 and ITRF14; b (in geodetic, Table 5) solutions in ITRF08 and ITRF14

4.2 Analysis

To this end, Tables 4 and 5 present the geocentric and geodetic coordinates of the NigNet GNSS stations at epoch 2015.9685, respectively. Furthermore, the time-dependent 14-parameter datum transformation relation as presented in Table 3 has been developed at epoch 2015.9685 (2015/12/20). First, to assess the accuracy and validity of the transformation parameters, coordinates of some of the stations at epoch 2015.9685 as obtained from GLOBK in this study were transformed to an epoch (2011.00) in which the Office of the Surveyor General of the Federation (OSGoF) last published their coordinates. Tables 6 and 7 present the ECEF and geodetic coordinates and from OSGoF and those obtained using the transformation parameters in Tables 3, 4 and 5, respectively.
Table 6

Transformed geocentric (ECEF) coordinates of NigNet in ITRF08 to epoch 2011.00 using that obtained from OSGoF

Stations

Coordinates from parameters to epoch 2011.00

Coordinates from OSGOF epoch 2011.00

X(m)

Y(m)

Z(m)

X(m)

Y(m)

Z(m)

MDGR

6,080,449.01428

1,418,433.39115

1,299,949.72885

6,080,449.31020

1,418,433.50620

1,299,949.42040

FUTY

6,145,058.26851

1,362,078.76812

1,029,390.22314

6,145,058.48550

1,362,078.88210

1,029,389.91230

GEMB

6,213,520.17239

1,228,500.26810

763,261.27930

6,213,520.30540

1,228,500.38660

763,260.95600

CGGT

6,201,032.02147

995,277.14949

1,113,815.81819

6,201,032.26630

995,277.24960

1,113,815.51850

CLBR

6,287,174.08361

922,979.32514

546,714.08852

6,287,174.16330

922,979.44880

546,713.76520

ABUZ

6,203,493.54500

833,088.59306

1,225,614.95558

6,203,493.81020

833,088.70460

1,225,614.62980

UNEC

6,284,298.13870

827,900.39694

708,988.91515

6,284,298.29670

827,900.51990

708,988.58530

OSGF

6,246,471.03300

820,848.62272

994,268.25665

6,246,471.24960

820,848.74400

994,267.92810

RUST

6,308,858.93534

772,229.79475

530,354.78307

6,308,859.04250

772,229.93130

530,354.45830

BKFP

6,211,960.02844

459,365.37528

1,368,115.37451

6,211,960.33600

459,365.48270

1,368,115.04300

ULAG

6,326,097.11517

375,575.99096

719,132.02554

6,326,097.29100

375,576.11170

719,131.68930

Table 7

Transformed geodetic coordinates of NigNet in ITRF08 to epoch 2011.00 using that obtained from OSGoF

 

Coordinates from parameters to epoch 2011.00

Coordinates from OSGF epoch 2011.00

Lat(o)

Long(o)

h(m)

Lat(o)

Long(o)

h(m)

MDGR

11.8380913018

13.13100269731

348.232

11.8380903963

13.1310017662

348.256

FUTY

9.3497435186

12.49779883391

247.390

9.3497426732

12.4977978863

247.392

GEMB

6.9172002632

11.18394150575

1795.643

6.9171993891

11.1839405985

1795.615

CGGT

10.1230954707

9.11831284289

916.428

10.1230948094

9.1183117765

916.432

CLBR

4.9503019252

8.35156968042

57.171

4.9503011371

8.3515687778

57.130

ABUZ

11.1517407832

7.64868831494

705.059

11.1517399270

7.6486873808

705.054

UNEC

6.4248068890

7.50499227431

254.392

6.4248060252

7.5049913378

254.391

OSGF

9.0276667198

7.48634270492

532.641

9.0276658561

7.4863418111

532.637

RUST

4.8018368080

6.97852227960

45.590

4.8018360187

6.9785214459

45.577

BKFP

12.4685775920

4.22924313986

250.001

12.4685767469

4.2292421925

250.000

ULAG

6.5173274292

3.39762444805

44.559

6.5173265996

3.3976234836

44.563

4.3 Statistics for validating transformation parameters

The accuracy, precision and reliability of the transformation parameters in Table 3 were evaluated by comparing solution obtained from the transformation parameters in ITRF08 and from OSGF using the performance indicators discussed in Sect. 3.5. Figure 4 is the scatter plot in this regard.
Fig. 4

ac Scatter plot of the correlation between coordinates obtained from OSGF and that computed using the developed transformation parameters in Table 3

The correlation value R, root mean square error (RMSE), normalized mean absolute error (NMAE) and reliability index (RI) are at the bottom right: (a) the plot in the X, (b) the plot in Y and (c) the plot in Z directions, respectively, of ECEF.

RMSE measures average square error. Zero values or near indicate close match. Therefore, the RMSE (0.00411 m) of the coordinates from the two data sources is an indication of close match. NMAE assesses the absolute deviation of computed coordinates from GLOBK and that of OSGF. Values of zero or near indicate close match and vice versa. The NMAE (1.267E−10 m) of the coordinates obtained from both sources showed a close match. The RI is an indication of how the two coordinate sources differ from each other; a near one value also indicates a close match. Therefore, from the two coordinate sources, the two data sources showed close match. The correlation coefficient of the data sources also yielded 1.0, which is a perfect correlation.

Similarly, [1] stated that the origin and scale between ITRF2014 and ITRF2008 are less than 5 mm. Therefore, the transformation parameters for ITRF2014 as developed in this study are also valid since the difference is within 5 mm.

5 Conclusions and recommendations

In this study, time-dependent geocentric datum transformation parameters for Nigeria using the NigNet tracking stations have been developed. The accuracy, precision and reliability of the transformation parameters using the R2, RMSE, NMAE and RI statistics validate the transformation parameters developed in this study. Also the origin and scale differences between ITRF2008 and ITRF2014 found to be within 5 mm also portray the reliability of the transformation parameters.

The significance of these results is fundamental in providing a variety of applications in areas such as geophysical hazard monitoring and assessment, sea-level monitoring, mining engineering, location based services, land boundary definition (international and local boundaries), environmental mapping, navigation, civil engineering and cadastral applications.

Based on the results of the study, the followings are hereby recommended:
  1. 1.

    The current trend by many countries is the realization of geocentric datum based on ITRF realization. Since the old MINNA datum is filled with many deficits, Nigeria should adopt the ITRF-based geocentric datum.

     
  2. 2.

    There should be awareness within the geospatial community on the need to move away from the old MINNA datum. This is a task vested on geospatial stakeholders such OSGoF.

     

Notes

Acknowledgements

The authors acknowledge the Office of the Surveyor General of Nigeria for providing the data used in this research. Also, the authors thank Mike Floyd of MIT for constantly providing valuable answers to our questions on GAMIT/GLOBK processing. We would also like to thank IGS for providing necessary geodetic products.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of GeomaticsAhmadu Bello UniversityZariaNigeria
  2. 2.Centre for Geodesy and Geodynamics, NASRDAToroNigeria
  3. 3.Department of PhysicsAhmadu Bello UniversityZariaNigeria

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