Realization of time-dependent geocentric datum transformation parameters for Nigeria
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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 parameters1 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].
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
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) | 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) | Position, velocity and frame realization | |
3 | SP3 precise ephemeris orbits | For GAMIT/GLOBK processing | |
4 | Ocean tide loading model (FES2004) | Correction for ocean tide loading | |
5 | Dry and wet Mmpping function (VMF1) | Incorporate and estimate tropospheric delay for both dry and wet mapping function | |
6 | Atmospheric tidal loading (ATL) and non-tidal atmospheric loading (ATML) | 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.
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
3.5 Test statistics for validating transformation parameters
4 Results and analysis
4.1 Results
Summary of ITRF08 and ITRF14 to geocentric datum of Nigeria 2015 (GDN15) transformation parameters and their uncertainties at reference epoch 2015.9685
ITRFyy | t_{x} (mm) | t_{y} (mm) | t_{z} (mm) | s_{c} (ppb) | r_{x} (mas) | r_{y} (mas) | r_{z} (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 |
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 |
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 |
4.2 Analysis
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 |
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 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 R^{2}, 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.
- 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.
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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