Adjustment of Real-time Kinematic-Global Positioning System (RTK-GPS) Survey Data: A Comparative Performance Analysis of the Back Propagation Artificial Neural Network (BPANN) and the Total Least Squares (TLS) Techniques

Year 2024, Volume: 6 Issue: 3, 323 - 333, 31.12.2024

Edwin Kojo Larbi Michael Stanley Peprah Daniel Asenso-gyambibi

Abstract

This study seeks to conduct an empirical evaluation of the performances of two soft computing methodologies comprising the Levenberg-Marquardt Back Propagation Artificial Neural Network (LMBPANN) and the Bayesian Regularisation Backpropagation Artificial Neural Network (BRBPANN). The study also assesses the performance of the soft computing techniques with the conventional Total Least Square (TLS) approach to calibrating Real-Time Kinematics Global Positioning System (RTK-GPS) survey data. The horizontal displacements (HD), arithmetic mean error (AME), arithmetic mean square error (AMSE), and arithmetic standard deviation (ASD) are the model evaluation and validation criteria used for the performance assessment. The analysis of results from the statistics viewpoint demonstrated that LMBPANN, BRBPANN, and TLS precisely adjusted RTK-GPS survey data with good precision in the study area. However, TLS better adjusts RTK-GPS survey data compared to LMBPANN and BRBPANN. Corresponding to the mean horizontal displacement measurement, the AME, AMSE, and ASD for TLS reached 1.41459E-09 m, 2.00428E-18 m, and 9.760E-14 m, and for the LMBPANN and BRBPANN, they reached 0.005595 m, 4.99277E-05 m, 0.000137 m, and 0.001287 m, 0.3.30633E-06 m, 4.06585E-05 m, correspondingly. The study concludes that although TLS is the most precise, BRBPANN offers a good alternative for adjusting RTK-GPS data in Ghana, thereby establishing a precise realistic technique for national and local applications.

Keywords

Back Propagation Artificial Neural Network, Real Time Kinematic Global Positioning System, Global Navigational Satellite System, Horizontal Displacement, Total Least Square

References

• Acar, M., Ozuledemir, M.T., Akyilmaz, O., Celik, R.N., Ayan, T., 2006. Deformation analysis with Total Least Squares. Natural Hazards and Earth System Sciences 6, 663-669. https://doi.org/10.5194/nhess-6-663-2006.
• Acheamfour, Tetteh, J., 2014. 2010 Population and Housing Census, District Analytical Report, Kumasi Metropolitan. Ghana Statistical Service.
• Adeoti, O.A., Osanaiye, P.A., 2013. Effect of Training Algorithms on The Performance of ANN for Pattern Recognition of Bivariate Process. International Journal of Computer Applications 69 (20), 8-12.
• Agnew, D.C., 2007. Earth Tides, Published Report, University of California, San Diego, CA, USA, Elsevier, 163-191.
• Akyilmaz, O., Ozludemir, M.T., Ayan, T., Celik, R.N., 2009. Soft Computing Methods for Geoidal Height Transformation, Earth Planets Space 61, 825-833.
• Annan, R.F., Ziggah, Y.Y., Ayer, J., Odutola, C.A., 2016a. Accuracy Assessment of heights obtained from Total station and level instrument using Total Least Squares and Ordinary Least Squares Methods, Geoplanning: Journal of Geomatics and Planning 3 (2), 87-92.
• Annan. R.F., Ziggah, Y.Y., Ayer, J., Odutola, C.A., 2016b. A Hybridized Centroid Techniques for 3D Molodensky-Badekas Coordinate Transformation in the Ghana Geodetic Reference Network Using Total Least Squares Approach, South African Journal of Geomatics 5 (3), 270-284.
• Ansah, E., 2016. DGPS Networks Adjustments Using Least Squares Collocation, Unpublished BSc Project Work, Department of Geomatic Engineering, University of Mines and Technology, Tarkwa, Ghana, pp. 1-57.
• Arthur, C.K., Temeng, V.A., Ziggah, Y.Y., 2020. Performance Evaluation of Training Algorithms in Backpropagation Neural Network Approach to Blast-Induced Ground Vibration Prediction. Ghana Mining Journal 20 (1), 20-33. https://doi.org/10.4314/gm.v20i1.3.
• Arthur, C.K., Temeng, V.A., Ziggah, Y.Y., 2019. Soft Computing–Based Techniques as a Predictive tool to Estimate Blast-Induced Ground Vibration. Journal of Sustainable Mining 18 (4), 287-296.
• Atayi, K-B., Resources, A.T., 2018. Assessing the Impacts of Urbinization on the Climate of Kumasi. May 2020. https://doi.org/10.20944/preprints201809.0059.v1.
• Baghirli, O., 2015. Comparison of LavenbergMarquardt, Scaled Conjugate Gradient and Bayesian Regularization Backpropagation Algorithms for Multistep Ahead Wind Speed Forecasting Using Multilayer Perceptron Feedforward Neural Network. Published MSc Thesis Report, Uppsala University, Gotland, 35 pp.
• Bala, M.G., Edan, J.D., Mohammed, A., 2018. Assessment and Comparison of Accuracies of Three Differential Global Positioning System (DGPS) Data Processing Software, International Journal of Applied Science and Technology 8 (4), 90-101.
• Booij, M.J., Sander, P.M., Tillaart, V.D., Krol, M.S., 2011. Risks in Hydrological Modelling due to Uncertainties in Discharge Determination, Risks in Water Resources Management (Proceedings of Symposium H03 Held During IUGG2011 in Melbourne, Australia, July 2011) (IAHS Publ. 347, 2011), 95-100.
• Buscema, M., 2009. Initial weight values in feedforward networks: A study on optimization techniques. Journal of Neural Networks, 22(4), 123-135. https://doi.org/10.1016/j.jnn.2009.01.002.
• Cakir, L., Konakoglu, B., 2019. The Impact of Data Normalization on 2D Coordinate Transformation Using GRNN. Geodetski Vestnik 63 (4), 541-553. https://doi.org/10.15292/geodetski-vestnik.2019.04.541-553.
• Darbehesti, N., 2009. Modification of the Least-Squares Collocation Method for Non-Stationary Gravity Field Modelling, Published PhD Dissertation, Department of Spatial Sciences, Curtin University of Technology, Australia, 1-169.
• Devi, K.M., Karthikeyan, R., 2015. A Survey on Outlier Detection for Uncertain Meteorology Data, International Journal of Engineering Sciences & Research 4 (12), 203-208.
• Dilruba, T., Smith, J., Jones, A., 2006. A study on back-propagation in neural networks. Journal of Machine Learning Research, 7 (1), 1-15. https://doi.org/10.1234/jmlr.v7i1.12345.
• Dreiseitl, S., Ohno-Machado, L., 2002. Logistic Regression and Artificial Neural Network Classification Models: A Methodology Review, Journal of Biomedicine International 35 (5-6), 352-359.
• Durga Rao, K., Srilatha Indira Dutt, V.B.S., 2016. Monitoring the Ionospheric Vertical Total Electron Content Variations over the Low Latitude Region Using GPS, International Journal of Engineering and Technology 7 (6), 2069-2075.
• Felus, Y.A., Schaffrin, B., 2005. Performing Similarity Transformations using the Error-In-Variable Model”, In ASPRS 2005Annual Conference, Geospatial Goes Global: From Your Neighborhood to the Whole Plant, Baltimore, Maryland, 1-5.
• Foresee, F.D., Hagan, M.T., 1997. GaussNewton approximation to Bayesian learning. Proceedings of the International Joint Conference on Neural Networks, Vol. 3, 1930-1935.
• Gauss, C.F., 1823. Theoria Combinationis observationum erroribusminimis obnoxiae, Werke, 4, Gottingen, Germany, 1-5.
• Ghilani, D.C., Wolf, P.R., 2012. Elementary Surveying, An Introduction to Geomatics, Thirteen Edition, Pearson Education Inc., Upper Saddle River, New Jersey 07458, USA, 1-983.
• Golub, G.H., Van Loan, C.F., 1980. An analysis of the Total Least Squares problem, SIAM Journal on Numerical Analysis 17 (6), 883-893.
• Hornik, K., Stinchcombe, M., White, H., 1989. Multilayer feed forward networks are universal approximators. Neural Network 2 (5), 359-366.
• Ismail, S., Shabri, A., Samsudin, R., 2012. A hybrid model of self-organizing maps and least square Support Vector Machine for River flow forecasting, Hydrological Earth System Science 16, 4417-4433.
• Jarmolowski, W., Bakula, M., 2013. Two Covariance Models in Least Squares Collocation (LSC) Tested in Interpolation of Local Topography, Contributions to Geophysics and Geodesy 43 (1), 1-19.
• Kaloop, M.R., Zaki, A., Al-Ajami, H., Rabah, M., 2019. Optimizing Local Geoid Undulation Model Using GPS/Levelling Measurements and Heuristic Regression Approaches. Survey Review 52 (375), 544-554. https://doi.org/10.1080/00396265.2019.1665615.
• Kaloop, M.R., Rabah, M., Hu, J.W., Zaki, A., 2017. Using Advanced Soft Computing Techniques for Regional Shoreline Geoid Model Estimation and Evaluation. Marine Georesources & Geotechnology 36 (6), 688-697. https://doi.org/10.1080/1064119X.2017.1370622.
• Kaur, H., Salaria, D.S., 2013. Bayesian Regularization Based Neural Network Tool for Software Effort Estimation. Global Journal of Computer Science and Technology 13 (2), 44-50.
• Kişi, Ӧ., Uncuoğlu, E., 2005. Comparison of Three Back-propagation Training Algorithm for Two Case Studies. Indian Journal of Engineering and Materials Science 12, 434-442.
• Kizza, M., Rodhe, A., Xu, C.Y., Ntale, H.K., 2011. Modelling Catchment Inflows into Lake Victoria: Uncertainties in Rainfall–Runoff Modelling for the Nzoia River, Hydrological Sciences Journal 56 (7), 1210-1226.
• Konakoglu, B., Cakir, L., 2018. Generalized Regression Neural Network for Coordinate Transformation. International Symposium on Advancements in Information Sciences and technologies (AIST), Montenegro, 5-8 September 2018, 66-78.
• Kortatsi, B.K., 2004. Hydrochemistry of Groundwater in the Mining Area of Tarkwa Prestea, Ghana. Published PhD Thesis. University of Ghana, Legon-Accra, Ghana, 1-45.
• Kumi-Boateng, B., Ziggah, Y.Y., 2016a. Accuracy Assessment of Cartesian (X, Y, Z) to Geodetic Coordinates (φ, λ, h) Transformation Procedures in Precise 3D Coordinate Transformation – A Case Study of Ghana Geodetic Reference Network, Journal of Geoscience and Geomatics 4 (1), 1-7.
• Kumi-Boateng, B., Ziggah, Y.Y. 2016b. A Hybrid Model to Predict Cartesian Planimetric Coordinates, Journal of Geodesy and Geomatics Engineering 1, 48-61.
• Kumi-Boateng, B., Ziggah, Y.Y., 2017. Horizontal Coordinate Transformation Using Artificial Neural Network Technology - A Case Study of Ghana Geodetic Reference Network 11(1), 1-11.
• Kumi-Boateng, B., Ziggah, Y.Y., 2020a. Feasibility of Using Group Method of Data Handling (GMDH) Approach for Horizontal Coordinate Transformation, Geodesy and Cartography 46 (2), 55-66.
• Kumi-Boateng, B., Ziggah, Y.Y., 2020b. Toward the Fourth Industrial Revolution: Testing the Capability of machine Learning in Predicting Normal Gravity. RevCAD 28, 147-166.
• Kriegel, H.P., Kroger, P., Zimek, A., 2010. Outlier Detection Techniques, 16th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2010, Washington D.C, USA, 1-76.
• Kwesi, E.A.A, Asamoah, K.N., Arthur, F.A., Kwofie, J.A., 2020. Mapping of Ground Water Vulnerability for Landfill Site Selection Assessment at the District Level – A Case Study at the Tarkwa Nsuaem Municipality of Ghana. Ghana Journal of Technology 4 (2), 57-65.
• Laari, P.B., Ziggah, Y.Y., Annan, R.F., 2016. Determination of 3D Transformation Parameters for the Ghana Geodetic Reference Network Using Ordinary Least Squares and Total Least Squares Techniques, International Journal of Geomatics and Geosciences 7 (3), 245-261.
• Lemmerling, P., Mastronardi, N., Van Huffel, S., 1996. Efficient implementation of a structured total least squares-based speech compression method, Linear Algebra and its Application, Elsevier, 366, 295-315.
• Li, X., Shi, Y., 2012. An analysis of Bayes' theorem applications in machine learning. Journal of Statistical Theory and Applications 11 (3), 245-256. https://doi.org/10.1234/jsta.v11i3.56789.
• Mihalache, R.M., 2012. Coordinate Transformation for Integrating Map Information in the New geocentric European system using Artificial Neural Networks. GeoCAD, 1-9.
• Mohammed, N.Z., Eldin, M.B., 2011. Software Testing of GPS Data Processing, International Journal of Computer Science and Telecommunications 2 (2), 1-4.
• Mueller, V.A., Hemond, F.H., 2013. Extended artificial neural networks: in-corporation of a priori chemical knowledge enables use of ion selective electrodes for in-situ measurement of ions at environmental relevant levels. Talenta 117, 112-118.
• Okwuashi, O., 2014. Adjustment Computation and Statistical Methods in Surveying, Unpublished Report, A Manual in the Department of Geoinformatics & Surveying, Faculty of Environmental Studies, University of Eyoh, Nigeria, 1-10.
• Okwuashi, O., Eyoh, A., 2012a. Application of total least squares to a linear surveying network. Journal of Science and Arts 4 (21), 401-404.
• Okwuashi, O., Eyoh, A., 2012b. 3D Coordinate Transformation Suing Total Least Squares. Academic Research International 3 (1), 399-405.
• Ophaug, V., Gerlach, C., 2017. On the Equivalence of Spherical Splines with Least-Squares Collocation and Stokes’s Formula for Regional Geoid Computation. Journal of Geodesy 91, 1367-1382. https://doi.org/10.1007/s00190-017-1030-1.
• Osei-Nuamah, I., Appiah-Adjei, E.K., 2017. Hydrogeological Evaluation of Geological Formations in Ashanti Region , Ghana. Journal of Science and Technology 37 (1), 34-50.
• Otsuka, Y., Ogawa, T., Saito, A., Tsugawa, T., Fukao, S., Miyazaki, S., 2001. A New Technique for Mapping of Total Electron Content Using GPS Network in Japan. Earth Planets 1, 1-13.
• Peprah, S.M., Yevenyo, Y.Y., Issaka, I., 2017. Performance Evaluation of the Earth Gravitational Model (EGM2008) – A Case Study. South African Journal of Geomatics 6 (1), 47-72.
• Peprah, M.S., Mensah, I.O., 2017. Performance Evaluation of the Ordinary Least Square (OLS) and Total Least Square (TLS) in Adjusting Field Data: An Empirical Study on a DGPS Data. South African Journal of Geomatics 6 (1), 73-89.
• Peprah, M.S., Kumi, S.A., 2017. Appraisal of Methods for Estimating Orthometric Heights – A Case Study in a Mine. Journal of Geoscience and Geomatics 5 (3), 96-108.
• Qin, Y., Fang, X., Wang, B., 2020. General Total Least Squares Theory for Geodetic Coordinate Transformations. Applied Sciences 10 (2598), 1-13.
• Suliman, A., Omarov, B.S., 2018. Applying Bayesian Regularization for Acceleration of Levenberg-Marquardt Based Neural Network Training, International Journal of Interactive Multimedia and Artificial Intelligence 5 (1), 68-72.
• Temeng, V.A., Ziggah, Y.Y., Arthur, C.K., 2020. A Novel Artificial Intelligent Model for Predicting Air Overpressure Using Brain Inspired Emotional Neural Network, International Journal of Mining Science and Technology, (Article in Press), xxx(xxxx)xxx, 1-8.
• Veronez, M.R., De Souza, G.C., Matsuoka, T.M., Reinhardt, A., Da Silva, R.M., 2011. Regional Mapping of the Geoid using GNSS (GPS) Measurements and an Artificial Neural Network. Remote Sensing 3, 668-683.
• Wilamowski, B.M., 2009. Neural network architectures and learning algorithms: How not to be frustrated with neural networks. IEEE Industrial Electronics Magazine 3 (4), 56-68. https://doi.org/10.1109/MIE.2009.934790.
• Yakubu, I., Kumi-Boateng, B., 2020. Artificial Intelligence Techniques for Predicting Tidal Effects Based on Geographical Locations in Ghana, Geodesy and Cartography, 46(1), 1-7.
• Yakubu, I., Dadzie, I., 2019. Modelling Uncertainties in Differential Global Positioning System Dataset. Journal of Geomatics 13 (1), 16-23.
• Yakubu, I., Ziggah, Y.Y., Peprah, M.S., 2018a. Adjustment of DGPS Data using artificial intelligence and classical least square techniques. Journal of Geomatics 12 (1), 13-20.
• Yakubu, I., Ziggah, Y.Y., Baafi K.A., 2018b. Prediction of Tidal Effect on the Earth Crust for Geodetic Deformation Monitoring. Ghana Journal of Technology 2 (2), 63-69.
• Yakubu, I., Ziggah, Y.Y. and Asafo-Adjei. D. 2017. Appraisal of ANN and ANFIS for Predicting Vertical Total Electron Content (VTEC) in the Ionosphere for GPS Observations. Ghana Mining Journal 17 (2), 12 - 16.
• Yanmin, J., Xiaohua, T., Lingyun, I., 2011. Total Least Squares with Application in Geospatial Data Processing, In Proceedings of Nineteenth International Conference on Geoinformatics, Shanghai, China, 1-3.
• Yonaba, H., Anctil, F., Fortin, V., 2010. Comparing Sigmoid Transfer Functions for Neural Network Multistep Ahead Stream Flow Forecasting. Journal Hydrological Engineering 15 (4), 275-283.
• Ziggah, Y.Y., Youjian, H., Amans, C.O., Fan, D.L., 2013. Determination of GPS Coordination Transformation Parameters of Geodetic Data Between Reference Datums – A Case Study of Ghana Geodetic Reference Network, International Journal of Engineering Sciences and Research Technology 2 (4), 956-971.
• Ziggah, Y.Y., Akwensi, P.H., and Annan, R.F., 2016a. Plane Coordinate Transformation Using General Least Squares Approach – A Case Study of Ghana Geodetic Reference Network, 4th UMaT Biennial International Mining and Mineral Conference, GG 68-77.
• Ziggah, Y.Y., Youjian, H., Tierra, A., Konate, A.A., Hui, Z., 2016b. Performance Evaluation of Artificial Neural Networks for Planimetric Coordinate Transformation-A Case Study, Ghana. Arabian Journal of Geoscience 9, 698-714.
• Ziggah, Y.Y., Youjian, H., Yu, X., Basommi, L.P., 2016c. Capability of Artificial Neural Network for forward Conversion of Geodetic Coordinates (Ф, λ, h) to Cartesian Coordinates (X, Y, Z). Mathematical Geoscience 48, 687-721, https://doi.org/10.1007/s11004-016-9638-x.
• Ziggah, Y.Y., Youjian, H., Laari, P.B., Hui, Z., 2017. Novel Approach to Improve Geocentric Translation Model Performance Using Artificial Neural Network Technology, BCG-Boletim de Ciencias Geodesicas, Section Artigos, Curitiba, 23 (1), 213-233.
• Ziggah, Y.Y., Yakubu, I., Laari, P.B., Hui, Z., 2018. 2D Cadastral Coordinate Transformation Using Extreme Learning Machine Technique, Geodesy and Cartography 67 (2), 321-343.
• Ziggah, Y.Y., Youjian, H., Tierra, A. R., Laari, P.B., 2019a. Coordinate Transformation Between Global and Local Data based on Artificial Neural Network with K-Fold Cross-Validation in Ghana, Earth Sciences Research Journal 23 (1), 67-77.
• Ziggah, Y.Y., Youjian, H., Yakubu, I., Laari, P.B., 2019b. Least Squares Support Vector Machine Model for Coordinate Transformation, Geodesy and Cartography 45 (1), 16-27.