Published

2022-02-07

A Modelling Study by Factorial Design on GNSS Positioning

Estudio de modelado por diseño factorial en posicionamiento de Sistemas Globales de Navegación Satelital

DOI:

https://doi.org/10.15446/esrj.v25n4.95060

Keywords:

factorial design, regression analysis, GNSS error sources, CORS (en)
diseño factorial; análisis de regresión; fuentes de error GNSS; estaciones de referencia en funcionamiento continuo; Sistemas Globales de Navegación Satelital (es)

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Although researchers have widely studied the analysis and modelling of error sources on Global Navigation Satellite Systems positioning, some of these errors have not been eliminated significantly and only some of the Global Navigation Satellite System’s data are modelled. The present work was undertaken to determine the effect of different variables, namely: season, the number of visible satellites, and dilution of precision on the efficiency of horizontal and vertical CORS (Continuously Operating Reference Stations) positioning. For this aim, the CORS data was collected at 14 different test points during 600 epochs with 1-second intervals. Factorial designs supply an efficient solution to understand the impact of several factors on a response variable. A full factorial design with three factors at two levels was applied for these purposes. According to the results of the full factorial design, all factors significantly affected the response variable. Also, the interaction effects of factors were analysed on the CORS horizontal and vertical positioning. The regression equations were obtained for all situations.

A pesar de que los investigadores han analizado y modelado ampliamente  las fuentes de error de posicionamiento en los Sistemas Globales de Navegación Satelital (GNSS, Global Navigation Satellite System), algunos de estos errores no se han eliminado significativamente. Y solo parte de esta información de los Sistemas Satelitales de Navegación Global ha sido modelada. Este trabajo se realiza con el fin de determinar los efectos de diferentes variables: temporada, número de satélites visibles, e imprecisión en la eficiencia de posicionamiento horizontal y vertical CORS  (estaciones de referencia en funcionamiento continuo). La información CORS se recolectó en 14 escenarios de prueba durante 600 períodos y con intervalos de un segundo para este objetivo. Los diseños factoriales proveen una solución eficiente para entender el impacto de varios factores ante una respuesta variable. En este trabajo se aplicó un diseño factorial completo con tres factores en dos niveles. Los efectos principales y de interacción de factores se analizaron con el posicionamiento CORS horizontal y vertical. De acuerdo con los resultados del diseño factorial completo, mientras que los efectos principales y de interacción de factores afectaron significativamente el error de posicionamiento horizontal, algunos efectos principales y de interacción de factores no afectaron el posicionamiento vertical CORS. También las ecuaciones de regresión se obtuvieron para todas las situaciones con el fin de investigar los otros niveles de factores seleccionados en la respuesta de variables.

References

Abad, P., & Suárez, J. P. (2004). Bi-factorial analysis for resolution of GPS equations. Journal of Computational and Applied Mathematics, 164–165, 1–10. https://doi.org/10.1016/j.cam.2003.11.006 DOI: https://doi.org/10.1016/j.cam.2003.11.006

Ahmad, K. A. (2015). Reliability Monitoring of GNSS Aided Positioning for Land Vehicle Applications in Urban Environments. Ph.D. Thesis, Universite de Toulouse, France.

Alkan, R. M., Ilçi, V., Ozulu, I. M. & Saka, M. H. (2015). A comparative study for accuracy assessment of PPP technique using GPS and GLONASS in urban areas. Measurement, 69, 1-8. https://doi.org/10.1016/j.measurement.2015.03.012 DOI: https://doi.org/10.1016/j.measurement.2015.03.012

Alkan, R. M., Saka, M. H., Ozulu, I. M. & İlçi, V. (2017). Kinematic precise point positioning using GPS and GLONASS measurements in marine environments. Measurement, 109, 36-43. https://doi.org/10.1016/j.measurement.2017.05.054 DOI: https://doi.org/10.1016/j.measurement.2017.05.054

Aykut, N. O., Gülal, E. & Akpinar, B. (2015). Performance of Single Base RTK GNSS Method versus Network RTK. Earth Sciences Research Journal, 19(2), 135–139. https://doi.org/10.15446/esrj.v19n2.51218 DOI: https://doi.org/10.15446/esrj.v19n2.51218

Bakici, S., Erkek, B., İlbey, A. & Kulaksiz, E. (2017). Business Model of CORS-TR (Tusaga-Aktif). 4th International Workshop on Geoinformation Science: GeoAdvances 2017, Safranbolu, Karabuk, Turkey, October, IV-4-W4(2017), 109-116. https://doi.org/10.5194/isprs-annals-IV-4-W4-109-2017 DOI: https://doi.org/10.5194/isprs-annals-IV-4-W4-109-2017

Banerjee, P. & Bose, A. (1996). Evaluation of GPS PDOP from elevation and azimuth of satellites. Indian Journal of Radio and Space Physics, 25, 110-113.

Box, G. E. P., Hunter, J. S. & Hunter, W. G. (2005). Statistics of Experimenters: Design, Innovation, and Discovery. John Wiley & Sons. 2nd ed., Wiley, Hoboken, 672 pp.

Brenneman, M. T., Morton, Y. T. & Zhou, Q. (2010). GPS Multipath Detection with ANOVA for Adaptive Arrays. IEEE Transactions on Aerospace and Electronic Systems, 46(3), 1171–1184. https://doi.org/10.1109/TAES.2010.5545181 DOI: https://doi.org/10.1109/TAES.2010.5545181

Busznyák, T., Pálfi, G., & Lakatos, I. (2019). On-board Diagnostic-based Positioning as an Additional Information Source of Driver Assistant Systems. Acta Polytechnica Hungarica, 16(5), 217–234. https://doi.org/10.12700/APH.16.5.2019.5.12 DOI: https://doi.org/10.12700/APH.16.5.2019.5.12

Cai, C. & Gao, Y. (2007). Precise Point Positioning Using Combined GPS and GLONASS Observations. Journal of Global Positioning Systems, 6(1), 13–22. DOI: https://doi.org/10.5081/jgps.6.1.13

Catania, P., Comparetti, A., Febo, P., Morello, G., Orlando, S., Roma, E. & Vallone, M. (2020). Positioning Accuracy Comparison of GNSS Receivers Used for Mapping and Guidance of Agricultural Machines. Agronomy, 10(7), 924. https://doi.org/10.3390/agronomy10070924 DOI: https://doi.org/10.3390/agronomy10070924

Chen, C. S., Chiu, Y. J., Lee, C. T., & Lin, J. M. (2013). Calculation of Weighted Geometric Dilution of Precision. Journal of Applied Mathematics, 953048, 1-10. https://doi.org/10.1155/2013/953048 DOI: https://doi.org/10.1155/2013/953048

Çoruh, S., Elevli, S. & Geyikçi, F. (2012). Statistical Evaluation and Optimization of Factors Affecting the Leaching Performance of Copper Flotation Waste. The Scientific World Journal, 758719, 1–8. https://doi.org/10.1100/2012/758719 DOI: https://doi.org/10.1100/2012/758719

Dogan, U., Uludag, M. & Demir, D. O. (2014). Investigation of GPS positioning accuracy during the seasonal variation. Measurement, 53, 91-100. https://doi.org/10.1016/j.measurement.2014.03.034 DOI: https://doi.org/10.1016/j.measurement.2014.03.034

Firuzabadì, D., & King, R. W. (2012). GPS precision as a function of session duration and reference frame using multi-point software. GPS Solutions, 16, 191–196. https://doi.org/10.1007/s10291-011-0218-8 DOI: https://doi.org/10.1007/s10291-011-0218-8

George, M. L., Rowlands, D., Price, M., & Maxey, J. (2005). The Lean Six Sigma Pocket Toolbook. McGraw Hill, New York.

Gülal, E., Erdoǧan, H., & Tiryakioǧlu, İ. (2013). Research on the stability analysis of GNSS reference stations network by time series analysis. Digital Signal Processing, 23(6), 1945-1957. https://doi.org/10.1016/j.dsp.2013.06.014 DOI: https://doi.org/10.1016/j.dsp.2013.06.014

Gündoğdu, T. K., Deniz, İ., Çalişkan, G., Şahin, E. S., & Azbar, N. (2016). Experimental design methods for bioengineering applications. Critical Reviews in Biotechnology, 36(2), 368-388. https://doi.org/10.3109/07388551.2014.973014 DOI: https://doi.org/10.3109/07388551.2014.973014

Gygi, C., Williams, B., & Gustafson, T. (2006). Six Sigma Workbook For Dummies. Wiley, Indiana. 320 pp.

İlçi, V. (2019). Accuracy comparison of real-time GNSS positioning solutions: Case study of Mid-North Anatolia. Measurement, 142, 40-47. https://doi.org/10.1016/j.measurement.2019.04.067 DOI: https://doi.org/10.1016/j.measurement.2019.04.067

Ismail, A. A., El-Midany, A. A., Ibrahim, I. A., & Matsunaga, H. (2008). Heavy metal removal using SiO2-TiO2 binary oxide: experimental design approach. Adsorption, 14(2008), 21–29. https://doi.org/10.1007/s10450-007-9042-4 DOI: https://doi.org/10.1007/s10450-007-9042-4

Karaim, M., Elsheikh, M., & Noureldin, A. (2018). GNSS Error Sources. Chapter 4 in Multifunctional Operation and Application of GPS. IntechOpen, Rijeka. https://doi.org/10.5772/intechopen.75493 DOI: https://doi.org/10.5772/intechopen.75493

Kavuri, N. C., Sahu, S., & Kundu, M. (2009). Bioleaching of Zinc Sulphide Ore Using Thiobacillus Ferrooxidans: Screening of Design Parameters Using Statistical Design of Experiments. The IUP Journal of Chemical Engineering, 1(1), 39–53. https://ssrn.com/abstract=1487464

Li, C., Teng, Y. & Kang, R. (2018). Some remarks on geometric dilution of precision (GDOP) at user level in multi-GNSS positioning. Advances in Space Research, 62(11), 3048-3052. https://doi.org/10.1016/j.asr.2018.08.029 DOI: https://doi.org/10.1016/j.asr.2018.08.029

Mason, R. L., Gunst, R. F., & Hess, J. L. (2003). Statistical Design and Analysis of Experiments: With Applications to Engineering and Science. 2nd ed. John Wiley & Sons, Hoboken, New Jersey, USA. https://doi.org/10.1002/0471458503 DOI: https://doi.org/10.1002/0471458503

Minitab. (2021). Statistical Software. https://www.minitab.com/en-us/ (last accessed October 2021)

Montgomery, D. (2001). Editorial: Research industrial statistics-Part I. In: Quality and Reliability Engineering International. 17(6), 3-4, John Wiley & Sons, Ltd. https://doi.org/10.1002/qre.449 DOI: https://doi.org/10.1002/qre.449

Navidi, W. (2008). Statistics for Engineers and Scientists. 3rd ed. McGraw-Hill Companies Inc., New York, USA, 933 pp.

Pirti, A. (2008). Accuracy analysis of GPS positioning near the forest environment. Croatian Journal of Forest Engineering, 29(2), 189–199.

Potter, K., Hagen, H., Kerren, A., & Dannenmann, P. (2006). Methods for presenting statistical information: The box plot. Visualization of large and unstructured data sets, 4, 97–106.

Raghunath, S., Malleswari, D. B. L., & Sridhar, K. (2011). Analysis of GPS errors during different times in a day. International Journal of Research in Computer Science, 2(1), 45–48. https://doi.org/10.7815/ijorcs.21.2011.014 DOI: https://doi.org/10.7815/ijorcs.21.2011.014

Saracoglu, A., & Sanli, D. U. (2020). Effect of meteorological seasons on the accuracy of GPS positioning. Measurement, 152, 107301. https://doi.org/10.1016/j.measurement.2019.107301 DOI: https://doi.org/10.1016/j.measurement.2019.107301

Seltman, H. J. (2018). Experimental Design and Analysis. Carnegie Mellon Univesrity, 428 pp. http://www.stat.cmu.edu/~hseltman/309/Book/Book.pdf

Sharma, S. (2019). Descriptive Statistics and Factorial Design. Ph.D. Thesis, Horizons University, Paris, France. https://www.researchgate.net/publication/333220406_Descriptive_Statistics#fullTextFileContent

Sisman, A. (2014a). An experimental design approach on georeferencing. Boletim de Ciências Geodésicas, 20(3), 548–561. https://doi.org/10.1590/s1982-21702014000300031 DOI: https://doi.org/10.1590/S1982-21702014000300031

Sisman, Y. (2014b). A Full-Factorial Design Approach for Coordinate Transformation. Arabian Journal for Science and Engineering, 39, 227–235. https://doi.org/10.1007/s13369-013-0864-y DOI: https://doi.org/10.1007/s13369-013-0864-y

Soler, T., Michalak, P., Weston, N. D., Snay, R. A., & Foote, R. H. (2006). Accuracy of OPUS solutions for 1- to 4-h observing sessions. GPS Solutions, 10(1), 45–55. https://doi.org/10.1007/s10291-005-0007-3 DOI: https://doi.org/10.1007/s10291-005-0007-3

Stone, J. M., & Powell, J. D. (1998). Precise Positioning with GPS near Obstructions by Augmentation with Pseudolites. IEEE 1998 Position Location and Navigation Symposium, 562–569. https://doi.org/10.1109/plans.1998.670213 DOI: https://doi.org/10.1109/PLANS.1998.670213

Svabensky, O., & Weigel, J. (2004). Optimized Technology for GPS Height Determination. FIG Working Week 2004, Athens, Greece, 22-27 May, 1–8. https://www.fig.net/resources/proceedings/fig_proceedings/athens/papers/ts07/ts07_6_svabensky_weigel.pdf

Teng, Y., & Wang, J. (2014). New Characteristics of Geometric Dilution of Precision (GDOP) for multi-GNSS constellations. Journal of Navigation, 67(6), 1018-1028. https://doi.org/10.1017/S037346331400040X DOI: https://doi.org/10.1017/S037346331400040X

Teng, Y., & Wang, J. (2016). A closed-form formula to calculate geometric dilution of precision (GDOP) for multi-GNSS constellations. GPS Solutions, 20, 331-339. https://doi.org/10.1007/s10291-015-0440-x DOI: https://doi.org/10.1007/s10291-015-0440-x

Teng, Y., Wang, J., & Huang, Q. (2015). Minimum of Geometric Dilution of Precision (GDOP) for five satellites with dual-GNSS constellations. Advances in Space Research, 56(2), 229-236. https://doi.org/10.1016/j.asr.2015.04.010 DOI: https://doi.org/10.1016/j.asr.2015.04.010

Verma, P., Hajra, K., Banerjee, P., & Bose, A. (2019). Evaluating PDOP in Multi-GNSS Environment. IETE Journal of Research, 1-8. https://doi.org/10.1080/03772063.2019.1666750 DOI: https://doi.org/10.1080/03772063.2019.1666750

Wang, Y., Huang, S., Xiang, W. & Pei, Y. (2011). Multipattern Road Traffic Crashes and Injuries: A Case Study of Xi’an City. Acta Polytechnica Hungarica, 8(4), 171–181.

Wang, Y., Zhao, X., Pang, C., Feng, B., Tong, H., & Zhang, L. (2019). BDS and GPS stand-alone and integrated attitude dilution of precision definition and comparison. Advances in Space Research, 63(9), 2972-2981. https://doi.org/10.1016/j.asr.2017.11.032 DOI: https://doi.org/10.1016/j.asr.2017.11.032

Wielgosz, P., Hadaś, T., Kłos, A., & Paziewski, J. (2019). Research on GNSS positioning and applications in Poland in 2015–2018. Geodesy and Cartography, 68(1), 87–119. https://doi.org/https://doi.org/10.24425/gac.2019.126089

Wing, M. G., Eklund, A., John, A., & Richard, K. (2008). Horizontal Measurement Performance of Five Mapping-Grade Global Positioning System Receiver Configurations in Several Forested Settings. Western Journal of Applied Forestry, 23(3), 166–171. https://doi.org/10.1093/wjaf/23.3.166 DOI: https://doi.org/10.1093/wjaf/23.3.166

Wu, J. C. F., & Hamada, M. S. (2009). Experiments: Planning, Analysis, and Optimization. 2nd. ed. A John Wiley & Sons. Inc., Hoboken, New Jersey. 760 pp.

Yoshimura, T., & Hasegawa, H. (2003). Comparing the precision and accuracy of GPS positioning in forested areas. Journal of Forest Research, 8(3), 147–152. https://doi.org/10.1007/s10310-002-0020-0 DOI: https://doi.org/10.1007/s10310-002-0020-0

Zheng, F., Lou, Y., Gu, S., Gong, X., & Shi, C. (2018). Modeling tropospheric wet delays with national GNSS reference network in China for BeiDou precise point positioning. Journal of Geodesy, 92, 545-560. https://doi.org/10.1007/s00190-017-1080-4 DOI: https://doi.org/10.1007/s00190-017-1080-4

How to Cite

APA

Ilci, V. and Sisman, Y. (2022). A Modelling Study by Factorial Design on GNSS Positioning. Earth Sciences Research Journal, 25(4), 391–396. https://doi.org/10.15446/esrj.v25n4.95060

ACM

[1]
Ilci, V. and Sisman, Y. 2022. A Modelling Study by Factorial Design on GNSS Positioning. Earth Sciences Research Journal. 25, 4 (Feb. 2022), 391–396. DOI:https://doi.org/10.15446/esrj.v25n4.95060.

ACS

(1)
Ilci, V.; Sisman, Y. A Modelling Study by Factorial Design on GNSS Positioning. Earth sci. res. j. 2022, 25, 391-396.

ABNT

ILCI, V.; SISMAN, Y. A Modelling Study by Factorial Design on GNSS Positioning. Earth Sciences Research Journal, [S. l.], v. 25, n. 4, p. 391–396, 2022. DOI: 10.15446/esrj.v25n4.95060. Disponível em: https://revistas.unal.edu.co/index.php/esrj/article/view/95060. Acesso em: 20 oct. 2024.

Chicago

Ilci, Veli, and Yasemin Sisman. 2022. “A Modelling Study by Factorial Design on GNSS Positioning”. Earth Sciences Research Journal 25 (4):391-96. https://doi.org/10.15446/esrj.v25n4.95060.

Harvard

Ilci, V. and Sisman, Y. (2022) “A Modelling Study by Factorial Design on GNSS Positioning”, Earth Sciences Research Journal, 25(4), pp. 391–396. doi: 10.15446/esrj.v25n4.95060.

IEEE

[1]
V. Ilci and Y. Sisman, “A Modelling Study by Factorial Design on GNSS Positioning”, Earth sci. res. j., vol. 25, no. 4, pp. 391–396, Feb. 2022.

MLA

Ilci, V., and Y. Sisman. “A Modelling Study by Factorial Design on GNSS Positioning”. Earth Sciences Research Journal, vol. 25, no. 4, Feb. 2022, pp. 391-6, doi:10.15446/esrj.v25n4.95060.

Turabian

Ilci, Veli, and Yasemin Sisman. “A Modelling Study by Factorial Design on GNSS Positioning”. Earth Sciences Research Journal 25, no. 4 (February 7, 2022): 391–396. Accessed October 20, 2024. https://revistas.unal.edu.co/index.php/esrj/article/view/95060.

Vancouver

1.
Ilci V, Sisman Y. A Modelling Study by Factorial Design on GNSS Positioning. Earth sci. res. j. [Internet]. 2022 Feb. 7 [cited 2024 Oct. 20];25(4):391-6. Available from: https://revistas.unal.edu.co/index.php/esrj/article/view/95060

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