Research Article
BibTex RIS Cite

Evaluation of zenith tropospheric delays estimated by different regression models

Year 2022, , 661 - 671, 18.07.2022

Ali Utku Akar , Cevat İnal

https://doi.org/10.28948/ngumuh.1088375

Abstract

Advances in artificial intelligence and machine learning provide alternative solutions to the problems in GNSS applications or enable to increase the efficiency of existing solutions. There are many errors encountered in GNSS and these errors pose a problem to users. The tropospheric delay effect is one of them. The increasing interest in GNSS technology as well as the use of learning algorithms in atmosphere/troposphere studies have made it important to create new models for tropospheric delay estimation. In this study, it was aimed to estimate the zenith tropospheric delay (ZTD) by using Radial Basis Function-Support Vector Regression (RBF-SVR), Ridge and Elastic-Net regression models. The new regression models trained according to machine learning was investigated its preferability as an alternative in ZTD estimation. For this reason, the results obtained from different methods were analyzed by comparing the ZTD models. From the analysis results, it was determined that the RBF-SVR model gave the best results, followed by the Elastic-Net and Ridge models. Afterward, the ZTD values obtained from the new models were compared with the Canadian Spatial Reference System–Precise Point Positioning (CSRS-PPP) ZTD values and the performance of the models was evaluated. According to the evaluation results, it was concluded that RBF-SVR is the most compatible model to CSRS-PPP.

Keywords

ZTD Estimation Machine learning RBF-SVR Ridge and elastic-net regression CSRS-PPP

References

  • V. B. Mendes, Modeling the neutral-atmospheric propagation delay in radiometric space techniques. UNB geodesy and geomatics engineering technical report 199(10), 1999.
  • A. Angrisano, S. Gaglione, C. Gioia, M. Massaro and U. Robustelli, Assessment of NeQuick ionospheric model for Galileo single-frequency users. Acta Geophysica, 61(6), 1457-1476, 2013. https://doi.org/10 .2478/s11600-013-0116-2.
  • M. Kahveci ve F. Yıldız, Uydularla Konum Belirleme Sistemleri (GPS/GNSS): Teori-Uygulama, 8. Basım, Nobel Yayıncılık, Ankara, 2017.
  • P. Tregoning and T. A. Herring, Impact of a priori zenith hydrostatic delay errors on GPS estimates of station heights and zenith total delays. Geophysical Research Letters, 33(23), 2006. https://doi.org/10. 1029/2006GL027706.
  • R. Dach, S. Lutz, P. Walser and P. Fridez, Bernese GNSS Software Version 5.2, User manual. Astronomical Institute, University of Bern, Bern Open Publishing, 2015. DOI: 10.7892/boris.72297, ISBN: 978-3-906813-05-9.
  • K. Wilgan, F. Hurter, A. Geiger, W. Rohm and J. Bosy, Tropospheric refractivity and zenith path delays from least-squares collocation of meteorological and GNSS data. Journal of Geodesy, 91(2), 117-134, 2017. https://doi.org/10.1007/s00190-016-0942-5.
  • P. Benevides, J. Catalao and G. Nico, Neural network approach to forecast hourly intense rainfall using GNSS precipitable water vapor and meteorological sensors. Remote Sensing, 11(8), 966, 2019. https://doi.org/10.3390/rs11080966.
  • S. Li, T. Xu, N. Jiang, H. Yang, S. Wang and Z. Zhang, Regional zenith tropospheric delay modeling based on least squares support vector machine using GNSS and ERA5 data. Remote Sensing, 13(5), 1004, 2021. https://doi.org/10.3390/rs13051004.
  • J. Böhm, A. Niell, P. Tregoning and H. Schuh, Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data. Geophysical research letters, 33(7), 2006. https://doi.org/10.1029/2005GL025546.
  • J. Boisits, D. Landskron and J. Böhm, VMF3o: the Vienna Mapping Functions for optical frequencies. Journal of Geodesy, 94(6), 1-11, 2020. https://doi.org/10.1007/s00190-020-01385-5.
  • H. S. Hopfield, Two‐quartic tropospheric refractivity profile for correcting satellite data. Journal of Geophysical research, 74(18), 4487-4499, 1969. https://doi.org/10.1029/JC074i018p04487.
  • J. Saastamoinen, Contributions to the theory of atmospheric refraction. Bulletin Géodésique (1946-1975), 105(1), 279-298, 1972. https://doi.org/10. 1007/BF02521844.
  • H. D. Black, An easily implemented algorithm for the tropospheric range correction. Journal of Geophysical Research: Solid Earth, 83(B4), 1825-1828, 1978. https://doi.org/10.1029/JB083iB04p01825.
  • J. Liu, X. Chen, J. Sun and Q. Liu, An analysis of GPT2/GPT2w+Saastamoinen models for estimating zenith tropospheric delay over Asian area. Advances in Space Research, 59(3), 824-832, 2017. https://doi.org/ 10.1016/j.asr.2016.09.019.
  • R. Leandro, M. Santos and R. Langley, UNB neutral atmosphere models: development and performance. In Proceedings of the 2006 national technical meeting of the institute of navigation, pp. 564-573, 2006.
  • S. Serrano-Vincenti, T. Condom, L. Campozano, J. Guamán and M. Villacís, An empirical model for rainfall maximums conditioned to tropospheric water vapor over the Eastern Pacific Ocean. Frontiers in Earth Science, 8, 198, 2020. https://doi.org/10.3389/ feart.2020.00198.
  • S. Li, T. Xu, Y. Xu, N. Jiang and L. Bastos, Forecasting GNSS Zenith Troposphere Delay by Improving GPT3 Model with Machine Learning in Antarctica. Atmosphere, 13(1), 78, 2022. https://doi.org/10. 3390/atmos13010078.
  • T. Hadas, F. N. Teferle, K. Kazmierski, P. Hordyniec and J. Bosy, Optimum stochastic modeling for GNSS tropospheric delay estimation in real-time. GPS solutions, 21(3), 1069-1081, 2017. https://doi.org/10. 1007/s10291-016-0595-0.
  • M. Ding, A neural network model for predicting weighted mean temperature. Journal of Geodesy, 92(10), 1187-1198, 2018. https://doi.org/10 .1007/s00190-018-1114-6.
  • M. Łoś, K. Smolak, G. Guerova and W. Rohm, GNSS-based machine learning storm nowcasting. Remote Sensing, 12(16), 2536, 2020. https://doi.org/10.3390/ rs12162536.
  • S. Manandhar, Y. H. Lee, Y. S. Meng, F. Yuan and J. T. Ong, GPS-derived PWV for rainfall nowcasting in tropical region. IEEE transactions on geoscience and remote sensing, 56(8), 4835-4844, 2018. 10.1109/TGRS.2018.2839899.
  • M. O. Selbesoğlu, Global Navigasyon Uydu Sistemleri (GNSS) Gözlemlerinden Elde Edilen Islak Troposfer Gecikmesinin Yapay Sinir Ağları ile Modellenmesi, Doktora Tezi, Yıldız Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Türkiye, 2017.
  • J. Deng, M. Xu, X. Yu and A. Zhang, Interpolation estimation method of tropospheric delay for long baseline network RTK based on support vector machine. In IOP Conference Series: Earth and Environmental Science, Vol. 192, No. 1, p. 012069. IOP Publishing, 2018. DOI: 10.1088/1755-1315/ 192/1/012069.
  • L. Miotti, E. Shehaj, A. Geiger, S. D'Aronco, J. D. Wegner, G. Moeller and M. Rothacher, Tropospheric delays derived from ground meteorological parameters: comparison between machine learning and empirical model approaches. In 2020 European Navigation Conference (ENC). pp. 1-10, IEEE, 2020.
  • M. Palaniswami and A. Shilton, Adaptive support vector machines for regression. In Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP’02. Vol. 2, pp. 1043-1049, IEEE, 2002.
  • V. Kecman, Learning and soft computing: support vector machines, neural networks, and fuzzy logic models. MIT press, 2001.
  • A. Mathur and G. M. Foody, Multiclass and binary SVM classification: Implications for training and classification users. IEEE Geoscience and remote sensing letters, 5(2), 241-245, 2008. DOI: 10.1109/LGRS.2008.915597.
  • R. Debnath and H. Takahashi, Kernel selection for the support vector machine. IEICE transactions on information and systems, 87(12), 2903-2904, 2004.
  • A. E. Hoerl and R. W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67, 1970.
  • R. R. Wilcox, Multicolinearity and ridge regression: results on type I errors, power and heteroscedasticity. Journal of Applied Statistics, 46(5), 946-957, 2019. https://doi.org/10.1080/02664763.2018.1526891.
  • G. James, D. Witten, T. Hastie and R. Tibshirani, Resampling methods. In An introduction to statistical learning (pp. 175-201). Springer, New York, NY, 2013. https://doi.org/10.1007/978-1-4614-7138-7_5.
  • J. Al-Jararha, New approaches for choosing the ridge parameters. Hacettepe Journal of Mathematics and Statistics, 47(6), 1625-1633, 2016.
  • J. Friedman, T. Hastie and R. Tibshirani, Regularization paths for generalized linear models via coordinate descent. Journal of statistical software, 33(1), 1, 2010.
  • H. Zou and T. Hastie, Regularization and variable selection via the elastic net. Journal of the royal statistical society: series B (statistical methodology), 67(2), 301-320, 2005. https://doi.org/10.1111/j.1467-9868.2005.00503.x.
  • R. J. Tibshirani, The lasso problem and uniqueness. Electronic Journal of statistics, 7, 1456-1490, 2013. DOI: 10.1214/13-EJS815.
  • S. Aslan ve T. Yıldız, Makine Öğrenmesinde Rastgele Oran ve Sıralı Küme Örneklemesi Yöntemlerinin Doğrusal Regresyon Modellerine Etkisi. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, 24(70), 29-36, 2022. https://doi.org/10.21205/deufmd.2022247004

Farklı regresyon modelleriyle kestirilen zenit troposferik gecikmelerin değerlendirilmesi

Year 2022, , 661 - 671, 18.07.2022

Ali Utku Akar , Cevat İnal

https://doi.org/10.28948/ngumuh.1088375

Abstract

Yapay zekâ ve makine öğrenimi alanındaki gelişmeler, GNSS uygulamalarındaki sorunlara alternatif çözümler sunmakta veya mevcut çözümlerin verimliliğini artırmaya imkân sağlamaktadır. GNSS’de karşılaşılan birçok hata vardır ve bu hatalar kullanıcılar için problem oluşturmaktadır. Troposferik gecikme bunlardan birisidir. GNSS teknolojisine ilginin artmasıyla beraber öğrenme algoritmalarının atmosfer/troposfer çalışmalarında kullanımı, troposferik gecikme kestirimi için yeni modellerin oluşturulmasını önemli hale getirmiştir. Bu çalışmada, Radyal Tabanlı Destek Vektör Regresyonu (RTF-DVR), Ridge ve Elastik-Net regresyon modelleriyle zenit troposferik gecikmenin (ZTD) kestirilmesi amaçlanmış, makine öğrenimi esasına göre eğitilmiş yeni regresyon modellerinin ZTD kestiriminde alternatif olarak tercih edilebilirliği araştırılmıştır. Bunun için farklı yöntemlerden elde edilen sonuç ZTD modelleri karşılaştırılarak analiz edilmiştir. Analiz sonuçlarından RTF-DVR modelinin daha iyi sonuçları verdiği, bunu Elastik-Net ve Ridge modellerinin takip ettiği tespit edilmiştir. Sonrasında yeni modellerden elde edilen ZTD değerleri, Canadian Spatial Reference System–Precise Point Positioning (CSRS-PPP) ZTD değerleriyle karşılaştırılıp modellerin performansı değerlendirilmiştir. Değerlendirme sonuçlarına göre, CSRS-PPP’ye en uyumlu modelin RTF-DVR olduğu sonucuna varılmıştır.

Keywords

RTF-DVR CSRS-PPP ZTD kestirimi Makine öğrenimi RTF-DVR Ridge ve elastik-net regresyonu CSRS-PPP

References

  • V. B. Mendes, Modeling the neutral-atmospheric propagation delay in radiometric space techniques. UNB geodesy and geomatics engineering technical report 199(10), 1999.
  • A. Angrisano, S. Gaglione, C. Gioia, M. Massaro and U. Robustelli, Assessment of NeQuick ionospheric model for Galileo single-frequency users. Acta Geophysica, 61(6), 1457-1476, 2013. https://doi.org/10 .2478/s11600-013-0116-2.
  • M. Kahveci ve F. Yıldız, Uydularla Konum Belirleme Sistemleri (GPS/GNSS): Teori-Uygulama, 8. Basım, Nobel Yayıncılık, Ankara, 2017.
  • P. Tregoning and T. A. Herring, Impact of a priori zenith hydrostatic delay errors on GPS estimates of station heights and zenith total delays. Geophysical Research Letters, 33(23), 2006. https://doi.org/10. 1029/2006GL027706.
  • R. Dach, S. Lutz, P. Walser and P. Fridez, Bernese GNSS Software Version 5.2, User manual. Astronomical Institute, University of Bern, Bern Open Publishing, 2015. DOI: 10.7892/boris.72297, ISBN: 978-3-906813-05-9.
  • K. Wilgan, F. Hurter, A. Geiger, W. Rohm and J. Bosy, Tropospheric refractivity and zenith path delays from least-squares collocation of meteorological and GNSS data. Journal of Geodesy, 91(2), 117-134, 2017. https://doi.org/10.1007/s00190-016-0942-5.
  • P. Benevides, J. Catalao and G. Nico, Neural network approach to forecast hourly intense rainfall using GNSS precipitable water vapor and meteorological sensors. Remote Sensing, 11(8), 966, 2019. https://doi.org/10.3390/rs11080966.
  • S. Li, T. Xu, N. Jiang, H. Yang, S. Wang and Z. Zhang, Regional zenith tropospheric delay modeling based on least squares support vector machine using GNSS and ERA5 data. Remote Sensing, 13(5), 1004, 2021. https://doi.org/10.3390/rs13051004.
  • J. Böhm, A. Niell, P. Tregoning and H. Schuh, Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data. Geophysical research letters, 33(7), 2006. https://doi.org/10.1029/2005GL025546.
  • J. Boisits, D. Landskron and J. Böhm, VMF3o: the Vienna Mapping Functions for optical frequencies. Journal of Geodesy, 94(6), 1-11, 2020. https://doi.org/10.1007/s00190-020-01385-5.
  • H. S. Hopfield, Two‐quartic tropospheric refractivity profile for correcting satellite data. Journal of Geophysical research, 74(18), 4487-4499, 1969. https://doi.org/10.1029/JC074i018p04487.
  • J. Saastamoinen, Contributions to the theory of atmospheric refraction. Bulletin Géodésique (1946-1975), 105(1), 279-298, 1972. https://doi.org/10. 1007/BF02521844.
  • H. D. Black, An easily implemented algorithm for the tropospheric range correction. Journal of Geophysical Research: Solid Earth, 83(B4), 1825-1828, 1978. https://doi.org/10.1029/JB083iB04p01825.
  • J. Liu, X. Chen, J. Sun and Q. Liu, An analysis of GPT2/GPT2w+Saastamoinen models for estimating zenith tropospheric delay over Asian area. Advances in Space Research, 59(3), 824-832, 2017. https://doi.org/ 10.1016/j.asr.2016.09.019.
  • R. Leandro, M. Santos and R. Langley, UNB neutral atmosphere models: development and performance. In Proceedings of the 2006 national technical meeting of the institute of navigation, pp. 564-573, 2006.
  • S. Serrano-Vincenti, T. Condom, L. Campozano, J. Guamán and M. Villacís, An empirical model for rainfall maximums conditioned to tropospheric water vapor over the Eastern Pacific Ocean. Frontiers in Earth Science, 8, 198, 2020. https://doi.org/10.3389/ feart.2020.00198.
  • S. Li, T. Xu, Y. Xu, N. Jiang and L. Bastos, Forecasting GNSS Zenith Troposphere Delay by Improving GPT3 Model with Machine Learning in Antarctica. Atmosphere, 13(1), 78, 2022. https://doi.org/10. 3390/atmos13010078.
  • T. Hadas, F. N. Teferle, K. Kazmierski, P. Hordyniec and J. Bosy, Optimum stochastic modeling for GNSS tropospheric delay estimation in real-time. GPS solutions, 21(3), 1069-1081, 2017. https://doi.org/10. 1007/s10291-016-0595-0.
  • M. Ding, A neural network model for predicting weighted mean temperature. Journal of Geodesy, 92(10), 1187-1198, 2018. https://doi.org/10 .1007/s00190-018-1114-6.
  • M. Łoś, K. Smolak, G. Guerova and W. Rohm, GNSS-based machine learning storm nowcasting. Remote Sensing, 12(16), 2536, 2020. https://doi.org/10.3390/ rs12162536.
  • S. Manandhar, Y. H. Lee, Y. S. Meng, F. Yuan and J. T. Ong, GPS-derived PWV for rainfall nowcasting in tropical region. IEEE transactions on geoscience and remote sensing, 56(8), 4835-4844, 2018. 10.1109/TGRS.2018.2839899.
  • M. O. Selbesoğlu, Global Navigasyon Uydu Sistemleri (GNSS) Gözlemlerinden Elde Edilen Islak Troposfer Gecikmesinin Yapay Sinir Ağları ile Modellenmesi, Doktora Tezi, Yıldız Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Türkiye, 2017.
  • J. Deng, M. Xu, X. Yu and A. Zhang, Interpolation estimation method of tropospheric delay for long baseline network RTK based on support vector machine. In IOP Conference Series: Earth and Environmental Science, Vol. 192, No. 1, p. 012069. IOP Publishing, 2018. DOI: 10.1088/1755-1315/ 192/1/012069.
  • L. Miotti, E. Shehaj, A. Geiger, S. D'Aronco, J. D. Wegner, G. Moeller and M. Rothacher, Tropospheric delays derived from ground meteorological parameters: comparison between machine learning and empirical model approaches. In 2020 European Navigation Conference (ENC). pp. 1-10, IEEE, 2020.
  • M. Palaniswami and A. Shilton, Adaptive support vector machines for regression. In Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP’02. Vol. 2, pp. 1043-1049, IEEE, 2002.
  • V. Kecman, Learning and soft computing: support vector machines, neural networks, and fuzzy logic models. MIT press, 2001.
  • A. Mathur and G. M. Foody, Multiclass and binary SVM classification: Implications for training and classification users. IEEE Geoscience and remote sensing letters, 5(2), 241-245, 2008. DOI: 10.1109/LGRS.2008.915597.
  • R. Debnath and H. Takahashi, Kernel selection for the support vector machine. IEICE transactions on information and systems, 87(12), 2903-2904, 2004.
  • A. E. Hoerl and R. W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67, 1970.
  • R. R. Wilcox, Multicolinearity and ridge regression: results on type I errors, power and heteroscedasticity. Journal of Applied Statistics, 46(5), 946-957, 2019. https://doi.org/10.1080/02664763.2018.1526891.
  • G. James, D. Witten, T. Hastie and R. Tibshirani, Resampling methods. In An introduction to statistical learning (pp. 175-201). Springer, New York, NY, 2013. https://doi.org/10.1007/978-1-4614-7138-7_5.
  • J. Al-Jararha, New approaches for choosing the ridge parameters. Hacettepe Journal of Mathematics and Statistics, 47(6), 1625-1633, 2016.
  • J. Friedman, T. Hastie and R. Tibshirani, Regularization paths for generalized linear models via coordinate descent. Journal of statistical software, 33(1), 1, 2010.
  • H. Zou and T. Hastie, Regularization and variable selection via the elastic net. Journal of the royal statistical society: series B (statistical methodology), 67(2), 301-320, 2005. https://doi.org/10.1111/j.1467-9868.2005.00503.x.
  • R. J. Tibshirani, The lasso problem and uniqueness. Electronic Journal of statistics, 7, 1456-1490, 2013. DOI: 10.1214/13-EJS815.
  • S. Aslan ve T. Yıldız, Makine Öğrenmesinde Rastgele Oran ve Sıralı Küme Örneklemesi Yöntemlerinin Doğrusal Regresyon Modellerine Etkisi. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, 24(70), 29-36, 2022. https://doi.org/10.21205/deufmd.2022247004
There are 36 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Geomatic Engineering
Authors

Ali Utku Akar 0000-0001-5639-9987

Cevat İnal 0000-0001-8980-2074

Publication Date July 18, 2022
Submission Date March 15, 2022
Acceptance Date April 7, 2022
Published in Issue Year 2022

Cite

APA Akar, A. U., & İnal, C. (2022). Farklı regresyon modelleriyle kestirilen zenit troposferik gecikmelerin değerlendirilmesi. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 11(3), 661-671. https://doi.org/10.28948/ngumuh.1088375
AMA Akar AU, İnal C. Farklı regresyon modelleriyle kestirilen zenit troposferik gecikmelerin değerlendirilmesi. NÖHÜ Müh. Bilim. Derg. July 2022;11(3):661-671. doi:10.28948/ngumuh.1088375
Chicago Akar, Ali Utku, and Cevat İnal. “Farklı Regresyon Modelleriyle Kestirilen Zenit Troposferik Gecikmelerin değerlendirilmesi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 11, no. 3 (July 2022): 661-71. https://doi.org/10.28948/ngumuh.1088375.
EndNote Akar AU, İnal C (July 1, 2022) Farklı regresyon modelleriyle kestirilen zenit troposferik gecikmelerin değerlendirilmesi. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 11 3 661–671.
IEEE A. U. Akar and C. İnal, “Farklı regresyon modelleriyle kestirilen zenit troposferik gecikmelerin değerlendirilmesi”, NÖHÜ Müh. Bilim. Derg., vol. 11, no. 3, pp. 661–671, 2022, doi: 10.28948/ngumuh.1088375.
ISNAD Akar, Ali Utku - İnal, Cevat. “Farklı Regresyon Modelleriyle Kestirilen Zenit Troposferik Gecikmelerin değerlendirilmesi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 11/3 (July 2022), 661-671. https://doi.org/10.28948/ngumuh.1088375.
JAMA Akar AU, İnal C. Farklı regresyon modelleriyle kestirilen zenit troposferik gecikmelerin değerlendirilmesi. NÖHÜ Müh. Bilim. Derg. 2022;11:661–671.
MLA Akar, Ali Utku and Cevat İnal. “Farklı Regresyon Modelleriyle Kestirilen Zenit Troposferik Gecikmelerin değerlendirilmesi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, vol. 11, no. 3, 2022, pp. 661-7, doi:10.28948/ngumuh.1088375.
Vancouver Akar AU, İnal C. Farklı regresyon modelleriyle kestirilen zenit troposferik gecikmelerin değerlendirilmesi. NÖHÜ Müh. Bilim. Derg. 2022;11(3):661-7.

download