Application of Principal Component Analysis (PCA) in Fuzzy Inference System (FIS) for Time-Series Modeling of Ionosphere

Document Type : Research Article


Assistant Professor, Department of Geoscience Engineering, Faculty of surveying, Arak University of Technology, Arak, Iran


The ionosphere is a layer of Earth's atmosphere extending from an altitude of 100 to more than 1000 km. Typically total electron content (TEC) is used to study the behavior and properties of the ionosphere. In fact, TEC is the total number of free electrons in the path between the satellite and the receiver. TEC varies greatly with time and space. TEC temporal frequencies can be considered on a daily, monthly, seasonal and annual basis. Understanding these variations is crucial in space science, satellite systems and positioning. Therefore, ionosphere time series modeling is very important. It requires a lot of observations to model the ionosphere temporal frequencies. As a result, it requires a model with high speed and accuracy. In this paper, a new method is presented for modeling the ionosphere time series. The principal component analysis (PCA) method is combined with the fuzzy inference system (FIS) and then, the ionosphere time series are modeled. The advantage of this combination is to increase the computational speed, reduce the convergence time to the optimal solution as well as increase the accuracy of the results. With the proposed model, the ionosphere can be analyzed at shorter time resolutions.
Principal component analysisis a statistical procedure that uses anorthogonal transformationto convert a set of observations of possibly correlated variables into a set of values oflinearly uncorrelatedvariables calledprincipal components.This transformation is defined in such a way that the first principal component has the largest possiblevariance, and each succeeding component in turn has the highest variance possible under the constraint that it isorthogonalto the preceding components. The resulting vectors are an uncorrelated orthogonal basis set. PCA is sensitive to the relative scaling of the original variables. Fuzzy inference systems (FIS) take inputs and process them based on the pre-specified rules to produce the outputs. Both the inputs and outputs are real-valued, whereas the internal processing is based on fuzzy rules and fuzzy arithmetic. FIS is the key unit of a fuzzy logic system having decision making as its primary work. It uses the “IF…THEN” rules along with connectors “OR” or “AND” for drawing essential decision rules.
To evaluate the proposed method of this paper, observations of Tehran's GNSS station, in 2016 have been used. This station is one of the International GNSS Service (IGS) in Iran. Therefore, its observations are easily accessible and evaluated. The statistical indices dVTEC = |VTECGPS-VTECmodel|, correlation coefficient and root mean square error (RMSE) are used to evaluate the new method. The statistical evaluations made on the dVTEC show that for the PCA-FIS combination model, this index has a lower numerical value than the FIS model without PCA as well as the global ionosphere map (GIM-TEC) and NeQuick empirical ionosphere model. The correlation coefficients are obtained 0.890, 0.704 and 0.697 for PCA-FIS, GIM and NeQuick models with respect to the GPS-TEC as a reference observation. Using the combination of PCA and FIS, the convergence speed to an optimal solution decreased from 205 to 159 seconds. Also, the RMSE of training and testing steps have also been significantly reduced. Northern, eastern, and height component analysis in precise point positioning (PPP) also show higher accuracy of the proposed model than the GIM and NeQuick model. The results of this paper show that the PCA-FIS method is a new method with precision, accuracy and high speed for time series modeling of TEC variations.


Main Subjects

Amerian, Y., Hossainali, M., Voosoghi, B. and Ghaffari Razin, M. R., 2010, Tomographic Reconstruction of the Ionospheric Électron Density in term of Wavelets. International Journal of Aerospace science and Technologie.
Austen, J.R., Franke, S.J. and Liu, C.H., 1988, Ionospheric imaging using computerized tomography. Radio Science, 23(3), 299-307.
Andreeva, E.S., Galinov, A.V., Kunitsyn, V.E., Mel’nichenko, Y.A., Tereshchenko, E.D., Filimonov, M.A. and Chernykov, S.M, 1990, Radio tomographic reconstructions of ionization dip in the plasma near the Earth. Journal of Experimental and Theoretical Physics Letter 52, 145–148.
Ansari, K., Panda, S. K., Althuwaynee, O. F. and Corumluoglu, O., 2017, Ionospheric TEC from the Turkish Permanent GNSS Network (TPGN) and comparison with ARMA and IRI models. Astrophys Space Sci., 362:178.
Amerian, Y., Voosoghi, B. and Hossainali, M.M., 2013a, regional ionosphere modeling in support of IRI and wavelet using GPS observations. Acta Geophysica, 61(5), 1246-1261.
Amerian, Y., Voosoghi, B. and Hossainali, M.M., 2013b, Regional improvement of IRI extracted ionospheric electron density by compactly supported base functions using GPS observations. Journal of Atmospheric and Solar-Terrestrial Physics 92 (2013) 23–30.
Abdi, N., Ardalan A.A. and Karimi, R. 2019, Rapid local ionosphere modeling based on Precise Point Positioning over Iran: A case study under 2014 solar maximum. Advances in Space Research. 2019, (63):937–949.
Akhoondzadeh, M., 2014, Investigation of GPS-TEC measurements using ANN method indicating seismo-273 ionospheric anomalies around the time of the Chile (Mw = 8.2) earthquake of 01 April 2014. Advance in space research., 54(9), 1768-1772.
Alken, P., Maute, A., Richmond, A. D., Vanhami , K. and Egbert, G. D., 2017, An application of principal component analysis to the interpretation of ionospheric current systems. J. Geophys. Res. Space Physics, 122, 5687–5708, doi:10.1002/2017JA024051.
Etemadfard, H. and Hossainali, M.M., 2016, Application of Slepian Theory for Improving the Accuracy of Global Ionosphere Models in the Arctic Region. J. Geophys. Res. Space Physics., 121(3), 2583-2594.
Feizi, R., Voosoghi, B. and Ghaffari Razin, M. R., 2019, Evaluation of the Efficiency of the Adaptive Neuro Fuzzy Inference System (ANFIS) in the Modeling of the Ionosphere Total Electron Content Time Series Case Study: Tehran Permanent GPS Station. JGST., 8 (4), 109-119.
Feizi, R., Voosoghi, B. and Ghaffari Razin, M.R, 2020, Regional modeling of the ionosphere using adaptive neuro-fuzzy inference system in Iran. Advances in space research.
Gao, Y., Liao, Z. and Liu, Z., 2002, Ionosphere Modeling Using Carrier Smoothed Ionosphere Observations from a Regional GPS Network. Geomatica, 56(2), 97-106.
Ghaffari Razin, M.R., Voosoghi, B. and Mohammadzadeh, A., 2015, Efficiency of artificial neural networks in map of total electron content over Iran. Acta Geod Geophys, DOI 10.1007/s40328-015-0143-3.
Ghaffari Razin, M.R. and Voosoghi, B., 2016, Wavelet neural networks using particle swarm optimization training in modeling regional ionospheric total electron content, Journal of Atmospheric and Solar–Terrestrial Physics, 149(2016), 21–30
Hirooka, S., Hattori, K. and Takeda, T., 2011, Numerical validations of neural-network-based ionospheric tomography for disturbed ionospheric conditions and sparse data, Radio Sci., 46, RS0F05, doi: 10.1029/2011RS004760.
Habarulema, J.B., McKinnell, L.-A., Cilliers, P.J. and Opperman, B.D.L., 2009, Application of neural networks to South African GPS TEC modelling. Adv. Space Res., 43(11), 1711–1720. doi:10.1016/j.asr.2008.08.020, 2009.
Komjathy, A. and Langley, R. B., 1996, An Assessment of Predicted and Measured Ionospheric Total Electron Content Using a Regional GPS Network. Proceedings of the National Technical Meeting of the Institute of Navigation, pp. 615-624.
Liu, Z. and Gao, Y., 2003, Ionospheric TEC predictions over a local area GPS reference network. GPS Solutions., 8(1), 23–29.
Liu, Z., 2004, Ionospheric Tomographic Modeling, UCGE Reports, Number 20198, University of CALGARY.
Lin, J.-W., 2012, Nonlinear principal component analysis in the detection of ionospheric electron content anomalies related to a deep earthquake (>300 km, M 7.0) on 1 January 2012, Izu Islands, Japan, J. Geophys. Res., 117, A06314, doi:10.1029/2012JA017614.
Mallika, I., Ratnam, D., Sivavaraprasad, G. and Raman, S., 2018, Implementation of Hybrid Ionospheric TEC Forecasting Algorithm Using PCA-NN Method. IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING.
Mars, P., Chen, J.R. and Nambiar, R., 1996, Learning Algorithms: Theory and Applications in Signal Processing, Control and Communications, CRC Press, Boca Raton, Florida, 1996.
Natali, M.P. and Meza, A., 2017, PCA and vTEC climatology at midnight over mid-latitude regions. Earth Planets Space 69, 168 (2017) doi:10.1186/s40623-017-0757-5
Rodrigo, F. Leandro., 2007, A New Technique to TEC Regional Modeling using a Neural Network. Geodetic Research Laboratory, Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, Canada.
Seeber, G., 2003, Satellite Geodesy, Foundations, Methods and Application, Walter de Gruyter, Berlin and New York, 531.
Sharifi, M.A. and Farzaneh, S., 2015, Regional TEC dynamic modeling based on Slepian functions. Advances in Space Research, 56(5):907-915.
Sharifi, M.A. and Farzaneh, S., 2014, The spatio-spectral localization approach to modeling VTEC over the western part of the USA using GPS observations. Advances in Space Research, 54 (6), 908-916.
Sabzehee, F., Farzaneh, S., Sharifi, M.A. and Akhoondzadeh, M., 2018, TEC Regional Modeling and prediction using ANN method and single frequency receiver over IRAN. ANNALS OF GEOPHYSICS. 2018; 61(1).
Talaat, E. R. and Zhu, X., 2016, Spatial and temporal variation of total electron content as revealed by principal component analysis. Annales Geophysicae, 34(12).
Takagi, T. and Sugeno, M., 1985, Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man and Cybernetics, 15(1), 116-132.