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

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 = |VTEC_GPS-VTEC_model|, 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.