System identification: theory for the user
System identification: theory for the user
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Time series analysis of the vertical total electron content (VTEC) is carried out in order to model variations in these observations dependent on time and frequency for various station-satellite pairs. The data of global positioning system (GPS) from four stations are processed in order to obtain the VTEC. The experiment was conducted on two successive days, the 12th and 13th April 2006 (days of year, DOY, 102-103). The mean of the squares of correlation coefficients (R^2) between time and short-term VTEC is 0.81, which shows high linear correlation for the linear trend component analysis of the time series. For each VTEC observation arc, one significant frequency value is found using the peak-peaking (PP) method in the frequency domain for the periodical component analysis. The stochastic component is modeled with a second-order autoregressive [AR(2)] model. VTEC is recovered by 98% combining trend, periodical and stochastic components. In order to analyze the efficiency of these models for prediction, a 5 min ahead prediction is carried out resulting in a 0.19 mean root mean squared error (RMSE). Also, good results were obtained for 10, 15 and 20 min ahead predictions in some VTEC observation arcs.