Comparison of statistical Holt-Winter models for forecasting the ionospheric delay using GPS observations

Abstract

The ionosphere is a notable source of error that disrupts the accuracy of the global position system (GPS) signal to the ground by changing the speed and direction of the signal propagation and in the process causing a delay in the signal. Therefore, forecasting the ionospheric delay is very important to reduce the GPS positioning error. In this work, statistical Holt-Winter method was chosen due to its suitability in forecasting time series with repeated seasonal patterns. This involved the forecast of ionospheric delays covering the period from October 2009 to December 2010 using GPS Ionospheric Scintillation and TEC Monitor (GISTM) over Universiti Kebangsaan Malaysia (UKM) station, at geographic coordinate of 2.55 °N, 101.46 °E. The comparisons of Additive and Multiplicative Holt-Winter models were done in terms of month-to-month error measurement, the difference of the actual and forecasting delay and the monthly average of the forecast. The maximum difference between actual and forecasting delay was estimated to be about 2 m. The accuracy of each model resulted in 77-91% for Additive and 78-92% for the multiplicative model during the period from morning to noon, while during the afternoon to nighttime period, the accuracy resulted in 68-92% and 70-93% for Additive and Multiplicative models, respectively. These results showed that the accuracy of the Multiplicative model in forecasting the ionospheric delay is better than that of Additive model going by its small error values and higher accuracy.