Abstract
Although the Klobuchar model is widely used in single-frequency GPS receivers, it cannot effectively correct the ionospheric delay. The Klobuchar model sets the night ionospheric delay as a constant, i.e., it cannot reflect temporal changes at night. The observation data of seventeen International Global Navigation Satellite System Service (IGS) stations within and around China from 2011 provided by the IGS center are used in this study to calculate the Total Electron Content (TEC) values using the Klobuchar model and the dual-frequency model. The Holt–Winters exponential smoothing model is used to forecast the error of the 7th day between the Klobuchar model and the dual-frequency model by using the error of the former six days. The forecast results are used to develop the sophisticated Klobuchar model when no epochs are missing, considering that certain reasons may result in some of the observation data being missing and weaken the relationship between each epoch in practical applications. We study the applicability of the sophisticated Klobuchar model when observation data are missing. This study deletes observation data of some epochs randomly and then calculates TEC values using the Klobuchar model. A cubic spline curve is used to restore the missing TEC values calculated in the Klobuchar mode. Finally, we develop the sophisticated Klobuchar model when N epochs are missing in China. The sophisticated Klobuchar model is compared with the dual-frequency model. The experimental results reveal the following: (1) the sophisticated Klobuchar model can correct the ionospheric delay more significantly than the Klobuchar model; (2) the sophisticated Klobuchar model can reflect the ionosphere temporal evolution, particularly at night, with the correct results increasing with increasing latitude; and (3) the sophisticated Klobuchar model can achieve remarkable correction results when N epochs are missing, with the correct results being nearly as good as that of the dual-frequency model when no epochs are missing.
Highlights
Satellite signals passing through the ionosphere may be influenced by the ionosphere
For a single-frequency Global Positioning System (GPS) receiver, different types of models or algorithms can be used to correct the ionospheric delay. These models are applied to the receivers and can be classified as follows: (1) Broadcast Ionospheric Models (BIMs), which include the Klobuchar model (BKM) in GPS [5], the NeQuick model in Galileo [6], the BeiDou satellite navigation System (BDS) ionospheric model [7], and the ionospheric grids that are broadcast by the Satellite-Based Augmentation System (SBAS) [8]; (2) Empirical Ionospheric Models (EIMs), such as the International Reference Ionosphere (IRI) model [9] and the Parameterized Ionospheric Model (PIM) [10]; and (3) Global Ionospheric Maps (GIM) provided by each International Global Navigation Satellite System Service (IGS) analysis center [11]
In the low-latitude area (PIMO), the corrective rate of sophisticated Klobuchar model (SKM) with no epochs missing improved by nearly 30% over BKM, while the RMSE improved by nearly 3 TECu during the day
Summary
Satellite signals passing through the ionosphere may be influenced by the ionosphere. For a single-frequency GPS receiver, different types of models or algorithms can be used to correct the ionospheric delay These models are applied to the receivers and can be classified as follows: (1) Broadcast Ionospheric Models (BIMs), which include the Klobuchar model (BKM) in GPS [5], the NeQuick model in Galileo [6], the BeiDou satellite navigation System (BDS) ionospheric model [7], and the ionospheric grids that are broadcast by the Satellite-Based Augmentation System (SBAS) [8]; (2) Empirical Ionospheric Models (EIMs), such as the International Reference Ionosphere (IRI) model [9] and the Parameterized Ionospheric Model (PIM) [10]; and (3) Global Ionospheric Maps (GIM) provided by each International Global Navigation Satellite System Service (IGS) analysis center [11]. These models use observational data to establish a model to calculate the TEC all over the world
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