## 1 Introduction  
The global positioning system (GPS), which was initially limited to military or surveying fields, has gradually been extended to ordinary industrial fields such as navigation and time synchronization. The types of GPS receivers are determined based on the performance required in each field, the price of the system, and the size of the market. For example, in the field of land surveying or bridge monitoring where high accuracy is required, high-end GPS receivers that support multi-frequency signals are used, including L1, which is the primary frequency, and L2 (1227.60 MHz), which is the secondary frequency. These receivers are used to estimate the ionospheric errors and are capable of receiving pseudorange and carrier-phase measurements. In the field of safety-of-life (SoL) service for aviation or maritime, GPS receivers that are capable of receiving L1 pseudorange and carrier-phase measurements are used. In the field of location-based service (LBS) or road systems, low-cost GPSreceivers that support the L1 single-frequency signal are used, the accuracy of which is approximately 5 m. As the price of the low-cost GPS chipsets has fallen below US one dollar and smartphones have become increasingly popular, the applications of global navigation satellite system (GNSS), such as car navigation, geo-tagging, and LBS, are likely to increase dramatically [1]. As the low-cost L1 single-frequency GPS receivers dominate most of the GPS market [2], there is a strong interest in enhancing their accuracy. Many types of augmentation systems have been developed for low-cost GPS receivers. Among them, the differential global positioning system (DGPS) is the most representative augmentation system. DGPS services have been established worldwide. They can be divided into so-called local-area DGPS (LADGPS) services for small areas, such as a country, and wide-area DGPS (WADGPS) services for larger areas such as an entire continent or even worldwide [3]. A single reference station (RS) in a LADGPS at a known location can estimate a range of error corrections for each GPS satellite in view. These error corrections are then broadcasted to users nearby an RS. By applying these corrections to the received signals, a user can typically improve the accuracy up to a range of 1-3 m [4]. However, as the distance between the user and the RS increases, the range decorrelation increases, thus reducing the accuracy. The positioning accuracy [3,4] reduces largely because of the spatial decorrelation such as ephemeris error and ionospheric and tropospheric delays. Furthermore, if a user moves away from the RS of the LADGPS while receiving the corrections, the error due to the spatial decorrelation cannot be ignored. In this case, it is possible to receive corrections from another RS that is getting closer while moving, but the discontinuity of the position can occur. To extend the service area using a few geosynchronous equatorial orbit (GEO) satellites and overcome the error due to the spatial decorrelation, the WADGPS has been proposed. This system is used to obtain a meter-level accuracy over a large region while using a fraction of the number of RSs. The general approach is to divide the total pseudorange error into its components and estimate the variation in each component over the entire region [5; 6; 7]. Hence, the accuracy does not depend on the proximity of the user to a single RS, such as that in the LADGPS [5]. However, the corrections regarding the ionospheric delay are broadcasted at maximum intervals of 300 s [8]. Although the intervals vary in different operating nations such as wide-area augmentation system (WAAS, USA), European geostationary navigation overlay service (EGNOS, Europe), and MTSAT satellite augmentation system (MSAS, Japan), the user needs to wait for a long time to receive all the corrections of the WADGPS.