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Objectives：Establishing a regional ionospheric total electron content (TEC) model from a single station is much more efficient than developing a global multistation model because of its small amount of data. However, the single⁃station regional ionospheric TEC model has a scope of application. Therefore, the study of the scope and accuracy of a single⁃station regional ionospheric TEC model can effectively provide high⁃precision ionospheric delay correction for single⁃frequency users in the region. Methods：With 2⁃to 15⁃order spherical harmonic functions, single⁃station regional ionospheric TEC models are established using global navigation satellite systems (GNSS) observations from 16 stations in the European region during day of year (DOY) 357—363 in 2017, a period of calm solar activity and without a magnetic storm. The average ionospheric TEC values and average root mean square (RMS) values at all grid points in the longitude–latitude ranges of 0°×0°, 10°×5°, 10°×10°, 10°×15°, 20°×15°, and 20°×20° are compared with those of global ionospheric products such as Center for Orbit Determination in Europe (CODE), International GNSS Monitoring and Assessment System (iGMAS), and International GNSS Service (IGS) for the determination of the scope of application and accuracy of the single⁃station regional ionospheric TEC models. Results：(1) The 16 single⁃station regional ionospheric TEC models based on 2⁃to⁃15⁃order spherical harmonic functions have the average TEC values within the value range of CODE, iGMAS, and IGS in different regions. In other words, within the latitude⁃longitude range of 20°×20°, the TEC values of the single⁃station regional ionospheric models established by the proposed method are comparable to those of CODE, iGMAS, and IGS. (2) The RMS values of regional ionospheric TEC models established with the data of 16 single stations and 2⁃to⁃15⁃order spherical harmonic functions are different from those of IGS beyond the latitude⁃longitude range of 10°×10°. The lower order of spherical harmonic functions in the latitude⁃longitude range of 10°×10° corresponds to smaller RMS values of the models. The accuracy of the single⁃station regional ionospheric TEC models based on low⁃order (2×2 or 3×3) spherical harmonic functions is similar to that of IGS in the 10°×10° range centered on a single station, namely that the applicable radius of the single⁃station regional ionospheric TEC models is about 600 km and the accuracy is about 1 TECU. (3) The single⁃station regional ionospheric TEC models are highly consistent with the IGS global ionospheric TEC model, which indicates that the accuracy of the single⁃station regional ionospheric TEC models based on low⁃order (2×2 or 3×3) spherical harmonic functions is comparable to that of the IGS global ionospheric TEC model. Conclusions：The results show that the single⁃station regional ionospheric TEC models based on low⁃order (2×2 or 3×3) spherical harmonic functions has the comparable accuracy to that of global iono⁃ spheric products such as CODE, iGMAS, and IGS, which is about 1.0 TECU, within the latitude ⁃longitude range of 10°×10° (radius < 600 km) centered on a single station. Thus, the global ionospheric TEC model can be replaced by the ionospheric TEC model established with data of a single station in a certain region (radius less than 600 km), with which the high⁃precision ionospheric delay correction can be efficiently provided for single⁃frequency users in the region. [ABSTRACT FROM AUTHOR]

The basic construction of BeiDou global satellite navigation system (BDS) has played a key role in promoting the development of global navigation satellite system, which provides an important guarantee for multi⁃constellation fusion positioning, navigation and timing. Multi⁃system fusion positioning provides users with more navigation information, and also provides a better guarantee for the realization of navigation performance indicators. At present, in order to ensure integrity, it is necessary to warn users when navigation service is unavailable. Due to satellite failure, the protection level exceeds its alert limit. However, under the condition of multi⁃frequency and multi⁃constellation, the number of satellites is sufficient. After a few satellite faults are eliminated quickly, the influence on the overall navigation accuracy is very small and no alarm is needed. A protection level reconstruction method based on robust estimation is proposed. The protection level is reconstructed by using robust information and posterior variance. In order to verify the feasibility of the algorithm, the accuracy and protection limits required by localizer performance with vertical guidance 200ft (LPV⁃200) approach phase are selected as the standard of this paper, and the global positioning system (GPS)/BDS combination of dynamic and static data are used for calculation and analysis. The GPS adopts L1 pseudo range observation, and the BDS adopts B1 pseudo range observation. Each group of experiments is divided into two parts, fault detection and elimination and the method of adding abnormal error is calculated respectively, the vertical protection level is calculated by the protection level calculation method based on a posteriori variance and the protection level reconstruction method based on robust estimation. The results show that our proposed method can reduce the alarm frequency on the premise of ensuring the positioning accuracy. [ABSTRACT FROM AUTHOR]