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Using Global Navigation Satellite Systems (GNSS) observation data for developing a high-precision ionospheric Total Electron Content (TEC) model is one of the essential subjects in ionospheric physics research and the application of satellite navigation correction. In this study, we integrate the Empirical Orthogonal Function (EOF) method with the TEC data provided by the Center for Orbit Determination in Europe (CODE), and observed by the dense GNSS receivers operated by the Crustal Movement Observation Network of China (CMONOC) to construct a regional ionospheric TEC model over China. The EOF analysis of CODE TEC in China from 1998 to 2010 shows that the first-order EOF component accounts for 90.3813% of the total variation of the ionospheric TEC in China. Meanwhile, the average value of CODE TEC is consistent with the spatial and temporal distribution characteristics of the first-order EOF base function, which mainly reflects the latitude and diurnal variations of TEC in China. The first-order coefficient after EOF decomposition shows an obvious 11-year period and semi-annual variations. The maximum amplitude of semi-annual variation mainly appears in March and October, which is closely associated with the variation in geographical longitude, the semi-annual change of the low-latitude electric field, and the ionospheric fountain effect. The second-order coefficient has an evident annual variation, the minimum amplitude mainly occurs in March, August, and September, and the amplitude values in the high solar activity years are more significant than those in the low solar activity years. The third-order coefficient mainly shows the characteristics of annual variation, and the fourth-order coefficient shows the noticeable semi-annual and annual variations. The third and fourth-order coefficients are both modulated by the solar activity index F10.7. The ionospheric TEC model in China, driven by CMONOC real-time GNSS observation data, can better reflect the latitude, local time and seasonal variation characteristics of ionospheric TEC over China. In particular, it can clearly show the spring and autumn asymmetry of ionospheric TEC in the low latitudes. The root mean square error of the absolute error between the model and the actual observation is mainly distributed around 2.45 TECU (1 TECU = 1016 electrons/m2). The values of the TEC model constructed in this study are closer to the actual observed values than those of the CODE TEC in China. [ABSTRACT FROM AUTHOR]

The precise point positioning service on B2b signal (PPP-B2b) is a real-time decimeter-level positioning service provided by the BeiDou-3 Global Navigation Satellite System (BDS-3). The service provides users with high-precision orbit and clock corrections through geostationary orbit (GEO) satellites, which means that the PPP-B2b service would be unusable if GEO satellites were blocked. In this study, the performance of PPP-B2b corrections and real-time positioning results during outages of the PPP-B2b service are comprehensively investigated. The results showed that PPP can achieve satisfactory accuracy during outages of the PPP-B2b service by extending the nominal validity of the received PPP-B2b corrections. After extending the PPP-B2b corrections for 10 min, for BDS-3 medium earth orbit (MEO) satellites, the mean root-mean-square error (RMSE) values of the extended orbit were 0.16 m, 0.26 m, and 0.23 m in the radial, along-, and cross-track directions, respectively. The accuracy of the BDS-3 inclined geostationary orbit (IGSO) satellites was slightly worse than that of the BDS-3 MEO satellites; for Global Positioning System (GPS) satellites, the mean RMSE values of the extended orbit were 0.11 m, 0.45 m, and 0.33 m in the radial, along-, and cross-track directions, respectively. In terms of the extended clock, the mean standard deviation (STD) reached 0.17 ns, 0.20 ns, and 0.22 ns after 10 min for the BDS-3 MEO, BDS-3 IGSO, and GPS satellites, respectively. The positioning performance maintained with the extended corrections during the PPP-B2b service outage was evaluated based on five stations in and around China. Our experiments showed that, as long as the interruption time does not exceed 10 min, the real-time positioning with extended PPP-B2b corrections can achieve a comparable accuracy with that obtained following PPP-B2b correction. [ABSTRACT FROM AUTHOR]

The advancements of Earth observations, remote sensing, communications and navigation augmentation based on low Earth orbit (LEO) platforms present strong requirements for accurate, real-time and autonomous navigation of LEO satellites. Precise onboard real-time orbit determination (RTOD) using the space-borne data of multiple global navigation satellite systems (multi-GNSS) becomes practicable along with the availability of multi-GNSS. We study the onboard RTOD algorithm and experiments by using America's Global Positioning System (GPS) and China's regional BeiDou Navigation Satellite System (BDS-2) space-borne data of the FengYun-3C satellite. A new pseudo-ambiguity parameter, which combines the constant phase ambiguity, the orbit and clock offset error of the GPS/BDS broadcast ephemeris in the line-of-sight (LOS), is defined and estimated in order to reduce the negative effect of the LOS error on onboard RTOD. The analyses on the variation of the LOS error in the GPS/BDS broadcast ephemeris indicate that the pseudo-ambiguity parameter could be modeled as a random walk, and the setting of the power spectral density in the random walk model decides whether the pseudo-ambiguity can be estimated reasonably and the LOS error could be reduced or not. For different types of GPS/BDS satellites, the LOS errors show different variation characteristics, so the power spectral density should be set separately and differently. A numerical search approach is presented in this paper to find the optimal setting of the power spectral density for each type of GPS/BDS satellite by a series of tests. Based on the optimal stochastic model, a 3-dimensional (3D) real-time orbit accuracy of 0.7–2.0 m for position and 0.7–1.7 mm/s for velocity could be achieved only with dual-frequency BDS measurements and the broadcast ephemeris, while a notably superior orbit accuracy of 0.3–0.5 m for position and 0.3–0.5 mm/s for velocity is achievable using dual-frequency GPS/BDS measurements, due to the absorption effect of the estimated pseudo-ambiguity on the LOS error of the GPS/BDS broadcast ephemeris. Compared to using GPS-alone data, the GPS/BDS fusion only marginally improves the onboard RTOD orbit accuracy by about 1–3 cm, but the inclusion of BDS satellites increases the number of the tracked GNSS satellites and thus speeds up the convergence of the filter. Furthermore, the GPS/BDS fusion could help suppress the local orbit errors, ensure the orbit accuracy and improve the reliability and availability of the onboard RTOD when fewer GPS satellites are tracked in some anomalous arcs. [ABSTRACT FROM AUTHOR]

Ionospheric total electron content (TEC) is important data for ionospheric morphology, and also an important parameter for ionospheric correction in Global Navigation Satellite System (GNSS) precise positioning, navigation, and radio science. In this study, we present a data assimilation model for regional ionosphere based on a local ensemble Kalman filter (LEnKF) with the International Reference Ionosphere 2016 (IRI-2016) model as the background, to assimilate ionospheric TEC observations from GNSS. To demonstrate the results, the TEC estimates from the Crustal Movement Observation Network of China (CMONOC), which is about 260 stations in China, are applied as observation. The assessments are performed against the TEC estimates from BeiDou Navigation Satellite System (BDS) geostationary earth orbit (GEO) and against the final products from the Center for Orbit Determination in Europe (CODE). The assimilation results are in good agreement with BDS GEO TEC and the CODE TEC on a quiet or disturbed day. The correlation coefficient after assimilation is increased by about 17% compared with that before assimilation, and the RMSE after assimilation is decreased by about 42% compared with that before assimilation. Furthermore, the assimilated method is also evaluated in the single-frequency precise point positioning (PPP). The experimental results indicate that the PPP/Assimilated method can improve the GNSS positioning accuracy more effectively in comparison to the PPP/CODE. These results reveal that the LEnKF method can be considered as a useful tool for ionospheric assimilation. [ABSTRACT FROM AUTHOR]

High-precision orbits of Low Earth Orbit (LEO) satellites are essential for many scientific applications, such as assessing the change in current global mean sea level, estimating the coefficients of gravity field, and so on. How to determinate the high-precision orbits for LEO satellites has gradually become an important research focus. HY2D is a new altimetry satellite of China, which is equipped with a Global Positioning System (GPS) and the third generations of the BeiDou Global Navigation Satellite System (BDS-3) in order to guarantee the reliability of orbital precision in radar altimetry mission. Therefore, this study adopts one month of spaceborne data to conduct the research of precise orbit determination (POD) for the HY2D satellite. Our analysis results are: (1) The standard deviation of residuals for the HY2D satellite based on spaceborne BDS and GPS data are 9.12 mm and 8.53 mm, respectively, and there are no significant systematic errors in these residuals. (2) The comparison results with Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS)-derived orbits indicate that the HY2D satellite, using spaceborne BDS and GPS data, can achieve the radial accuracy of 1.4~1.5 cm, and the mean three-dimensional (3D) accuracy are 5.3 cm and 4.3 cm, respectively, which can satisfy high-precision altimetry applications. (3) By means of satellite laser ranging (SLR), the accuracy of Global Navigation Satellite System (GNSS)-derived orbits of HY2D is approximately 3.3 cm, which reflects that the model strategies are reliable. [ABSTRACT FROM AUTHOR]

The characteristics and performance of satellite clocks are important to the positioning, navigation, and timing (PNT) services of Global Navigation Satellite System (GNSS) users. Although China's BeiDou-3 Navigation Satellite System (BDS-3) has been fully operational for more than one year, there is still a lack of comprehensive research on the onboard clocks of the entire BDS-3 constellation. In this study, the precise clock products of GeoForschungsZentrum (GFZ) from day-of-year (DOY) 1, 2021 to DOY 300, 2021 were used to analyze the characteristics and performance of BDS-3 onboard clocks from the following aspects: clock bias, frequency, drift rate, fitting residuals, periodicity, and frequency stability. Compared with BDS-2, the clock quality of BDS-3 satellites has been greatly improved, but there are still jumps in the clock offsets and frequency series of BDS-3 clocks. The drift rate of BDS-3 clocks varies within the range between − 2 × 10 − 18   and   2 × 10 − 18   s / s 2 . The daily model fitting residuals of passive hydrogen masers (PHM) on BDS-3 medium Earth orbit (MEO), inclined geosynchronous orbit (IGSO), and geostationary (GEO) satellites are 0.15, 0.28, and 0.46 ns, respectively. The overlapping Allan deviation (OADEV) of BDS-3 MEO clocks is 4 . 0   ×   10 − 14   s / s at a time interval of 1000 s. The PHMs on BDS-3 MEO satellites exhibit fewer periodic signals than those of Rb clocks. In addition, the precise clock offsets of the BDS-3 PHMs carried on the MEO, IGSO, and GEO satellites show different periodicities, which are similar to those of the corresponding types of BDS-2 satellites. [ABSTRACT FROM AUTHOR]

BeiDou Global Navigation Satellite System (BDS-3) provides a regional Precise Point Positioning (PPP) service, called PPP-B2b, for users in China and surrounding areas through B2b signal transmitted from its three geostationary earth orbit (GEO) satellites. The information broadcasted by the B2b signal include satellite orbit corrections, satellite clock offset corrections, and differential code bias (DCB) corrections of BDS-3 satellites. In this study, the accuracies of PPP-B2b corrections along with real-time PPP performance are comprehensively evaluated referenced to precise orbit and clock products from GFZ and the precise DCB products from CAS. The result indicates that the accuracy of the BDS-3 broadcast orbit is similar to that of the PPP-B2b real-time orbit. The PPP-B2b clock offset correction improved the satellite clock offset precision of the BDS-3 broadcast ephemeris. The Signal-in-Space Range Error (SISRE) of broadcast ephemeris and PPP-B2b are calculated, which are 0.536 and 1.24 m, respectively. The large SISRE value of PPP-B2b is caused by the satellite-specified systematic bias to IGS final products. The positioning performance evaluation of real-time PPP with B2b service is carried out and compared with the real-time product provided by Wuhan University (WHU) based on the eight IGS MGEX stations in China and surrounding countries. The positioning accuracy of static positioning mode with PPP-B2b service achieved centimeter-level accuracy in the selected station, and that of kinematic positioning mode achieved decimeter-level accuracy. The availability rate of PPP-B2b corrections in the surrounding area of China, however, degrades from 88.76% to 60.91% in the selected stations. The accuracy of the PPP solution using PPP-B2b correction is better than that of using WHU real-time product within China. The positioning performance of stations located at the boundary of the PPP-B2b service area, however, is affected by the number of PPP-B2b available satellites. The positioning accuracy in kinematic positioning mode is worse than that of using WHU real-time precise product. [ABSTRACT FROM AUTHOR]

On 31 July 2020, the Beidou global navigation satellite system (BDS-3) was officially announced as being commissioned. In addition to offering global positioning, navigation, and timing (PNT) services, BDS-3 also provides precise point positioning (PPP) augmentation services. The satellite orbit correction, clock correction and code bias correction of BDS-3 and other global navigation satellite systems (GNSS) are broadcast by the BDS-3 geostationary earth orbit (GEO) satellites through the PPP-B2b signal. The PPP-B2b service is available for users in China and the surrounding area. In this study, an initial assessment of the PPP-B2b service is presented, with collected 3-day PPP-B2b messages. Based on broadcast ephemeris and PPP-B2b messages, the precise satellite orbits and clock offsets can be recovered. This precision is evaluated with the precise ephemeris from the GeoForschungsZentrum Potsdam (GFZ) analysis center as references. The results indicate that the accuracy of BDS-3 satellite orbits in the direction of radial, along-track, and cross-track is 0.138, 0.131, and 0.145 m, respectively, and for GPS a corresponding accuracy of 0.104, 0.160, and 0.134 m, respectively, could be obtained. The precision of clock offsets can reach a level of several centimeters for both GPS and BDS-3. Both the performance of static PPP and kinematic PPP are evaluated using the observations from four international GNSS monitoring assessment service (iGMAS) stations. Regarding static PPP, the average convergence time is 17.7 min to achieve a horizontal positioning accuracy of better than 0.3 m, and a vertical positioning accuracy of better than 0.6 m. The average positioning accuracy in the direction of east, north, and up-directions are 2.4, 1.6, and 2.3 cm. As to kinematic PPP, the average RMS values of positioning errors in the direction of east, north, and up are 8.1 cm, 3.6 cm, and 8.0 cm after full convergence. [ABSTRACT FROM AUTHOR]

Ionospheric delay is a crucial error source and determines the source of single-frequency precise point positioning (SF-PPP) accuracy. To meet the demands of real-time SF-PPP (RT-SF-PPP), several international global navigation satellite systems (GNSS) service (IGS) analysis centers provide real-time global ionospheric vertical total electron content (VTEC) products. However, the accuracy distribution of VTEC products is nonuniform. Proposing a refinement method is a convenient means to obtain a more accuracy and consistent VTEC product. In this study, we proposed a refinement method of a real-time ionospheric VTEC model for China and carried out experiments to validate the model effectiveness. First, based on the refinement method and the Centre National d'Études Spatiales (CNES) VTEC products, three refined real-time global ionospheric models (RRTGIMs) with one, three, and six stations in China were built via GNSS observations. Second, the slant total electron content (STEC) and Jason-3 VTEC were used as references to evaluate VTEC accuracy. Third, RT-SF-PPP was used to evaluate the accuracy in the positioning domain. Results showed that even if using only one station to refine the global ionospheric model, the refined model achieved a better performance than CNES and the Center for Orbit Determination in Europe (CODE). The refinement model with six stations was found to be the best of the three refinement models. [ABSTRACT FROM AUTHOR]

For single-frequency Global Navigation Satellite Systems (GNSSs) users, ionospheric delay is the main error source affecting the accuracy of positioning. Applying a broadcast ionospheric correction model to mitigate the ionospheric delay is essential for meter-to-decimeter-level accuracy positioning. To provide support for real-time single-frequency operations, particularly in the China area, we assessed the performance of three broadcast ionospheric correction models, namely, the Neustrelitz total electron content (TEC) broadcast model (NTCM-BC), the BeiDou global broadcast ionospheric delay correction model (BDGIM), and the Klobuchar model. In this study, the broadcast coefficients of Klobuchar and BDGIM are obtained from the navigation data files directly. Two sets of coefficients of NTCM-BC for China and global areas are estimated. The slant total electron contents (STEC) data from more than 80 validation stations and the final vertical TEC (VTEC) data of the Center for Orbit Determination in Europe (CODE) are used as independent benchmarks for comparison. Compared to GPS STEC during the period of Day of Year (DOY) 101~199, 2019, the ionospheric correction ratio of NTCM-BC, BDGIM, and Klobuchar are 79.4%, 64.9%, and 57.7% in China, respectively. For the global area, the root-mean-square (RMS) errors of these three models are 3.67 TECU (1 TECU = 1016 electrons/m2), 5.48 TECU, and 8.92 TECU, respectively. Compared to CODE VTEC in the same period, NTCM-BC, BDGIM, and Klobuchar can correct 72.6%, 69.8%, and 61.7% of ionospheric delay, respectively. Hence, NTCM-BC is recommended for use as the broadcast ionospheric model for the new-generation BeiDou satellite navigation system (BDS) and its satellite-based augmentation system. [ABSTRACT FROM AUTHOR]