Ionospheric delay as the major error source needs to be properly handled in multi-GNSS (Global Navigation Satellite System) single-frequency positioning and the different ionospheric models exhibit apparent performance difference. In this study, two single-frequency positioning solutions with different ionospheric corrections are utilized to comprehensively analyze the ionospheric delay effects on multi-frequency and multi-constellation positioning performance, including standard point positioning (SPP) and ionosphere-constrained precise point positioning (PPP). The four ionospheric models studied are the GPS broadcast ionospheric model (GPS-Klo), the BDS (BeiDou Navigation Satellite System) broadcast ionospheric model (BDS-Klo), the BDS ionospheric grid model (BDS-Grid) and the Global Ionosphere Maps (GIM) model. Datasets are collected from 10 stations over one month in 2019. The solar remained calm and the ionosphere was stable during the test period. The experimental results show that for single-frequency SPP, the GIM model achieves the best accuracy, and the positioning accuracy of the BDS-Klo and BDS-Grid model is much better than the solution with GPS-Klo model in the N and U components. For the single-frequency PPP performance, the average convergence time of the ionosphere-constrained PPP is much reduced compared with the traditional PPP approach, where the improvements are of 11.2%, 11.9%, 21.3% and 39.6% in the GPS-Klo-, BDS-Klo-, BDS-Grid- and GIM-constrained GPS + GLONASS + BDS single-frequency PPP solutions, respectively. Furthermore, the positioning accuracy of the BDS-Grid- and GIM-constrained PPP is generally the same as the ionosphere-free combined single-frequency PPP. Through the combination of GPS, GLONASS and BDS, the positioning accuracy and convergence performance for all single-system single-frequency SPP/PPP solutions can be effectively improved.

The accuracy of the timing group delay (TGD) transmitted in the broadcast ephemeris is an important factor that affects the service performance of a GNSS system. In this contribution, an apparent bias is found by comparing the orbit and clock difference using half-year data of the BeiDou navigation satellite system (BDS) broadcast ephemeris and precise post-processed products. The bias differs at each satellite on each frequency and shows a general systematic difference between BDS-2 and BDS-3. We attribute this to the satellite-dependent TGD bias of the BDS broadcast ephemeris, which is subsequently calibrated. Moreover, to calibrate the bias independently, a network solution strategy is proposed based on 87 globally distributed multi-GNSS experiment (MGEX) stations spanning 25 weeks. The estimated bias shows good agreement with the values observed from the orbit and clock comparison. For the validation of the bias, we compared the signal-in-space range error (SISRE) performance with and without the TGD bias correction. The results show that the SISRE of the BDS improved from 0.71, 0.81, and 1.40 m to 0.64, 0.66, and 0.64 m in the B1I, B3I, and B1I/B3I frequencies. For BDS-3, the SISRE is well within 0.50 m after the bias correction. To further validate the bias, a week’s data were collected at 97 globally distributed MGEX stations. When the TGD bias is corrected, the root mean square (RMS) of single point positioning (SPP) can be improved by 5.6, 8.4, and 21.6% in the B1I, B3I, and B1I/B3I frequencies. Meanwhile, the SISRE and SPP assessment results also indicate that the TGD bias should be corrected by each satellite rather than only corrected between BDS-2 and BDS-3.

We proposed an extended geometry and probability model (EGAPM) to analyze the performance of various kinds of (Global Navigation Satellite System) GNSS+ constellation design scenarios in terms of satellite visibility and dilution of precision (DOP) et al. on global and regional scales. Different from conventional methods, requiring real or simulated satellite ephemerides, this new model only uses some basic parameters of one satellite constellation. Verified by the reference values derived from precise satellite ephemerides, the accuracy of visible satellite visibility estimation using EGAPM gets an accuracy better than 0.11 on average. Applying the EGAPM to evaluate the geometry distribution quality of the hybrid GNSS+ constellation, where highly eccentric orbits (HEO), quasi-zenith orbit (QZO), inclined geosynchronous orbit (IGSO), geostationary earth orbit (GEO), medium earth orbit (MEO), and also low earth orbit (LEO) satellites included, we analyze the overall performance quantities of different constellation configurations. Results show that QZO satellites perform slightly better in the Northern Hemisphere than IGSO satellites. HEO satellites can significantly improve constellation geometry distribution quality in the high latitude regions. With 5 HEO satellites included in the third-generation BeiDou navigation satellite system (BDS-3), the average VDOP (vertical DOP) of the 30° N–90° N region can be decreased by 16.65%, meanwhile satellite visibility can be increased by 38.76%. What is more, the inclusion of the polar LEO constellation can significantly improve GNSS service performance. When including with 288 LEO satellites, the overall DOPs (GDOP (geometric DOP), HDOP (horizontal DOP), PDOP (position DOP), TDOP (time DOP), and VDOP) are decreased by about 40%, and the satellite visibility can be increased by 183.99% relative to the Global Positioning System (GPS) constellation.