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For precise position services, the real-time precise point positioning (PPP) is a promising technology. The real-time PPP performance is expected to be improved by multi-system combination. The performance of real-time multi-system PPP needs to be periodically investigated, with the increasing number of available satellites and the continuously improved quality of real-time precise products of satellite clocks and orbits. In this study, a comprehensive performance assessment is conducted for the four-system integrated real-time PPP (FSIRT-PPP) with GPS, BDS, Galileo and GLONASS in both static and kinematic modes. The datasets from 118 stations spanning approximately a month are used for analysis, and the real-time stream CLK93 is employed. The superior performance of FSIRT-PPP is validated by comparing with the results of GPS/BDS, GPS/Galileo, GPS/GLONASS, GPS-only, BDS-only, Galileo-only and GLONASS-only cases. The FSIRT-PPP using ionospheric-free (IF) combined observables can achieve a convergence time of 10.9, 4.8 and 11.8 min and a positioning accuracy of 0.4, 0.5 and 0.7 cm in the static mode in the east, north and up directions, respectively, while the derived statistic is 15.4, 7.0 and 16.4 min, and 1.6, 1.2 and 3.4 cm in the kinematic mode in the three directions, respectively. Moreover, we also compare the position solutions of real-time PPP adopting IF combined and uncombined (UC) observables, and prove the mathematical equivalence between the two PPP models in the converged stage, provided that there are no external ionospheric corrections or constraints given to the estimated ionospheric delays in the UC model. The difference between the fully converged positioning accuracy of IF-based and UC-based real-time PPP is marginal, but the UC-based real-time PPP has longer convergence time due to the influence of the significant unmodeled time-varying errors in the real-time precise products as well as the different parameterization between them. For completeness, the real-time kinematic PPP results in harsh environments and the post-processed PPP results are also presented.

The proper handling of code biases is essential for realizing precise ionospheric modeling, positioning and timing. It is common to treat code biases in a differential mode as a differential code bias (DCB). With the modernization of GPS and GLONASS and the implementation of Galileo and BDS, the traditional DCB calibrations are complex and not easily extendable to different frequencies and modulations. An alternative treatment of code biases is to use observable-specific signal biases (OSBs). In this contribution, all possible OSBs are estimated for the latest GNSS and analyzed from the perspectives of precision, consistency and stability. The precisions of the GPS and Galileo OSBs are significantly better than those of the GLONASS and BDS OSBs. Considering the inter-frequency bias (IFB) of GLONASS and the inter-system bias (ISB) of BDS can improve the precisions of their OSB estimates. OSB comparisons among different agencies reveal that GPS and Galileo show good agreement at the level of 0.2–0.3 ns, while the differences of the GLONASS and BDS OSBs reach 0.5–1.0 ns. In addition, agreement of 0.4–0.5 ns is demonstrated for IGSO and MEO OSBs, while the consistency of GEO OSBs is worse by a factor of 2–3. The stability of the OSB estimates is at the level of 0.03–0.09 ns for GPS, 0.10–0.25 ns for Galileo, 0.14–0.48 ns for GLONASS, and 0.16–0.44 ns for BDS. In general, the BDS-3 OSB estimates show better stability than the BDS-2 OSBs. Moreover, the code biases at the same or at a close central frequency show similar performance. This is particularly obvious for Galileo and BDS, which adopt the dual-frequency constant envelope multiplexing (DCEM) technique. For instance, the code bias estimates of C5Q, C5X, C7Q, and C8Q are close to each other for individual Galileo satellites, and the BDS code biases of C5P, C7Z, and C8X are comparable to each other.

Low-orbit satellites have the advantages of rapid observation geometric changes and strong reception signals. The LEOs play a significant role in accelerating the convergence speed of precise point positioning, and help to provide high-precision positioning services indoors or in areas with severe signal obstruction. However, due to the constraint of the orbit height of low orbit satellites, a larger number of satellites are needed to achieve global coverage compared with medium and high orbit satellites. This paper proposes a LEO constellation design method based on dual-objective optimization, which uses fewer satellites to achieve global coverage. The PPP performance under different boundary conditions is analyzed through simulation. The method proposed in this paper can be widely used in the design of LEO satellite navigation augmentation system, and the research results provide reference and support for the corresponding system demonstration and analysis.

A low earth orbit (LEO) constellation can support broadband Internet access and can also be a platform for navigation augmentation for global navigation satellite systems. LEO satellites have the potential to transmit very strong navigation signals; they also show rapid changes in spatial geometry as they come closer to earth and travel faster over stations than satellites in medium or high orbits do. Before the establishment of a LEO-based navigation augmentation system, constellation design is a critical task. Previous LEO constellations have usually employed single polar or near-polar orbits for global coverage, resulting in fewer visible satellites at low latitudes. We propose and optimize several hybrid LEO-augmented constellations using a genetic algorithm to realize globally even coverage. When there are 100 LEO satellites, the average numbers of visible satellites during a regression period are 5.49, 5.44 and 5.47, with standard deviations of 0.44, 0.18 and 0.28, for the optimized hybrid polar-orbit/Walker, orthogonal circular-orbit/Walker and Walker/Walker constellations, respectively. For the hybrid orthogonal circular-orbit/Walker constellation type, the necessary numbers of LEO satellites to realize globally even coverage with six visible satellites are 109, 172 and 221 for elevation mask angles of 7°, 15° and 20°, respectively. For coverages with four and five visible satellites with an elevation mask angle of 7°, the required numbers of satellites are 90 and 93, respectively. All proposed hybrid constellations can provide 100% global coverage availability with one to three visible satellites for broadband Internet access.

The School of Geodesy and Geomatics (SGG) at Wuhan University has been generating GPS fractional cycle bias (FCB) products for users to realize ambiguity-fixed precise point positioning (PPP) since 2015. Along with the development of multiple Global Navigation Satellite Systems (GNSS), there is an urgent need to provide multi-GNSS FCB products for the PPP ambiguity resolution (AR) with multi-constellation observations. This study focuses on the multi-GNSS FCB estimation, in which the FCB products of GPS, Galileo, BDS and QZSS are generated. We describe here the detailed estimation method and the significant improvements to the new service. The FCB quality, as well as the PPP AR performance, is evaluated. The mean standard deviations of wide-lane FCBs relative to CODE are 0.019, 0.005, 0.015 and 0.008 cycles, while those of narrow-lane are 0.021, 0.021, 0.057 and 0.010 cycles for GPS, Galileo, BDS and QZSS, respectively. The comparison with CNES GPS and Galileo FCBs indicates their good consistency with the corresponding FCBs. Compared with GPS-only PPP AR, the convergence time and time to first fix of the four-system PPP AR can be reduced by 27.3 and 29.4% in the static mode, respectively, while the corresponding improvements are 42.6 and 51.9% in the kinematic mode, respectively. These results demonstrate that our SGG FCB service can provide high-precision and reliable four-system FCB corrections for worldwide users to conduct ambiguity-fixed PPP processing.

The fusion of low earth orbit (LEO) constellation and Global Navigation Satellite Systems (GNSS) can increase the number of visible satellites and optimize spatial geometry, which is expected to improve the performance of precise point positioning (PPP) ambiguity resolution (AR). In addition, the multi-frequency signals of LEO satellites can bring a variety of observation combinations, which is potential to further improve the efficiency of PPP AR. In this contribution, multi-frequency PPP AR was achieved with the augmentation of different LEO constellations. Three types of LEO constellations were designed with 60, 192, and 288 satellites. Moreover, the corresponding observation data were simulated with the GNSS observations over the ground stations. The LEO constellations were designed to transmit navigation signals on three frequencies: L1, L2, and L5 at 1575.42, 1227.6, and 1176.45 MHz, respectively, which are consistent with the GPS signals. For PPP AR, the uncalibrated phase delay (UPD) products of GNSS and LEO were estimated first. Furthermore, the quality of UPD products was also analyzed. The research findings show that the performance of estimated LEO UPD is comparable to that of GNSS UPD. Based on the UPD products, LEO-augmented multi-GNSS PPP AR can be achieved. Numerous results show that the performance of single-system and multi-GNSS PPP AR can be significantly improved by introducing the LEO constellations. The augmentation performance is more remarkable in the case of increasing LEO satellites. The time to first fix (TTFF) of the GREC fixed solution can be shortened from 7.1 to 4.8, 1.1, and 0.7 min, by introducing observations of 60-, 192-, and 288-LEO constellations, respectively. The positioning accuracy of multi-GNSS fixed solutions is also improved by about 60%, 80%, and 90% with the augmentation of 60-, 192-, and 288-LEO constellations, respectively. Compared to the dual-frequency solutions, the triple-frequency LEO-augmented PPP fixed solution presents a better performance. The TTFF of GREC fixed solutions is shortened to 33 s with the augmentation of 288-LEO constellation under the triple-frequency environment. It is worth indicating that the 288-satellite LEO-only PPP AR was conducted in dual-frequency and triple-frequency modes, respectively. The averaged TTFFs of both modes are 71.8 s and 55.2 s, respectively. It indicates that LEO constellation with 288 satellites is capable of achieving high-precision positioning independently and shows an even better performance than GNSS-only solutions.

The BDS-3 basic system has already been established, starting to provide global service. As a new generation navigation system, the BDS-3 adopts a global ionospheric model, called BDGIM. Single-frequency users can use the BDGIM along with nine ionospheric parameters broadcasted in the navigation message to perform ionospheric correction. This paper analyzes the deficiency of the current BDS and GPS Klobuchar models, and then by using the high precision CODE’s global ionospheric map (GIM) as a reference, the precision of BDGIM model is evaluated. Finally, the performance of applying this model to the positioning is verified by experimental data. The results show that the global accuracy of the BDGIM model is about 3.6 TECU, which is better than that of the Klobuchar model and more uniform on a global scale. In terms of the BDS standard point positioning, ionospheric correction with the BDGIM model obtains higher accuracy compared to that with the Klobuchar model, especially in the vertical direction.

Global navigation satellite system (GNSS) orbits are traditionally determined by observation data of ground stations, which usually need even global distribution to ensure adequate observation geometry strength. However, good tracking geometry cannot be achieved for all GNSS satellites due to many factors, such as limited ground stations and special stationary characteristics for the geostationary Earth orbit (GEO) satellites in the BeiDou constellation. Fortunately, the onboard observations from low earth orbiters (LEO) can be an important supplement to overcome the weakness in tracking geometry. In this contribution, we perform large LEO constellation-augmented multi-GNSS precise orbit determination (POD) based on simulated GNSS observations. Six LEO constellations with different satellites numbers, orbit types, and altitudes, as well as global and regional ground networks, are designed to assess the influence of different tracking configurations on the integrated POD. Then, onboard and ground-based GNSS observations are simulated, without regard to the observations between LEO satellites and ground stations. The results show that compared with ground-based POD, a remarkable accuracy improvement of over 70% can be observed for all GNSS satellites when the entire LEO constellation is introduced. Particularly, BDS GEO satellites can obtain centimeter-level orbits, with the largest accuracy improvement being 98%. Compared with the 60-LEO and 66-LEO schemes, the 96-LEO scheme yields an improvement in orbit accuracy of about 1 cm for GEO satellites and 1 mm for other satellites because of the increase of LEO satellites, but leading to a steep rise in the computational time. In terms of the orbital types, the sun-synchronous-orbiting constellation can yield a better tracking geometry for GNSS satellites and a stronger augmentation than the polar-orbiting constellation. As for the LEO altitude, there are almost no large-orbit accuracy differences among the 600, 1000, and 1400 km schemes except for BDS GEO satellites. Furthermore, the GNSS orbit is found to have less dependence on ground stations when incorporating a large number of LEO. The orbit accuracy of the integrated POD with 8 global stations is almost comparable to the result of integrated POD with a denser global network of 65 stations. In addition, we also present an analysis concerning the integrated POD with a partial LEO constellation. The result demonstrates that introducing part of a LEO constellation can be an effective way to balance the conflict between the orbit accuracy and computational efficiency.

It is widely known that in real-time kinematic (RTK) solution, the convergence and ambiguity-fixed speeds are critical requirements to achieve centimeter-level positioning, especially in medium-to-long baselines. Recently, the current status of the global navigation satellite systems (GNSS) can be improved by employing low earth orbit (LEO) satellites. In this study, an initial assessment is applied for LEO constellations augmented GNSS RTK positioning, where four designed LEO constellations with different satellite numbers, as well as the nominal GPS constellation, are simulated and adopted for analysis. In terms of aforementioned constellations solutions, the statistical results of a 68.7-km baseline show that when introducing 60, 96, 192, and 288 polar-orbiting LEO constellations, the RTK convergence time can be shortened from 4.94 to 2.73, 1.47, 0.92, and 0.73 min, respectively. In addition, the average time to first fix (TTFF) can be decreased from 7.28 to 3.33, 2.38, 1.22, and 0.87 min, respectively. Meanwhile, further improvements could be satisfied in several elements such as corresponding fixing ratio, number of visible satellites, position dilution of precision (PDOP) and baseline solution precision. Furthermore, the performance of the combined GPS/LEO RTK is evaluated over various-length baselines, based on convergence time and TTFF. The research findings show that the medium-to-long baseline schemes confirm that LEO satellites do helpfully obtain faster convergence and fixing, especially in the case of long baselines, using large LEO constellations, subsequently, the average TTFF for long baselines has a substantial shortened about 90%, in other words from 12 to 2 min approximately by combining with the larger LEO constellation of 192 or 288 satellites. It is interesting to denote that similar improvements can be observed from the convergence time.