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.

In recent years, the development of new constellations including Galileo, BeiDou Navigation Satellite System (BDS) and Quasi-Zenith Satellite System (QZSS) have undergone dramatic changes. Since January 2018, about 30 satellites of the new constellations have been launched and most of the new satellites have been included in the precise orbit and clock products provided by the Multi Global Navigation Satellite System (Multi-GNSS) Experiment (MGEX). Meanwhile, critical issues including antenna parameters, yaw-attitude models and solar radiation pressure models have been continuously refined for these new constellations and updated into precise MGEX orbit determination and precise clock estimation solutions. In this context, MGEX products since 2018 are herein assessed by orbit and clock comparisons among individual analysis centers (ACs), satellite laser ranging (SLR) validation and precise point positioning (PPP) solutions. Orbit comparisons showed 3D agreements of 3–5 cm for Galileo, 8–9 cm for BDS-2 inclined geosynchronous orbit (IGSO), 12–18 cm for BDS-2 medium earth orbit (MEO) satellites, 24 cm for BDS-3 MEO and 11–16 cm for QZSS IGSO satellites. SLR validations demonstrated an orbit accuracy of about 3–4 cm for Galileo and BDS-2 MEO, 5–6 cm for BDS-2 IGSO, 4–6 cm for BDS-3 MEO and 5–10 cm for QZSS IGSO satellites. Clock products from different ACs generally had a consistency of 0.1–0.3 ns for Galileo, 0.2–0.5 ns for BDS IGSO/MEO and 0.2–0.4 ns for QZSS satellites. The positioning errors of kinematic PPP in Galileo-only mode were about 17–19 mm in the north, 13–16 mm in the east and 74–81 mm in the up direction, respectively. As for BDS-only PPP, positioning accuracies of about 14, 14 and 49 mm could be achieved in kinematic mode with products from Wuhan University applied.

Traditional precise orbit determination (POD) for low Earth orbit (LEO) satellites relies on observations from ground stations and onboard receivers. Although the accuracy can reach centimeter level, there are still problems such as insufficient autonomous operation capability. The inter-satellite link (ISL) is a link used for communication between satellites and has a function of dual-way ranging. Numerous studies have shown that observational data using ISLs can be adopted for POD of navigation satellites. In this contribution, we mainly focus on LEO satellites POD with ISLs. First, we design LEO constellations with different numbers of satellites and ISL measurements, based on which the constellations are simulated. Then rough tests of POD using different link topologies are carried out. The results show that in the 60-LEO constellation the average 3-dimensional (3D) orbital errors are 0.112 m using “4-connected” link topology with constant 4 links per satellite and 0.069 m using “all-connected” link topology with theoretically maximum numbers of links. After that, we carry out refined POD experiments with several sets of satellite numbers and different observation accuracy. The results show the higher link ranging accuracy and the more numbers of links bring higher POD precision. POD with ISLs gets bad performance in the case of center of gravity reference when link ranging accuracy is poor and numbers of links are small. When the link accuracy is 40 cm, average 3D orbital errors of 60-LEO constellation are 0.358 m, which can only meet the demand of autonomous navigation. With the constraint of the right ascension of the ascending node (RAAN), POD using ISLs reaches an extremely high precision when adopting a spatial reference provided by navigation satellites. For 120-LEO constellation, the average 3D orbital errors are 0.010 m; for 192-LEO constellation, the errors are 0.006 m.

The precise point positioning-real-time kinematic (PPP-RTK) method, which could achieve instantaneous ambiguity resolution (AR) with the regional atmospheric corrections, has been recognized as a preferred alternative for emerging applications such as self-driving cars, unmanned aerial vehicles, and mobile robots. Nevertheless, the performance of PPP-RTK is limited by the distribution and interstation distance of regional networks. Presently, the rapid development of the low Earth orbit (LEO) constellation brings innovative opportunities for satellite navigation. The fusion of LEO and global navigation satellite system (GNSS), which brings significant improvement in satellite visibility and spatial geometry, is expected to further enhance the performance of PPP-RTK and finally provide a wide-area and high-precision positioning service. In this study, we propose a novel LEO-augmented PPP-RTK model that leverages massive LEO observations and atmospheric augmented information. The spatial–temporal characteristics of uncalibrated phase delays (UPDs) and network-derived atmospheric corrections for fast-moving LEO satellites are analyzed, and their effectiveness on rapid AR is demonstrated. The positioning performance is comprehensively investigated with multiscale regional networks. The results indicate that the positioning accuracy of the traditional PPP-RTK can be improved by 15%–27% and 20%–40% with the augmentation of 144-LEO and 360-LEO constellations, respectively. Moreover, by incorporating the 360-LEO constellation, the time required for the first fix can be reduced to less than 1 and 10 s for network spacings of 400 and 800 km, respectively, exhibiting a significant improvement of 88%–92% compared with the traditional PPP-RTK method. These findings demonstrate the potential of LEO-augmented PPP-RTK to provide rapid (even instantaneous) centimeter-accurate positioning for an unlimited number of users over a large coverage area.

As the first hybrid-constellation global navigation system, China’s BeiDou navigation satellite system (BDS) has been fully constructed since July 2020 and provides open services for worldwide users. Due to the natural sensitivity of satellite tracking techniques to geocenter motion, BDS has the capability to determine the geocenter coordinates (GCC). This study aims to improve the precision of geocenter coordinates derived from BDS. To that end, 3-year sets of daily geocenter coordinates have been determined with BDS observations. Different solar radiation pressure (SRP) models, including the empirical CODE orbit model (ECOM), the extended ECOM model (ECOM2), and the a priori box-wing along with the ECOM model (BW + ECOM), have been applied for the BDS geocenter estimation. We show that the BW + ECOM model is beneficial in recovering the geocenter motion. Compared to the ECOM, the BW + ECOM model appears to mitigate the draconitic signal of BDS, which reduces the annual amplitude of the GCC-Z by a factor of 2.9. On the other hand, the amplitude of the 3 cpy signal is also reduced by a factor of 2.9. Furthermore, we studied the impact of BDS constellation configuration on the geocenter estimation. The results indicate that the inclusion of IGSO satellites significantly mitigates the spurious signals in the spectra of the GCC-Z. The amplitudes of the annual signal and 3 cpy signal are reduced by (28%, 14%), (33%, 61%), and (31%, 9%) for ECOM, ECOM2, and BW + ECOM cases, respectively. Meanwhile, the amplitude of the 7-day signal related to the orbital period of MEO satellites is also reduced by 32–45%. Thus, the BW + ECOM model and the MEO+IGSO hybrid configuration are recommended for BDS to determine the geocenter coordinates. However, despite these improvements, a significant annual signal with an amplitude of 20.2 mm and a visible 3 cpy signal with an amplitude of 6.1 mm still exist when compared to the Satellite Laser Ranging (SLR) solution.