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.

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.

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.

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.

The satellite-induced systematic biases were identified to exist in the code observations from BeiDou navigation satellite system (BDS) satellites using multipath (MP) combinations. The current correction model for satellite-induced code bias (SICB) does not take into account the consistency of MP combinations, which limits the accuracy of the developed model. Both the cycle slips and different tracking of a satellite at different stations can affect the absolute values of MP combinations, although the variations remain unchanged. An improved SICB piecewise linear correction model as a function of elevations is proposed. We estimate the model parameters for each frequency and for each satellite. The single-difference of MP combinations in the domain of elevation angles is carried out to remove the unknown ambiguities and stable hardware delays so that the SICB modeling is free of the effects of MP combination inconsistency. In addition, a denser elevation node separation of 1°, rather than the 10° usually employed by the traditional model, is used to describe the more precise SICB variations. The SICB corrections show significant differences among orbit types and frequency bands. The SICB variations have much less effect on Inclined Geosynchronous Orbit (IGSO) satellites than on Medium Earth Orbit (MEO) satellites for the regional BDS (BDS-2). The B1 signal has the largest SICB corrections, which can be up to 0.9 m close to zenith for BDS-2 MEO satellites, and the B2 signal follows. After adding the SICB corrections to the code observations, the elevation-dependent code biases vanish, and we can obtain improved code observations. After applying the improved SICB correction model, the root mean square (RMS) values of MP combination time series are reduced by 7%, 6% and 2%, and 18%, 14% and 5% on the B1, B2 and B3 frequencies for the BDS-2 IGSO and MEO satellites, respectively. For comparison, we also establish the traditional SICB correction model. With the traditional SICB correction model, the corresponding RMS MP combinations are smaller than those of uncorrected MP series, but slightly larger than those of corrected MP series using the improved SICB correction model. To validate the effectiveness and correctness of our proposed model, single-frequency precise point positioning (PPP) processing with BDS-2 MEO and IGSO satellites is conducted. An accuracy improvement of 24%, 19% and 89%, and 7%, 7% and 6% for the single-frequency PPP applying the improved SICB corrections over the case without SICB corrections and the case using the traditional SICB corrections in east, north and vertical directions is achieved, respectively. Although only centimeter-level SICB variations could be observed for the two legacy signals B1 and B3 and the three new navigation signals B1C, B2a and B2b transmitted by the satellites of global BDS demonstration system (BDS-3S), we still establish an effective SICB correction model on the B1 and B3 frequencies for BDS-3S IGSO satellites, and the RMS MP combinations are reduced by 1–4% after applying the improved SICB corrections.

Global navigation satellite systems (GNSS) water vapor tomography is an important technique to obtain the three-dimensional distribution of atmospheric water vapor. The rapid development of low Earth orbit (LEO) constellations has led to a richer set of observations, which brings new expectations for water vapor tomography. This paper analyzes the influence of LEO constellation-augmented multi-GNSS(LCAMG)on the tomography, in terms of ray distribution, tomography accuracy, and horizontal resolution, by simulating LEO constellation data. The results show that after adding 288 LEO satellites to GNSS, the 30-min ray distribution effect of GNSS can be achieved in 10 min, which can effectively shorten the observation time by 66.7%. In the 10-min observation time, the non-repetitive effective observation value of LCAMG is 2.38 times that of GNSS, and the accuracy is 1.27% higher than that of GNSS. Compared with GNSS and the global positioning system (GPS), at a horizontal resolution of 13 × 14, the proportion of empty voxels in LCAMG reduces by 5.22% and 22.53%, respectively.