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Currently, the Global Navigation Satellite System (GNSS) mainly uses the satellites in Medium Earth Orbit (MEO) to provide position, navigation, and timing (PNT) service. The weak navigation signals limit its usage in deep attenuation environments, and make it easy to interference and counterfeit by jammers or spoofers. Moreover, being far away to the Earth results in relatively slow motion of the satellites in the sky and geometric change, making long time needed for achieved centimeter positioning accuracy. By using the satellites in Lower Earth Orbit (LEO) as the navigation satellites, these disadvantages can be addressed. In this contribution, the advantages of navigation from LEO constellation has been investigated and analyzed theoretically. The space segment of global Chinese BeiDou Navigation Satellite System consisting of three GEO, three IGSO, and 24 MEO satellites has been simulated with a LEO constellation with 120 satellites in 10 orbit planes with inclination of 55 degrees in a nearly circular orbit (eccentricity about 0.000001) at an approximate altitude of 975 km. With simulated data, the performance of LEO constellation to augment the global Chinese BeiDou Navigation Satellite System (BeiDou-3) has been assessed, as one of the example to show the promising of using LEO as navigation system. The results demonstrate that the satellite visibility and position dilution of precision have been significantly improved, particularly in mid-latitude region of Asia-Pacific region, once the LEO data were combined with BeiDou-3 for navigation. Most importantly, the convergence time for Precise Point Positioning (PPP) can be shorted from about 30 min to 1 min, which is essential and promising for real-time PPP application. Considering there are a plenty of commercial LEO communication constellation with hundreds or thousands of satellites, navigation from LEO will be an economic and promising way to change the heavily relay on GNSS systems.

While few phase bias streams are available from the IGS Real-time Service Phase, such products are essential to enable PPP ambiguity resolution. Satellite phase biases and clocks should be estimated when fixing undifferenced ambiguities in a network solution, which is troublesome in real time and thus usually not done in practice. This study estimates real-time GPS/Galileo/BDS ambiguity-fixed multi-frequency raw phase biases from GNSS observation modeling. Multi-frequency narrow-lane and wide-lane uncalibrated phase delays (UPDs) are first extracted from the float ambiguities of the stations. Multi-frequency raw ambiguities are then resolved to form unambiguous carrier-range observations. Finally, the satellite phase observable-specific signal biases (phase OSBs) are estimated directly from the real-time network data processing using carrier-range observations only. The approach has been applied to generate real-time phase bias products at the Wuhan IGS analysis center. Real-time products are routinely calculated by 180 globally distributed stations. This study validates the approach and associated products using one week of data. The results show that triple-frequency kinematic PPP-AR based on the ambiguity-fixed phase OSBs can converge in 7.2 min on average, while those based on UPD products take 11.2 min to converge. The other software, PRIDE PPP-AR is used to validate the high-precision static positioning performance of the real-time OSB products. The results show that 82%, 85% and 76% of GPS, Galileo and BDS-3 narrow-lane ambiguities can be resolved successfully among global stations, achieving a mean positioning accuracy of 3.1, 3.0 and 6.0 mm for the east, north and up components.

Integer ambiguity resolution is the key for achieving the highest accuracy with Precise Point Positioning (PPP) and for significantly reducing the convergence time. Unfortunately, due to hardware phase biases originating from the satellites and receiver, fixing the phase ambiguities to their correct integer number is difficult in PPP. Nowadays, various institutions and analysis centers of the International GNSS Service (IGS) provide satellite products (orbits, clocks, biases) based on different strategies, which allow PPP with integer ambiguity resolution (PPP-AR) for GPS and Galileo. We present the theoretical background and practical application of the satellite products from CNES, CODE, SGG, and TUG. They are tested in combined GPS and Galileo PPP-AR solutions calculated using our in-house software raPPPid. The numerical results show that the choice of satellite product has an influence on the convergence time of the fixed solution. The satellite product of CODE performs better than the following, in the given order: SGGCODE, SGGGFZ, TUG, CNES, and SGGCNES. After the convergence period, a similar level of accuracy is achieved with all these products. With these satellite products and observations with an interval of 30 s, a mean convergence time of about 6 min to centimeter-level 2D positioning is achieved. Using high-rate observations and an observation interval of 1 s, this period can be reduced to a few minutes and, in the best case, just one minute.

With the advancement of multi-frequency and multi-constellation GNSS signals and the introduction of observable-specific bias (OSB) products, the uncombined precise point positioning (PPP) model has grown more prevalent. However, this model faces challenges due to the large number of estimated parameters, resulting in strong correlations between state parameters, such as clock errors, ionospheric delays, and hardware biases. This can slow down the convergence time and impede ambiguity resolution. We propose two methods to improve the triple-frequency uncombined PPP-AR model by integrating ambiguity constraints. The first approach makes use of the resolved ambiguities from dual-frequency ionosphere-free combined PPP-AR processing and incorporates them as constraints into triple-frequency uncombined PPP-AR processing. While this approach requires the implementation of two filters, increasing computational demands and thereby limiting its feasibility for real-time applications, it effectively reduces parameter correlations and facilitates ambiguity resolution in post-processing. The second approach incorporates fixed extra-wide-lane (EWL) and wide-lane (WL) ambiguities directly, allowing for rapid convergence, and is well suited for real-time processing. Results show that, compared to the uncombined PPP-AR model, integrating N1 and N2 constraints reduces averaged convergence time from 8.2 to 6.4 min horizontally and 13.9 to 10.7 min vertically in the float solution. On the other hand, integrating EWL and WL ambiguity constraints reduces the horizontal convergence to 5.9 min in the float solution and to 4.6 min for horizontal and 9.7 min for vertical convergence in the fixed solution. Both methods significantly enhance the ambiguity resolution in the uncombined triple-frequency PPP model, increasing the validated fixing rate from approximately 80% to 89%.

Ambiguity resolution (AR) is a core technology that helps to speed up convergence time and increase positioning accuracy for precise point positioning (PPP), and the performance of PPP-AR is based on the quality of ambiguity resolution products. Real-time PPP-AR becomes a reality as users can now obtain publicly accessible real-time observable-specific signal bias (OSB) products from the Centre National d’Etudes Spatiales (CNES). Therefore, an analysis of the quality of OSB products and an evaluation of the performance of PPP-AR are required to promote the application of real-time positioning. For a total of 31 days between day of year (DOY) 121 and 151 in 2021, observation data were collected from 90 stations, and the OSB products were used to assess the experiments. As for the quality of the OSB products, the data availability (DA) of the GPS and Galileo satellites was greater than 97%, whereas that of BDS was less than 60%; the maximum fluctuation value (MAX) and standard deviation (STD) of the GPS, Galileo, and BDS satellites were 0.045 and 0.012; 0.081 and 0.028; and 0.292 and 0.085 cycles, respectively. In terms of ambiguity residuals using the OSB products, the wide-lane (WL) residual percentages within ±0.25 cycles for the GPS, Galileo, BDS-2, and BDS-3 systems were more than 92%, and the narrow-lane (NL) residual percentages within ±0.25 cycles for the four systems were 92%, 89%, 79%, and 60%, respectively. With regard to the performance of PPP-AR, the GPS+Galileo solution showed the best performance in the kinematic positioning mode, in which the mean root mean square (RMS) of positioning accuracy was 1.06, 1.27, and 2.85 cm for the east (E), north (N), and up (U) components, respectively, and the mean convergence time reached 9.6 min. In the static positioning mode, the mean convergence times of the GPS-only and GPS+Galileo solutions were 11.4 min and 8.0 min, respectively, and both of their mean RMS for positioning accuracy reached 0.79, 0.95, and 1.48 cm for the E, N, and U components, respectively. However, the addition of BDS did not further enhance the performance of multi-GNSS PPP-AR in either the kinematic or static positioning mode due to the poor quality of the real-time BDS products. More importantly, a prediction method was proposed to avoid re-convergence and to enhance the reliability of PPP-AR in the event of short-time missing real-time OSB products and to improve the positioning accuracy and the ambiguity fixed rate.

Real-time Kinematic (RTK) positioning provides centimeter-level positioning accuracy within several seconds, but it has to rely on a nearby base station. Although Precise Point Positioning (PPP) supplies precise positions with one receiver, its convergence time takes several tens of minutes, which makes PPP not well suited for real-time kinematic applications where a rapid convergence is required. PPP-RTK integrates the benefits of PPP and RTK, which actually is PPP augmented by a ground GNSS network. The satellite orbit, clock offsets, signal biases, ionospheric and tropospheric corrections are determined based on this GNSS network, modeled as state space information and transmitted to PPP users. By applying these State Space Representation (SSR) corrections, a real-time kinematic PPP-RTK approach is developed and implemented, which can instantly resolve the ambiguities to integers and realize rapid convergence. In a static scenario, it realized an instant ambiguity resolution and a rapid convergence within 2 s in more than 90% of 120 hourly sessions. The PPP-RTK has been applied and evaluated in a kinematic scenario on the highway. The horizontal positioning errors are almost lower than 0.1 m except for the time of passing through bridges. After passing bridges, the PPP-RTK successfully resolved ambiguities within 2 s in 90.6% of the cases and achieved convergence in horizontal within 5 s in more than 90% of the cases. The PPP-RTK with a precision of 0.1 m and rapid convergence of several seconds benefits the precise navigation of automobile on the highway, which will support the development of autonomous driving in future.

The long convergence time required to achieve high-precision position solutions with integer ambiguity resolution-enabled precise point positioning (PPP-RTK) is driven by the presence of ionospheric delays. When precise real-time ionospheric information is available and properly applied, it can strengthen the underlying model and substantially reduce the time required to achieve centimeter-level accuracy. In this study, we present and analyze the real-time PPP-RTK user performance using ionospheric corrections from multi-scale regional networks during a day with medium ionospheric disturbance. It is the goal of this contribution to measure the impact the network dimension has on the ambiguity-resolved user position through the predicted ionospheric corrections. The user-specific undifferenced ionospheric corrections are computed at the network side, along with the satellite phase biases needed for single-receiver ambiguity resolution, using the best linear unbiased predictor. Such corrections necessitate the parameterization of an estimable user receiver code bias, on which emphasis is given in this study. To this end, we process GPS dual-frequency data from four four-station evenly distributed CORS networks in the United States with varying station spacings in order to evaluate if and to what extent the ionospheric corrections from multi-scale networks can improve the user convergence times. Based on a large number of samples, our experimental results showed that sub-10 cm horizontal accuracy can be achieved almost instantaneously in the ionosphere-weighted partially-ambiguity-fixed kinematic PPP-RTK solutions based on corrections from a network with 68 km spacing. Most of the solutions (90%) were shown to require less than 6.0 min, compared to the ionosphere-float PPP solutions that needed 68.5 min. In case of sparser networks with 115, 174 and 237 km spacing, 50% of the horizontal positioning errors are shown to become less than one decimeter after 1.5, 4.0 and 7.0 min, respectively, while 90% of them require 10.5, 16.5 and 20.0 min. We also numerically demonstrated that the user’s convergence times bear a linear relationship with the network density and get shorter as the density increases, for both full and partial ambiguity resolution.

Real-time satellite clock offsets are key in realizing real-time precise point positioning (PPP). Typically, tens of minutes are required for re-convergence because many tropospheric and ambiguity parameters are estimated in the clock offset estimation when the interruption of observation data occasionally occurs. This contribution proposes a rapid re-convergence method for multi-global navigation satellite system (GNSS) real-time satellite clock offset estimation. In case of a few seconds of interruption, the dual-thread integer ambiguity resolution method is proposed. The float clock offset, uncalibrated phase delay, fixed and float ambiguities, clock offset with IAR, zenith wet delay (ZWD) and inter-system bias (ISB) are generated in a slow thread, in which the fixed and float ambiguities, ZWD and ISB are used in a quick thread to achieve rapid re-convergence. Observations from 60 globally distributed stations were processed using the proposed method. The experimental results show that rapid re-convergence, fast estimation and high-precision clock offsets can be achieved. The re-convergence time of clock offset estimation was 0.14, 0.15, 0.74, 0.36 and 2.48 min for the GPS, Galileo, BDS-2, BDS-3 and GLONASS, respectively. Most satellite clock offsets can realize instantaneous re-convergence. The clock offset standard deviations are 0.028, 0.024, 0.069, 0.043 and 0.125 ns, respectively. The computation times were 21.4 and 1.7 s for the slow and quick threads, respectively. Compared to the float PPP solutions, the positioning accuracy of the PPP-AR was improved by 53.9, 29.9 and 18.2% from 1.80 to 0.83 cm, 1.57 to 1.10 cm and 3.63 to 2.97 cm for the east, north and up components, respectively. In case of interruptions lasting from a few minutes to tens of minutes, the ZWD, ambiguities and ISB information before interruption are used in the clock offset estimation, and a strong constraint is imposed on the normal equation, i.e., a large value (e.g., 105) is used instead of the diagonal value of the normal equation matrix corresponding to each estimated parameter. Experimental results show that rapid re-convergence can be achieved for GPS and Galileo with an interruption of 10 min, whereas the rapid re-convergence cannot be achieved for BDS-2, BDS-3 and GLONASS because of the impact of satellite orbit accuracy, error model, and neglection of the inter-frequency bias, respectively.

The main challenge of dual-frequency precise point positioning (PPP) is that it requires about 30 min to obtain centimeter-level accuracy or to succeed in the first ambiguity-fixing. Currently, PPP is generally conducted with GPS only using the ionosphere-free combination. We adopt a single-differenced (SD) between-satellite PPP model to combine the GPS and GLONASS raw dual-frequency carrier phase measurements, in which the GPS satellite with the highest elevation is selected as the reference satellite to form the SD between-satellite measurements. We use a 7-day data set from 178 IGS stations to investigate the contribution of GLONASS observations to both ambiguity-float and ambiguity-fixed SD PPP solutions, in both kinematic and static modes. In ambiguity-fixed PPP, we only attempt to fix GPS integer ambiguities, leaving GLONASS ambiguities as float values. Numerous experimental results show that PPP with GLONASS and GPS requires much less convergence time than that of PPP with GPS alone. For ambiguity-float PPP, the average convergence time can be reduced by 45.9 % from 22.9 to 12.4 min in static mode and by 57.9 % from 40.6 to 17.7 min in kinematic mode, respectively. For ambiguity-fixed PPP, the average time to the first-fixed solution can be reduced by 27.4 % from 21.6 to 15.7 min in static mode and by 42.0 % from 34.4 to 20.0 min in kinematic mode, respectively. Experimental results also show that the less the GPS satellites are used in float PPP, the more significant is the reduction in convergence time when adding GLONASS observations. In addition, on average, more than 4 GLONASS satellites can be observed for most 2-h observation sessions. Nearly, the same improvement in convergence time reduction is achieved for those observations.

This study proposes a model using 5G time-of-arrival data to assist global navigation satellite system precise point positioning ambiguity resolution. Specifically, the model addresses the problem of PPP requiring a long convergence time in partially satellite-occluded GNSS environments, such as urban canyons. First, we apply the ionosphere-free PPP model to estimate uncalibrated phase delays. Next, we combine real 5G data with GNSS data to determine whether introducing 5G observations will decrease the convergence time of the PPP solution. Experimental results reveal that the 5G-assisted PPP model can effectively improve the convergence efficiency of the float solution, lower the fixed time, and achieve greater positional reliability. Notably, the combination of GPS, BDS, and 5G with a sampling interval of 1 s obtains a fixed solution in an average of 1.12 min. Moreover, 5G-assisted GNSS positioning effectively compensates for partial satellite occlusion, optimizes the PDOP value, and speeds up ambiguity fixing. The introduction of three and more 5G base stations helps to obtain fixed solutions within 9 min when it is difficult to obtain fixed solutions relying only on GNSS. Our findings have important implications for improving the widespread applicability and effectiveness of satellite-based navigation systems in light of increasing urbanization and the rise of signal-occluding environments.