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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 Real-Time Global Navigation Satellite System (GNSS) Precise Positioning Service (RTPPS) is recognized as the most promising system by providing precise satellite orbit and clock corrections for users to achieve centimeter-level positioning with a stand-alone receiver in real-time. Although the products are available with high accuracy almost all the time, they may occasionally suffer from unexpected significant biases, which consequently degrades the positioning performance. Therefore, quality monitoring at the system-level has become more and more crucial for providing a reliable GNSS service. In this paper, we propose a method for the monitoring of real-time satellite orbit and clock products using a monitoring station network based on the Quality Control (QC) theory. The satellites with possible biases are first detected based on the outliers identified by Precise Point Positioning (PPP) in the monitoring station network. Then, the corresponding orbit and clock parameters with temporal constraints are introduced and estimated through the sequential Least Square (LS) estimator and the corresponding Instantaneous User Range Errors (IUREs) can be determined. A quality indicator is calculated based on the IUREs in the monitoring network and compared with a pre-defined threshold. The quality monitoring method is experimentally evaluated by monitoring the real-time orbit and clock products generated by GeoForschungsZentrum (GFZ), Potsdam. The results confirm that the problematic satellites can be detected accurately and effectively with missed detection rate and false alarm rate . Considering the quality alarms, the PPP results in terms of RMS of positioning differences with respect to the International GNSS Service (IGS) weekly solution in the north, east and up directions can be improved by 12%, 10% and 27%, respectively.

Realtime satellite clock corrections are usually estimated using undifferenced phase and range observations from a global network. Because a large number of ambiguity parameters must be estimated, the computation is time-consuming. Consequently, only a sparse global network of limited number of stations is processed by most IGS Realtime Analysis Centers with an update rate of 5 s. In addition, it is very desirable to build the capability to simultaneously estimate clock corrections for multi-GNSS constellations. Although the estimation can be sped up by epoch-differenced observations that eliminate ambiguities, the derived clocks can contain a satellite-specific bias that diminishes the contribution of range observations. We introduce a computationally efficient approach for realtime clock estimation. Both the epoch-differenced phase and undifferenced range observations are used together to estimate the epoch-differenced satellite clocks and the initial clock bias for each satellite and receiver. The biased clock corrections accumulated from the estimated epoch-differenced clocks are then aligned with the estimated clock biases and provided as the final clock corrections to users. The algorithm is incorporated into the EPOS-RT software developed at GFZ (GeoForschungsZentrum) and experimentally validated with the IGS global network. The comparison with the GFZ rapid products shows that the accuracy of the clock estimation with the new approach is comparable with that of the undifferenced approach, whereas the computation time is reduced to one-tenth. As a result, estimation of high-rate satellite clocks from a large reference network and tracking satellites of multi-GNSS constellations becomes achievable.

Real-time multi-GNSS precise point positioning (PPP) requires the support of high-rate satellite clock corrections. Due to the large number of ambiguity parameters, it is difficult to update clocks at high frequency in real-time for a large reference network. With the increasing number of satellites of multi-GNSS constellations and the number of stations, real-time high-rate clock estimation becomes a big challenge. In this contribution, we propose a decentralized clock estimation (DECE) strategy, in which both undifferenced (UD) and epoch-differenced (ED) mode are implemented but run separately in different computers, and their output clocks are combined in another process to generate a unique product. While redundant UD and/or ED processing lines can be run in offsite computers to improve the robustness, processing lines for different networks can also be included to improve the clock quality. The new strategy is realized based on the Position and Navigation Data Analyst (PANDA) software package and is experimentally validated with about 110 real-time stations for clock estimation by comparison of the estimated clocks and the PPP performance applying estimated clocks. The results of the real-time PPP experiment using 12 global stations show that with the greatly improved computational efficiency, 3.14 cm in horizontal and 5.51 cm in vertical can be achieved using the estimated DECE clock.

High-precision positioning from Global Navigation Satellite Systems (GNSS) has garnered increased interest due to growing demand in various applications, like autonomous car navigation and precision agriculture. Precise Point Positioning (PPP) offers a distinct advantage over differential techniques by enabling precise position determination of a GNSS rover receiver through the use of external corrections sourced from either the Internet or dedicated correction satellites. However, PPP’s implementation has been challenging due to the need to mitigate numerous GNSS error sources, many of which are eliminated in differential techniques such as Real-Time Kinematics (RTK) or overlooked in Standard Point Positioning (SPP). This paper extensively reviews PPP’s error sources, such as ionospheric delays, tropospheric delays, satellite orbit and clock errors, phase and code biases, and site displacement effects. Additionally, this article examines various PPP models and correction sources that can be employed to address these errors. A detailed discussion is provided on implementing the standard dual-frequency (DF)-PPP to achieve centimeter- or millimeter-level positioning accuracy. This paper includes experimental examples of PPP implementation results using static data from the International GNSS Service (IGS) station network and a kinematic road test based on the actual trajectory to showcase DF-PPP development for practical applications. By providing a fusion of theoretical insights with practical demonstrations, this comprehensive review offers readers a pragmatic perspective on the evolving field of Precise Point Positioning.

The technology of precise point positioning - real time kinematic (PPP - RTK) can realize regional accurate positioning. However, poor quality atmospheric corrections can greatly impact the integer ambiguity resolution. The low reliability of interpolated corrections may arise from blocked transmission of the updated corrections, atmospheric disturbance, and when the user is located outside the service area. Therefore, to maintain a continuous ambiguity-fixed state in an inaccurate correction observation environment, we propose a novel stop-and-go (SAG) kinematic positioning method. Integer ambiguities inherited from the last epoch are used to estimate the ionospheric errors of the current epoch using an inversion calculation method. Unmodeled errors contained in the ionospheric corrections are also considered. We then experimentally compare the proposed method and traditional PPP - RTK and SAG methods with the results of the PPP-ambiguity resolution calculation using geomagnetic storm-influenced data. All indicators, including the number of fixed ambiguities, errors of corrections, successful fix rate, and correct fix rate, confirm the superiority of the proposed method. The proposed method achieves a horizontal correct fix rate of 98% and maintains the vertical correct fix rate above 96% throughout the day. It is proved that for most of the time the novel method can provide continuous ambiguity-fixed solutions for users in an inaccurate correction observation environment.

The recent access to GNSS (Global Navigation Satellite System) phase observations on smart devices, enabled by Google through its Android operating system, opens the possibility to apply precise positioning techniques using off-the-shelf, mass-market devices. The target of this work is to evaluate whether this is feasible, and which positioning accuracy can be achieved by relative positioning of the smart device with respect to a base station. Positioning of a Google/HTC Nexus 9 tablet was performed by means of batch least-squares adjustment of L1 phase double-differenced observations, using the open source goGPS software, over baselines ranging from approximately 10 m to 8 km, with respect to both physical (geodetic or low-cost) and virtual base stations. The same positioning procedure was applied also to a co-located u-blox low-cost receiver, to compare the performance between the receiver and antenna embedded in the Nexus 9 and a standard low-cost single-frequency receiver with external patch antenna. The results demonstrate that with a smart device providing raw GNSS phase observations, like the Nexus 9, it is possible to reach decimeter-level accuracy through rapid-static surveys, without phase ambiguity resolution. It is expected that sub-centimeter accuracy could be achieved, as demonstrated for the u-blox case, if integer phase ambiguities were correctly resolved.

A regional zenith tropospheric delay (ZTD) empirical model, referred to as SHAtropE (SHanghai Astronomical observatory tropospheric delay model—Extended), is developed and provides tropospheric propagation delay corrections for users in China and the surrounding areas with improved accuracy. The SHAtropE model was developed based on the ZTD time series of the continuous GNSS sites from the Crustal Movement Observation Network of China (CMONOC) and GNSS sites of surrounding areas. It combines the exponential and periodical functions and is provided as regional grids with a resolution of 2.5° × 2.0° in longitude and latitude. At each grid point, the exponential function converts the ZTD from the site height to the ellipsoid, and the periodical terms, including both annual and semi-annual periods, describe ZTD’s temporal variation. Moreover, SHAtropE also provides the predicted ZTD uncertainty, which is valuable in Precise Point Positioning (PPP) with ZTD being constrained for faster convergence. The data of 310 GNSS sites over 7 years were used to validate the new model. Results show that the SHAtropE ZTD has an accuracy of 3.5 cm in root mean square (RMS) quantity, which has a mean improvement of 35.2% and 5.4% over the UNB3m (5.4 cm) and GPT3 (3.7 cm) models, respectively. The predicted uncertainty of SHAtropE ZTD shows seasonal variations, where the values are larger in summer than in winter. By applying the SHAtropE model in the static PPP, the convergence time of GPS-only and BDS-only solutions are reduced by 8.1% and 14.5% respectively compared to the UNB3m model, and the reductions are 6.9% and 11.2% respectively for the GPT3 model. As no meteorological data are required for the implementation of the model, the SHAtropE could thus be a refined tropospheric model for GNSS users in mainland China and the surrounding areas. The method of modeling the ZTD uncertainty can also be used in further global tropospheric delay modeling.

GNSS positioning in urban scenarios suffers for the scarce visibility of satellites. Integration with 5G services for positioning could improve this situation. In this paper, the digital surface models (DSMs) relevant to different urban scenarios, namely residential streets and urban canyons, are simulated around one observer in northern Italy (Milano) for one day of the year chosen as an example. The time series of the number of in-view GNSS satellites, their geometry and the derived quality indexes (position dilution of precision (PDOP)) are computed and analyzed. As expected, in urban canyons, a significant number of epochs does not provide four satellites within view, and many more epochs present really mediocre PDOPs. In residential streets, the situation is always quite fair. Different geometric configurations of 5G base stations are simulated around the observer. The availability of 5G times of arrival (ToAs) and their differences (TDoAs) is hypothesized, and the integration of these observations with GNSS pseudoranges is analyzed, again in terms of the PDOPs. In residential streets, 5G availability improves the positioning. In urban canyons, the optimal configuration of 5G base stations (five base stations around the observer) completely solves the positioning problem for all the epochs of the day. Less favorable configurations (four and three base stations) improve epochs with poor PDOPs in a GNSS-only configuration. They allow the positioning of epochs with few satellites but cannot completely replace the GNSS.

On February 11, 2019, four additional Galileo satellites were put into service, approaching the completion of the European global navigation satellite system constellation. For the first time, the performance of Galileo system in terms of high-accuracy precise point positioning (PPP) can be evaluated. The results presented in this paper are based on one full week (February 11–17, 2019) of post-processed kinematic positioning for a set of fixed stations at a 30-s sampling. Due to the availability of precise Galileo orbit and “integer” clock products, delivered by CNES/CLS Analysis Center of International GNSS Service, the impact of Galileo ambiguity resolution on the positioning results is also quantified. The precision using Galileo-only measurements in the East, North and Up directions is 10 mm, 7 mm and 33 mm for PPP and 6 mm, 5 mm and 28 mm for PPP-AR (PPP with ambiguity resolution) (1 sigma), respectively. These results shall represent the future performance of the Galileo system for kinematic post-positioning. They also indicate the important future contribution of Galileo to high-accuracy multi-GNSS applications.