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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 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.

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.

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.

The real-time estimation of the wide-lane and narrow-lane Uncalibrated Phase Delay (UPD) of satellites is realized by real-time data received from regional reference station networks; The properties of the real-time UPD product and its influence on real-time precise point positioning ambiguity resolution (RTPPP-AR) are experimentally analyzed according to real-time data obtained from the regional Continuously Operating Reference Stations (CORS) network located in Tianjin, Shanghai, Hong Kong, etc. The results show that the real-time wide-lane and narrow-lane UPD products differ significantly from each other in time-domain characteristics; the wide-lane UPDs have daily stability, with a change rate of less than 0.1 cycle/day, while the narrow-lane UPDs have short-term stability, with significant change in one day. The UPD products generated by different regional networks have obvious spatial characteristics, thus significantly influencing RTPPP-AR: the adoption of real-time UPD products employing the sparse stations in the regional network for estimation is favorable for improving the regional RTPPP-AR up to 99%; the real-time UPD products of different regional networks slightly influence PPP-AR positioning accuracy. After ambiguities are successfully fixed, the real-time dynamic RTPPP-AR positioning accuracy is better than 3 cm in the plane and 8 cm in the upward direction.

In this contribution, we present a GPS+GLONASS+BeiDou+Galileo four-system model to fully exploit the observations of all these four navigation satellite systems for real-time precise orbit determination, clock estimation and positioning. A rigorous multi-GNSS analysis is performed to achieve the best possible consistency by processing the observations from different GNSS together in one common parameter estimation procedure. Meanwhile, an efficient multi-GNSS real-time precise positioning service system is designed and demonstrated by using the multi-GNSS Experiment, BeiDou Experimental Tracking Network, and International GNSS Service networks including stations all over the world. The statistical analysis of the 6-h predicted orbits show that the radial and cross root mean square (RMS) values are smaller than 10 cm for BeiDou and Galileo, and smaller than 5 cm for both GLONASS and GPS satellites, respectively. The RMS values of the clock differences between real-time and batch-processed solutions for GPS satellites are about 0.10 ns, while the RMS values for BeiDou, Galileo and GLONASS are 0.13, 0.13 and 0.14 ns, respectively. The addition of the BeiDou, Galileo and GLONASS systems to the standard GPS-only processing, reduces the convergence time almost by 70 %, while the positioning accuracy is improved by about 25 %. Some outliers in the GPS-only solutions vanish when multi-GNSS observations are processed simultaneous. The availability and reliability of GPS precise positioning decrease dramatically as the elevation cutoff increases. However, the accuracy of multi-GNSS precise point positioning (PPP) is hardly decreased and few centimeter are still achievable in the horizontal components even with 40 ∘ elevation cutoff. At 30 ∘ and 40 ∘ elevation cutoffs, the availability rates of GPS-only solution drop significantly to only around 70 and 40 %, respectively. However, multi-GNSS PPP can provide precise position estimates continuously (availability rate is more than 99.5 %) even up to 40 ∘ elevation cutoff (e.g., in urban canyons).

Starting from 2016, the raw Global Navigation Satellite System (GNSS) measurements can be extracted from the Android Nougat (or later) operating systems. Since then, GNSS smartphone positioning has been given much attention. A high number of related publications indicates the importance of the research in this field, as it has been doing in recent years. Due to the cost-effectiveness of the GNSS smartphones, they can be employed in a wide variety of applications such as cadastral surveys, mapping surveying applications, vehicle and pedestrian navigation and etc. However, there are still some challenges regarding the noisy smartphone GNSS observations, the environment effect and smartphone holding modes and the algorithm development part which restrict the users to achieve high-precision smartphone positioning. In this review paper, we overview the research works carried out in this field with a focus on the following aspects: first, to provide a review of fundamental work on raw smartphone observations and quality assessment of GNSS observations from major smart devices including Google Pixel 4, Google Pixel 5, Xiaomi Mi 8 and Samsung Ultra S20 in terms of their signal strengths and carrier-phase continuities, second, to describe the current state of smartphone positioning research field until most recently in 2021 and, last, to summarize major challenges and opportunities in this filed. Finally, the paper is concluded with some remarks as well as future research perspectives.

The update of the Android system and the emergence of the dual-frequency GNSS chips enable smartphones to acquire dual-frequency GNSS observations. In this paper, the GPS L1/L5 and Galileo E1/E5a dual-frequency PPP (precise point positioning) algorithm based on RTKLIB and GAMP was applied to analyze the positioning performance of the Xiaomi Mi 8 dual-frequency smartphone in static and kinematic modes. The results showed that in the static mode, the RMS position errors of the dual-frequency smartphone PPP solutions in the E, N, and U directions were 21.8 cm, 4.1 cm, and 11.0 cm, respectively, after convergence to 1 m within 102 min. The PPP of dual-frequency smartphone showed similar accuracy with geodetic receiver in single-frequency mode, while geodetic receiver in dual-frequency mode has higher accuracy. In the kinematic mode, the positioning track of the smartphone dual-frequency data had severe fluctuations, the positioning tracks derived from the smartphone and the geodetic receiver showed approximately difference of 3–5 m.

Within the framework of differential augmentation, this paper introduces the basic technical framework and performance of the BeiDou Global Navigation Satellite System (BDS-3) Satellite-Based Augmentation System (BDSBAS), including orbit products, satellite clock offset products, ionosphere and its integrity performance. The basic principle of BDS-3 Precise Point Positioning (PPP-B2b) is expounded, the similarities and differences between the PPP service provided by BDS-3 and International Global Navigation Satellite System (GNSS) Service (IGS) are discussed, and the limitations of PPP-B2b are analyzed. Since both the BDSBAS and PPP-B2b utilize a ground monitoring station network to determine the satellite orbits and clock offset corrections, and broadcast differential corrections through the three Geostationary Orbit (GEO) satellites of BDS-3, the feasibility of the co-construction of BDSBAS and PPP-B2b is analyzed, strategies for the infrastructure sharing and correction broadcasting are presented, and the influences of BDSBAS correction broadcasting strategy adjustment are evaluated. In addition, it assesses the possibility of broadcasting differential corrections through the Inclined Geosynchronous Orbit (IGSO) satellites of BDS-3, and the feasibility of augmenting satellite navigation with Low Earth Orbit (LEO) satellites.