Search Results (49)

The performance of the MADOCA-PPP (Multi-GNSS Orbit and Clock Augmentation-Precise Point Positioning) wide-range ionospheric correction requires further investigation during periods of high ionospheric activity, particularly regarding its impact on the convergence time and positioning accuracy of both PPP and PPP with Ambiguity Resolution (PPP-AR). Thus, the present study selects the month with the highest average Kp index between January 2023 and May 2025 and conducts positioning analyses at nine stations. Results indicate that applying wide-range ionospheric corrections reduces PPP convergence time by 47% in static mode and 54% in kinematic mode. When these corrections are integrated into PPP-AR, they shorten the convergence time by 69% in static mode and 72% in kinematic mode. Moreover, PPP-AR enhanced with wide-range ionospheric corrections achieves the highest positioning accuracy across both modes: in static mode, the horizontal and vertical root mean square errors (RMSEs) are approximately 5.2 cm and 6.9 cm, respectively, while in kinematic mode, these values are 5.6 cm and 8.0 cm. These findings demonstrate that the wide-range ionospheric corrections provided by the MADOCA-PPP service effectively enhance PPP performance during periods of heightened ionospheric activity. Full article

This study investigates the horizontal positioning accuracy of a low-cost, multi-frequency GNSS receiver operating in static mode using a newly released PPP-RTK correction service delivering localized corrections. To the authors’ knowledge, this represents one of the first performance evaluations of this service, which optimizes correction data based on the approximate receiver location. The results are compared against those from the previous version of the service, which provided non-localized corrections. Analyses were conducted in both the time and frequency domains, employing robust statistical tools to characterize error behavior. The localized service achieved a mean horizontal error of approximately 0.020 m and a 95% Circular Error Probable (CEP95) of 0.046 m, in line with its declared performance. By contrast, the earlier non-localized service yielded a mean horizontal error of approximately 0.074 m and a CEP95 of 0.124 m under comparable static conditions, confirming the significant improvement achieved by localized corrections. Spectral and wavelet analyses revealed a dominant 33 mHz harmonic in the positioning error, corresponding to the 30 s update period of atmospheric corrections, indicating a periodic influence arising from the correction stream. Continuous wavelet analysis further identified intervals in which this harmonic was absent, during which positioning accuracy improved markedly (CEP95 reduced to 0.019 m). To properly address the non-Gaussian nature of the error distribution, bias-corrected and accelerated (BCa) bootstrap methods were applied to estimate confidence intervals. Overall, the results demonstrate the benefits of localized corrections, while emphasizing the importance of accounting for the temporal structure of correction data in PPP-RTK performance assessments. Future developments will focus on kinematic scenarios and adaptive filtering strategies to mitigate periodic errors induced by correction updates. Full article

GNSS Precise Point Positioning (PPP) technology has been applied to the time transfer for a long time, enabling time synchronization between two arbitrary stations on a global scale. Over the past decade, Low Earth Orbit (LEO) satellite constellations have been developed to enhance GNSS, offering rapid geometry configuration variations that can accelerate PPP convergence and enhance the time link performance. In this contribution, LEO observations are integrated into GNSS to enhance the real-time PPP time transfer. Simulated LEO constellations with varying numbers of satellites are used to assess their impact on real-time PPP time transfer performance. One week of observation data from 11 globally distributed stations is used to generate 10 time links, and five experimental schemes are designed: (1) GPS/BDS-3/Galileo solution (GCE), (2) GCE with 120 LEO satellites (GCE+120L), (3) GCE with 180 LEO satellites (GCE+180L), (4) GCE with 240 LEO satellites (GCE+240L), and (5) GCE with 300 LEO satellites (GCE+300L). Results showed that compared to the GCE solution, integrating 120, 180, 240, and 300 LEO satellites increases the average number of observed satellites from 23.4 to 30.6, 34.1, 37.7, and 41.3, respectively, while reducing Time Dilution of Precision (TDOP) values from 0.547 to 0.424, 0.391, 0.363, and 0.342, respectively. Using 30 s observations, the average convergence time to STD of time link errors better than 0.1 ns is reduced from 7.95 to 5.94, 4.83, 4.46, and 4.45 min in static mode, with improvements of 25.3%, 39.2%, 43.9%, and 44.0%, respectively, and from 8.75 to 6.18, 5.17, 4.89, and 4.72 min in kinematic mode, with improvements of 29.3%, 40.8%, 44.1%, and 46.0%, respectively. Using 1 s observations, Scenarios GCE+120L, GCE+180L, GCE+240L, and GCE+300L can achieve 1 ns convergence within 1 min. The time link precision was also found to be significantly improved, i.e., from 0.337 to 0.243 ns in static mode with improvements of 27.9%, and from 0.377 to 0.253 ns in kinematic mode with improvements of 32.9%. The time link stability is significantly enhanced for averaging times between 60 and 20,000 s in both static and kinematic modes, with a maximum improvement of nearly 50%. These results have demonstrated that integrating LEO satellites can significantly enhance real-time PPP time transfer performance. Full article

This research examines the performance of the affordable Xiaomi 11T smartphone in static positioning mode. Static Global Navigation Satellite System (GNSS) measurements are acquired over a two-hour period with a known reference point, spanning three consecutive days. The acquired data are processed, employing both real-time and post-processing Precise Point Positioning (PPP) solutions using GPS-only, Galileo-only, and the combined GPS/Galileo datasets. To correct the satellite and clock errors, the instantaneous Centre National d’Études Spatiales (CNES), the final Le Groupe de Recherche de Géodésie Spatiale (GRG), GeoForschungsZentrum (GFZ), and Wuhan University (WUM) products were applied. The results demonstrate that sub-30 cm positioning accuracy is achieved in the horizontal direction using real-time and final products. Additionally, sub-50 cm positioning accuracy is attained in the vertical direction for the real-time and post-processed solutions. Furthermore, the real-time products achieved three-dimensional (3D) position accuracies of 40 cm, 29 cm, and 20 cm using GPS-only, Galileo-only, and the combined GPS/Galileo observations, respectively. The final products achieved 3D position accuracies of 24 cm, 26 cm, and 28 cm using GPS-only, Galileo-only, and the combined GPS/Galileo measurements, respectively. The attained positioning accuracy can be used in some land use and urban planning applications. Full article

The performance of Precise Point Positioning (PPP) using different Global Navigation Satellite System (GNSS) product sets, including broadcast ephemerides, International GNSS Service Real-Time Service (IGS-RTS) corrections, Galileo High Accuracy Service (HAS) corrections, and precise products from the Center for Orbit Determination in Europe (CODE) Multi-GNSS Experiment (MGEX), has been evaluated. The availability of solutions, convergence time, position accuracy and Zenith Tropospheric Delay (ZTD) estimation across these products were analyzed using simulated real-time and postprocessing static modes, using data from globally distributed stations with a 1 s observation interval. The results indicate that precise products from the MGEX provide the highest accuracy, achieving centimeter-level precision in post-processed mode. Real-time simulated solutions, such as HAS and IGS-RTS, deliver promising results, with Galileo HAS meeting its target accuracy of 20 cm horizontally and 40 cm vertically and a convergence time under 5 min. However, Global Positioning System (GPS) performance within HAS is limited by a significantly lower correction availability—around 67% on average compared to over 95% for Galileo—which negatively impacts PPP performance. ZTD estimation results show that real-time services (HAS, IGS-RTS) achieved errors within 1–3 cm, sufficient for meteorological applications. This study highlights the growing importance of HAS in real-time positioning applications and suggests further improvements in GPS for enhanced performance. Full article

Nowadays, several smartphones on the market provide multi-frequency multi-constellations GNSS measurements, including carrier phase ones, allowing the achievement of high-accuracy positioning by exploiting Real Time Kinematic (RTK) or Precise Point Positioning (PPP) techniques. This paper will showcase the effectiveness of using smartphone measurements for RTK under different scenarios and for different applications using baselines of different lengths. The impact of the smartphone’s antenna on the solution will also be analysed. The assessment will be performed by evaluating different key performance indicators, including the time to first fix and the horizontal/vertical accuracy. This paper shows that around a 99% fix position can be achieved even using the smartphones’ antennas for the static case under open sky conditions. Moreover, high percentages of fix solutions can also be achieved in kinematic mode by ad hoc tuning of the RTK algorithm. Full article

The BeiDou global navigation satellite system (BDS-3) and Galileo systems both broadcast satellite signals on five frequencies, which can form many observation combinations with dual-frequency ionospheric-free (DFIF) precise point positioning (PPP). This study analyzes the PPP static and kinematic performance of a total of eight different DFIF combinations, including BDS-3’s B1C/B2a, B1C/B3I, B1I/B2b, and B1I/B3I and Galileo’s E1/E5, E1/E6, E1/E5a, and E1/E5b combinations. A 10-day dataset from 60 Multi-GNSS Experiment (MGEX) stations was adopted. The root mean square error (RMSE) of the PPP was tested in the north, east, and up (NEU), horizontal (H), and three-dimensional (3D) components. The PPP accuracy of BDS-3 was comparable with that of Galileo. Both BDS-3 and Galileo signals allow for independent PPP processing both in static and kinematic modes. When the 3D error was used as the evaluation criterion, the order of the combinations in which the positioning accuracy gradually deteriorated was as follows: E1/E5, B1C/B3I, B1I/B2b, E1/E6, B1I/B3I, E1/E5b, E1/E5a, and B1C/B2a; The 3D RMSE values for the best combination, E1/E5, and the worst combination, B1C/B2a, were 1.06 cm and 1.43 cm, respectively; the positioning accuracies of all combinations remained at the level of 1 cm in static mode. In kinematic mode, the order of the combinations in which the PPP accuracy gradually deteriorated was as follows: E1/E5, E1/E5a, E1/E5b, B1I/B2b, B1I/B3I, B1C/B2a, B1C/B3I, and E1/E6. The 3D RMSE values for the best combination, E1/E5, and the worst combination, B1C/B2a, were 3.89 cm and 1.95 cm, respectively. The best results could be achieved with the E1/E5 combination, which outperforms the worst combination, E1/E6, by about 1 cm. Full article

Precise Point Positioning (PPP), coupled with the ambiguity resolution (AR) method, has demonstrated substantial potential in fields like agricultural navigation and airborne mapping. However, there remains a notable deficiency in the comprehensive comparative evaluation of its performance when using rapid and real-time satellite products, especially for mass low-cost receivers. Stations equipped with geodetic and low-cost receivers are analyzed in kinematic and static mode. In the kinematic mode, the GPS+Galileo-combined PPP, employing ambiguity fixing with “WHU” rapid products, achieves the highest positioning accuracy of 0.9 cm, 0.9 cm, and 2.6 cm in the North, East, and Up components, respectively. Real-time PPP using “CNT” products attains accuracies of 2.1 cm, 2.7 cm, and 4.8 cm for these components, utilizing GPS ambiguity-fixed PPP. BDS positioning accuracy is inferior to standalone GPS, but improves when the number of visible BDS satellites exceeds 10. Convergence time analysis shows that approximately 38.2 min are required for single GPS or BDS PPP using the “WHU” products and geodetic receivers, which can be reduced to 18.5 min for dual-system combinations and further to 14.8 min for triple-system combinations. The time can be further reduced by ambiguity fixing. In the static mode, multi-GNSS combination does not significantly impact convergence times, which are more influenced by the precision of the products used. Real-time products require approximately 22 min to achieve horizontal accuracy below 0.1 m, while rapid products reach this accuracy within 10 min. For PPP using low-cost GNSS receivers, more than two hours are necessary to achieve an accuracy better than 0.1 m for kinematic PPP, which is considerably longer than the convergence time observed at MGEX stations. However, the accuracy achieved after convergence, as well as the performance of static PPP, is comparable to that of MGEX stations. Full article

Compared to the traditional ionospheric-free (IF) precise point positioning (PPP) model, the undifferenced and uncombined (UU) PPP has the advantages of lower observation noise and the ability to obtain ionospheric information. Thanks to the IGS (International GNSS Service), real-time service (RTS) can provide RT vertical total electron content (VTEC) products, and an enhanced RT UU-PPP based on the RT-VTEC constraints can be achieved. The global performance of the BeiDou Navigation Satellite System-2 (BDS-2) and BDS-3 joint RT UU-PPP using different RTS products was investigated. There is not much difference in the RTS orbit accuracy of medium earth orbit (MEO) satellites among all analysis centers (ACs), and the optimal orbit accuracy is better than 5, 9, and 7 cm in the radial, along-track, and cross-track directions, respectively. The orbit accuracy of inclined geosynchronous orbit (IGSO) satellites is worse than that of MEO satellites. Except for CAS of 0.46 ns, the RTS clock accuracy of MEO satellites for other ACs achieves 0.2–0.27 ns, and the corresponding accuracy is about 0.4 ns for IGSO satellites. In static positioning, due to the limited accuracy of RT-VTEC, the convergence time of the enhanced RT UU-PPP is longer than that of RT IF-PPP for most ACs and can be better than 25 and 20 min in the horizontal and vertical components, respectively. After convergence, the 3D positioning accuracy of the static RT UU-PPP is improved by no more than 8.7%, and the optimal horizontal and vertical positioning accuracy reaches 3.5 and 7.0 cm, respectively. As for the kinematic mode with poor convergence performance, with the introduction of RT-VTEC constraints, the convergence time of RT UU-PPP can be slightly shorter and reaches about 55 and 60 min in the horizontal and vertical components, respectively. Both the horizontal and vertical positioning accuracies of the kinematic RT UU-PPP can be improved and achieve around 7.5 and 10 cm, respectively. Full article

Although deformations are mostly insignificant, they can be catastrophic when accumulated to certain amounts. Precise point positioning (PPP) can work with one receiver, preventing problems caused by the base station constrain upon employment of current methods such as real-time kinematics (RTK). However, current methods employing PPP focus on high-frequency monitoring such as earthquake or geological calamity monitoring, and these methods are not suitable for structures. Thus, this study proposes a new method for the deformation monitoring of structures via PPP. First, we obtained the coordinate sequence of structures via static PPP when setting the interval. Then, we transformed the coordinates to the same coordinate system with the same basis. Finally, we decomposed the sequences via empirical mode decomposition (EMD) to obtain a low-frequency part, which is the deformation of the target structure. The result of the monitoring experimentation on IGS stations shows that the monitoring index, $S^d$, of the sequence under different intervals using this method could be 1–2 mm on average in the directions of E, N, and U, which is much better than the original monitoring sequence. Alongside that, it prevented a fall in accuracy when the interval decreased. Therefore, all results proved the feasibility and validity of the method. Full article

Real-Time (RT) Precise Point Positioning (PPP) uses precise satellite orbits and clock corrections, and employs a separate receiver for positioning. With the growing demand, RT PPP is becoming an increasingly popular research topic. The ambiguity resolution (AR) can significantly improve the positioning accuracy and convergence time of PPP, so it is essential to study PPPAR in RT mode. In this paper, 37 MGEX stations from around the world are chosen, and the RT orbit, clock, and phase biases products broadcast by the Centre National d’Etudes Spatiales (CNES) are applied to PPPAR. Additionally, the residuals of the RT phase biases products, convergence time, and positioning accuracy are investigated. The results indicate that GPS products have the best quality of AR, with wide-lane (WL) and narrow-lane (NL) residuals of 98.9% and 95.3%, respectively, within ±0.25 cycles. Within ±0.25 cycles, the WL and NL residuals of the Galileo are 98.2% and 94.3%, respectively. Within ±0.25 cycles, the (Beidou Navigation Satellite System) BDS has a poor quality of AR, with WL and NL residuals of 97.3% and 73.1%, respectively. Due to the poor quality of the BDS AR, the convergence time of the BDS is not calculated in this paper. The convergence time of other systems is significantly reduced after AR processing, and the convergence time of the GPS/Galileo combination is the fastest, being 17.14 min in kinematic mode and only 11.85 min in static mode. The positioning accuracy of the GPS, Galileo, GPS/Galileo, and GPS/Galileo/BDS in the E and U directions is significantly improved after PPPAR. Full article

Real-time GNSS PPP is commonly used for high-precision positioning, but its utility is constrained by factors that necessitate extended convergence periods for a dependable accuracy. Multipath, as an unmodeled error, significantly curtails PPP performance in time-constrained scenarios. Approximately 31 consecutive days of multi-GNSS data from the satellite positioning service of the German national survey (SAPOS) network were collected to evaluate the effectiveness of multipath correction for real-time PPP ambiguity resolution (AR). Using principal component analysis (PCA) to extract the common-mode error (CME) from observation residuals prior to multipath modeling, a multipath hemispherical map (MHM) and sidereal filtering (SF) approach were employed to alleviate the effects of multipath and assess the efficacy of multipath correction in real-time PPP-AR. The average RMS reductions of the carrier-phase and pseudorange residual of multi-GNSS were 25.5% and 20.1% with MHM ${}_{0.5}$, while being 24.4% and 18.3% using SF. With MHM ${}_{0.5}$ correction, the TTFF reductions were approximately 7.0%, 17.7%, 37.5%, and 23.7% for G/GE/GC/GEC kinematic PPP-AR, respectively; and the convergence times for G/GE/GC PPP-AR were reduced to 18.2, 11.7, and 8.6 min, while GEC achieved an average convergence time of 7.1 min; a remarkable improvement compared to the multipath-uncorrected result (18 min). Moreover, 80% of the stations achieved convergence within 10 min, while 40% achieved convergence within 5 min. The kinematic positioning accuracy for the GEC solution improved from 0.97, 0.88, and 2.07 cm, to 0.94, 0.70, and 1.72 cm. In the static results, the TTFF shortened by 30.1%, 19.1%, and 20.1% for G/GE/GC, and the GEC decreased from 10.5 to 9.7 min; the average convergence time for G/GE/GC shortened to 13.0, 10.0, and 11.3 min, and for GEC shortened from 12.5 to 8.3 min. For the GPS-only solution, 78.3% of stations achieved convergence within 15 min. Similarly, for the GE scheme, the convergence time was primarily concentrated within 10 min, and for GC and GEC, with the application of enhanced multipath error correction, some of the stations even achieved convergence of PPP-AR within 5 min. The static positioning accuracy for GEC PPP was 0.50, 0.30, and 0.71 cm for the east, north, and up components. Full article

With the continuous construction and development of the BeiDou navigation satellite system (BDS), its positioning performance is constantly being improved. In this study, the positioning performance of different frequency combinations of BDS-3/GPS/Galileo in the Asia-Pacific region was investigated. The precision products of Wuhan University and the observation data of nine MGEX stations were selected to compare and analyze the B1I\B1C\B2a\B3I and L1\E1 pseudo-range Standard Point Positioning (SPP) and B1IB2a\B1IB3I\B1CB2a\B1CB3I\B2aB3I\L1L2\E1E5a precise point positioning (PPP) performance, while B1I\B3I\L1 SPP and B1IB3I PPP were investigated using BDS-2 with QZSS supplemented with BDS-3 and GPS. The experimental results showed that the positioning precision of BDS-3/GPS/Galileo SPP was in the order of B1C > E1 > L1 > B1I > B3I > B2a, and it was not significantly improved after BDS-2 and QZSS were added. Moreover, for the PPP of different frequency combinations, the convergence speed was in the order of L1L2 > B1IB3I > E1E5a > B1CB3I > B1CB2a > B1IB2a > B2aB3I. After adding BDS-2, B1IB3I improved by about 11% in static mode and 27% in kinematic mode, which was similar to the L1L2 frequency combination. The positioning precision of different frequency combinations of BDS-3/GPS/Galileo was B1IB3I > B1CB3I > L1L2 > E1E5a > B1B2a > B1CB2a > B2aB3I. In static mode, after adding BDS-2, B1IB3I did not show significant improvement in the plane direction, and showed ~61% improvement in the elevation direction, and ~67% in the three-dimensional (3D) direction. In kinematic mode, after adding BDS-2, B1IB3I was improved by about 16% in the E direction, the N direction did not show significant change, it improved by ~38% in the U direction and by ~70% in the 3D direction. In general, the positioning performance of BDS-3 was slightly better than those of GPS and Galileo in the Asia-Pacific region, and it is believed that with the continuous development of BDS, its positioning performance will surely be improved further. Full article

The development of low-cost dual-frequency global navigation satellite system (GNSS) receivers in recent years has enabled the use of these devices in numerous applications. In the monitoring of natural hazards, such as landslides, these devices can be considered suitable sensors. In this work, dual-frequency GNSS receivers and antennas were used for setting up near-real-time continuous low-cost GNSS monitoring systems (LGMSs) under field conditions. The SimpleRTK2B board, which integrates the u-blox ZED-F9P dual-frequency GNSS chip and the survey-calibrated GNSS antenna are the main components of the GNSS system. The LGMS was installed and tested for six months in the Laze landslide located in the northwestern part of Slovenia. A total of four GNSS systems were deployed, three of which were located in pillars in the landslide itself and one in a stable area. Open-source software was used to postprocess the acquired data, providing daily coordinates in static relative and precise point positioning (PPP) positioning modes. The results of six months of near-real-time monitoring showed that the Laze landslide was stable during this period, with only minor changes in the vertical component. The trend of decreasing ellipsoid height was evident at all stations, although it was in the range of a few millimeters. To validate the results in static relative positioning mode, the coordinate differences between low-cost and high-end geodetic GNSS instruments were estimated and found to be in the range of 5 mm or less, while the difference between horizontal and spatial positions was less than 7 mm for all stations. The same data were processed in PPP, vertical displacements were not detected as in the static relative positioning mode due to the lower accuracy of the method itself. Considering the six-month performance of a low-cost GNSS system under field conditions, it can be emphasized that these devices are capable of performing near real-time continuous monitoring of slow movements with high accuracy and decreased costs. In addition, an experimental test was performed to identify the size of detected displacements in real-time kinematic (RTK). Based on the achieved results, it was concluded that 20 mm spatial displacements are detectable with LGMSs in RTK considering only 15 s of observations. Full article

It has been proven that precise point positioning (PPP) is a well-established technique to obtain high-precision positioning in the order between centimeters and millimeters. In this context, different studies have been carried out to evaluate the performance of PPP in static mode as a possible alternative to the relative method. However, only a few studies have evaluated the performance of a large number of different open-source software programs and have focused extensively on online free PPP services. Therefore, in this paper, a comprehensive comparison of processing in static mode between different open-source software and the online free PPP services is developed. For the evaluation, different GNSS observation files collected at 45 International GNSS Service (IGS) stations distributed worldwide were processed in static PPP mode. Within this frame of reference, ten open-source PPP software and five online free PPP services were studied. The results from the processing strategy demonstrate that it is possible to obtain precision in the order of millimeters with both open-source software and online PPP services. In addition, online PPP services experienced better performance than some other specialized PPP software. In summary, the results show that the daily solutions for the E (East), N (North), and U (Up) components estimated by the ten open-source software and by the five online free PPP services can reach millimeter precision for some stations. Among the open-source software, the PRIDE-PPPAR presented the best performance with a Root Mean Square Error (RMSE) of 5.52, 5.40, and 6.79 mm in the E, N, and U components, respectively. Alternatively, in the case of the online free PPP services, the APPS and CSRS-PPP produced the most accurate results, with RMSE values less than 12 mm for the three components. Finally, the open-source software and online free PPP services experienced similar positioning performance in the horizontal and vertical components, demonstrating that both can be implemented in static mode without compromising the accuracy of the measurement. Full article