Search Results (88)

GNSS Precise Point Positioning (PPP) technology has been extensively applied to post-processing international comparisons between UTC/TAI times and real-time time transfer, predominantly in static configurations. However, with the swift advancement of intelligent and unmanned systems, there is an urgent need for research into kinematic time transfer. This paper introduces a kinematic model Galileo/GPS integrated PPP time transfer approach leveraging the Galileo High Accuracy Service (HAS). The study utilized observational data from seven stations spanning 22 days. The findings indicate that under static conditions, GPS, Galileo, and Galileo/GPS PPP, when supported by the Galileo HAS, can achieve time transfer with sub-nanosecond precision. In kinematic scenarios, the accuracy of single-system PPP time transfer is comparatively lower, with frequent re-convergence events leading to significant accuracy degradation (exceeding 1 ns). However, in cases where re-convergence is infrequent due to a limited number of satellites, sub-nanosecond time transfer is still attainable. The Galileo/GPS integrated PPP time transfer effectively mitigates the issue of re-convergence, ensuring sub-nanosecond accuracy across all links (0.48 ns). Consequently, it is recommended to employ a multi-system integration approach for kinematic PPP time transfer, particularly when utilizing the Galileo HAS. In terms of frequency stability, GPS, Galileo, and Galileo/GPS PPP demonstrate short-term stability (over 960 s) of (5.29 × 10⁻¹³, 3.34 × 10⁻¹³, and 1.60 × 10⁻¹³), respectively, and long-term stability (over 15,360 s) of (1.49 × 10⁻¹³, 1.02 × 10⁻¹³, and 4.06 × 10⁻¹⁴), respectively. Full article

Real-time ionospheric products can accelerate the convergence of real-time precise point positioning (PPP) to improve the real-time positioning services of global navigation satellite systems (GNSSs), as well as to achieve continuous monitoring of the ionosphere. This study applied an extended Kalman filter (EKF) to total electron content (TEC) modeling, proposing a regional real-time EKF-based ionospheric model (REIM) with a spatial resolution of 1° × 1° and a temporal resolution of 1 h. We examined the performance of REIM through a 7-day period during geomagnetic storms. The post-processing model from the China Earthquake Administration (IOSR), CODG, IGSG, and the BDS geostationary orbit satellite (GEO) observations were utilized as reference. The consistency analysis showed that the mean deviation between REIM and IOSR was 0.97 TECU, with correlation coefficients of 0.936 and 0.938 relative to IOSR and IGSG, respectively. The VTEC mean deviation between REIM and BDS GEO observations was 4.15 TECU, which is lower than those of CODG (4.68 TECU), IGSG (5.67 TECU), and IOSR (6.27 TECU). In the real-time single-frequency PPP (RT-SF-PPP) experiments, REIM-augmented positioning converges within approximately 80 epochs, and IGSG requires 140 epochs. The REIM-augmented east-direction positioning error was 0.086 m, smaller than that of IGSG (0.095 m) and the Klobuchar model (0.098 m). REIM demonstrated high consistencies with post-processing models and showed a higher accuracy at IPPs of BDS GEO satellites. Moreover, the correction results of the REIM model are comparable to post-processing models in RT-SF-PPP while achieving faster convergence. Full article

This article aims to examine the real-time precise point positioning (PPP) solution’s accuracy utilizing the low-cost dual-frequency multi-constellation U-blox ZED-F9P module and real-time GNSS orbit and clock products from five analysis centers, including Bundesamt für Kartographie und Geodäsie (BKG), Centre National d’Etudes Spatiales (CNES), International GNSS Service (IGS), Geo Forschungs Zentrum (GFZ), and GNSS research center of Wuhan University (WHU). Three-hour static quad-constellation GNSS measurements are collected from ZED-F9P modules and geodetic grade Trimble R4s receivers over a reference station in Aswan City, Egypt, for a period of three consecutive days. Since a multi-GNSS PPP processing model is applied in the majority of the previous studies, this study employs the single-constellation GNSS PPP solution to process the acquired datasets. Different single-constellation GNSS PPP scenarios are adopted, namely, GPS PPP, GLONASS PPP, Galileo PPP, and BeiDou PPP models. The obtained PPP solutions from the low-cost module are validated for the positioning and precipitable water vapor (PWV) domains. To provide a reference positioning solution, the post-processed dual-frequency geodetic-grade GNSS PPP solution is applied; additionally, as the station under investigation is not a part of the IGS reference station network, a new technique is proposed to estimate reference PWV values. The findings reveal that the GPS and Galileo 3D position’s accuracy is within the decimeter level, while it is within the meter level for both the GLONASS and BeiDou models. Additionally, millimeter-level PWV precision is obtained from the four PPP models. Full article

Although the traditional Carrier-to-Code Leveling (CCL) method can provide ideal slant total electron content (STEC) observables for establishing ionospheric models, it must rely on dual-frequency (DF) receivers, which results in high hardware costs. In this study, an ionosphere-weight (IW) single-frequency (SF) precise point positioning (PPP) method for extracting STEC observables is proposed, and multi-global navigation satellite system (GNSS)-integrated processing is adopted to improve the spatial resolution of the ionospheric model. To investigate the advantages of this novel method, 41 European stations are used to establish the regional ionospheric model, and both low- and high-solar-activity conditions are considered. The results show that the IW SFPPP-derived regional ionospheric model has a significantly better quality of vertical total electron content (VTEC) than the CCL method when using the final global ionospheric map (GIM) as a reference, especially in areas with sparse monitoring stations. Compared with the CCL method, the RMS VTEC accuracy of the IW SFPPP method can be improved by 17.4% and 12.7% to 1.09 and 2.83 total electron content unit (TECU) in low- and high-solar-activity periods, respectively. Regarding GNSS carrier-phase-derived STEC variation (dSTEC) as the reference, the dSTEC accuracy of the IW SFPPP method is comparable to that of the CCL method, and its RMS values are about 1.5 and 2.8 TECU in low- and high-solar-activity conditions, respectively. This indicates that the proposed method using SF-only observations can achieve the same external accord accuracy as the CCL method in regional ionospheric modeling. Full article

In the conventional PPP-RTK mode, the platform and users act only as the generator and the utilizer of ionospheric corrections, respectively. In sparse reference station networks or regions with an active ionosphere, high-precision modeling still faces challenges. This study utilizes the concept of crowdsourcing and treats users as dynamic reference stations. By continuously feeding back ionospheric information to the platform, high-spatial-resolution modeling is achieved. Additionally, weight factors related to user positions are incorporated into conventional polynomial models to transform the regional ionosphere model from a common model into customized models, thereby providing more personalized services for different users. Validation was conducted with a sparse reference network with an average inter-station distance of approximately 391 km. While increasing the number of crowdsourcing users generally improves modeling performance, the enhancement also depends on their spatial distribution; that is, crowdsourcing users primarily provide localized improvements in their vicinity. Therefore, crowdsourcing users should ideally be uniformly distributed across the whole network. Compared with the conventional common model, the proposed customized model can more effectively characterize the irregular physical characteristics of the ionosphere, and the modeling accuracy is improved by about 12% to 41% in different scenarios. Furthermore, the performance of single-frequency PPP-RTK was verified on the terminal. In general, both crowdsourcing enhancement and the customized model can accelerate the convergence speed of the float solutions and improve positioning accuracy to varying degrees, and the epoch fix rate of the fixed solutions is also significantly improved. Full article

The availability of raw Global Navigation Satellites System (GNSS) measurements in Android smartphones fosters advancements in high-precision positioning for mass-market devices. However, challenges like inconsistent pseudo-range and carrier phase observations, limited dual-frequency data integrity, and unidentified hardware biases on the receiver side prevent the ambiguity resolution of smartphone GNSS. Consequently, relying solely on GNSS for high-precision positioning may result in frequent cycle slips in complex conditions such as deep urban canyons, underpasses, forests, and indoor areas due to non-line-of-sight (NLOS) and multipath conditions. Inertial/GNSS fusion is the traditional common solution to tackle these challenges because of their complementary capabilities. For pedestrians and smartphones with low-cost inertial sensors, the usual architecture is Pedestrian Dead Reckoning (PDR)+ GNSS. In addition to this, different GNSS processing techniques like Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) have also been integrated with INS. However, integration with PDR has been limited and only with Kalman Filter (KF) and its variants being the main fusion techniques. Recently, Factor Graph Optimization (FGO) has started to be used as a fusion technique due to its superior accuracy. To the best of our knowledge, on the one hand, no work has tested the fusion of GNSS Post-Processed Kinematics (PPK) and PDR on smartphones. And, on the other hand, the works that have evaluated the fusion of GNSS and PDR employing FGO have always performed it using the GNSS Single-Point Positioning (SPP) technique. Therefore, this work aims to combine the use of the GNSS PPK technique and the FGO fusion technique to evaluate the improvement in accuracy that can be obtained on a smartphone compared with the usual GNSS SPP and KF fusion strategies. We improved the Google Pixel 4 smartphone GNSS using Post-Processed Kinematics (PPK) with the open-source RTKLIB 2.4.3 software, then fused it with PDR via KF and FGO for comparison in offline mode. Our findings indicate that FGO-based PDR+GNSS–PPK improves accuracy by 22.5% compared with FGO-based PDR+GNSS–SPP, which shows smartphones obtain high-precision positioning with the implementation of GNSS–PPK via FGO. Full article

The long convergence time and non-robust positioning accuracy are the main factors limiting the application of precision single-point positioning (PPP) in kinematic vehicle navigation. Therefore, a dual/triple-frequency multi-constellation PPP-RTK method with atmospheric augmentation is proposed to achieve cm-level reliable kinematic positioning. The performance was assessed using a set of static station and kinematic vehicle positioning experiments conducted in Wuhan. In the static experiments, instantaneous convergence within 1 s and centimeter-level positioning accuracy were achieved for PPP-RTK using dual-frequency observation. For the kinematic experiments, instantaneous convergence was also achieved for dual-frequency PPP-RTK in open areas, with RMS of 2.6 cm, 2.6 cm, and 7.5 cm in the north, east, and up directions, respectively, with accuracy similar to short-baseline real-time kinematic positioning (RTK). Horizontal positioning errors of less than 0.1 m and 3D positional errors of less than 0.2 m were 99.54% and 98.46%, respectively. Additionally, after the outage of GNSS and during satellite reduction in obstructed environments, faster reconvergence and greater accuracy stability were realized compared with PPP without atmospheric enhancement. Triple-frequency PPP-RTK was able to further enhance the robustness and accuracy of positioning, with RMS of 2.2 cm, 2.0 cm, and 7.3 cm, respectively. In summary, a performance similar to RTK was achieved based on dual-frequency PPP-RTK, demonstrating that PPP-RTK has the potential for lane-level navigation. Full article

The multi-global navigation satellite system (GNSS) undifferenced and uncombined precise point positioning (UU-PPP), as a high-precision ionospheric observables extraction technology superior to the traditional carrier-to-code leveling (CCL) method, has received increasing attention. In previous research, only dual-frequency (DF) or multi-frequency (MF) observations are used to extract slant ionospheric delay with the UU-PPP. To reduce the cost of ionospheric modeling, the feasibility of extracting ionospheric observables from the multi-GNSS single-frequency (SF) UU-PPP was investigated in this study. Meanwhile, the between-satellite single-differenced (SD) method was applied to remove the effects of the receiver differential code bias (DCB) with short-term time-varying characteristics in regional ionospheric modeling. In the assessment of the regional real-time (RT) between-satellite SD ionospheric model, the internal accord accuracy of the SD ionospheric delay can be better than 0.5 TECU, and its external accord accuracy within 1.0 TECU is significantly superior to three global RT ionospheric models. With the introduction of the proposed SD ionospheric model into the multi-GNSS kinematic RT SF-PPP, the initialization speed of vertical positioning errors can be improved by 21.3% in comparison with the GRAPHIC (GRoup And PHase Ionospheric Correction) SF-PPP model. After reinitialization, both horizontal and vertical positioning errors of the SD ionospheric constrained (IC) SF-PPP can be maintained within 0.2 m. This proves that the proposed SDIC SF-PPP model can enhance the continuity and stability of kinematic positioning in the case of some GNSS signals missing or blocked. Compared with the GRAPHIC SF-PPP, the horizontal positioning accuracy of the SDIC SF-PPP in kinematic mode can be improved by 37.9%, but its vertical positioning accuracy may be decreased. Overall, the 3D positioning accuracy of the SD ionospheric-constrained RT SF-PPP can be better than 0.3 m. Full article

In just one year, Spaceopal and its partners developed the Galileo HAS Performance Characterization User Algorithm for the EU Agency for the Space Programme (EUSPA). The Galileo HAS User Terminal (HAUT) hosts the Galileo HAS Performance Characterization User Algorithm. The Galileo HAS User Terminal is a portable, configurable and autonomous device powered by a triple-frequency Galileo and GPS receiver and calculates a single- (Galileo) or multi-constellation (Galileo + GPS) Galileo HAS and Open Service (OS) positioning, velocity and time (PVT) solution. The User Terminal can be configured to retrieve Galileo HAS corrections either from Galileo Signal-in-Space (SIS) over E6-B or Internet Data Distribution (IDD) over NTRIP in an RTCM3 format and works in different frequency combinations that can be configured by the user. The User Terminal is a robust device (IP64) with multiple communication and logging capabilities. The Galileo HAS Initial Service was declared on 24 January by the European Commission, and provides free-of-charge, high-accuracy Precise Point Positioning (PPP) corrections (orbits, clocks) and code biases for Galileo and GPS to achieve real-time improved user positioning performance. The Galileo HAS Service Definition Document (SDD) and the HAS SIS Interface Control Document (HAS SIS ICD) are freely available to users on the web portal of the European GNSS Service Centre and HAS Internet Data Distribution Interface Control Documents (HAS IDD ICD) are available after registration. Using the Galileo HAS User Terminal, this article presents the results of Galileo HAS User Terminal’s performance, configuring the User Algorithm to assume static dynamics. It is to be noted that this configuration provides a significant performance benefit with respect to a configuration compatible with kinematic operation. Preliminary results indicate the Galileo HAS User Terminal achieves excellent accuracy. Full article

The use of high-precision positioning systems in modern navigation applications is crucial since location data is one of the most important pieces of information in Industry 4.0, especially for robots operating outdoors. In the modernization process of global navigation satellite system (GNSS) positioning, precise point positioning (PPP) has demonstrated its effectiveness in comparison to traditional differential positioning methods over the past thirty years. However, various challenges hinder the integration of PPP techniques into Internet of Things (IoT) systems for robot localization, with accuracy being a primary concern. This accuracy is impacted by factors such as satellite availability and signal disruptions in outdoor environments, resulting in less precise determination of satellite observations. Effectively addressing various GNSS errors is crucial when collecting PPP observations. The paper investigates the trade-off between kinematic PPP accuracy and cost effectiveness, through the examination of various influencing factors, including the choice of GNSS system (single or mixed), observation type (single or dual frequency), and satellite geometry. This research investigates kinematic PPP accuracy variation on a 10.4 km observed track based on different factors, using the GNSS system (single or mixed), and observation type (single or dual frequency). It can be concluded that mixed (GPS/GLONASS) dual frequency offers a 3D position accuracy of 9 cm, while mixed single frequency offers a 3D position accuracy of 13 cm. In industry, the results enable manufacturers to select suitable robot localization solutions according to the outdoor working environment (number of available satellites), economical constraint (single or dual frequency), and 3D position accuracy. Full article

Differential Code Bias (DCB) is a crucially systematic error in satellite positioning and ionospheric modeling. This study aims to estimate the BeiDou-3 global navigation satellite system (BDS-3) satellite DCBs by using the single-frequency (SF) uncombined Precise Point Positioning (PPP) model. The experiment utilized BDS-3 B1 observations collected from 25 International GNSS Service (IGS) stations located at various latitudes during March 2023. The results reveal that the accuracy of estimating B1I-B3I DCBs derived from single receiver exhibits latitude dependence. Stations in low-latitude regions show considerable variability in the root mean square (RMS) of absolute offsets for satellite DCBs estimation, covering a wide range of values. In contrast, mid- to high-latitude stations demonstrate a more consistent pattern with relatively stable RMS values. Moreover, it has been observed that the stations situated in the Northern Hemisphere display a higher level of consistency in the RMS values when compared to those in the Southern Hemisphere. When incorporating estimates from all 25 stations, the RMS of the absolute offsets in satellite DCBs estimation consistently remained below 0.8 ns. Notably, after excluding 8 low-latitude stations and utilizing data from the remaining 17 stations, the RMS of absolute offsets in satellite DCBs estimation decreased to below 0.63 ns. These enhancements underscore the importance of incorporating a sufficient number of mid- and high-latitude stations to mitigate the effects of ionospheric variability when utilizing SF observations for satellite DCBs estimation. Full article

Differential code bias (DCB) of satellite is an error that cannot be ignored in precise positioning, timing, ionospheric modeling, satellite clock correction, and ambiguity resolution. The completion of the third generation of BeiDou Navigation Satellite System (BDS-3) has extended DCB to multichannel code bias observations and observable-specific signal bias (OSB). In this paper, the DCB and OSB products provided by the Chinese Academy of Sciences (CAS) are analyzed and compared. The DCB parameters for the BDS satellites are applied in both single- and dual-frequency single point positioning (SPP), and the results are intensively investigated. Based on the satellite DCB parameters of the BDS, the performance of precise point positioning (PPP) with different frequency combinations is also analyzed in terms of positioning accuracy and convergence time. The standard deviations (STDs) of DCBs at each signal pair fluctuate from 0.2 ns to 1.5 ns. The DCBs of BDS-2 are slightly more stable than those of BDS-3. The mean values and STDs of C2I and C7I OSBs for BDS-2 are at the same level and are numerically smaller than their counterparts for the C6I OSBs. The mean OSBs for each signal of the BDS-3, excluding C2I, fluctuate between 12.35 ns and 12.94 ns, and the STD fluctuates between 2.11 ns and 3.10 ns. The DCBs and OSBs of the BDS-3 of the IGSO satellites are more stable than those of the MEO satellites. The corrections for TGD and DCB are able to improve the accuracy of single-frequency SPP by 44.09% and 44.07%, respectively, and improve the accuracy of dual-frequency SPP by 6.44% and 12.85%, respectively. The most significant improvements from DCB correction are seen in single-frequency positioning with B1I and dual-frequency positioning with B2a+B3I. DCB correction can improve the horizontal and three-dimensional positioning accuracy of the dual-frequency PPP of different ionosphere-free combinations by 13.53% and 13.84% on average, respectively, although the convergence is slowed. Full article

Currently, there are two main methods for single-epoch decimeter-level precise point positioning (PPP); one is a model based on ambiguity-fixed ionosphere-free (AFIF) observations, and the other is based on uncombined (UC) PPP. The implementation of these two models requires both extra-wide-lane (EWL) and wide-lane (WL) ambiguity fixing. Different from the existing methods, this paper proposes a multi-frequency ionosphere-reduced (IR) PPP model suitable for single-epoch decimeter-level positioning. Based on Galileo five-frequency data, the optimal selection strategy of IR combinations is first studied with ionosphere, noise level and wavelength factors considered. Then, based on the selected IR combination, two IR PPP models, namely IR(EST) and IR(IGN), are established according to whether ionosphere parameters are estimated or ignored. Finally, the proposed models are verified with real tracked data from globally distributed stations, and further compared with the existing AFIF/UC models in terms of positioning performance and time consumption. The relationship between the ionosphere equivalent ranging error and satellite elevation in the IR models is analyzed. The lower the elevation is, the larger the residual ranging error is, and its impact on positioning is weakened by downweighting its observations and adjusting the cut-off elevation during the partial ambiguity fixing (PAF) process. The results show that the performance of the two IR models is basically the same, and both can achieve horizontal and vertical accuracies better than 20 cm and 40 cm, respectively. Compared with the existing AFIF/UC models, the proposed IR models can achieve similar decimeter-level accuracy with only one step of EWL ambiguity fixing, and at the same time, the IR models have varying degrees of improvement in time consumption: 38% shorter than the AFIF model and 97% shorter than the UC model. Full article

Real−time single−frequency precise point positioning (PPP) is a promising low−cost technique for achieving high−precision navigation with sub−meter or centimeter−level accuracy. However, its effectiveness depends heavily on the availability and quality of the real−time ionospheric state estimations required for correcting the delay in global navigation satellite system (GNSS) signals. In this study, the dynamic mode decomposition (DMD) model is used with global ionospheric vertical total electron content (vTEC) RMS maps to construct 24 h global ionospheric vTEC RMS map forecasts. These forecasts are assimilated with C1P forecast products, and L1 single−frequency positioning solutions are compared with different ionospheric correction models. The study examines the impact of assimilating predicted RMS data and evaluates the presented approach’s practicality in utilizing the IGRG product. The results show that the IGSG RMS prediction−based model improves positioning accuracy up to five hours ahead and achieves comparable results to other models, making it a promising technique for obtaining high−precision navigation. Full article

Due to the lack of coverage of IGS in Africa, especially over North Africa, and the construction revolution of infrastructure in Egypt, a geodetic CORS stations network was established in 2012. These CORS stations are operated by the Egyptian Surveying Authority (Egy. SA) and cover the whole of Egypt. The paper presents a fully developed regional ionosphere model (RIM) depending on the Egyptian CORS stations. The new model and the PPP solution were obtained using Bernese GNSS V. 5.2 software. An observation data series of eight days (DOY 201–208)/2019 was used in this study. Eighteen stations were used to develop the RIM model for each day; fifteen stations were used to validate the new RIM model. A static SF-PPP solution was obtained using the CODE-GIM and RIM models. Comparing the outcomes to the reference network solution, based on the recently developed RIM model, the solution showed a mean error of 0.06 m in the East direction, 0.13 m in the North direction, and 0.21 m in the height direction. In the East, North, and height directions, this solution improves the SF-PPP result achieved by the Global Ionosphere Maps (CODE-GIM) model by 60%, 68%, and 77%, respectively. Full article