Search Results (55)

The undifferenced and uncombined (UDUC) model preserves raw code and carrier-phase observations for each frequency, avoiding differencing or ionosphere-free combinations. This approach enables the direct estimation of atmospheric parameters. However, the stochastic characteristics of these parameters, particularly ionospheric delay, are often oversimplified or based on empirical assumptions, limiting the accuracy and convergence speed of Precise Point Positioning (PPP). To address this issue, this study introduces a stochastic constraint model based on the power spectral density (PSD) of ionospheric variations. The PSD describes the distribution of ionospheric delay variance across temporal frequencies, thereby providing a physically meaningful constraint for modeling their temporal correlations. Integrating this PSD-derived stochastic model into the UDUC framework improves both ionospheric delay estimation and PPP performance, especially under disturbed ionospheric conditions. This paper presents a BDS PPP/PPP-AR method that estimates the ionospheric power spectral density (IPSD) in real time. Vondrak smoothing is applied to suppress noise in ionospheric observations before IPSD estimation. Experimental results demonstrate that the proposed approach significantly improves convergence time and positioning accuracy. Compared to the empirical IPSD model, the PPP mode using the estimated IPSD reduced horizontal and vertical convergence times by 11.1% and 13.2%, and improved the corresponding accuracies by 15.7% and 12.6%, respectively. These results confirm that real-time IPSD estimation, coupled with Vondrak smoothing, establishes an adaptive and robust ionospheric modeling framework that enhances BDS PPP and PPP-AR performance under varying ionospheric conditions. Full article

In LEO constellation–augmented navigation, the transmitting antenna phase center offset (PCO) and the equipment delay associated with the downlink signals of LEO satellites constitute major error sources that must be precisely characterized. Previous studies primarily focused on single or small-scale satellite scenarios, lacking comprehensive evaluations regarding the influence of constellation scale, orbital altitude, ground station configuration, and various error sources. To address this gap, we propose a joint estimation method utilizing observations from a limited number of regional ground stations in China that simultaneously track GNSS and LEO satellites. The method is specifically designed to accommodate practical constraints on ground station distribution within China. Initially, a batch least-squares estimation strategy is employed to simultaneously determine the ionosphere-free PCO and initial equipment delays for all LEO satellites in a constellation-wide solution. Subsequently, the estimated PCO parameters are fixed, and the equipment delays are further refined using a precise point positioning (PPP) approach. To systematically evaluate the method’s performance under realistic conditions, we analyze the impact of orbital altitude, constellation size, ground station number, data processing duration, and orbit/clock biases through comprehensive simulations. The results indicate: (1) the Z-direction component of the PCO (pointing toward the Earth’s center) and equipment delay is more sensitive to orbit and clock errors; (2) Increasing the number of LEO satellites generally improves the estimation accuracy of equipment delays, but the marginal gain diminishes as the constellation size expands; (3) sub-centimeter PCO accuracy and equipment delay accuracies better than 3 cm can still be achieved using only 3–4 regionally distributed ground stations over an observation period of 5–7 days. Full article

As contemporary society and the global economy become increasingly dependent on satellite-based systems, the need for reliable and resilient positioning, navigation, and timing (PNT) services has never been more critical. This study investigates the impact of the geomagnetic storm that occurred in May 2024 on the performance of global navigation satellite system (GNSS) low-cost permanent stations. The research evaluates the influence of ionospheric disturbances on both positioning performance and raw GNSS observations. Two days were analyzed: 8 May 2024 (DOY 129), representing quiet ionospheric conditions, and 11 May 2024 (DOY 132), coinciding with the peak of the geomagnetic storm. Precise Point Positioning (PPP) and static relative positioning techniques were applied to data from a low-cost GNSS station (DYVA), supported by comparative analysis using a nearby geodetic-grade station (TRDS00NOR). The results showed that while RMS positioning errors remained relatively stable over 24 h, the maximum errors increased significantly during the storm, with the 3D positioning error nearly doubling on DOY 132. Short-term analysis revealed even larger disturbances, particularly in the vertical component, which reached up to 3.39 m. Relative positioning analysis confirmed the vulnerability of single-frequency (L1) solutions to ionospheric disturbances, whereas dual-frequency (L1+L2) configurations substantially mitigated errors, highlighting the effectiveness of ionosphere-free combinations during storm events. In the second phase, raw GNSS observation quality was assessed using detrended GPS L1 carrier-phase residuals and signal strength metrics. The analysis revealed increased phase instability and signal degradation on DOY 132, with visible cycle slips occurring between epochs 19 and 21. Furthermore, the average signal-to-noise ratio (SNR) decreased by approximately 13% for satellites in the northwest sky sector, and a 5% rise in total cycle slips was recorded compared with the quiet day. These indicators confirm the elevated measurement noise and signal disruption associated with geomagnetic activity. These findings provide a quantitative assessment of low-cost GNSS receiver performance under geomagnetic storm conditions. This study emphasizes their utility for densifying GNSS infrastructure, particularly in regions lacking access to geodetic-grade equipment, while also outlining the challenges posed by space weather. Full article

Ensuring Global Navigation Satellite System (GNSS) integrity, which provides operational reliability via fault detection, is important for safety-critical applications using high-precision techniques like Precise Point Positioning (PPP) and Real-Time Kinematic (RTK). Ionospheric errors, from atmospheric free electrons, challenge this integrity by introducing variable uncertainties into positioning solutions. This study investigates how ionospheric error modeling spatial resolution impacts protection level (PL) calculations, a metric defining positioning error bounds with high confidence. A comparative evaluation was conducted in low-latitude (Guangdong) and mid-latitude (Shandong) regions, contrasting large-scale with small-scale grid-based ionospheric models from regional GNSS networks. Experimental results show small-scale grids improve characterization of localized ionospheric variability, reducing ionospheric residual standard deviation by approximately 30% and enhancing PL precision. Large-scale grids show limitations, especially in active low-latitude conditions, leading to conservative PLs that reduce system availability and increase missed fault detection risks. A user-side PL computation framework incorporating this high-resolution ionospheric residual uncertainty improved system availability to 94.7% and lowered misleading and hazardous outcomes by over 80%. This research indicates that refined, high-resolution ionospheric modeling improves operational reliability and safety for high-integrity GNSS applications, particularly under diverse and challenging ionospheric conditions. Full article

The International Bureau of Weights and Measures (BIPM) currently mainly uses GPS time transfer for the calculation of UTC. In order to enhance the reliability of the time links, the common-view (CV) and Precise Point Positioning (PPP) time transfer performance of the dual-frequency ionosphere-free combination for BRUX-SPT0, NIST-USN7, and BRUX-USN7 links was evaluated, including GPS (P1 & P2), Galileo (E1 & E5a), and BDS-3 (B1I & B3I, B1I & B2a, B1C & B3I, B1C & B2a). The experimental results show that the precision and average frequency stability (AFT) of BDS-3 B1C & B2a CV and PPP links are better than those of BDS-3 B1I & B3I, B1I & B2a, and B1C & B3I links. Compared to the GPS P1 & P2 and BDS-3 B1C & B2a CV links, the Galileo E1 & E5a links have the highest precision. In addition, the precision of GPS PPP links outperforms the BDS-3 and Galileo links. The short-term FT (frequency stability) of GPS PPP links is better than that of BDS-3 B1C & B2a PPP links. When the average time is greater than 4.3 h, however, the BDS-3 B1C & B2a PPP link’s AFT is significantly improved compared with the Galileo PPP links. 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

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%. Full article

The legacy Global Navigation Satellite System (GNSS) satellite clock offsets obtained by the dual-frequency undifferenced (UD) ionospheric-free (IF) model absorb the code and phase time-variant hardware delays, which leads to the inconsistency of the precise satellite clock estimated by different frequencies. The dissimilarity of the satellite clock offsets generated by different frequencies is called the inter-frequency clock bias (IFCB). Estimates of the IFCB typically employ epoch-differenced (ED) geometry-free ionosphere-free (GFIF) observations from global networks. However, this method has certain theoretical flaws by ignoring the receiver time-variant biases. We proposed a new undifferenced model coupled with satellite clock offsets, and further converted the IFCB into the code and phase time-variant mixed observable-specific signal bias (OSB) to overcome the defects of the traditional model and simplify the bias correction process of multi-frequency precise point positioning (PPP). The new model not only improves the mixed OSB performance, but also avoids the negative impact of the receiver time-variant biases on the satellite mixed OSB estimation. The STD and RMS of the original OSB can be improved by 7.5–60.9% and 9.4–66.1%, and that of ED OSB (it can reflect noise levels) can be improved by 50.0–87.5% and 60.0–88.9%, respectively. Similarly, the corresponding PPP performance for using new mixed OSB is better than that of using the traditional IFCB products. Thus, the proposed pseudorange and phase time-variant mixed OSB concept and the new undifferenced model coupled with satellite clock offsets are reliable, applicable, and effective in multi-frequency PPP. Full article

Integrated water vapor (IWV) is a crucial parameter for tropospheric sounding and weather prediction applications. IWV is essentially calculated using observations from global navigation satellite systems (GNSS). Presently, the Galileo satellite system is further developed, including more visible satellites that transmit multi-frequency signals. This study aims to evaluate the accuracy of real-time IWV estimated from a triple-frequency Galileo-only precise point positioning (PPP) processing model utilizing E₁, E_5a, E_5b, and E₅ observations, which is not addressed by the previous studies. For this purpose, Galileo datasets from 10 global reference stations spanning various 4-week periods in the winter, spring, summer, and fall seasons are acquired. To process the acquired datasets, dual- and triple-frequency ionosphere-free PPP solutions are used, including E₁E_5a PPP, E₁E_5aE_5b PPP, and E₁E₅E_5b PPP solutions. The publicly available real-time products from the Centre National d’Etudes Spatiales (CNES) are utilized. The real-time IWV values are computed and then validated with the European Centre for Medium-Range Weather Forecasting (ECMWF) reanalysis products (ERA5) counterparts. The findings demonstrate that the root mean square error (RMSE) of the estimated IWV is less than 3.15 kg/m² with respect to the ECMWF ERA5 counterparts. Furthermore, the E₁E_5aE_5b PPP and E₁E₅E_5b PPP models enhance the IWV’s accuracy by about 11% and 16%, respectively, compared with the E₁E_5a PPP model. Full article

Global Navigation Satellite System (GNSS) signals experience delays when passing through the atmosphere due to the presence of free electrons in the ionosphere and air density in the non-ionized part of the atmosphere, known as the troposphere. The Precise Point Positioning (PPP) technique demonstrates highly accurate positioning along with Zenith Tropospheric Delay (ZTD) estimation. ZTD estimation is valuable for various applications including climate modelling and determining atmospheric water vapor. Current GNSS network resolutions are not completely sufficient for the scale of a few kilometres that regional climate and weather models are increasingly adopting. The Centipede-RTK network is a low-cost option for increasing the spatial resolution of tropospheric monitoring. This study is motivated by the question of whether low-cost GNSS networks can provide a viable alternative without compromising data quality or precision. This study compares the performance of the low-cost Centipede-RTK network in calculating the Zenith Tropospheric Delay (ZTD) to that of the existing EUREF Permanent Network (EPN), using two alternative software packages, RTKLIB demo5 version and CSRS-PPP version 3, to ensure robustness and software independence in the findings. This investigation indicated that the ZTD estimations from both networks are almost identical when processed by the CSRS-PPP software, with the highest mean difference being less than 3.5 cm, confirming that networks such as Centipede-RTK could be a reliable option for dense precise atmospheric monitoring. Furthermore, this study revealed that the Centipede-RTK network, when processed using CSRS-PPP, provides ZTD estimations that are very similar and consistent with the EUREF ZTD product values. These findings suggest that low-cost GNSS networks like Centipede-RTK are viable for enhancing network density, thus improving the spatial resolution of tropospheric monitoring and potentially enriching climate modelling and weather prediction capabilities, paving the way for broader application and research in GNSS meteorology. Full article

Global navigation satellite system (GNSS) provides users with all-weather, continuous, high-precision positioning, navigation, and timing (PNT) services. In the operation and use of GNSS, the influence of the space environment is a factor that must be considered. For example, during geomagnetic storms, a series of changes in the Earth’s magnetosphere, ionosphere, and upper atmosphere affect GNSS’s positioning performance. To investigate the positioning performance of global satellite navigation systems during geomagnetic storms, this study selected three geomagnetic storm events that occurred from September to December 2023. Utilizing the global positioning system (GPS)/Beidou navigation satellite system (BDS) dual-system, kinematic precise point positioning (PPP) experiments were conducted, and the raw observational data from 100 stations worldwide was analyzed. The experimental results show that the positioning accuracy of some stations in high-latitude areas decreases significantly when using the conventional Geometry Free (GF) cycle-slip detection threshold during geomagnetic storms, which means that the GF is no longer applicable to high-precision positioning services. Meanwhile, there is no significant change in the satellite signal strengths received at the stations during the period of the decrease in positioning accuracy. Analyzing the cycle-slip rates for stations where abnormal accuracy occurred, it was observed that stations experiencing a significant decline in positioning accuracy exhibited serious cycle-slip misjudgments. To improve the kinematic PPP accuracy during magnetic storms, this paper proposes an adaptive threshold for cycle-slip detection and designs five experimental strategies. After using the GF adaptive threshold, the station positioning accuracy improved significantly. It achieved the accuracy level of the quiet period, while the cycle-slip incidence reached the average level. During magnetic storms, the ionosphere changes rapidly, and the use of the traditional GF constant threshold will cause serious cycle-slip misjudgments, which makes the dynamic accuracy in high latitude areas and some mid-latitude areas uncommon, while the use of the GF adaptive threshold can alleviate this phenomenon and improve the positioning accuracy in the high-latitude regions and some of the affected mid-latitude areas during the magnetic storms. Full article

When processing the carrier phase, the global navigation satellite system (GNSS) grants the highest precision for geodetic measurements. The analysis centers (ACs) from the International GNSS Service (IGS) provide different data such as precise clock data, precise orbits, reference frame, ionosphere and troposphere data, as well as other geodetic products. Each individual AC has its own strategy for delivering the abovementioned products, with one of the key elements being the cutoff elevation angle. Typically, this angle is arbitrarily chosen using generic values without studying the impact of this choice on the obtained results, in particular when very precise positions are considered. This article addresses this issue. To this end, the article has two key sections, and the first is to evaluate the impact of using the two different cutoff elevation angles that are most widely used: (a) 3 degrees cutoff and (b) 10 degrees cutoff elevation angle. This analysis is completed in two major parts: (i) the analysis of the root mean square (RMS) for the carrier phase and (ii) the analysis of the station position in terms of repeatability. The second key section of the paper is a comprehensive carrier phase analysis conducted by adopting a new approach using a mean of the 25-point average RMS (A-RMS) and the single-point RMS and using an ionosphere-free linear combination. By using the ratio between the 25-point average RMS and the single-point RMS we can define the type of scatter that dominates the phase solution. The analyzed data span a one-year period. The tested GNSS stations belong to the EUREF Permanent Network (EPN) and the International GNSS Service (IGS). These comprise 55 GNSS stations, of which only 23 GNSS stations had more than 95% data availability for the entire year. The RMS and A-RMS are analyzed in conjunction with the precipitable water vapor (PWV), which shows clear signs of temporal correlation. Of the 23 GNSS stations, three stations show an increase of around 50% of the phase RMS when using a 3° cutoff elevation angle, and only four stations have a difference of 5% between the phase RMS when using both cutoff elevation angles. When using the A-RMS, there is an average improvement of 37% of the phase scatter for the 10° cutoff elevation angle, whereas for the 3° cutoff elevation angle, the improvement is around 33%. Based on studying this ratio, four stations indicate that the scatter is dominated by the stronger-than-usual dominance of long-period variations, whereas the others show short-term noise. In terms of station position repeatability, the weighted root mean square (WRMS) is used as an indicator, and the results between the differences of using a 3° and 10° cutoff elevation angle strategy show a difference of −0.16 mm for the North component, −0.21 mm for the East component and a value of −0.75 mm for the Up component, indicating the importance of using optimal cutoff angles. 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

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

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