Search Results (20)

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

Satellite navigation is an essential component of the national infrastructure. Space weather and ionospheric conditions are the prime sources of GNSS (global navigation satellite system) positioning, navigation, and timing (PNT) service disruptions and degradations. Protection, toughening, and augmentation (PTA) of GNSS PNT services require novel approaches in ionospheric effects mitigation. Standard global ionospheric correction models fail in the mitigation of high-dynamics and local ionospheric disturbances. Here, we demonstrate that in the case of the short-term fast-developing geomagnetic storm, a machine learning-based environment-aware GNSS ionospheric correction model for sub-equatorial regions may provide a substantial improvement over the existing global Klobuchar model, considered a benchmark. The proposed machine learning-based model utilises just the geomagnetic field density component observations as a predictor to estimate TEC/GNSS ionospheric delay as the prediction model target. Further research is needed to refine the methodology of machine learning model development selection and validation and to establish an architecture-agnostic framework for GNSS PTA development. Full article

Topside total electron content (TEC) data measured by COSMIC/FORMAT-3 during 2008 and 2016 were used to analyze and model the global plasmaspheric electron content (PEC) above 800 km with the help of the empirical orthogonal function (EOF) analysis method, and the potential role of the proposed PEC model in helping Global Navigation Satellite System (GNSS) users derive accurate slant TEC (STEC) from existing high-precision vertical TEC (VTEC) products was validated. A uniform gridded PEC dataset was first obtained using the spherical harmonic regression method, and then, it was decomposed into EOF basis modes. The first four major EOF modes contributed more than 99% of the total variance. They captured the pronounced latitudinal gradient, longitudinal differences, hemispherical differences, diurnal and seasonal variations, and the solar activity dependency of global PEC. A second-layer EOF decomposition was conducted for the spatial pattern and amplitude coefficients of the first-layer EOF modes, and an empirical PEC model was constructed by fitting the second-layer basis functions related to latitude, longitude, local time, season, and solar flux. The PEC model was designed to be driven by whether solar proxy or parameters derived from the Klobuchar model meet the real-time requirements. The validation of the results demonstrated that the proposed PEC model could accurately simulate the major spatiotemporal patterns of global PEC, with a root-mean-square (RMS) error of 1.53 and 2.24 TECU, improvements of 40.70% and 51.74% compared with NeQuick2 model in 2009 and 2014, respectively. Finally, the proposed PEC model was applied to conduct a vertical-slant TEC conversion experiment with high-precision Global Ionospheric Maps (GIMs) and dual-frequency carrier phase observables of more than 400 globally distributed GNSS sites. The results of the differential STEC (dSTEC) analysis demonstrated the effectiveness of the proposed PEC model in aiding precise vertical-slant TEC conversion. It improved by 18.52% in dSTEC RMS on a global scale and performed better in 90.20% of the testing days compared with the commonly used single-layer mapping function. Full article

Low Earth Orbit (LEO) constellations have recently gained tremendous attention in the navigational field due to their larger constellation size, faster geometry variations, and higher signal power levels than Global Navigation Satellite Systems (GNSS), making them favourable for Position, Navigation, and Timing (PNT) purposes. Satellite signals are heavily attenuated from the atmospheric layers, especially from the ionosphere. Ionospheric delays are, however, expected to be smaller in signals from LEO satellites than GNSS due to their lower orbital altitudes and higher carrier frequency. Nevertheless, unlike for GNSS, there are currently no standardized models for correcting the ionospheric errors in LEO signals. In this paper, we derive a new model called Interpolated and Averaged Memory Model (IAMM) starting from existing International GNSS Service (IGS) data and based on the observation that ionospheric effects repeat every 11 years. Our IAMM model can be used for ionospheric corrections for signals from any satellite constellation, including LEO. This model is constructed based on averaging multiple ionospheric data and reflecting the electron content inside the ionosphere. The IAMM model’s primary advantage is its ability to be used both online and offline without needing real-time input parameters, thus making it easy to store in a device’s memory. We compare this model with two benchmark models, the Klobuchar and International Reference Ionosphere (IRI) models, by utilizing GNSS measurement data from 24 scenarios acquired in several European countries using both professional GNSS receivers and Android smartphones. The model’s behaviour is also evaluated on LEO signals using simulated data (as measurement data based on LEO signals are still not available in the open-access community; we show a significant reduction in ionospheric delays in LEO signals compared to GNSS. Finally, we highlight the remaining open challenges toward viable ionospheric-delay models in an LEO-PNT context. Full article

In this study, the NeQuick G and Klobuchar models are evaluated by monitoring performance issues related to ionosphere activity for single-frequency users. The effects of radio frequency (RF) signal propagation through the ionosphere may have a significant impact on satellite communication and navigation systems because of geomagnetic field geometry near the magnetic equator and in the proximity to the high- and low-latitude zones. An ongoing challenge is determining how accurate the ionospheric models employed by existing Global Navigation Satellite Systems (GNSSs) are. This work investigates the patterns of total electron content (TEC) fluctuations over distinct zones from 1 January 2019 to 30 June 2022. Measurements are collected at station networks deployed worldwide. Firstly, monthly and seasonal variations of TECs are analysed. Secondly, the TEC ’availability’ parameter, as the percentage of time when the TEC error is compliant with the specification of the Galileo Single-Frequency Ionosphere Algorithm (’NeQuick G’ model), is introduced. The TEC error defines the difference between (a) the model TEC, obtained by either the NeQuick G or the Klobuchar model over a given station, and (b) the reference TEC, based on observations from networks of GNSS receivers. Finally, the position, velocity, and time (PVT), along with broadcast group delays (BGDs) are analysed and the PVT accuracy is compared between the NeQuick G and Klobuchar models. In 3.5 years, the seasonal behaviour of TEC shows maxima during the March and October equinox and minima during the June and December solstice. Moreover, an increase in the TEC values and the amount of TEC errors are visible as we are approaching the next solar maximum. Preliminary results show a larger associated positioning error using the Klobuchar than the NeQuick G model. However, the difference is zone-dependent, most evident in equatorial regions. This collaborative study of the GRC, NMA, TUW, and SRC was performed under the Framework Partnership Agreements (GSA/GRANT/04/2016). Full article

Global navigation satellite systems (GNSS) provide a great data source about the ionosphere state. These data can be used for testing ionosphere models. We studied the performance of nine ionospheric models (Klobuchar, NeQuickG, BDGIM, GLONASS, IRI-2016, IRI-2012, IRI-Plas, NeQuick2, and GEMTEC) both in the total electron content (TEC) domain—i.e., how precise the models calculate TEC—and in the positioning error domain—i.e., how the models improve single frequency positioning. The whole data set covers 20 years (2000–2020) from 13 GNSS stations, but the main analysis involves data during 2014–2020 when calculations are available from all the models. We used single-frequency positioning without ionospheric correction and with correction via global ionospheric maps (IGSG) data as expected limits for errors. Improvements against noncorrected solution were as follows: GIM IGSG—22.0%, BDGIM—15.3%, NeQuick2—13.8%, GEMTEC, NeQuickG and IRI-2016—13.3%, Klobuchar—13.2%, IRI-2012—11.6%, IRI-Plas—8.0%, GLONASS—7.3%. TEC bias and mean absolute TEC errors for the models are as follows: GEMTEC—−0.3 and 2.4 TECU, BDGIM—−0.7 and 2.9 TECU, NeQuick2—−1.2 and 3.5 TECU, IRI-2012—−1.5 and 3.2 TECU, NeQuickG—−1.5 and 3.5 TECU, IRI-2016—−1.8 and 3.2 TECU, Klobuchar—1.2 and 4.9 TECU, GLONASS—−1.9 and 4.8 TECU, and IRI-Plas—3.1 and 4.2 TECU. While TEC and positioning domains differ, new-generation operational models (BDGIM and NeQuickG) could overperform or at least be at the same level as classical empirical models. Full article

Ionospheric error is one of the largest errors affecting global navigation satellite system (GNSS) users in open-sky conditions. This error can be mitigated using different approaches including dual-frequency measurements and corrections from augmentation systems. Although the adoption of multi-frequency devices has increased in recent years, most GNSS devices are still single-frequency standalone receivers. For these devices, the most used approach to correct ionospheric delays is to rely on a model. Recently, the empirical model Neustrelitz Total Electron Content Model for Galileo (NTCM-G) has been proposed as an alternative to Klobuchar and NeQuick-G (currently adopted by GPS and Galileo, respectively). While the latter outperforms the Klobuchar model, it requires a significantly higher computational load, which can limit its exploitation in some market segments. NTCM-G has a performance close to that of NeQuick-G and it shares with Klobuchar the limited computation load; the adoption of this model is emerging as a trade-off between performance and complexity. The performance of the three algorithms is assessed in the position domain using data for different geomagnetic locations and different solar activities and their execution time is also analysed. From the test results, it has emerged that in low- and medium-solar-activity conditions, NTCM-G provides slightly better performance, while NeQuick-G has better performance with intense solar activity. The NTCM-G computational load is significantly lower with respect to that of NeQuick-G and is comparable with that of Klobuchar. Full article

Unmanned aerial vehicles (UAVs) have become very popular tools for geoinformation acquisition in recent years. They have also been applied in many other areas of life. Their navigation is highly dependent on global navigation satellite systems (GNSS). The European Geostationary Navigation Overlay Service (EGNOS) is intended to support GNSSs during positioning, mainly for aeronautical applications. The research presented in this paper concerns the analysis of the positioning quality of a modified GPS/EGNOS algorithm. The calculations focus on the source of ionospheric delay data as well as on the aspect of smoothing code observations with phase measurements. The modifications to the algorithm concerned the application of different ionospheric models for position calculation. Consideration was given to the EGNOS ionospheric model, the Klobuchar model applied to the GPS system, the Klobuchar model applied to the BeiDou system, and the NeQuick model applied to the Galileo system. The effect of removing ionospherical corrections from GPS/EGNOS positioning on the results of the determination of positioning quality was also analysed. The results showed that the original EGNOS ionospheric model maintains the best accuracy results and a better correlation between horizontal and vertical results than the other models examined. The additional use of phase-smoothing of code observations resulted in maximum horizontal errors of approximately 1.3 m and vertical errors of approximately 2.2 m. It should be noted that the results obtained have local characteristics related to the area of north-eastern Poland. Full article

Single point positioning (SPP) can meet the requirements of the majority of real-time time transfer applications. Meanwhile, a single-frequency (SF) receiver is cheaper than a dual-frequency receiver. However, SPP performance can be greatly affected by large pseudorange observation noise. Phase smoothing the pseudorange is an effective approach to reduce pseudorange noise. Since the classical phase-smoothed pseudorange algorithm does not account for the effect of ionosphere delay, we propose a BDGIM-based phase-smoothed pseudorange algorithm to eliminate the ionospheric delay and apply it to BeiDou Navigation Satellite System (BDS-3) SPP time transfer. In this paper, we first evaluate the performance of the BeiDou global ionospheric delay correction model (BDGIM) and compare it with that of the BeiDou Klobuchar model to determine if it is practical to incorporate the BDGIM into our suggested method. The performance of the BDGIM is better than that of the Klobuchar model. The mean RMS value of the BDGIM is 2.6 Total Electron Content Unit (TECU). The average ionospheric correction rate of the BDGIM is 75.5%. Then, we investigate the performance of the improved SF SPP time transfer. The performance of the improved SPP time transfer is much better than that of the traditional SPP time transfer. Compared with the traditional time transfer, the average Type A uncertainty of the improved time transfer is 2.08 ns, which is reduced by about 11.1% from the time transfer without it. Regarding frequency stability, the modified Allan deviations of the improved time transfer are 1.43E-12 and 1.68E-13 at 960 s and 61,440 s, with improvements of 51.2% and 59.9%, respectively. Full article

The broadcast ionospheric model is one of the main methods for eliminating ionospheric delay errors for the Global Navigation Satellite Systems (GNSS) single-frequency users. GPS Klobuchar model (GPSK8) is the widely used broadcast ionospheric model for GPS, while BDS usually implements the BDS Klobuchar model (BDSK8) and BeiDou Global Broadcast Ionospheric Delay Correction Model (BDGIM). Geomagnetic storms may cause interference within the ionosphere and near-Earth space, compromising the accuracy of ionospheric models and adversely affecting the navigation satellite systems. This paper analyzes the static Standard Point Positioning (SPP) accuracy of GPS and BDS by implementing the broadcast ionospheric models and then investigates the impact of strong geomagnetic storms occurring in 2021 on positioning accuracy. The results show that the global 3D positioning accuracy (95%) of GPS + GPSK8, BDS + BDSK8, and BDS + BDGIM are 3.92 m, 4.63 m, and 3.50 m respectively. BDS has a better positioning accuracy in the northern hemisphere than that of the southern hemisphere, while the opposite is valid for GPS. In the mid-latitude region of the northern hemisphere, BDS + BDSK8 and BDS + BDGIM have similar positioning accuracy and are both better than GPS + GPSK8. The positioning accuracy after applying those three broadcast ionospheric models shows the superior performances of winter and summer over spring and autumn (based on the northern hemisphere seasons). With the exception of during winter, nighttime accuracy is better than that of daytime. The strong geomagnetic storm that occurred on the day of year (DOY) 132, 2021 has an impact on the positioning accuracy for only a small number of stations; however, the global average positioning accuracy is not significantly affected. The strong geomagnetic storms that occurred in DOY 307 and DOY 308 have a significant impact on the positioning accuracy of dozens of stations, and the global average positioning accuracy is affected to a certain extent, with some stations experiencing a serious loss of accuracy. Decreased degrees in positioning accuracy is proportional to the intensity of the geomagnetic storm. Of the 33 IGS Multi-GNSS Experiment (MGEX) stations worldwide, those located in the low and mid-latitudes are more significantly affected by the geomagnetic storms compared with higher latitudes. Evident fluctuations of the positioning errors existed during the strong geomagnetic storms, with an increase in extreme values, particularly in the up direction. Full article

The broadcast ionospheric model is mainly used to correct the ionospheric delay error for single-frequency users. Since the BeiDou global ionospheric delay correction model (BDGIM) is a novel broadcast ionospheric model for BDS-3, its performance was analyzed through single point positioning (SPP) in this study. Twenty-two stations simultaneously receiving B1C, B2a, B1I and B3I signals were selected from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) tracking networks for the SPP experiments. The differential code bias (DCB) parameters were used to correct the hardware delays in the signals of B1C and B2a. The results showed that the BDGIM performs the best in high-latitude areas, and can effectively improve the positioning accuracy compared with the Klobuchar model. The average 3D positioning accuracy of the four civil signals can reach 3.58 m in high-latitude areas. The positioning accuracies with the BDGIM in the northern hemisphere are better than those in the southern hemisphere, and the global average 3D positioning accuracy of the four civil signals is 4.60 m. The performance of the BDGIM also shows some seasonal differences. The BDGIM performs better than the Klobuchar model on the days of spring equinox and winter solstice, while the opposite is true on the days of summer solstice and autumn equinox. On the day of winter solstice, the average 3D accuracies with the BDGIM on the signals of B1C, B2a, B1I and B3I are 4.13 m, 5.32 m, 4.40 m and 4.49 m, respectively. Although the SPP accuracies are to some extent affected by the geomagnetic storm, the BDGIM generally performs better and are more resistant to the geomagnetic storm than the Klobuchar model. Full article

IONORING (IONOspheric RING) is a tool capable to provide the real-time monitoring and modeling of the ionospheric Total Electron Content (TEC) over Italy, in the latitudinal and longitudinal ranges of 35°N–48°N and 5°E–20°E, respectively. IONORING exploits the Global Navigation Satellite System (GNSS) data acquired by the RING (Rete Integrata Nazionale GNSS) network, managed by the Istituto Nazionale di Geofisica e Vulcanologia (INGV). The system provides TEC real-time maps with a very fine spatial resolution (0.1° latitude x 0.1° longitude), with a refresh time of 10 min and a typical latency below the minute. The TEC estimated at the ionospheric piercing points from about 40 RING stations, equally distributed over the Italian territory, are interpolated using locally (weighted) regression scatter plot smoothing (LOWESS). The validation is performed by comparing the IONORING TEC maps (in real-time) with independent products: (i) the Global Ionospheric Maps (GIM) - final product- provided by the International GNSS Service (IGS), and (ii) the European TEC maps from the Royal Observatory of Belgium. The validation results are satisfactory in terms of Root Mean Square Error (RMSE) between 2 and 3 TECu for both comparisons. The potential of IONORING in depicting the TEC daily and seasonal variations is analyzed over 3 years, from May 2017 to April 2020, as well as its capability to account for the effect of the disturbed geospace on the ionosphere at mid-latitudes. The IONORING response to the X9.3 flare event of September 2017 highlights a sudden TEC increase over Italy of about 20%, with a small, expected dependence on the latitude, i.e., on the distance from the subsolar point. Subsequent large regional TEC various were observed in response to related follow-on geomagnetic storms. This storm is also used as a case event to demonstrate the potential of IONORING in improving the accuracy of the GNSS Single Point Positioning. By processing data in kinematic mode and by using the Klobuchar as the model to provide the ionospheric correction, the resulting Horizontal Positioning Error is 4.3 m, lowering to, 3.84 m when GIM maps are used. If IONORING maps are used as the reference ionosphere, the error is as low as 2.5 m. Real-times application and services in which IONORING is currently integrated are also described in the conclusive remarks. Full article

As one of the main errors that affects Global Navigation Satellite System (GNSS) positioning accuracy, ionospheric delay also affects the improvement of smartphone positioning accuracy. The current ionospheric error correction model used in smartphones has a certain time delay and low accuracy, which is difficult to meet the needs of real-time positioning of smartphones. This article proposes a method to use the real-time regional ionospheric model retrieved from the regional Continuously Operating Reference Stations (CORS) observation data to correct the GNSS positioning error of the smartphone. To verify the accuracy of the model, using the posterior grid as the standard, the electron content error of the regional ionospheric model is less than 5 Total Electron Content Unit (TECU), which is about 50% higher than the Klobuchar model, and to further evaluate the impact of the regional ionosphere model on the real-time positioning accuracy of smartphones, carrier-smoothing pseudorange and single-frequency Precise Point Positioning (PPP) tests were carried out. The results show that the real-time regional ionospheric model can significantly improve the positioning accuracy of smartphones, especially in the elevation direction. Compared with the Klobuchar model, the improvement effect is more than 34%, and the real-time regional ionospheric model also shortens the convergence time of the elevation direction to 1 min. (The convergence condition is that the range of continuous 20 s is less than 0.5 m). Full article

Space-based augmentation system (SBAS) provides correction information for improving the global navigation satellite system (GNSS) positioning accuracy in real-time, which includes satellite orbit/clock and ionospheric delay corrections. At SBAS service area boundaries, the correction is not fully available to GNSS users and only a partial correction is available, mostly satellite orbit/clock information. By using the geospatial correlation property of the ionosphere delay information, the ionosphere correction coverage can be extended by a spatial extrapolation algorithm. This paper proposes extending SBAS ionosphere correction coverage by using a biharmonic spline extrapolation algorithm. The wide area augmentation system (WAAS) ionosphere map is extended and its ionospheric delay error is compared with the GPS Klobuchar model. The mean ionosphere error reduction at low latitude is 52.3%. The positioning accuracy of the extended ionosphere correction method is compared with the accuracy of the conventional SBAS positioning method when only a partial set of SBAS corrections are available. The mean positioning error reduction is 44.8%, and the positioning accuracy improvement is significant at low latitude. Full article

A new approach is presented to improve the spatial and temporal resolution of the Vertical Total Electron Content (VTEC) estimates for regional positioning applications. The proposed technique utilises a priori information from the Global Ionosphere Maps (GIMs) of the Center for Orbit Determination in Europe (CODE), provided in terms of Spherical Harmonic (SH) coefficients of up to degree and order 15. Then, it updates the VTEC estimates using a new set of base-functions (with better resolution than SHs) while using the measurements of a regional GNSS network. To achieve the highest accuracy possible, our implementation is based on a transformation of the GIM/CODE VTECs to their equivalent coefficients in terms of (spherical) Slepian functions. These functions are band-limited and reflect the majority of signal energy inside an arbitrarily defined region, yet their orthogonal property is remained. Then, new dual-frequency GNSS measurements are introduced to a Least Squares (LS) updating step that modifies the Slepian VTEC coefficients within the region of interest. Numerical application of this study is demonstrated using a synthetic example and ground-based GPS data in South America. The results are also validated against the VTEC estimations derived from independent GPS stations (that are not used in the modelling), and the VTEC products of international centres. Our results indicate that, by using 62 GPS stations in South America, the ionospheric delay estimation can be considerably improved. For example, using the new VTEC estimates in a Precise Point Positioning (PPP) experiment improved the positioning accuracy compared to the usage of GIM/CODE and Klobuchar models. The reductions in the root mean squared of errors were ∼23% and 25% for a day with moderate solar activity while 26% and ∼35% for a day with high solar activity, respectively. Full article