Global Navigation Satellite System Products Research Articles

Real-Time LEO Satellite Orbits Based on Batch Least-Squares Orbit Determination with Short-Term Orbit Prediction

The augmentation of the Global Navigation Satellite System (GNSS) by Low Earth Orbit (LEO) satellites is proposed as an effective method to improve the precision and shorten the convergence time of Precise Point Positioning (PPP). Serving as navigation satellites in the future, LEO satellites need to be provided with their high-accuracy orbits in real-time. This would potentially enable the high-accuracy real-time LEO satellite clock determination, and eventually facilitate the high-accuracy ground-based positioning. Studies have been performed to achieve such real-time orbits using a Kalman filter in both the kinematic and reduced-dynamic modes. Batch Least-Squares (BLS) adjustment delivers more stable orbits in near-real-time, as it performs better phase screening. However, it suffers from longer delays compared to the Kalman filter. With the LEO satellite orbit prediction strategies improved over time, this latency can be bridged by short-term orbit prediction. In this study, using real-time GNSS satellite products, the real-time LEO satellite orbits are obtained based on the batch least-squares adjustment and short-term prediction. LEO ephemeris parameters are generated within specific prediction time windows. Using real data from the 500 km GRACE C satellite and 810 km Sentinel-3B satellite, the near-real-time BLS Precise Orbit Determination (POD) results exhibit good accuracy with an Orbital User Range Error (OURE) of 2–4 cm using different real-time GNSS products. A range of delays of the BLS POD processes are assumed, based on tests performed on different processing machines, leading to various prediction windows, from 3–8 min to 12–17 min that correspond to the real-time usage. The orbital prediction errors are shown to be highly correlated with the orbital height and the prediction time. The computational efficiency thus becomes essential to reduce the prediction errors for a certain LEO satellite. For advanced processing units leading to a prediction window shorter or equal to 6–11 min, one can expect a total real-time orbital error budget of 3–5 cm, provided that an appropriate prediction strategy is applied and high-quality GNSS products are used. For a given fitting interval, the ephemeris fitting errors are generally related to the number of ephemeris parameters and the orbital height. Compared with the prediction errors, the ephemeris fitting errors do not play a significant role in the total error budget when using 22 ephemeris parameters.

Machine learning-based prediction of Alpine foehn events using GNSS troposphere products: first results for Altdorf, Switzerland

Abstract. Remote sensing of water vapour using the Global Navigation Satellite System (GNSS) is a well-established technique and reliable data source for numerical weather prediction (NWP). However, one of the phenomena rarely studied using GNSS are foehn winds. Since foehn winds are associated with significant humidity gradients between two sides of a mountain range, tropospheric estimates from GNSS are also affected by their occurrence. Time series reveal characteristic features like distinctive minima and maxima as well as a significant decrease in the correlation between the stations. However, detecting such signals becomes increasingly difficult for large datasets. Therefore, we suggest the application of machine learning algorithms for the detection and prediction of foehn events by means of GNSS troposphere products. This initial study develops a new, machine learning-based method for detection and prediction of foehn events at the Swiss station Altdorf by utilising long-term time series of high-quality GNSS troposphere products. Data from the Automated GNSS Network Switzerland (AGNES) and various GNSS sites from neighbouring countries as well as records of an operational foehn index are used to investigate the performance of several different classification algorithms based on appropriate statistical metrics. The two best-performing algorithms are fine tuned and tested in four dedicated experiments using different feature setups. The results are promising, especially when reprocessed GNSS products are utilised and the most dense station setup is used. Detection- and alarm-based measures reach levels between 66 %–80 % for both tested algorithms and thus are comparable to those from studies using data from meteorological stations and NWP. For operational prediction, limitations due to the availability and quality of GNSS products in near-real time (NRT) exist. However, they might be mitigated to a significant extent by provision of additional NRT products and improved data processing in the future. Results also outline benefits for the results when including geographically relevant stations (e.g. high-altitude stations) in the utilised datasets.

GNSS Storm Nowcasting Demonstrator for Bulgaria

Global Navigation Satellite System (GNSS) is an established atmospheric monitoring technique delivering water vapour data in near-real time with a latency of 90 min for operational Numerical Weather Prediction in Europe within the GNSS water vapour service (E-GVAP). The advancement of GNSS processing made the quality of real-time GNSS tropospheric products comparable to near-real-time solutions. In addition, they can be provided with a temporal resolution of 5 min and latency of 10 min, suitable for severe weather nowcasting. This paper exploits the added value of sub-hourly real-time GNSS tropospheric products for the nowcasting of convective storms in Bulgaria. A convective Storm Demonstrator (Storm Demo) is build using real-time GNSS tropospheric products and Instability Indices to derive site-specific threshold values in support of public weather and hail suppression services. The Storm Demo targets the development of service featuring GNSS products for two regions with hail suppression operations in Bulgaria, where thunderstorms and hail events occur between May and September, with a peak in July. The Storm Demo real-time Precise Point Positioning processing is conducted with the G-Nut software with a temporal resolution of 15 min for 12 ground-based GNSS stations in Bulgaria. Real-time data evaluation is done using reprocessed products and the achieved precision is below 9 mm, which is within the nowcasting requirements of the World Meteorologic Organisation. For the period May–September 2021, the seasonal classification function for thunderstorm nowcasting is computed and evaluated. The probability of thunderstorm detection is 83%, with a false alarm ration of 38%. The added value of the high temporal resolution of the GNSS tropospheric gradients is investigated for a storm case on 24–30 August 2021. Real-time tropospheric products and classification functions are integrated and updated in real-time on a publicly accessible geoportal.

A new European service to share GNSS Data and Products

This paper describes the new GNSS data and product services that have been developed within the context of the EPOS (European Plate Observing System) European Research Infrastructure Consortium (ERIC), which is part of the European Strategy Forum on Research Infrastructures. These services, optimized for Solid Earth research applications, endeavour to harmonise, and standardise Global Navigation Satellite System (GNSS) data collection and processing. They have been implemented by the members of the GNSS Data & Products (EPOS-GNSS), one of the Thematic Core Services (TCS) of EPOS with the active support of national and pan-European infrastructures (in particular the Regional Reference Frame Sub-Commission for Europe (EUREF) of the International Association of Geodesy). The optimized use of data from dozens of diverse European GNSS networks, installed not specifically for geodynamic studies, created additional requirements from an organizational and technical point of view, the solutions for which we describe in this article. The data flows from data suppliers and analysis centers to the various TCS Data & Product Portals are described, as well as their integration into the overall EPOS system. This is made through GLASS (GNSS Linkage Advanced Software System), a dedicated software package developed since 2016, whose architecture and functionalities are detailed here. Time series and other GNSS products computed at the several analysis centers are described as are the quality control steps that are performed. Finally, several user cases are presented that demonstrate how different stakeholders (from data providers to scientists) can benefit from the efforts being carried out by the EPOS- GNSS community.

Improved precise kinematic LEO orbits based on the raw observation approach

Observing Earth’s gravity field variations by means of precise orbits is nowadays a common practice next to dedicated gravity field satellite missions. The reason for using kinematic orbits of low earth orbiting (LEO) satellites for gravity field estimates instead of dynamic or reduced-dynamic orbits is based on the fact that kinematic orbits do not include a priori information about the gravity field. To achieve highly accurate gravity field estimates through the use of LEO satellite positions, it is of paramount importance to determine these positions as precisely as possible. We investigated whether it is possible to improve the accuracy of the kinematic orbits that had been processed by our working group in the past. For this purpose we modified our processing approach, which is based on an iterative least-squares adjustment using raw observations, and re-processed the kinematic orbits for several satellite missions such as CHAMP, GRACE, GRACE Follow-On, Jason, MetOp, Swarm, Sentinel, TanDEM-X and TerraSAR-X. The modifications include that we are now processing global navigation satellite system (GNSS) constellations in-house and that the phase ambiguities are fixed to integer values. In this paper we discuss these modifications. We show that the consistent in-house processing of the GNSS products already significantly improves the orbit determination, since the use of the these GNSS products mitigates the performance degradation. Furthermore, we present that an additional enhancement through integer ambiguities can be achieved.

Accuracy Analysis of GNSS Hourly Ultra-Rapid Orbit and Clock Products from SHAO AC of iGMAS

With the development of the global navigation satellite system(GNSS), the hourly ultra-rapid products of GNSS are attracting more attention due to their low latency and high accuracy. A new strategy and method was applied by the Shanghai Astronomical Observatory (SHAO) Analysis Center (AC) of the international GNSS Monitoring and Assessment Service (iGMAS) for generating 6-hourly and 1-hourly GNSS products, which mainly include the American Global Positioning System (GPS), the Russian Global’naya Navigatsionnaya Sputnikova Sistema (GLONASS), the European Union’s Galileo, and the Chinese BeiDou navigation satellite system (BDS). The 6-hourly and 1-hourly GNSS orbit and clock ultra-rapid products included a 24-h observation session which is determined by 24-h observation data from global tracking stations, and a 24-h prediction session which is predicted from the observation session. The accuracy of the 1-hourly orbit product improved about 1%, 31%, 13%, 11%, 23%, and 9% for the observation session and 18%, 43%, 45%, 34%, 53%, and 15% for the prediction session of GPS, GLONASS, Galileo, BDS Medium Earth Orbit (MEO), Inclined Geosynchronous Orbit (IGSO), and GEO orbit, when compared with reference products with high accuracy from the International GNSS service (IGS).The precision of the 1-hourly clock products can also be seen better than the 6-hourly clock products. The accuracy and precision of the 6-hourly and 1-hourly orbit and clock verify the availability and reliability of the hourly ultra-rapid products, which can be used for real-time or near-real-time applications, and show encouraging prospects.

Navigator Notes

Navigator Notes

Removing day-boundary discontinuities on GNSS clock estimates: methodology and results

Global navigation satellite system (GNSS) satellites are equipped with very stable atomic clocks that can be used for assessing the models and strategies involved in the estimation processes, where the clock estimates should present high stability. For instance, GNSS products (including satellite and receiver clocks) are computed on daily basis, i.e., with the data of each day being processed independently from other days. This choice produces the well-known day-boundary discontinuities (DBDs) on clock estimates that stem from the estimation process, rather than to the nature of the atomic clock itself. The aim of the present contribution is to propose a strategy to estimate the satellite and receiver clock offsets that is capable to reduce the DBDs observed in the products of different analysis centers (ACs) within the International GNSS Service (IGS), ultimately improving the accuracy of clock estimates. Our approach relies on the use of unambiguous, undifferenced and uncombined carrier phase measurements collected by a network of permanent receivers on ground. The strategy considers the carrier phase hardware delays and assumes their possible variations along time. Our daily data processing aims to maintaining the natural continuity over days of the carrier phase measurements after integer ambiguity resolution (IAR), even if IAR is performed on daily batches. We compare our clock estimations with those computed by different IGS ACs, evaluating the linear behavior of the satellite atomic clocks on the day change. The results show the removal of DBD on clock estimates computed with the continuous and unambiguous carrier phase measurements. This DBD improvement may benefit the statistical characterization of long-term phenomena correlated with the on-board clocks.

POD of small LEO satellites based on precise real-time MADOCA and SBAS-aided PPP corrections

For real-time precise orbit determination (POD) of low earth orbit (LEO) satellites, high-accuracy global navigation satellite system (GNSS) orbit and clock products are necessary in real time. Recently, the Japanese multi-GNSS advanced demonstration of orbit and clock analysis precise point positioning (PPP) service and the new generation of the Australian/New Zealand satellite-based augmentation system (SBAS)-aided PPP service provide free and precise GNSS products that are directly broadcast through the navigation and geostationary earth orbit satellites, respectively. With the high quality of both products shown in this study, a 3D accuracy of centimeters can be achieved in the post-processing mode for the reduced-dynamic orbits of small LEO satellites having a duty cycle down to 40% and at sub-dm to dm level for the kinematic orbits. The results show a promising future for high-accuracy real-time POD onboard LEO satellites benefiting from the precise free-of-charge PPP corrections broadcast by navigation systems or SBAS.

A collocation framework to retrieve tropospheric delays from a combination of GNSS and InSAR

High spatio-temporal variability of atmospheric water vapor affects microwave signals of Global Navigation Satellite Systems (GNSS) and Interferometric Synthetic Aperture Radar (InSAR). A better knowledge of the distribution of water vapor improves both GNSS- and InSAR-derived data products. In this work, we present a collocation framework to combine and retrieve zenith and (relative) slant tropospheric delays. GNSS and InSAR meteorological products are combined aiming at a better retrieval of the atmospheric water vapor. We investigate the combination approach with synthetic and real data acquired in the Alpine region of Switzerland. Based on a closed-loop validation with simulated delays, a few mm accuracy is achieved for the GNSS-InSAR combination in terms of retrieved ZTDs. Furthermore, when real delays are collocated, the combination results are more congruent with InSAR computed products. This research is a contribution to improve the spatio-temporal mapping of tropospheric delays by combining GNSS-derived and InSAR-derived delays.

Comparative analysis of real-time kinematic and PPP techniques in dynamic environment

The main objective of this study is to assess the performance of the relative Real-time Kinematic (RTK) Global Navigation Satellite System (GNSS) Methods; i.e., Single-baseline & Network RTK, and Real-time Precise Point Positioning (RT-PPP); i.e., Trimble CenterPoint Real Time eXtended (RTX) Correction Service in a dynamic environment. For this purpose, a kinematic test was done within a vessel in Obruk Lake Dam in Çorum province, Turkey. The test area was situated in a deep valley and surrounded by high hills covered with dense trees. The real-time coordinates of each measurement epoch were simultaneously determined with Single-baseline RTK, Network RTK, and RTX RT-PPP methods by using three GNSS receivers. The real-time coordinates obtained from both RTK and RT-PPP methods were compared against the post-processed relative solution epoch-by-epoch. The results show that, the 3D position accuracies of real-time methods were found as ±6 cm, ±3 cm and ±7 cm for Single-baseline RTK, Network RTK and RT-PPP methods, respectively. This study demonstrates that although the Network RTK methods provided the best solution among the others, the positioning did not conduct most of the time due to the loss of cellular connection. This was also partially valid for the Single-baseline RTK method because the corrections from the base station via radio-link couldn’t be received due to the rough terrain conditions. However, it was possible to make positioning with RTX Real-time PPP technique using satellite delivery GNSS products (corrections) continuously and in a robust manner within the cm-level accuracy. Our study showed that the use of the global multi-GNSS RTX correction service outcompetes conventional RTK methods with providing consistent, reliable, and seamless cm-level accurate positioning almost without any interruption especially in challenging marine environments with severe terrain obstructions.

Network Effects and Handling of the Geocenter Motion in Multi‐GNSS Processing

AbstractBoth, the network configuration and the way of terrestrial reference frame (TRF) realization, affect the global geodetic products delivered from the Global Navigation Satellite Systems (GNSS) data processing. The purpose of this study is to analyze the differences in GNSS products, such as station coordinates, Earth rotation parameters, geocenter coordinates (GCC), and satellite orbits delivered from the double‐difference multi‐GNSS (GPS, GLONASS, and Galileo) processing, which may arise from (1) using a homogeneous and inhomogeneous network of multi‐GNSS stations, (2) different approaches to the TRF realization using minimum constraint conditions, and (3) different approaches to handling of GCC in GNSS global processing. The questionable quality of GCC delivered from the global GNSS solutions is described with a special attention to network effects and system‐specific parameters. We found that Galileo can provide GCC, whose quality corresponds to the GPS series. Moreover, the GCC from Galileo is of a better quality than those based on GLONASS data, despite the same number of nominal orbital planes and a much lower number of active satellites. When the No‐Net‐Translation constraint is not applied on the GNSS network, the station coordinate repeatability is worsened by about 70%, 55%, and 25% for the north, east, and up components, respectively, compared to the solution when applying No‐Net‐Translation and when having the network origin consistent with the international TRF. We thus infer that the No‐Net‐Translation condition is mandatory in global GNSS solutions.

Validation of the EGSIEM GRACE Gravity Fields Using GNSS Coordinate Timeseries and In-Situ Ocean Bottom Pressure Records

Over the 15 years of the Gravity Recovery and Climate Experiment (GRACE) mission, various data processing approaches were developed to derive time-series of global gravity fields based on sensor observations acquired from the two spacecrafts. In this paper, we compare GRACE-based mass anomalies provided by various processing groups against Global Navigation Satellite System (GNSS) station coordinate time-series and in-situ observations of ocean bottom pressure. In addition to the conventional GRACE-based global geopotential models from the main processing centers, we focus particularly on combined gravity field solutions generated within the Horizon2020 project European Gravity Service for Improved Emergency Management (EGSIEM). Although two validation techniques are fully independent from each other, it is demonstrated that they confirm each other to a large extent. Through the validation, we show that the EGSIEM combined long-term monthly solutions are comparable to CSR RL05 and ITSG2016, and better than the other three considered GRACE monthly solutions AIUB RL02, GFZ RL05a, and JPL RL05.1. Depending on the GNSS products, up to 25.6% mean Weighted Root-Mean-Square (WRMS) reduction is obtained when comparing GRACE to the ITRF2014 residuals over 236 GNSS stations. In addition, we also observe remarkable agreement at the annual period between GNSS and GRACE with up to 73% median WRMS reduction when comparing GRACE to the 312 EGSIEM-reprocessed GNSS time series. While the correspondence between GRACE and ocean bottom pressure data is overall much smaller due to lower signal to noise ratio over the oceans than over the continents, up to 50% agreement is found between them in some regions. The results fully confirm the conclusions found using GNSS.

A two-stage tropospheric correction model combining data from GNSS and numerical weather model

We have developed a new concept for providing tropospheric augmentation corrections. The two-stage correction model combines data from a Numerical Weather Model (NWM) and precise ZTDs estimated from Global Navigation Satellite System (GNSS) permanent stations in regional networks. The first-stage correction is generated using the background NWM forecast only. The second-stage correction results from an optimal combination of the background model data and GNSS (near) real-time tropospheric products. The optimum correction is achieved when using NWM for the hydrostatic delay modeling and for vertical scaling, while GNSS products are used for correcting the non-hydrostatic delay. The method is assessed in several variants including study of the combination of NWM and GNSS data, spatial densification of the original NWM grid, and GNSS ZTD densification using tropospheric linear horizontal gradients. The first-stage correction can be characterized by overall accuracy of about 10 mm for ZTD (1-sigma). The second-stage correction supported with GNSS tropospheric products improved the first-stage correction by a factor of 2–4 in terms of the ZTD accuracy and by a factor of 2.5 in terms of its spatio-temporal stability.

Impact and Implementation of Higher‐Order Ionospheric Effects on Precise GNSS Applications

AbstractHigh precision Global Navigation Satellite Systems (GNSS) positioning and time transfer require correcting signal delays, in particular higher‐order ionospheric (I2+) terms. We present a consolidated model to correct second‐ and third‐order terms, geometric bending and differential STEC bending effects in GNSS data. The model has been implemented in an online service correcting observations from submitted RINEX files for I2+ effects. We performed GNSS data processing with and without including I2+ corrections, in order to investigate the impact of I2+ corrections on GNSS products. We selected three time periods representing different ionospheric conditions. We used GPS and GLONASS observations from a global network and two regional networks in Poland and Brazil. We estimated satellite orbits, satellite clock corrections, Earth rotation parameters, troposphere delays, horizontal gradients, and receiver positions using global GNSS solution, Real‐Time Kinematic (RTK), and Precise Point Positioning (PPP) techniques. The satellite‐related products captured most of the impact of I2+ corrections, with the magnitude up to 2 cm for clock corrections, 1 cm for the along‐ and cross‐track orbit components, and below 5 mm for the radial component. The impact of I2+ on troposphere products turned out to be insignificant in general. I2+ corrections had limited influence on the performance of ambiguity resolution and the reliability of RTK positioning. Finally, we found that I2+ corrections caused a systematic shift in the coordinate domain that was time‐ and region‐dependent and reached up to −11 mm for the north component of the Brazilian stations during the most active ionospheric conditions.

First Observations of GNSS Ionospheric Scintillations From DemoGRAPE Project

The Istituto Nazionale di Geofisica e Vulcanologia leads an international project funded by the Italian National Program for Antarctic Research, called Demonstrator of Global Navigation Satellite System (GNSS) Research and Application for Polar Environment (DemoGRAPE), in partnership with Politecnico di Torino, Istituto Superiore Mario Boella, and with South African National Space Agency and the Brazilian National Institute of Space Physics, as key collaborators. DemoGRAPE is a new prototype of support for the satellite navigation in Antarctica. Besides the scientific interest, the accuracy of satellite navigation in Antarctica is of paramount importance since there is always the danger that people and vehicles can fall into a crevasse during a snowstorm, when visibility is limited and travel is restricted to following specified routes using satellite navigation systems. The variability of ionospheric delay and ionospheric scintillation are two of the primary factors which affect the accuracy of satellite navigation. The project will provide a demonstrator of cutting edge technology for the empirical assessment of the ionospheric delay and ionospheric scintillations in the polar regions. The scope of the project includes new equipment for the recording and dissemination of GNSS data and products installed at the South African and Brazilian bases in Antarctica. The new equipment will facilitate the exchange of software and derived products via the Cloud computing technology infrastructure. The project portal is accessible at www.demogrape.net. We report the first Global Navigation Satellite System (GNSS) signal scintillations observed in Antarctica.

Mapping GPS multipath: a case study for the lunar laser ranger timing antenna at HartRAO

Accounting for multipath in Global Navigation Satellite Systems (GNSS) is a difficult task and an important one, especially during the pre-investigation phase for the installation of a permanent GNSS station for positioning or timing applications. Sites with a high level of multipath can cause positioning errors or timing errors resulting in the quality of GNSS products (position or timing) becoming degraded by several metres or nanoseconds. We investigate and attempt to map multipath as part of the site investigation for the installation of the timing antenna for lunar laser ranging applications at the Hartebeesthoek Radio Astronomy Observatory (HartRAO). A high-resolution wavelet power spectrum and a standard deviation parameter are used to map multipath in both the time and frequency domain as well as spatial variations on the sky plot. The high standard deviation values on the sky map are attributed to reflections due to shrubs or trees on the site, while smaller standard deviation areas are attributed to bare soil or less vegetated as this would give constant reflection over time provided the ground has constant moisture. We conclude that the site is suitable for installation of the timing antenna and that a mask of 15°-20° elevation angle will be applied to the timing antenna to minimise multipath at lower elevations.

Benchmark campaign and case study episode in central Europe for development and assessment of advanced GNSS tropospheric models and products

Abstract. Initial objectives and design of the Benchmark campaign organized within the European COST Action ES1206 (2013–2017) are described in the paper. This campaign has aimed to support the development and validation of advanced Global Navigation Satellite System (GNSS) tropospheric products, in particular high-resolution and ultra-fast zenith total delays (ZTDs) and tropospheric gradients derived from a dense permanent network. A complex data set was collected for the 8-week period when several extreme heavy precipitation episodes occurred in central Europe which caused severe river floods in this area. An initial processing of data sets from GNSS products and numerical weather models (NWMs) provided independently estimated reference parameters – zenith tropospheric delays and tropospheric horizontal gradients. Their provision gave an overview about the product similarities and complementarities, and thus a potential for improvements of a synergy in their optimal exploitations in future. Reference GNSS and NWM results were intercompared and visually analysed using animated maps. ZTDs from two reference GNSS solutions compared to global ERA-Interim reanalysis resulted in accuracy at the 10 mm level in terms of the root mean square (rms) with a negligible overall bias, comparisons to Global Forecast System (GFS) forecasts showed accuracy at the 12 mm level with the overall bias of −5 mm and, finally, comparisons to mesoscale ALADIN-CZ forecast resulted in accuracy at the 8 mm level with a negligible total bias. The comparison of horizontal tropospheric gradients from GNSS and NWM data demonstrated a very good agreement among independent solutions with negligible biases and an accuracy of about 0.5 mm. Visual comparisons of maps of zenith wet delays and tropospheric horizontal gradients showed very promising results for future exploitations of advanced GNSS tropospheric products in meteorological applications, such as severe weather event monitoring and weather nowcasting. The GNSS products revealed a capability of providing more detailed structures in atmosphere than the state-of-the-art numerical weather models are able to capture. In an initial study on the contribution of hydrometeors (e.g. cloud water, ice or snow) to GNSS signal delays during severe weather, the effect reached up to 17 mm, and it was suggested that hydrometeors should be carefully accounted for within the functional model. The reference products will be further exploited in various specific studies using the Benchmark data set. It is thus going to play a key role in these highly interdisciplinary developments towards better mutual benefits from advanced GNSS and meteorological products.

Speed Adaptation in Urban Road Network Management

Abstract Various forecasting schemes have been proposed to manage traffic data, which is collected by videos cameras, sensors, and mobile phone services. However, these are not sufficient for collecting data because of their limited coverage and high costs for installation and maintenance. To overcome the limitations of these tools, we introduce a hybrid scheme based on intelligent transportation system (ITS) and global navigation satellite system (GNSS). Applying the GNSS to calculate travel time has proven efficient in terms of accuracy. In this case, GNSS data is managed to reduce traffic congestion and road accidents. This paper introduces a short-time forecasting model based on real-time travel time for urban heterogeneous road networks. Travel time forecasting has been achieved by predicting travel speeds using an optimized exponential moving Average (EMA) model. Furthermore for speed adaptation in heterogeneous road networks, it is necessary to introduce asuitable control strategy for longitude, based on the GNSS. GNSS products provide worldwide and real-time services using precise timing information and, positioning technologies.

Distribution and mitigation of higher‐order ionospheric effects on precise GNSS processing

Higher‐order ionospheric effects (I2+) are one of the main limiting factors in very precise Global Navigation Satellite Systems (GNSS) processing, for applications where millimeter accuracy is demanded. This paper summarizes a comprehensive study of the I2+ effects in range and in GNSS precise products such as receiver position and clock, tropospheric delay, geocenter offset, and GNSS satellite position and clock. All the relevant higher‐order contributions are considered: second and third orders, geometric bending, and slant total electron content (dSTEC) bending (i.e., the difference between the STEC for straight and bent paths). Using a realistic simulation with representative solar maximum conditions on GPS signals, both the effects and mitigation errors are analyzed. The usage of the combination of multifrequency L band observations has to be rejected due to its increased noise level. The results of the study show that the main two effects in range are the second‐order ionospheric and dSTEC terms, with peak values up to 2 cm. Their combined impacts on the precise GNSS satellite products affects the satellite Z coordinates (up to +1 cm) and satellite clocks (more than ±20 ps). Other precise products are affected at the millimeter level. After correction the impact on all the precise GNSS products is reduced below 5 mm. We finally show that the I2+ impact on a Precise Point Positioning (PPP) user is lower than the current uncertainties of the PPP solutions, after applying consistently the precise products (satellite orbits and clocks) obtained under I2+ correction.