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Estimating inter-system biases (ISBs) is important in multi-constellation Global Navigation Satellite System (GNSS) processing. The present study aims to evaluate and screen out an optimal estimation strategy of ISB for multi-GNSS kinematic precise point positioning (PPP). The candidate strategies considered for ISB estimation are white noise process (ISB-WN), random walk process (ISB-RW), constant (ISB-CT) and eliminated by between-satellite single-differenced observations (ISB-SD). We first present the mathematical model of ISB derived from the observation combination among different GNSSs, and we demonstrate the equivalence between ISB-WN and ISB-SD in the Kalman filter. In order to evaluate the performance of these four ISB solution strategies, we implement kinematic PPP with 1-month static data from 112 International GNSS service stations and two-hour dynamic vehicular data collected in an urban case. For comparison, precise orbit and clock products from the Center for Orbit Determination in Europe (CODE), GeoForschungsZentrum in Germany (GFZ) and Wuhan University (WHU) are employed in our experiments. The results of static tests show that the positioning accuracy is comparable among the four strategies, but ISB-CT performs slightly better in convergence time. In the kinematic test, there are more cycle slips than static test, and the ISB-CT improves the positioning accuracy by 15.7%, 38.9% and 63.2% in east, north and up components, and reduces the convergence time by 60.1% comparing with the other strategies. Moreover, both the static and kinematic tests prove the consistence among CODE, GFZ and WHU precise products and the equivalence between ISB-WN and ISB-SD strategies. Finally, more, i.e., the same amount of cycle slips as for the dynamic data, are artificially added to the static data to conduct the pseudo-kinematic test. The result shows that ISB-CT improves the positioning accuracy and convergence time by 19.2% and 24.4%, respectively. The study is funded by Laoshan Laboratory (LSKJ202205104, LSKJ202205104_01), National Key Research and Development Program of China (2020YFB0505800, 2020YFB0505804), National Natural Science Foundation of China (42004012), Natural Science Foundation of Shandong Province, China (ZR2020QD048) and by the project RTI2018-094295-B-I00 funded by the MCIN/AEI 1013039/501100011033 which is co-funded by the FEDER program.

Several X-class solar flares (SFs) with different intensities and locations on the solar disk occurred in September 2017. Among them, the X9.3 SF on 6 September 2017 was the most intensive SF in the 24th solar cycle. In this study, we investigated and compared the ionospheric response to the different X-class SFs and their impacts on the Global Positioning System (GPS) kinematic precise point positioning (PPP) solutions. We aim to study the mechanism behind the positioning degradation from the perspective of the impacts of the SF-induced ionosphere disturbance on the GPS data processing. By comparing the sudden ionospheric disturbance (SID) induced by the SFs, we observed that the SID is controlled by the intensity, the location, and the duration time of the SF. We found that the SID induced by the SF may deteriorate the cycle slip (CS) detection algorithms seriously. The threshold of the CS detection observables is sensitive to the SID, making the CS easier to be falsely detected. On the other hand, for the SF that occurred during the recovery phase of the geomagnetic storm, as the case of the X8.2 SF, the effects of the SF can reduce the precision of the GPS measurements, thus affecting the positioning accuracy. These mechanisms are essential and significant for the accuracy and stability of the kinematic PPP solution obtained with GPS during the SF events. The study is funded by National Natural Science Foundation of China (Nos. 42004012 and 42004025), Natural Science Foundation of Shandong Province, China (No. ZR2020QD048), State Key Laboratory of Geo-Information Engineering (No. SKLGIE2019-Z-2-2), State Key Laboratory of Geodesy and Earth's Dynamics (No. SKLGED-2021-3-4), and by the project RTI2018-094295-B-I00 funded by the MCIN/AEI 10.13039/501100011033, which is cofunded by the FEDER programme. We appreciate the discussion on the amplitude scintillation and IF-sigma from high-rate geodetic GNSS data with Dr. Xiaomin Luo from China University of Geosciences (Wuhan) and Prof. Juan, J. M. from Universitat Politecnica de Catalunya (UPC), Spain. The authors are also thankful to the reviewers for the instructive comments and suggestions on the manuscript.

We focus on the impacts of the polar cap ionospheric sporadic-E (Es) layer that occurred at Resolute Bay, Canada, on September 5, 2012, on the quality of the Global Positioning System (GPS) observable and the positioning performance. Mainly, we are concerned about the relationship between the thin Es layer and the ionosphere scintillation and the reason behind the degraded positioning performance during the event of the polar cap Es. The results show that the polar cap Es can trigger weak-to-moderate amplitude scintillation and the maximum positioning errors in the up component for the Ionospheric-Free Precise Point Positioning (IF-PPP) model can reach up to 0.51 m while that for the Uncombined PPP (UC-PPP) model can reach 1.20 m. The maximum positioning errors occur simultaneously with the time of the maximum amplitude scintillation induced by the polar cap Es. The degraded positioning performance can be attributed mostly to falsely detected cycle slips (CSs), which are influenced by the polar cap Es layer-induced scintillation. To mitigate this, we propose the 3-sigma rule to determine the threshold of the CS detection observables. The preliminary results show that compared with the commonly adopted threshold values, the positioning accuracy improvement in the up component is 14.1% for the IF-PPP model while the corresponding improvement is 40.8% for the UC-PPP model, suggesting that the high accuracy positioning performance can be achieved in the high latitude region by statistic characterization of the CS thresholds. The study is funded by the National Natural Science Foundation of China (No.42004012, 42004025), Natural Science Foundation of Shandong Province, China(No.ZR2020QD048),State Key Laboratory of Geo-Information Engineering (No.SKLGIE2019-Z-2-2), State Key Laboratory of Geodesy and Earth Dynamics (No. SKLGED-2021-3-4) and by the project RTI2018-094295-B-I00 funded by the MCIN/AEI 10.13039/501100011033 which is co-founded by the FEDER program. We acknowledge the usage of the GAMP package for the positioning performances at https://www.ngs.noaa.gov/gps-toolbox/. We thank the anonymous reviewers and Editors for the comments and suggestions, which significantly improve the quality of the manuscript.

The Galileo High Accuracy Service (HAS) is a new capability of the European Global Navigation Satellite System that is currently under development. The Galileo HAS will start providing satellite orbit and clock corrections (i.e. non-dispersive effects) and soon it will also correct dispersive effects such as inter-frequency biases and, in its full capability, ionospheric delay. We analyse here an ionospheric correction system based on the fast precise point positioning (Fast-PPP) and its potential application to the Galileo HAS. The aim of this contribution is to present some recent upgrades to the Fast-PPP model, with the emphasis on the model geometry and the data used. The results show the benefits of integer ambiguity resolution to obtain unambiguous carrier phase measurements as input to compute the Fast-PPP model. Seven permanent stations are used to assess the errors of the Fast-PPP ionospheric corrections, with baseline distances ranging from 100 to 1000 km from the reference receivers used to compute the Fast-PPP corrections. The 99% of the GPS and Galileo errors in well-sounded areas and in mid-latitude stations are below one total electron content unit. In addition, large errors are bounded by the error prediction of the Fast-PPP model, in the form of the variance of the estimation of the ionospheric corrections. Therefore, we conclude that Fast-PPP is able to provide ionospheric corrections with the required ionospheric accuracy, and realistic confidence bounds, for the Galileo HAS. Open Access funding provided thanks to the CRUECSIC agreement with Springer Nature. The present work was supported in part by the European Space Agency contract IONO4HAS 4000128823/19/NL/AS, by the project RTI2018-094295-B-I00 funded by the MCIN/AEI 10.13039/501100011033 which is co-founded by the FEDER programme and by the Horizon 2020 Marie Skłodowska-Curie Individual Global Fellowship 797461 NAVSCIN.

Monitoring spatiotemporal variations of ionospheric vertical total electron content (VTEC) is crucial for space weather and satellite positioning. In the present study, an enhanced neural network (ENN) model is proposed to capture the changing characteristics of ionospheric VTEC and compared with the traditional mathematical models, i.e. the POLYnomial (POLY) model, generalized trigonometric series function and spherical harmonic function (SHF) model. The ionospheric VTEC data obtained from 31 permanent global positioning system stations in the southwest region of China on 26 August and 8 September, 2017, were used to test the performance of the mentioned models under different Solar-geomagnetic conditions. The ENN model is derived from the ensemble learning method, and the disadvantage that simple backpropagation neural network learners that are not robust enough is weakened by the ENN model. After statistical analysis and single-frequency precise point positioning (SF-PPP) experiments, it is demonstrated that the ENN model is superior to the above three mathematical models, regardless of the solar-geomagnetic conditions. In terms of mean absolute error, root mean square error, standard deviation, and mean absolute percentage error, the ENN model outperforms the SHF model, which is the best mathematical model in the analysis, by 40.7%, 30.20%, 29.88%, 38.04% under quiet solar-geomagnetic conditions, and by 37.66%, 29.93%, 30.96%, 32.01% under active solar-geomagnetic conditions. In addition, the accuracy of the SF-PPP is greatly affected by the error caused by ionosphere. In the static SF-PPP experiment of this study, the ENN model can better correct ionospheric error. Under quiet and active solar-geomagnetic conditions, the SF-PPP accuracy can be improved by 85.1% and 85.2% with the ionosphere delay correction from the ENN model.

With great potential for being applied to Internet of Things (IoT) applications, the concept of cloud-based Snapshot Real Time Kinematics (SRTK) was proposed and its feasibility under zero-baseline configuration was confirmed recently by the authors. This article first introduces the general workflow of the SRTK engine, as well as a discussion on the challenges of achieving an SRTK fix using actual snapshot data. This work also describes a novel solution to ensure a nanosecond level absolute timing accuracy in order to compute highly precise satellite coordinates, which is required for SRTK. Parameters such as signal bandwidth, integration time and baseline distances have an impact on the SRTK performance. To characterize this impact, different combinations of these settings are analyzed through experimental tests. The results show that the use of higher signal bandwidths and longer integration times result in higher SRTK fix rates, while the more significant impact on the performance comes from the baseline distance. The results also show that the SRTK fix rate can reach more than 93% by using snapshots with a data size as small as 255 kB. The positioning accuracy is at centimeter level when phase ambiguities are resolved at a baseline distance less or equal to 15 km. This research was funded by Albora Technologies and Universitat Politècnica de Catalunya with industrial PhD grant number DI 082 from the Generalitat de Catalunya; This research was partially funded by the Spanish Ministry of Science and Innovation project RTI2018-094295-B-I00. P.C. has been partially supported by the NSF under Awards CNS-1815349 and ECCS-1845833

Global navigation satellite system (GNSS) satellites are equipped with very stable atomic clocks that can be used for assess-ing 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 consid-ers 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. The present work was supported in part by the European Space Agency contract (REL-GAL) N.4000122402/17/NL/IB, by the Spanish Ministry of Science, Innovation and Universities project RTI2018-094295-B-I00 and by the Horizon 2020 Marie Skłodowska-Curie Individual Global Fellowship 797461 NAVSCIN. The authors acknowledge the use of data and products provided by the International GNSS Service

The GNSS LABoratory tool (gLAB) is an interactive educational suite of applications for processing data from the Global Navigation Satellite System (GNSS). gLAB is composed of several data analysis modules that compute the solution of the problem of determining a position by means of GNSS measurements. The present work aimed to improve the pre-fit outlier detection function of gLAB since outliers, if undetected, deteriorate the obtained position coordinates. The methodology exploits robust statistical tools for regression provided by the Flexible Statistics and Data Analysis (FSDA) toolbox, an extension of MATLAB for the analysis of complex datasets. Our results show how the robust analysis FSDA technique improves the capability of detecting actual outliers in GNSS measurements, with respect to the present gLAB pre-fit outlier detection function. This study concludes that robust statistical analysis techniques, when applied to the pre-fit layer of gLAB, improve the overall reliability and accuracy of the positioning solution. This work was supported in part by the Spanish Ministry of Science, Innovation and Universities project RTI2018-094295-B-I00 and in part by the Horizon 2020 Marie Skłodowska-Curie Individual Global Fellowship 797461 NAVSCIN.

In this study, midlatitude summer nighttime anomalies (MSNAs) are analyzed via observations and tidal/planetary wave features using measurements from the Formosat-3/Constellation Observing System for Meteorology, Ionosphere, and Climate (F3C) for 2007, a year with low solar activity, and 2014, a year with high solar activity. The total ionospheric electron content, ECion, an integrated quantity derived from F3C measurements, was used to compare the observational data. The ECion values were derived from accurate radio-occultation-retrieved electron density profiles without assuming spherical symmetry and from a model that separated the ground total electron content into the plasmaspheric and the ionospheric electron content contributions. An analysis of the ECion data set confirmed that MSNAs were present in three different regions of the world for the months surrounding the local summer solstice during both 2007 and 2014. In the southern hemisphere, the so-called Weddell Sea Anomaly showed a maximum increase in ECion, measured as the difference between nighttime and midday values, that was more than three times that in the northern MSNAs. For each individual MSNA, the corresponding maximum increases in electron content were similar between the two years analyzed, so they were not significantly affected by solar activity. Then, linear least-square fit to the frequency–wave number basis functions was used to derive the tidal and planetary wave components contributing to MSNAs. The main component that appears to produce the Weddell Sea Anomaly is D0, followed by SPW1, DW2, and DE1, in this order, which make secondary but still relevant contributions. The presence of MSNAs in the northern hemisphere was clearly supported by the migrating tide SW2 in combination with DE1. SW2 also supported an early morning MSNA being observed in the northern hemisphere. The main tidal and planetary wave signatures producing the MSNAs did not significantly differ between 2007 and 2014.

Scintillation is a particular type of space weather perturbation occurred when the signals from the Global Navigation Satellite System (GNSS) traverse irregularities in the ionosphere; the upper layer of the Earth atmosphere. This produces rapid variations on the refraction index and, when the size of the irregularities is close to the Fresnel length of the frequencies used in GNSS frequencies, can also produce diffractive effects affecting the signal amplitude and the tracking of the carrier-phase measurements. Under these conditions, techniques delivering a High Accuracy Service (HAS) are severely degraded in terms of positioning accuracy and availability. The research group of Astronomy and Geomatics has recently introduced the Geodetic Detrending to perform scintillation studies. The GD method removes slowly-varying effects (i.e., trends) in the GNSS signals, such as the satellite movement, the on-board atomic clock offset, and the tropospheric delay (the atmosphere layer from sea level up to 50 km in height). Once the trends are removed, the GD technique allows studying effects of shorter time-scale –rapid fluctuations–of the GNSS signals, with the focus on the identification and correction of discontinuities, the so-called “cycle-slips”, on the geodetically de-trended GNSS carrier-phase measurements. Ultimately, once the cycle-slips problem is mitigated, the HAS can be re-stored under scintillation conditions. The authors acknowledge the use of data and products provided by the International GNSS Service.

Signals from a Global Navigation Satellite System (GNSS) can be disturbed along the propagation ray path from the satellites to the receivers. The presence of irregularities in the electron density in the near-Earth space environment can cause refraction and/or diffraction in the electromagnetic signals used by GNSS. This causes fast fluctuations of the GNSS signals known as scintillation. Currently, specialized Ionospheric Scintillation Monitoring Receivers (ISMRs) are used to characterize the intensity (or amplitude) and the phase scintillation. ISMRS are capable of sampling GNSS carrier-phase measurements at high-rate (e.g. 50 to 100 Hz) and must be equipped with a highly stable clock. In contrast, the present contribution studies the climatology of scintillation at high- and low- latitudes for both hemispheres and for a long temporal series, with measurements gathered by conventional geodetic receivers with a sampling frequency of 1 Hz that belong to the International GNSS Service (IGS) network. The derivation of S4 (amplitude scintillation) and ?? (phase scintillation) parameters uses a novel technique based in a precise Geodetic Detrending (GD) of the carrier-phase measurements, as in Precise Point Positioning (PPP). Amplitude and phase scintillation have been statistically characterized by means of the cumulative distribution functions (CDF) of S4 and ?? parameters. The thresholds for moderate and intense scintillation periods are established from the 99% and 99.9% percentiles of the CDFs as 0.25 and 0.45 for ?? values and 0.3 and 0.5 for S4 values, respectively. The large temporal series analyzed allows relating high-activity periods to severe space weather events such as geomagnetic storms at high-latitudes, to local times from 19h to midnight at low-latitudes and studying the seasonal dependencies. We conclude that the GD method is a powerful tool to perform scintillation studies and that it can be applied to individual (i.e. uncombined) signal frequencies. The authors acknowledge the use of data and products provided by the International GNSS Service. Data from the Ionospheric Monitoring Experimentation Plan and Instrument Development (MONITOR) from the European Space Agency (ESA) has been used. The research reported in this paper was financially supported in part by the ESA under contract 4000120868/17/NL/AF and in part by the Spanish Ministry of Science, Innovation and Universities project RTI2018-094295-B-I00 belonging to the RETOS 2018 call.

Time synchronization is one of the main applications of Global Navigation Satellite System (GNSS). Indeed, GNSS satellites are equipped with highly stable atomic clocks, which can be used as clock references. In particular, Galileo constellation satellites are equipped with Rubidium and Hydrogen-maser frequency standards that have a long-term (1-day) stability at the level of 10-14 for intervals of 104 s. However, in order to use these clocks as references, their time offsets must be estimated from measurements collected on ground. In this sense, the effectiveness of these references depends on the accuracy and stability of such estimates. For that reason, the International GNSS Service (IGS) is providing satellite solutions with a nominal accuracy of 75 ps (i.e. better than 3 cm). The clock accuracy is assessed by evaluating the discontinuities over consecutive days, computed independently. These discontinuities appear because of the correlations between the different parameters, which are estimated jointly with the satellite clocks (e.g. receiver clocks or carrier phase ambiguities). Therefore, satellite clocks depend on the robustness of the different models used in the estimation process. For the Galileo satellites, the inter-day discontinuities are at the level of 0.5 ns. These large jumps are due to the minor number of Galileo satellites available than in GPS, which results in a reduced number of fixed carrier phase ambiguities (other solutions from other IGS analysis centers present similar features). In this work we present a refinement of the method for estimating satellite and receiver clocks, which is able to reduce these discontinuities and, consequently, to improve the accuracy of the satellite clock estimations (according to the above-mentioned IGS metric applied). Some of the main characteristics of this new approach are 1) the use of unambiguous carrier phases, 2) processing several constellations and several frequencies and 3) considering the temperature dependency of the phase biases.

The Multi-constellation Global Navigation Satellite System (Multi-GNSS) has become the standard implementation of high accuracy positioning and navigation applications. It is well known that the noise of code and phase measurements depend on GNSS constellation. Then, Helmert variance component estimation (HVCE) is usually used to adjust the contributions of different GNSS constellations by determining their individual variances of unit weight. However, HVCE requires a heavy computation load. In this study, the HVCE posterior weighting was employed to carry out a kinematic relative Multi-GNSS positioning experiment with six short-baselines from day of year (DoY) 171 to 200 in 2019. As a result, the HVCE posterior weighting strategy improved Multi-GNSS positioning accuracy by 20.5%, 15.7% and 13.2% in east-north-up (ENU) components, compared to an elevation-dependent (ED) priori weighting strategy. We observed that the weight proportion of both code and phase observations for each GNSS constellation were consistent during the entire 30 days, which indicates that the weight proportions of both code and phase observations are stable over a long period of time. It was also found that the quality of a phase observation is almost equivalent in each baseline and GNSS constellation, whereas that of a code observation is different. In order to reduce the time consumption of the HVCE method without sacrificing positioning accuracy, the stable variances of unit weights of both phase and code observations obtained over 30 days were averaged and then frozen as a priori information in the positioning experiment. The result demonstrated similar ENU improvements of 20.0%, 14.1% and 11.1% with respect to the ED method but saving 88% of the computation time of the HCVE strategy. Our study concludes with the observations that the frozen variances of unit weight (FVUW) could be applied to the positioning experiment for the next 30 days, that is, from DoY 201 to 230 in 2019, improving the positioning ENU accuracy of the ED method by 18.1%, 13.2% and 10.6%, indicating the effectiveness of the FVUW.

Users of the Global Navigation Satellite System (GNSS) using a single-frequency receiver need to use an Ionospheric Correction Algorithm (ICA) to compensate the delay introduced by the Ionosphere on radio waves. The European GNSS, Galileo, uses an ICA named NeQuick-G since it is an adaptation to real time use of the 3D climatological model NeQuick, whereas the American Global Positioning Service (GPS) uses the Klobuchar ICA, which was also adopted initially by the Chinese GNSS, Beidou. In an effort to foster the adoption of NeQuick-G by final users, two implementations in C language were made publicly available by the European Space Agency (ESA) and the Joint Research Centre (JRC) of the European Commission (EC) respectively. The latter, was chosen to be integrated in the GNSS laboratory tool suite (gLAB), developed by the research group of Astronomy and Geomatics (gAGE) of the Universitat Politecnica de Catalunya (UPC) because its open license and its processing speed. The aim of the present contribution is to compare the Slant Total Electron Content (STEC) predictions of the two aforementioned ICAs and assess their differences in the navigation domain using the gLAB tool. For this purpose, we have used multi-frequency data for several hundreds of stations distributed worldwide belonging to the International GNSS Service (IGS) network. For each first day of the month during year 2019, the outcomes STECs of the two ICAs have been compared in terms of accuracy, availability and execution time. For completeness and inter-comparisons, STEC from post-processed Global Ionospheric Maps from IGS have been also been accounted for. Then, for each station involved in the experiment, positioning errors have been analyzed while using the different ionospheric corrections. The authors acknowledge the use of data and products provided by the International GNSS Service. The research reported in this paper has been partially supported by the Horizon 2020 Marie Skłodowska-Curie Individual Global Fellowship 797461 NAVSCIN and by the Spanish Ministry of Science, Innovation and Universities project RTI2018-094295-B-I00 a.

Single-frequency users of the global navigation satellite system (GNSS) must correct for the ionospheric delay. These corrections are available from global ionospheric models (GIMs). Therefore, the accuracy of the GIM is important because the unmodeled or incorrectly part of ionospheric delay contributes to the positioning error of GNSS-based positioning. However, the positioning error of receivers located at known coordinates can be used to infer the accuracy of GIMs in a simple manner. This is why assessment of GIMs by means of the position domain is often used as an alternative to assessments in the ionospheric delay domain. The latter method requires accurate reference ionospheric values obtained from a network solution and complex geodetic modeling. However, evaluations using the positioning error method present several difficulties, as evidenced in recent works, that can lead to inconsistent results compared to the tests using the ionospheric delay domain. We analyze the reasons why such inconsistencies occur, applying both methodologies. We have computed the position of 34 permanent stations for the entire year of 2014 within the last Solar Maximum. The positioning tests have been done using code pseudoranges and carrier-phase leveled (CCL) measurements. We identify the error sources that make it difficult to distinguish the part of the positioning error that is attributable to the ionospheric correction: the measurement noise, pseudorange multipath, evaluation metric, and outliers. Once these error sources are considered, we obtain equivalent results to those found in the ionospheric delay domain assessments. Accurate GIMs can provide single-frequency navigation positioning at the decimeter level using CCL measurements and better positions than those obtained using the dual-frequency ionospheric-free combination of pseudoranges. Finally, some recommendations are provided for further studies of ionospheric models using the position domain method.

At present most low-cost GNSS receivers operate one frequency in the L band. For themone of the largest error contributions is the delay of radio signals in the Ionosphere. NeQuick-Gisthe official ionospheric correction algorithm (ICA), which has been adopted for Galileo, the EuropeanGNSS Programme. The NeQuick-G implementation is complex when compared with other ICAs. Itis also demanding in terms of computational resources. The Joint Research Centre completed areference implementation of NeQuick-G based on the official document“Ionospheric CorrectionAlgorithm for Galileo Single Frequency Users”provided by the European Global Navigation SatelliteSystems Agency. The rationale behind the JRC implementation of NeQuick-G was the intent to write anindependent source code from scratch, without using the pseudo-codes from the reference documentand solely relying on the physics descriptions. Using such implementation as baseline, this paperdescribes an optimization attempt of the official pseudo-code from an algorithmic perspective. Theobjective was to reduce the computational load while not sacrificing the performance. The newproposed integration method is able to speed up calculations to 21% and 49% with respect the twoofficial integration algorithms. The overall computational burden depends on the number of operations,which is eventually closely correlated to the number of calls of the ionospheric model. This underlinesthe quest tofind an integration method reducing this number of calls. Moreover, based on thefindings of this study, the authors strongly recommend revisiting the convergence control of theintegration routines introduced in (European Commission, 2016, https://www.gsc-europa.eu/sites/default/files/sites/all/files/Galileo_Ionospheric_Model.pdf).

The characterization of Galileo Open Service signal-in-space (SiS) represents an essential input to Safety-of-Life (SoL) applications like Horizontal ARAIM (Advanced Receiver Autonomous Integrity Monitoring) and SBAS (Satellite Based Augmentation System) in particular EGNOS V3. This paper describes the IFMEA (Integrity Failure Mode and Effect Analysis) process that has been implemented for Galileo in order to conduct in a structured way the analysis of events critical for Safety-of-Life applications (referred to as Feared Events, FE) based on accumulated measurement history and design documentation analysis. The different steps of the established process are described which encompass measurement collection and post-processing, design analysis, root cause identification, reporting and archiving in form of a database. The process is leading to the identification of improvement recommendations in order to mitigate the re-occurrence of observed events. Moreover this paper provides insight into the Galileo Feared Event characterization, along with an analysis versus overall Safety-of-Life needs and the extrapolation to future Galileo configurations. It comprises the identification of anomalies in the satellites’ signal-in-space that could impact the positioning integrity. Several SiS threat offline monitors have been developed for the Galileo Feared Event characterization that allow identifying anomalies in both the navigation message and code and carrier phase observations. The focus is put on the characterization results in terms of Feared Event probabilities of occurrence and related magnitudes.The underlying mathematical approach for the derivation of the Feared Eventprobabilities as a function of the number of Feared Events and the observation period is described in this paper.The characterization results confirm the high quality of the code and carrier phase signals (based on an observation period of about 3.5 years of the Galileo constellation). For the message related anomalies including the broadcast orbit and clock prediction errors, the latest results are limited due to a limited observation period (about 2.5 years of Galileo constellation after the declaration of Galileo Initial Services). After extrapolation to a future Galileo configuration, the Feared Event probabilities achieve low and very promising levels.

Ionospheric scintillation causes rapid fluctuations of measurements from Global Navigation Satellite Systems (GNSSs), thus threatening space-based communication and geolocation services. The phenomenon is most intense in equatorial regions, around the equinoxes and in maximum solar cycle conditions. Currently, ionospheric scintillation monitoring receivers (ISMRs) measure scintillation with high-pass filter algorithms involving high sampling rates, e.g. 50 Hz, and highly stable clocks, e.g. an ultra-low-noise Oven-Controlled Crystal Oscillator. The present paper evolves phase scintillation indices implemented in conventional geodetic receivers with sampling rates of 1 Hz and rapidly fluctuating clocks. The method is capable to mitigate ISMR artefacts that contaminate the readings of the state-of-the-art phase scintillation index. Our results agree in more than 99.9% within ± 0.05 rad (2 mm) of the ISMRs, with a data set of 8 days which include periods of moderate and strong scintillation. The discrepancies are clearly identified, being associated with data gaps and to cycle-slips in the carrier-phase tracking of ISMR that occur simultaneously with ionospheric scintillation. The technique opens the door to use huge databases available from the International GNSS Service and other centres for scintillation studies. This involves GNSS measurements from hundreds of worldwide-distributed geodetic receivers over more than one Solar Cycle. This overcomes the current limitations of scintillation studies using ISMRs, as only a few tens of ISMRs are available and their data are provided just for short periods of time.

This work presents recent and ongoing updates to the free and open-source advanced interactive multi-purpose package for processing and analysing Global Navigation Satellite System (GNSS) data, named GNSS-Lab Tool suite (gLAB). The updates have been performed in the framework of two projects funded by the European Space Agency (ESA), namely, the “gLAB upgrade for European Geostationary Navigation Overlay System (EGNOS) Data processing” and “Upgrade of gLAB Tool for Double Frequency Multi-Constellation (DFMC)”. We examine various sets of results obtained with actual data using the Satellite Based Augmentation System (SBAS) corrections and the Differential GNSS (DGNSS) mode. Specifically, we introduce the Global Monitoring System (GMS) that routinely assesses the performance of the SBAS and DGNSS solutions using multiple station networks. That is, the Stanford-ESA integrity diagram, the Worst Integrity Ratio (WIR) maps, continuity risk, among other types of performance monitoring. Lastly, we present the ongoing update to the gLAB tool that focusses on the implementation of multi-frequency and multi-constellation data processing capabilities.

Fast Precise Point Positioning (Fast-PPP) provides Global Navigation Satellite System corrections in real-time. Satellite orbits and clock corrections are shown to be accurate to a few centimeters and a few tenths of a nanosecond which, together with the determination of the fractional part of the ambiguities, enable global high-accuracy positioning with undifferenced Integer Ambiguity Resolution. The new global ionospheric model is shown to provide corrections accurate at the level of 1 Total Electron Content Unit over well-sounded areas and Differential Code Biases at the level of tenths of a nanosecond. These corrections are assessed with permanent receivers, treated as rovers, located at 100 to 800 kilometers from the reference stations of the ionospheric model. Fast-PPP achieves decimeter-level of accuracy after few minutes, several times faster than single- and dual-frequency ionospheric-free solutions, using a month of Global Positioning System data close to the last Solar Maximum and including equatorial rovers.

This is a pre-print of an article published in GPS Solutions. The final authenticated version is available online at: https://doi.org/10.1007/s10291-018-0753-7. The study is funded by National Key Research and Development Program of China (2016YFB0501902), National Natural Science Foundation of China (41574025, 41574013, 41731069), Spanish Ministry of Science and Innovation project (CGL2015-66410-P), The Hong Kong RGC Joint Research Scheme (E-PolyU501/16) and State Key Laboratory of Geo-Information Engineering (SKLGIE2015-M-2-2). The calibration errors on experimental slant total electron content (TEC) determined with global positioning system (GPS) observations is revisited. Instead of the analysis of the calibration errors on the carrier phase leveled to code ionospheric observable, we focus on the accuracy analysis of the undifferenced ambiguity-fixed carrier phase ionospheric observable determined from a global distribution of permanent receivers. The results achieved are: (1) using data from an entire month within the last solar cycle maximum, the undifferenced ambiguity-fixed carrier phase ionospheric observable is found to be over one order of magnitude more accurate than the carrier phase leveled to code ionospheric observable and the raw code ionospheric observable. The observation error of the undifferenced ambiguity-fixed carrier phase ionospheric observable ranges from 0.05 to 0.11 total electron content unit (TECU) while that of the carrier phase leveled to code and the raw code ionospheric observable is from 0.65 to 1.65 and 3.14 to 7.48 TECU, respectively. (2) The time-varying receiver differential code bias (DCB), which presents clear day boundary discontinuity and intra-day variability pattern, contributes the most part of the observation error. This contribution is assessed by the short-term stability of the between-receiver DCB, which ranges from 0.06 to 0.17 TECU in a single day. (3) The remaining part of the observation errors presents a sidereal time cycle pattern, indicating the effects of the multipath. Further, the magnitude of the remaining part implies that the code multipath effects are much reduced. (4) The intra-day variation of the between-receiver DCB of the collocated stations suggests that estimating DCBs as a daily constant can have a mis-modeling error of at least several tenths of 1 TECU.

Scintillation is one of the most challenging problems in Global Navigation Satellite Systems (GNSS) navigation. This phenomenon appears when the radio signal passes through ionospheric irregularities. These irregularities represent rapid changes on the refraction index and, depending on their size, they can produce also diffractive effects affecting the signal amplitude and, eventually producing cycle slips. In this work, we show that the scintillation effects on the GNSS signal are quite different in low and high latitudes. For low latitude receivers, the main effects, from the point of view of precise navigation, are the increase of the carrier phase noise (measured by σϕ) and the fade on the signal intensity (measured by S4) that can produce cycle slips in the GNSS signal. With several examples, we show that the detection of these cycle slips is the most challenging problem for precise navigation, in such a way that, if these cycle slips are detected, precise navigation can be achieved in these regions under scintillation conditions. For high-latitude receivers the situation differs. In this region the size of the irregularities is typically larger than the Fresnel length, so the main effects are related with the fast change on the refractive index associated to the fast movement of the irregularities (which can reach velocities up to several km/s). Consequently, the main effect on the GNSS signals is a fast fluctuation of the carrier phase (large σϕ), but with a moderate fade in the amplitude (moderate S4). Therefore, as shown through several examples, fluctuations at high-latitude usually do not produce cycle slips, being the effect quite limited on the ionosphere-free combination and, in general, precise navigation can be achieved also during strong scintillation conditions.

A high-accuracy Global Ionosphere Model (GIM) is significant for precise positioning and navigating with the Global Navigation Satellite System (GNSS), as well as space weather applications. To obtain a precise GIM, it is critical to take both the ionospheric observable and mathematical model into consideration. In this contribution, the undifferenced ambiguity-fixed carrier-phase ionospheric observable is first determined from a global distribution of permanent receivers. Accuracy assessment with a co-located station experiment shows that the observational errors affecting the ambiguity-fixed carrier-phase ionospheric observables range from 0.10 to 0.35 Total Electron Content Units (TECUs, where 1 TECU = 10 16 e − / m 2 and corresponds to 0.162 m on the Global Positioning System, GPS L1 frequency), indicating that the ambiguity-fixed carrier-phase ionospheric observable is over one order of magnitude more accurate than the carrier-phase leveled-code one (from 1.21 to 3.77 TECUs). Second, to better model the structure of the ionosphere, a two-layer GIM has been built based on the above carrier-phase observable. Preliminary global accuracy evaluation demonstrates that the accuracy of the two-layer GIM is below 1 TECU and about 2 TECUs during low and high solar activity periods. Third, the single-frequency point positioning experiment is adopted to test the ionosphere mitigation effects of the GIMs. Positioning results demonstrate that the single-frequency positioning accuracy can be improved by more than 30% using the undifferenced ambiguity-fixed ionospheric observable-derived two-layer GIM, compared with that using the carrier-phase leveled-code ionospheric observable-based single-layer GIM.

Ionospheric scintillation produces strong disruptive effects on global navigation satellite system (GNSS) signals, ranging from degrading performances to rendering these signals useless for accurate navigation. The current paper presents a novel approach to detect scintillation on the GNSS signals based on its effect on the ionospheric-free combination of carrier phases, i.e. the standard combination of measurements used in precise point positioning (PPP). The method is implemented using actual data, thereby having both its feasibility and its usefulness assessed at the same time. The results identify the main effects of scintillation, which consist of an increased level of noise in the ionospheric-free combination of measurements and the introduction of cycle-slips into the signals. Also discussed is how mis-detected cycle-slips contaminate the rate of change of the total electron content index (ROTI) values, which is especially important for low-latitude receivers. By considering the effect of single jumps in the individual frequencies, the proposed method is able to isolate, over the combined signal, the frequency experiencing the cycle-slip. Moreover, because of the use of the ionospheric-free combination, the method captures the diffractive nature of the scintillation phenomena that, in the end, is the relevant effect on PPP. Finally, a new scintillation index is introduced that is associated with the degradation of the performance in navigation.

© 2015, Springer-Verlag Berlin Heidelberg. The characterization of the accuracy of ionospheric models currently used in global navigation satellite systems (GNSSs) is a long-standing issue. The characterization remains a challenging problem owing to the lack of sufficiently accurate slant ionospheric determinations to be used as a reference. The present study proposes a methodology based on the comparison of the predictions of any ionospheric model with actual unambiguous carrier-phase measurements from a global distribution of permanent receivers. The differences are separated as hardware delays (a receiver constant plus a satellite constant) per day. The present study was conducted for the entire year of 2014, i.e. during the last solar cycle maximum. The ionospheric models assessed are the operational models broadcast by the global positioning system (GPS) and Galileo constellations, the satellite-based augmentation system (SBAS) (i.e. European Geostationary Navigation Overlay System (EGNOS) and wide area augmentation system (WAAS)), a number of post-process global ionospheric maps (GIMs) from different International GNSS Service (IGS) analysis centres (ACs) and, finally, a more sophisticated GIM computed by the research group of Astronomy and GEomatics (gAGE). Ionospheric models based on GNSS data and represented on a grid (IGS GIMs or SBAS) correct about 85 % of the total slant ionospheric delay, whereas the models broadcasted in the navigation messages of GPS and Galileo only account for about 70 %. Our gAGE GIM is shown to correct 95 % of the delay. The proposed methodology appears to be a useful tool to improve current ionospheric models.

We introduce a methodology to extract the separate contributions of the ionosphere and the plasmasphere to the vertical total electron content, without relying on a fixed altitude to perform that separation. The method combines two previously developed and tested techniques, namely, the retrieval of electron density profiles from radio occultations using an improved Abel inversion technique and a two-component model for the topside ionosphere plus protonosphere. Taking measurements of the total electron content from global ionospheric maps and radio occultations from the Constellation Observing System for Meteorology, Ionosphere, and Climate/FORMOSAT-3 constellation, the ionospheric and plasmaspheric electron contents are calculated for a sample of observations covering 2007, a period of low solar and geomagnetic activity. The results obtained are shown to be consistent with previous studies for the last solar minimum period and with model calculations, confirming the reversal of the winter anomaly, the hemispheric asymmetry of the semiannual anomaly, and the existence in the plasmasphere of an annual anomaly in the South American sector of longitudes. The analysis of the respective fractional contributions from the ionosphere and the plasmasphere to the total electron content shows quantitatively that during the night the plasmasphere makes the largest contribution, peaking just before sunrise and during winter. On the other hand, the fractional contribution from the ionosphere reaches a maximum value around noon, which is nearly independent of season and geomagnetic latitude.

Fast precise point positioning (Fast-PPP) is a satellite-based navigation technique using an accurate real-time ionospheric modeling to achieve high accuracy quickly. In this paper, an end-to-end performance assessment of Fast-PPP is presented in near-maximum Solar Cycle conditions; from the accuracy of the Central Processing Facility corrections, to the user positioning. A planetary distribution of permanent receivers including challenging conditions at equatorial latitudes, is navigated in pure kinematic mode, located from 100 to 1300 km away from the nearest reference station used to derive the ionospheric model. It is shown that satellite orbits and clocks accurate to few centimeters and few tenths of nanoseconds, used in conjunction with an ionosphere with an accuracy better than 1 Total Electron Content Unit (16 cm in L1) reduce the convergence time of dual-frequency Precise Point Positioning, to decimeter-level (3-D) solutions. Horizontal convergence times are shortened 40% to 90%, whereas the vertical components are reduced by 20% to 60%. A metric to evaluate the quality of any ionospheric model for Global Navigation Satellite System is also proposed. The ionospheric modeling accuracy is directly translated to mass-market single-frequency users. The 95th percentile of horizontal and vertical accuracies is shown to be 40 and 60 cm for single-frequency users and 9 and 16 cm for dual-frequency users. The tradeoff between the formal and actual positioning errors has been carefully studied to set realistic confidence levels to the corrections.

Best Presentation Award, 27th. International Technical Meeting of Satellite Division of the Instutute of Navigation (ION GNSS+2014) The ionosphere plays an important role in satellite-based navigation, either in standard navigation, with single frequency mass-market receivers, or in precise navigation, with dual frequency receivers. In this work, the requirements of a real-time ionospheric model suitable for GNSS applications are explored, in terms of accuracy and confidence bounds. Key factors for an ionospheric determination better than 1 Total Electron Content Unit (TECU) (16 centimeters in L1) are shown to be whether the model has been derived using an ambiguity-fixing strategy and the number of layers used to reproduce the ionospheric delay. Different models are assessed both in mid-latitudes and equatorial regions, near the Solar Cycle maximum. It will be shown how dual-frequency users take benefit from a precise modelling of the ionosphere. If accurate enough, the convergence of the navigation filter is reduced to achieve high accuracy positioning quickly, (i.e., the Fast Precise Point Positioning technique). Satellite orbits and clocks computed for Fast-PPP will be shown to be accurate to few centimeters and few tenths of nanoseconds, respectively. Single-frequency users correct its measurements with the predictions provided by any ionospheric model. Thence, the accuracy of the Fast-PPP ionospheric corrections is directly translated to the measurements modelling and, consequently, to the user solution. Horizontal and vertical 95% accuracies are shown to be better than 36 and 63 centimeters for single-frequency users and 11 and 15 centimeters for dual-frequency users. The assessment is done for several locations, including the equatorial region, for a month of data close to the last Solar Maximum. The trade-off between the formal and actual positioning errors has been carefully studied by means of the Stanford plots to set realistic confidence bounds to the corrections. Award-winning

This work presents the first results obtained on real time positioning applying the algorithms developed by our research group and using the data from the IGS-RT network, in order to confirm previous feasibility studies. Real-time user receivers at hundreds of kilometres far from the nearest reference station, which achieve precise positioning after few minutes of a cold start, will be presented and analyzed.

Satellite Navigation has become a keystone for the development of Europe and its citizens. It is then essential to provide adequate educational programmes so to ensure a prepared workforce for the GNSS sector in Europe. In this context, ESA has launched a complete Satellite Navigation Educational program, called EDUNAV, aiming at providing up-to-date GNSS based educational material and educational tools. The GNSS-Lab (gLAB) Educational Software Tool is part of this ESA EDUNAV initiative. gLAB, developed under ESA Contract by the research group of Astronomy and Geomatics (gAGE) from the Universitat Politecnica de Catalunya (UPC), is an interactive educational multipurpose package to process and analyse GNSS data. gLAB performs precise modeling of GNSS observables (pseudorange and carrier phase) at the centimetre level, allowing both standalone GPS positioning and PPP. Every single error contributor may be assessed independently, which, in turn, provides a major educational benefit. gLAB is adapted to a variety of standard formats like RINEX-3.00, SP3, ANTEX and SINEX files, among others. Moreover, functionality is also included for GPS, Galileo and GLONASS, allowing performing some data analysis with real multi-constellation data. The gLAB software tool is quite flexible, able to run under Linux and Windows operating systems and is provided free of charge by ESA to universities and GNSS professionals.

The final publication is available at Springer via http://dx.doi.org/10.1007/s10291-017-0634-5 We address two main problems related to the receiver and satellite differential code biases (DCBs) determination. The first issue concerns the drifts and jumps experienced by the DCB determinations of the International GNSS Service (IGS) due to satellite constellation changes. A new alignment algorithm is introduced to remove these nonphysical effects, which is applicable in real time. The full-time series of 18 years of Global Positioning System (GPS) satellite DCBs, computed by IGS, are realigned using the proposed algorithm. The second problem concerns the assessment of the DCBs accuracy. The short- and long-term receiver and satellite DCB performances for the different Ionospheric Associate Analysis Centers (IAACs) are discussed. The results are compared with the determinations computed with the two-layer Fast Precise Point Positioning (Fast-PPP) ionospheric model, to assess how the geometric description of the ionosphere affects the DCB determination and to illustrate how the errors in the ionospheric model are transferred to the DCB estimates. Two different determinations of DCBs are considered: the values provided by the different IAACs and the values estimated using their pre-computed Global Ionospheric Maps (GIMs). The second determination provides a better characterization of DCBs accuracy, as it is confirmed when analyzing the DCB variations associated with the GPS Block-IIA satellites under eclipse conditions, observed mainly in the Fast-PPP DCB determinations. This study concludes that the accuracy of the IGS IAACs receiver DCBs is approximately 0.3–0.5 and 0.2 ns for the Fast-PPP. In the case of the satellite DCBs, these values are about 0.12–0.20 ns for IAACs and 0.07 ns for Fast-PPP.

The Abel inversion method is the classic approach to retrieve electron density profiles from radio occultation measurements, assuming that the electron density is only dependent upon height. In the early 2000s, the total electron content (TEC)-aided inversion method was introduced, where horizontal gradients in the electron density distribution are taken into account by using information from an external model of total electron content (TEC). We show how the quality of the chosen external ionospheric model influences the radio occultation retrievals. Using a two-layer TEC model, the 68% percentiles of the global error distributions of retrieved critical frequency and bottomside ionospheric electron content for 2014 improve more than 30%, with regard to the classic Abel inversion results. In a well-sounded region like Europe, this improvement raises to about 40–45%, while 10% improvement is achieved using two-layer maps with regard to the retrievals using single-layer TEC maps. We point out that using the TEC to describe the horizontal gradient incurs an implicit mismodeling that, until now, has not been taken into account. A new technique is presented that, thanks to TEC modeling by means of two layers, can assess the impacts of such mismodeling. From this technique, a method to select the most accurate radio occultation retrievals is applied to demonstrate that the resulting errors in the retrieved critical frequencies for the European region are smaller than 7% in nearly 82% of the cases, very similar to the relative difference between measurements of two nearby ionosondes.

This work reviews an ionospheric activity indicator useful for identifying disturbed periods affecting the performance of Global Navigation Satellite System (GNSS). This index is based in the Along Arc TEC Rate (AATR) and can be easily computed from dual-frequency GNSS measurements. The AATR indicator has been assessed over more than one Solar Cycle (2002–2017) involving about 140 receivers distributed world-wide. Results show that it is well correlated with the ionospheric activity and, unlike other global indicators linked to the geomagnetic activity (i.e. DST or Ap), it is sensitive to the regional behaviour of the ionosphere and identifies specific effects on GNSS users. Moreover, from a devoted analysis of different Satellite Based Augmentation System (SBAS) performances in different ionospheric conditions, it follows that the AATR indicator is a very suitable mean to reveal whether SBAS service availability anomalies are linked to the ionosphere. On this account, the AATR indicator has been selected as the metric to characterise the ionosphere operational conditions in the frame of the European Space Agency activities on the European Geostationary Navigation Overlay System (EGNOS). The AATR index has been adopted as a standard tool by the International Civil Aviation Organization (ICAO) for joint ionospheric studies in SBAS. In this work we explain how the AATR is computed, paying special attention to the cycle-slip detection, which is one of the key issues in the AATR computation, not fully addressed in other indicators such as the Rate Of change of the TEC Index (ROTI). After this explanation we present some of the main conclusions about the ionospheric activity that can extracted from the AATR values during the above mentioned long-term study. These conclusions are: (a) the different spatial correlation related with the MOdified DIP (MODIP) which allows to clearly separate high, mid and low latitude regions, (b) the large spatial correlation in mid latitude regions which allows to define a planetary index, similar to the geomagnetic ones, (c) the seasonal dependency which is related with the longitude and (d) the variation of the AATR value at different time scales (hourly, daily, seasonal, among others) which confirms most of the well-known time dependences of the ionospheric events, and finally, (e) the relationship with the space weather events.

Users of the global navigation satellite system (GNSS) operating with a single-frequencyreceiver must use an ionospheric correction algorithm (ICA) to account for the delay introduced onradio waves by the upper atmosphere. Galileo, the European GNSS, uses an ICA named NeQuick-G. In an effort to foster the adoption of NeQuick-G by final users, two implementations in Clanguage have been recently made available to the public by the European Space Agency (ESA)and the Joint Research Centre (JRC) of the European Commission (EC), respectively. The aim ofthe present contribution is to compare the slant total electron content (STEC) predictions of thetwo aforementioned implementations of NeQuick-G. For this purpose, we have used actual multi-constellation and multi-frequency data for several hundreds of stations distributed worldwidebelonging to the Multi GNSS Experiment (MGEX) network of the International GNSS Service (IGS).For each first day of the month during year 2019, the STECs of the two NeQuick-G versions werecompared in terms of accuracy, consistency, availability, and execution time. Our study concludesthat both implementations of NeQuick-G perform equivalently. Indeed, in over 99.998% of the 2125million STECs computed, the output is exactly coincident. In contrast, 0.002% of the whole set ofSTECs for those rays are tangent to the Earth, the behavior of both implementations differs. Weconfirmed the discrepancy by processing radio-occultation actual measurements from a COSMIC-2 low Earth orbit satellite. We selected the JRC version of the Galileo ICA to be integrated intothe GNSS LABoratory (gLAB) tool suite, because its open license and its processing speed (it is13.88% faster than the ESA version). NeQuick-G outperforms the GPS ICA in STEC residuals up to12.15 TECUs (percentile 96.23th) and in the 3D position errors, up to 5.76 m (percentile 99.18th) forcode-pseudorange positioning. This work was supported in part by the Spanish Ministry of Science, Innovation andUniversities project RTI2018-094295-B-I00 and in part by the Horizon 2020 Marie Skłodowska-Curie Individual Global Fellowship 797461 NAVSCIN.