Innovation: The European Way

June 1, 2014  - By 0 Comments

Performance of the Galileo Single-Frequency Ionospheric Correction During In-Orbit Validation

By Roberto Prieto-Cerdeira, Raül Orús-Pérez, Edward Breeuwer, Rafael Lucas-Rodriguez, and Marco Falcone

INNOVATION INSIGHTS with Richard Langley

INNOVATION INSIGHTS with Richard Langley

OFF TO A GOOD START. That’s how we might characterize the European Galileo satellite navigation system. The official beginning of the Galileo program occurred on May 26, 2003, when the European Union and the European Space Agency officially agreed on the first stage of the program (although some work on system concepts took place earlier). The first two prototype or development satellites, Galileo In-Orbit Validation Element-A (GIOVE-A) and GIOVE-B, were launched on December 28, 2005, and April 26, 2008, respectively. The satellites successfully validated key technologies for the full Galileo constellation and secured the system’s frequency allocations.

The first two In-Orbit Validation (IOV) satellites were launched by a single rocket on October 21, 2011, and the third and fourth IOV satellites were similarly launched on October 12, 2012. The two GIOVE satellites and first two IOV satellites provided an opportunity to use Galileo-only receiver measurements and after-the-fact precise satellite orbit and clock data to compute the position of a receiver’s antenna. Joined by two colleagues, I was pleased to report our successful attempt using dual-frequency carrier-phase and pseudorange data collected on May 17, 2012, in an article in the September 2012 issue of this magazine. The two GIOVE satellites were subsequently retired.

The four IOV satellites began transmitting navigation messages with valid ephemerides in March, 2013, and this paved the way for the first real-time single-frequency pseudorange Galileo position fix using the broadcast messages on the morning of March 12 at the Navigation Laboratory of the European Space Research and Technology Centre in Noordwijk, the Netherlands. The position fix included compensation for the effect of the ionosphere on the Galileo signals.

The signals from GNSS satellites travel through the ionosphere on their way to receivers on or near the Earth’s surface. The free electrons populating this region of the atmosphere affect the propagation of the signals, changing their speed and direction of travel. This results in a delay in the arrival of the modulated components of the signals (from which pseudorange measurements are made) and an advance in the phases of the signals’ carrier waves (affecting carrier-phase measurements). The ionosphere is a dispersive medium for radio signals, so by making measurements simultaneously on two frequencies transmitted by a satellite, most of the effect of the ionosphere can be removed. However, single-frequency devices such as most vehicle navigation and handheld receivers don’t have the luxury of dual-frequency correction. These devices must rely on a single-frequency correction model. The coefficients for such a model are included in the navigation messages transmitted by all GPS satellites. Known as the Ionospheric Correction Algorithm or Klobuchar Algorithm, it removes at least 50 percent of the ionosphere’s effect.

The Galileo satellites also include the parameters of an ionospheric algorithm, called NeQuick G, in their navigation messages. In this month’s column, the Galileo system design team describes the novel European way for modeling the ionosphere for single-frequency users and compares its performance to the current GPS approach.


“Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas.


Radiowave propagation of GNSS signals is affected by the Earth’s atmosphere and the characteristics of the local environment surrounding the receiver. GNSS systems are based on the broadcasting of radiowave ranging signals in the microwave domain (mainly in the so-called L-band, although some new systems like the Indian Regional Navigation Satellite System are also expected to broadcast in the S-band). These electromagnetic signals may suffer from a number of impairments as they propagate from a satellite to a receiver. In considering these effects, we can divide the Earth’s atmosphere into two parts: the electrically neutral atmosphere (primarily the lowest part, the troposphere), whose main effect is a group delay on the navigation signal due to water vapor and the gas components of the dry air, which, for microwave frequencies, is non-dispersive (independent of frequency); and the ionosphere, the ionized part of the atmosphere. The local environment may affect the navigation signal in various ways, too, such as signal fading or complete signal blockage by vegetation or obstacles such as buildings, and multipath, where the signal is broadened in the time and frequency domains due to reflections and diffraction by surrounding objects. In this article, we will discuss the effect of the ionosphere on GNSS signals and how it is being dealt with by the Galileo satellite navigation system.

The ionosphere owes its existence to solar radiation, primarily extreme ultraviolet light. The radiation ionizes the atoms and molecules in the upper atmosphere at heights of less than a hundred kilometers to a few kilometers above the Earth’s surface, producing a sea of ions and free electrons (collectively known as a plasma). This region is responsible for a number of dispersive (frequency-dependent) effects on navigation signals. Chief among these is a persistent delay of the pseudorandom noise (PRN) ranging codes (and the advance of the phase of the underlying carrier waves), thereby introducing positioning and timing errors if not compensated for. Signals are also susceptible to scintillations — rapid variations of amplitude and/or phase of the signals due to diffraction and refraction caused by plasma irregularities. Furthermore, the ionosphere can bend the signal path, resulting in a slightly longer path than the straight path, and rotate the polarization of the signal.

The ionospheric refractive index (the ratio of the speed of propagation of electromagnetic waves in a vacuum to the speed of their propagation in a medium) is related to the number of free electrons along the propagation path. For this purpose, the total electron content (TEC) is defined as the electron density in a cross-section of 1 square meter, integrated along a slant (or vertical) path between two points (such as a satellite and a receiver). It is often expressed in TEC units (TECU) where 1 TECU = 1016 electrons per meter squared = 0.1624 meters of delay at the GPS L1 frequency.  According to the electron density, the mechanisms responsible for such ionization, and the dynamics, the ionosphere is usually sub-classified in layers of different characteristics: D, E, F1, and F2, with the latter largely responsible for the ionospheric effects on GNSS.

All of the propagation effects due to the ionosphere depend on a number of factors such as time of the day, location, season, and solar activity. There is also an interaction between solar activity, the ionosphere, and the Earth’s magnetic field, which, at times, can result in a significant disturbance of the ionosphere, as happens during geomagnetic storms. On a long timescale, solar activity follows a periodic, approximately 11-year, cycle. And spatially, the behavior of the ionosphere can be broadly classified into four main regions: the equatorial anomaly regions, located at around ±15-20º on either side of the magnetic equator, usually presenting the largest TEC values; mid-latitude regions, where the daytime TEC values are usually less than half the values found in the equatorial anomaly regions; and the auroral and polar regions, which present moderate TEC values but with larger variability than at mid-latitudes due to the characteristics of the geomagnetic field.

If we ignore some smaller, higher-order terms, the ionospheric group delay (the delay of the “group” of waves making up the PRN ranging code modulations) may be expressed in meters as 40.3 sTEC / f2, where sTEC is slant TEC in electrons per meter squared, calculated along the straight propagation path between receiver and satellite, and f is the carrier frequency in hertz. This effect introduces ranging errors of several meters if not corrected. The higher order terms usually account for differences at the millimeter level (rising to centimeter level during extreme ionospheric disturbances) and may be safely neglected for code ranging. The effect on the carrier phase has the same magnitude as the code delay, but of opposite sign, meaning that the carrier phase is advanced while propagating through the ionosphere. Since the group delay is dispersive, its effect can be mitigated using linear combinations of signals at two separate frequencies.

For single-frequency receivers, GNSSes often rely on correction models driven by broadcast data. For example, with GPS, the Ionospheric Correction Algorithm (ICA, also known as the Klobuchar algorithm) uses eight broadcast coefficients to describe the ionosphere, which is represented as a two-dimensional thin-shell model (the vTEC is assumed to be concentrated in a two-dimensional shell at a given height, relying on an analytical mapping or obliquity function to convert between vTEC and sTEC depending on the elevation angle of the received signal). This model is very efficient in terms of computational complexity, and it usually removes more than 50 percent of the ionospheric error, particularly at mid-latitudes.

Galileo and NeQuick G

Galileo provides dual-frequency services able to mitigate the effects of the ionosphere, but also services to single-frequency users. For a Galileo single-frequency receiver, an algorithm has been developed based on an adaptation of the NeQuick electron density model.

With the launch of the Galileo In-Orbit Validation (IOV) satellites and the initial navigation message broadcast, for the first time the end-to-end performance of the single-frequency correction algorithm for Galileo could be analyzed. The objective of the IOV phase was to launch the first four operational Galileo satellites and to deploy the first version of a completely new ground segment. During this phase, the European Space Agency (ESA) needed to validate — in the operational environment — all space, ground, and user components and their interfaces, prior to full system deployment, including the single-frequency correction algorithm performance starting from April 2013. Results were obtained for the period up to March 2014, coinciding with the maximum of solar cycle 24 and including three equinoxes with increased solar activity. In this article, we present performance results showing that the algorithm is capable of correcting more than 70 percent of the ionospheric group delay error under nominal ionospheric conditions, using only the reduced Galileo infrastructure during IOV (four satellites and a partial set of the Galileo sensor or monitoring stations).

The Algorithm. The Galileo single-frequency correction algorithm is based on an adaptation of the three-dimensional NeQuick electron density model, driven by an effective ionization level calculated with three broadcast ionospheric coefficients.

The original NeQuick model is a three-dimensional and time-dependent ionospheric electron density model based on an empirical climatological representation of the ionosphere, which predicts monthly mean electron density from analytical profiles, depending on solar-activity-related input values: sunspot number or solar flux, month, geographic latitude and longitude, height and UT. It allows us to calculate the TEC through numerical integration of electron density along a path between a beginning and an end point crossing the ionosphere. As an example, a global vTEC map obtained with NeQuick is illustrated in FIGURE 1. The first version of this model (NeQuick1) was incorporated into a previous version of the International Telecommunication Union (ITU) recommendation ITU-R P.532 for TEC estimation in radiowave propagation predictions. Researchers have continued development of the model with updated formulations, and version NeQuick2 is the one currently recommended by the ITU.

FIGURE 1. Global vTEC map obtained with the NeQuick electron density model for a sunspot number of 150 at 13h UT in the month of April (grid resolution 2.5 degrees × 2.5 degrees).

FIGURE 1. Global vTEC map obtained with the NeQuick electron density model for a sunspot number of 150 at 13h UT in the month of April (grid resolution 2.5 degrees × 2.5 degrees).

The NeQuick model has been adapted for Galileo single-frequency ionospheric corrections (for convenience, the Galileo version is known as NeQuick G) in order to derive real-time predictions based a single input parameter, Az, which is determined using three coefficients broadcast in the navigation message. The three coefficients are used in a second-degree polynomial as a function of the modified dip latitude (MODIP) of the receiver, to determine Az, which replaces the solar flux input parameter of the parent NeQuick model, with the following equation:

INN-E1(1)

where ai0-2 are the three broadcast coefficients. MODIP is expressed in degrees. A grid table of MODIP values versus geographical location is provided together with the algorithm. A map showing five different MODIP regions is presented in FIGURE 2, each region usually presenting different behavior.

FIGURE 2. MODIP regions. Contours are modified dip latitudes.

FIGURE 2. MODIP regions. Contours are modified dip latitudes.

The performance of the Galileo single-frequency ionospheric algorithm, designed to reach a correction capability of at least 70 percent of the ionospheric code delay, had been assessed in the past using GPS data only and using GPS plus Galileo In-Orbit Validation Element satellite data for an offline estimation of the broadcast parameters.

Since the first successful autonomous real-time Galileo-based position fix on March 12, 2013, the Galileo navigation messages have been broadcast by the four IOV spacecraft to the external user community, including the ionospheric broadcast parameters determined with IOV-only observations.

Experiment Period and Performance Indicators

To analyze the performance of the single-frequency ionospheric correction, a number of performance indicators were used:

  • The root-mean-square (RMS) error of the ionospheric model in meters of L1 code delay, for one station and one day.
  • The relative correction capability, expressed as an RMS percentage, defined as:

INN-E2(2)
where STECref is the reference STEC and STECNeQuickG is the STEC obtained with the Galileo correction model. The factor 66 is used to avoid the fact that small absolute errors, which are relatively large due to small reference values, inflate the correction capability; it is linked to a target correction of 70 percent with a minimum absolute threshold of 20 TECU (30 percent of 66 TECU is about 20 TECU).

Performance verification has been assessed for the period from April 2013 to March 2014, which includes the secondary peak of the current solar maximum. The Galileo broadcast data used for this test are the Az coefficients broadcast by the four Galileo IOV satellites. It is important to remember that during the period of this assessment, the IOV infrastructure was reduced with respect to the target full operational capability, including the generation of the ionospheric parameters: four IOV satellites (no other GNSS satellites were used in the estimation) and a reduced number of monitoring stations.

Since the ionospheric correction performance assessment can be done independently of the Galileo signals and analysis of performance is preferred over independent data and locations, reference STEC estimated using dual-frequency observables from GPS at stations from the International GNSS Service (IGS), distributed around the world, were selected for the correction capability performance assessment. This resulted in observations of six to nine satellites for any epoch and with more than 120 stations per day, which assured good global coverage for the test. Performance has been computed individually for each set of broadcast parameters. For this aspect of ionospheric correction assessment, the differences between GPS and full constellation Galileo geometries are considered to be negligible.

As a reference for comparative purposes, for some cases the results have been compared to those obtained with the GPS ICA correction model using the broadcast parameters from GPS satellites.

The reference ionosphere STEC values were computed using dual-frequency carrier-phase GPS observables from IGS stations at a sampling rate of 300 seconds, and using IGS final global ionospheric maps (GIMs) to level the geometry-free combination of carrier phases. In this context, the IGS GIMs are employed to align the geometry-free or ionospheric combination, LI, to compute the ambiguity term (BI) for each satellite-to-receiver arc:
INN-E3(3)

where LI represents the linear combination between signals at frequencies f1 and f2INN-E3a is the ionospheric delay in meters of LI; and BI is composed of several terms: station and satellite phase inter-frequency biases (INN-KLI and INN-KLIJ respectively), LI phase ambiguity (λ1N1jλ2N2j), phase wind-up, multipath, and noise. And i corresponds to the station and j to the satellite.

Then, in order to compute the corresponding BI term for each satellite-receiver continuous arc, the sTEC prediction of the GIM (sTECGIM_map) is computed for each satellite ionospheric pierce point, and then the average is computed as follows:
INN-E4(4)

where the indices i, j, and α correspond to the receiver, satellite, and arc indicator respectively, and the average is performed over the corresponding continuous (no cycle slips) arc (α) of data. INN-E4a  is estimated following the mapping function and the procedures to interpolate in space and time recommended by IGS for GIM maps represented in ionosphere-exchange (IONEX) format.

With this estimation, the aligned STEC can be obtained as:
INN-E5(5)

which is the STEC used as an accurate sTEC estimation or “truth”  reference value.

Results

The first analysis that we performed was the daily RMS error and correction capability for all stations. Most days have shown very promising performance. To see different levels of performance, results for one “bad” day and one typical “good” day, in the period of experimentation, are presented in FIGURE 3. It is observed that even for the “bad” day, the correction capability is above 70 percent, except for some stations in the equatorial regions. This performance is exceeded significantly for the “good” day, with RMS residual ionospheric errors below 1.5 meters for L1 even at low latitudes.

FIGURE 3a. Performance of the Galileo single-frequency ionospheric correction when using the E11 satellite broadcast, “bad day”  RMS error in meters of L1.

FIGURE 3a. Performance of the Galileo single-frequency ionospheric correction when using the E11 satellite broadcast, “bad day” RMS error in meters of L1.

FIGURE 3b. Performance of the Galileo single-frequency ionospheric correction when using the E11 satellite broadcast, “good day” RMS error in meters of L1.

FIGURE 3b. Performance of the Galileo single-frequency ionospheric correction when using the E11 satellite broadcast, “good day” RMS error in meters of L1.

FIGURE 3c. Performance of the Galileo single-frequency ionospheric correction when using the E11 satellite broadcast, “good day” correction capability in percent.

FIGURE 3c. Performance of the Galileo single-frequency ionospheric correction when using the E11 satellite broadcast, “good day” correction capability in percent.

FIGURE 3d. Performance of the Galileo single-frequency ionospheric correction when using the E11 satellite broadcast, “good day”  correction capability in percent.

FIGURE 3d. Performance of the Galileo single-frequency ionospheric correction when using the E11 satellite broadcast, “good day” correction capability in percent.

The evolution of the RMS residual error both for Galileo NeQuick G and GPS ICA from April 2013 to March 2014 are presented in FIGURE 4. In this figure, ionospheric activity at the equinoxes is clearly observed in the degradation of performance, and the influence of increased solar activity from October 2013 to March 2014 is also evident.

FIGURE 4. Global daily RMS ionospheric residual error in meters of L1 after correction with Galileo NeQuick G (red) and GPS ICA (blue) from April 2013 to March 2014.

FIGURE 4. Global daily RMS ionospheric residual error in meters of L1 after correction with Galileo NeQuick G (red) and GPS ICA (blue) from April 2013 to March 2014.

The residual error of the Galileo correction model is already at the level of the expected capability for the full constellation. It also shows better performance as compared to the GPS ICA model, especially at equatorial latitudes.

The level of correction capability for each station for the Galileo NeQuick G model and the GPS ICA model are presented in FIGURE 5 for a quiet day in May 2013 and an active day during the spring equinox in 2014.

FIGURE 5. RMS correction capability (percent, with a lower bound of 20 TECU) of Galileo NeQuick G correction models for day 127, 2013.

FIGURE 5a. RMS correction capability (percent, with a lower bound of 20 TECU) of Galileo NeQuick G correction models for day 127, 2013.

FIGURE 5b. RMS correction capability (percent, with a lower bound of 20 TECU) of GPS ICA correction models for day 127, 2013.

FIGURE 5b. RMS correction capability (percent, with a lower bound of 20 TECU) of GPS ICA correction models for day 127, 2013.

FIGURE 5c. RMS correction capability (percent, with a lower bound of 20 TECU) of Galileo NeQuick G correction models for day 80, 2014.

FIGURE 5c. RMS correction capability (percent, with a lower bound of 20 TECU) of Galileo NeQuick G correction models for day 80, 2014.

FIGURE 5d. RMS correction capability (percent, with a lower bound of 20 TECU) of GPS ICA (right) correction models for day 80, 2014.

FIGURE 5d. RMS correction capability (percent, with a lower bound of 20 TECU) of GPS ICA (right) correction models for day 80, 2014.

Effect in the Positioning Domain. We have performed two analyses to assess the correction performance in the positioning domain: one using GPS observables and one with Galileo-only observables. In both cases, we used three ionospheric delay mitigation methods: the dual-frequency ionosphere-free combination, the single-frequency GPS ICA correction algorithm, and the single-frequency Galileo NeQuick G correction algorithm.

The performance of the correction algorithm in the positioning domain using GPS observables was performed with data from two stations: Noordwijk in The Netherlands (a mid- to high-latitude station) and Malindi in Kenya (a low-latitude station) for the day of year (doy) 172 of 2013. Results are presented in FIGURES 6 and 7 showing good performance of the NeQuick G correction, in particular at low latitude. The results do not include code smoothing neither for single-frequency nor dual-frequency positioning. In the results, it may be observed that, as expected, the noise level for single-frequency positioning is much lower than that of ionosphere-free, but a higher bias may be present (the residual mean ionospheric error).

FIGURE 6a. Horizontal GPS positioning error on L1 using single-frequency NeQuick G correction (blue), L1 and GPS ICA (red) and dual-frequency ionosphere-free (green) for mid-latitude station in Noordwijk (doy 172, 2013).

FIGURE 6a. Horizontal GPS positioning error on L1 using single-frequency NeQuick G correction (blue), L1 and GPS ICA (red) and dual-frequency ionosphere-free (green) for mid-latitude station in Noordwijk (doy 172, 2013).

FIGURE 6b. Vertical GPS positioning error on L1 using single-frequency NeQuick G correction (blue), L1 and GPS ICA (red) and dual-frequency ionosphere-free (green) for mid-latitude station in Noordwijk (doy 172, 2013).

FIGURE 6b. Vertical GPS positioning error on L1 using single-frequency NeQuick G correction (blue), L1 and GPS ICA (red) and dual-frequency ionosphere-free (green) for mid-latitude station in Noordwijk (doy 172, 2013).

FIGURE 7a. Horizontal GPS positioning error on L1 and single-frequency NeQuick G correction (blue), L1 and GPS ICA (red) and dual-frequency ionosphere-free (green) for low-latitude station in Malindi (doy 172, 2013).

FIGURE 7a. Horizontal GPS positioning error on L1 and single-frequency NeQuick G correction (blue), L1 and GPS ICA (red) and dual-frequency ionosphere-free (green) for low-latitude station in Malindi (doy 172, 2013).

FIGURE 7b. Vertical GPS positioning error on L1 and single-frequency NeQuick G correction (blue), L1 and GPS ICA (red) and dual-frequency ionosphere-free (green) for low-latitude station in Malindi (doy 172, 2013).

FIGURE 7b. Vertical GPS positioning error on L1 and single-frequency NeQuick G correction (blue), L1 and GPS ICA (red) and dual-frequency ionosphere-free (green) for low-latitude station in Malindi (doy 172, 2013).

Positioning domain analysis with Galileo-only observations using the four Galileo IOV satellites, and applying the NeQuick G correction, was evaluated for a station in Washington, D.C., for doy 245, 2013, including E1-only, E5a-only, and dual-frequency E1-E5a ionosphere-free observations. (E1 is centered at the GPS L1 frequency, while E5a is centered at the GPS L5 frequency.)  These results are presented in FIGURE 8. The single-frequency positioning performance is considered promising considering the limited number of satellites.

FIGURE 8a. Horizontal Galileo IOV positioning error on E1 and single-frequency NeQuick G correction (blue), E5a and single-frequency NeQuick G correction (red) and dual-frequency E1-E5a ionosphere-free (green) for mid-latitude station in Washington (doy 245, 2013).

FIGURE 8a. Horizontal Galileo IOV positioning error on E1 and single-frequency NeQuick G correction (blue), E5a and single-frequency NeQuick G correction (red) and dual-frequency E1-E5a ionosphere-free (green) for mid-latitude station in Washington (doy 245, 2013).

FIGURE 8b. Vertical Galileo IOV positioning error on E1 and single-frequency NeQuick G correction (blue), E5a and single-frequency NeQuick G correction (red) and dual-frequency E1-E5a ionosphere-free (green) for mid-latitude station in Washington (doy 245, 2013).

FIGURE 8b. Vertical Galileo IOV positioning error on E1 and single-frequency NeQuick G correction (blue), E5a and single-frequency NeQuick G correction (red) and dual-frequency E1-E5a ionosphere-free (green) for mid-latitude station in Washington (doy 245, 2013).

Conclusions

The performance of the Galileo single-frequency ionospheric correction algorithm, based on NeQuick G, was evaluated using the broadcast navigation messages from the four Galileo IOV satellites, both in correction capability and in the positioning domain for the period April 2013 to March 2014. Despite the reduced infrastructure (broadcast ionospheric parameters estimated using only the IOV satellites at a limited number of monitoring stations), the performance shows promising results, in particular for low-latitude regions where the ionosphere is more problematic and, as expected, it has been confirmed that the correction performance is correlated with solar activity.

Acknowledgments

The NeQuick electron density model was developed by the Abdus Salam International Center of Theoretical Physics in Trieste, Italy, and the University of Graz in Austria. The adaptation of NeQuick for the Galileo single-frequency ionospheric correction algorithm (NeQuick G) was performed by ESA and involved the original developers of NeQuick and other European ionospheric scientists under various ESA projects.

Note to Manufacturers

The publication of the NeQuick G model and the Galileo single-frequency correction algorithm is under preparation for public release by the European Commission.


ROBERTO PRIETO-CERDEIRA is a propagation engineer in the European Space Agency (ESA) at the European Space Research and Technology Centre (ESTEC) in Noordwijk, The Netherlands, responsible for the activities related to radiowave propagation for GNSS and satellite mobile communications.

RAUL ORUS-PEREZ is a propagation engineer at ESTEC, working on activities related to radiowave propagation in the troposphere and ionosphere for GNSS and other ESA projects.

EDWARD BREEUWER is the system integration and verification manager in the Galileo Project Office at ESTEC, responsible for the organization and coordination of all testing activities at the system level. He had overall responsibility for the IOV test campaign.

RAFAEL LUCAS-RODRIGUEZ is the Galileo Services Engineering Manager for the Galileo project at ESTEC.

MARCO FALCONE is the System Manager in the Galileo Project Office at ESTEC.


Further Reading

• Development of NeQuick Ionospheric Model

“A New Version of the NeQuick Ionosphere Electron Density Model” by B. Nava, P. Coïsson, and S.M. Radicella in Journal of Atmospheric and Solar-Terrestrial Physics, Vol. 70, No. 15, December 2008, pp. 1856–1862, doi: 10.1016/j.jastp.2008.01.015.

“A Family of Ionospheric Models for Different Uses” by G. Hochegger, B. Nava, S.M. Radicella, and R. Leitinger in Physics and Chemistry of the Earth, Part C: Solar, Terrestrial & Planetary Science, Vol. 25, No. 4, 2000, pp. 307–310, doi : 10.1016/S1464-1917(00)00022-2.

“An Analytical Model of the Electron Density Profile in the Ionosphere” by G. Di Giovanni and S.M. Radicella in Advances in Space Research, Vol. 10, No. 11, 1990, pp. 27–30, doi: 10.1016/0273-1177(90)90301-F.

• Evaluation of the Galileo Single-Frequency Ionospheric Model

“Assessment of NeQuick Ionospheric Model for Galileo Single-Frequency Users” by A. Angrisano, S. Gaglione, C. Giola, M. Massaro, and U. Robustelli in Acta Geophysica, Vol. 61, No. 6, December 2013, pp. 1457–1476, doi: 10.2478/s11600-013-0116-2.

Ionosphere Modelling for Galileo Single Frequency Users by B. Bidaine, Ph.D. thesis, Université de Liège, Liège, Belgium, October 2012.

“GIOVE-A Experimentation Campaign: Ionospheric Related Data Analysis” by R. Orus and R. Prieto-Cerdeira in Proceedings of NAVITEC 2008, the 4th ESA Workshop on Satellite Navigation User Equipment Technologies: GNSS User Technologies in the Sensor Fusion Era, Noordwijk, The Netherlands, December 10–12, 2008.

“Assessment of the Ionospheric Correction Algorithm for GALILEO Single Frequency Receivers” by R. Prieto-Cerdeira, R. Orus, and B. Arbesser-Rastburg in Proceedings of NAVITEC 2006, the 3rd ESA Workshop on Satellite Navigation User Equipment Technologies, Noordwijk, The Netherlands, December 11–13, 2006.

“Advanced Ionospheric Modelling for GNSS Single Frequency Users” by M.A Aragón Ángel and F. Amarillo Fernández in the Proceedings of PLANS 2006, the Institute of Electrical and Electronics Engineers / Institute of Navigation Position, Location and Navigation Symposium, San Diego, California, April 24–27, 2006, pp. 110–120, doi: 10.1109/PLANS.2006.1650594.

• GPS Ionospheric Model

“Ionospheric Time-delay Algorithm for Single-frequency GPS Users” by J.A. Klobuchar in IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-23, No. 3, May 1987, pp. 325–331, doi: 10.1109/TAES.1987.310829

Ionospheric Effects on GPS” by J.A. Klobuchar in GPS World, Vol. 2, No. 4, April 1991, pp. 48–51.

• Ionospheric Effects on GNSS

GPS, the Ionosphere, and the Solar Maximum” by R.B. Langley in GPS World, Vol. 11, No. 7, July 2000, pp. 44–49.

• International GNSS Service Ionosphere Map Exchange Format

IONEX: The IONosphere Map EXchange Format Version 1 by S. Schaer, W. Gurtner, and J. Feltens, February 25, 1998.

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