This year’s European Navigation Conference in Bordeaux, France, got underway with “Good news from up there .…”
Galileo’s seventh and eighth satellites launched successfully in late March, the European Space Agency (ESA) plans four more satellites to reach orbit in 2015, and space maneuvers for Galileo 5 and 6 have been completed, with a recovery plan currently under study. ESA happily confirms that satellites 7 and 8 are in good position, under control, and behaving very well.
Fiammetta Diani, deputy head of Market Development for the European GNSS Agency (GSA), followed her keynote opener with “… some good news also from down here.”
The GSA predicts that the installed base of GNSS devices will triple by 2023, with per capita rates of 2.5 in North America, and 2.3 in Europe and Russia. Around the rest of the world, in eight years nearly every person, on average, will possess a GNSS device.
Axelle Pomies of Galileo Services, an association of industry players active in GNSS applications, stressed the need for a comprehensive, assertive industry policy to support the development of EGNOS/Galileo downstream sector, leading to growth, job creation and autonomy for Europe. She previewed the mid-May publication of a draft position paper in this regard, for wide consultation within the European downstream sector. Follow www.galileo-services.org for its first appearance.
Concluding the ENC plenary, Florence Ghiron of Topos Aquitaine, a regional council of satnav and intelligent transport companies in southwest France, focused on opportunities and risks for small-to-medium enterprises. One of her points: the long development paths of public and regulatory policy do not help SMEs grow.
The Galileo Services and Topos Aquitaine presentations receive more lengthy treatment in my online column mentioned above.
Diani and Ghiron closed with a call to return to Bordeaux in October for the Intelligent Transport Systems World Congress, themed “Towards Intelligent Mobility: Better Use of Space.” GNSS looks to take a more central role than ever in this far-reaching economic segment. Good news — for us — indeed.
The monitoring station in Brazil uses a Septentrio PolaRxS receiver to monitor the ionosphere, a Septentrio AsteRx3 to perform tests static and kinematic tests, and three RTK Altus APS3 receivers (one as a base station and two as rovers.)
After 27 months of intensive research, a project team funded under the European Union’s 7th Framework Programme has come up with a solution to counter the problem of ionospheric disturbance affecting GNSS signals.
The CALIBRA project recently showcased a commercially applicable approach to mitigate the phenomenon’s impact on high-accuracy GNSS positioning techniques. In two demonstrations, the project’s newly developed algorithm was successfully tested in actual precision agriculture and offshore operations.
Solar flares can cause ionospheric disturbance, a sudden increase in radio-wave absorption that often delays the propagation of signals and ultimately affects positioning. The problem has kept researchers busy for years.
The CALIBRA project team has been participating in this global research effort by focusing on Brazil, which is one of the most exposed regions due to its proximity to the magnetic equator. Add to this that the sun is at its peak of activity since it entered its new 11-year cycle in 2010.
The project achieved three main milestones. First, the team confirmed that ionospheric scintillation and variations in total electron content (TEC) had a direct impact on the functioning of high accuracy GNSS techniques, such as Precise Point positioning (PPP) and real-time kinematic (RTK) positioning. Then a suitable metric was established to characterize these ionospheric disturbances. Finally, the project produced a short-term empirical model for forecasting TEC and scintillation. A regional TEC map was developed which proved advantageous for use in Brazil and, to counter scintillation, a number of approaches for the mitigation of this phenomenon were proposed and their benefit demonstrated.
The project exploited the CIGALA-CALIBRA network and database — a network of ionospheric scintillation monitor receivers with a web interface (the ISMR Query tool), which collects more than 10 million observations on GPS, GLONASS, Galileo, BeiDou and other global navigation systems every day. Since it was launched in December 2014, this data has helped assist users from more than 20 countries because of the software’s visualization and mining techniques.
In light of this success, CALIBRA partners INGV (Istitute Nazionale di Geofisica e Vulcanologia) filed a patent for their forecasting model, and a new spin-off company — SpacEarth Technology — was set up. SpacEarth’s main purpose is to secure the software’s commercialization in relevant applications and services, while also improving and adapting it to evolving market needs.
The project’s results promise to considerably reduce downtime and financial losses caused by ionospheric disturbance in Brazil and other regions of the world. Learn more about the project here.
Langley, a professor at the University of New Brunswick, is working with the Jet Propulsion Laboratory in California to better understand how the ionosphere is disturbed by a variety of phenomena including solar outbursts and other natural hazards such as tsunamis. They are using the signals from GPS satellites to probe the ionosphere with the signals being picked up by receivers both on the ground and in low-Earth-orbiting satellites. The research could help find ways to mitigate ionospheric interference to GPS signals themselves as well as to other types of radio communications.
“GPS satellites are much higher than the ionosphere,” Langley told CBC News reporter Shane Fowler. “So the signals from the satellites have to come down through the ionosphere to receivers on or near the Earth’s surface. And as they come down through the ionosphere they get a little distorted. When you see auroras in the sky, that’s when you can tell the ionosphere is a bit disturbed. The average consumer may not notice these variances, but high-precision applications, like for scientific applications, we actually always see the effect of the ionosphere.”
Screen capture from CBC news video.
The research could also help develop early-detection systems for tsunamis. “The energy from that water displacement actually propagates up all the way into the atmosphere, all the way to the ionosphere,” Langley told CBC. “It basically moves around the electrons up there and GPS signals coming down from the satellites, through the ionosphere, pick up those small variations. It has the potential to save a lot of lives.”
Solar flares can also affect GPS signals. The Carrington Event, a solar storm in 1859, knocked out some of Earth’s telegraph systems. “The effect on the Earth’s magnetic field was so strong that currents were set up,” Langley told the CBC. “Those currents were so strong that telegraphs could run without batteries. There was enough current from this disturbance that it could run the telegraphs. And in some cases there was too much and rumour has it started small fires. Luckily we haven’t had one of those again; it seems to be a one-in-100-year, or a one-in-a-200-year, event.”
Editor’s note: GPS World Innovation editor Richard Langley has co-authored a study, described below, exploring how irregularities in Earth’s upper atmosphere can distort GPS signals, an important step toward mitigation.
The Aurora Borealis viewed by the crew of Expedition 30 on board the International Space Station. The sequence of shots was taken on February 7, 2012 from 09:54:04 to 10:03:59 GMT, on a pass from the North Pacific Ocean, west of Canada, to southwestern Illinois. Image Credit: NASA/JSC
News from the Jet Propulsion Laboratory
When you don’t know how to get to an unfamiliar place, you probably rely on a smartphone or other device with a GPS module for guidance. You may not realize that, especially at high latitudes on our planet, signals traveling between GPS satellites and your device can get distorted in Earth’s upper atmosphere.
Researchers at NASA’s Jet Propulsion Laboratory (JPL), Pasadena, Calif., in collaboration with the University of New Brunswick in Canada, are studying irregularities in the ionosphere, a part of the atmosphere centered about 217 miles (350 kilometers) above the ground that defines the boundary between Earth and space. The ionosphere is a shell of charged particles (electrons and ions), called plasma, that is produced by solar radiation and energetic particle impact.
The new study, published in the journal Geophysical Research Letters, compares turbulence in the auroral region to that at higher latitudes, and gains insights that could have implications for the mitigation of disturbances in the ionosphere. Auroras are spectacular multicolored lights in the sky that mainly occur when energetic particles driven from the magnetosphere, the protective magnetic bubble that surrounds Earth, crash into the ionosphere below it. The auroral zones are narrow oval-shaped bands over high latitudes outside the polar caps, which are regions around Earth’s magnetic poles. This study focused on the atmosphere above the Northern Hemisphere.
“We want to explore the near-Earth plasma and find out how big plasma irregularities need to be to interfere with navigation signals broadcast by GPS,” said Esayas Shume. Shume is a researcher at JPL and the California Institute of Technology in Pasadena, and lead author of the study.
If you think of the ionosphere as a fluid, the irregularities comprise regions of lower density (bubbles) in the neighborhood of high-density ionization areas, creating the effect of clumps of more and less intense ionization. This “froth” can interfere with radio signals including those from GPS and aircraft, particularly at high latitudes.
The size of the irregularities in the plasma gives researchers clues about their cause, which help predict when and where they will occur. More turbulence means a bigger disturbance to radio signals.
“One of the key findings is that there are different kinds of irregularities in the auroral zone compared to the polar cap,” said Anthony Mannucci, supervisor of the ionospheric and atmospheric remote sensing group at JPL. “We found that the effects on radio signals will be different in these two locations.”
The researchers found that abnormalities above the Arctic polar cap are of a smaller scale — about 0.62 to 5 miles (1 to 8 kilometers) — than in the auroral region, where they are 0.62 to 25 miles (1 to 40 kilometers) in diameter.
Why the difference? As Shume explains, the polar cap is connected to solar wind particles and electric fields in interplanetary space. On the other hand, the region of auroras is connected to the energetic particles in Earth’s magnetosphere, in which magnetic field lines close around Earth. These are crucial details that explain the different dynamics of the two regions.
CAScade, Smallsat and IOnospheric Polar Explorer (CASSIOPE) is a made-in-Canada small satellite from the Canadian Space Agency. It is comprised of three working elements that use the first multi-purpose small satellite platform from the Canadian Small Satellite Bus Program. Image Credit: Canadian Space Agency
To look at irregularities in the ionosphere, researchers used data from the Canadian Space Agency satellite Cascade Smallsat and Ionospheric Polar Explorer (CASSIOPE), which launched in September 2013. The satellite covers the entire region of high latitudes, making it a useful tool for exploring the ionosphere.
The data come from one of the instruments on CASSIOPE that looks at GPS signals as they skim the ionosphere. The instrument was conceived by researchers at the University of New Brunswick.
“It’s the first time this kind of imaging has been done from space,” said Attila Komjathy, JPL principal investigator and co-author of the study. “No one has observed these dimensional scales of the ionosphere before.”
The research has numerous applications. For instance, aircraft flying over the North Pole rely on solid communications with the ground; if they lose these signals, they may be required to change their flight paths, Mannucci said. Radio telescopes may also experience distortion from the ionosphere; understanding the effects could lead to more accurate measurements for astronomy.
“It causes a lot of economic impact when these irregularities flare up and get bigger,” he said.
NASA’s Deep Space Network, which tracks and communicates with spacecraft, is affected by the ionosphere. Komjathy and colleagues also work on mitigating and correcting for these distortions for the DSN. They can use GPS to measure the delay in signals caused by the ionosphere and then relay that information to spacecraft navigators who are using the DSN’s tracking data.
“By understanding the magnitude of the interference, spacecraft navigators can subtract the distortion from the ionosphere to get more accurate spacecraft locations,” Mannucci said.
Other authors on the study were Richard B. Langley of the Geodetic Research Laboratory, University of New Brunswick, Fredericton, New Brunswick, Canada; and Olga Verkhoglyadova and Mark D. Butala of JPL. Funding for the research came from NASA’s Science Mission Directorate in Washington. JPL, a division of the California Institute of Technology in Pasadena, manages the Deep Space Network for NASA.
The company PlanetiQ plans to use GNSS to make real-time weather forecasts. PlanetiQ plans to launch a commercial weather satellite constellation by 2017, composed of 12 to 18 small satellites that will capture data as GNSS satellites pass through Earth’s orbital horizon.
The satellites will use radio occultation to collect data that will supplement computer models on weather, producing more accurate and timely weather forecasts and assessments, PlanetiQ said. The satellites will measure how GPS, GLONASS, and BeiDou radio waves bend as they travel through the atmosphere, a technique that provides snapshots of temperature, pressure and water vapor, as well as insight into whether solar storms are active in the ionosphere, reports Discovery News.
Figure credit: PlanetiQ.
More than 30,000 occultation measurements can be collected each day.
PlanetiQ is one of five companies in the United States looking to commercialize weather forecasting. GeoOptics is working on a similar system and plans to launch its first satellite this year.
Explore further:
PlanetiQ President and CEO Anne Hale Miglarese discussed the project on The Weather Channel in August 2014.
Attila Komjathy, a NASA Jet Propulsion Laboratory principal investigator and adjunct professor in the University of New Brunswick’s Department of Geodesy and Geomatics Engineering, was named a Fellow of the Institute of Navigation in January for his work on remote sensing of the Earth’s ionosphere using signals from GNSS.
NASA is soliciting research on remote sensing techniques that use GNSS for studying the Earth’s environment.
Specifically, the announcement says NASA “seeks innovative approaches to the development of Global Navigation Satellite System (GNSS) remote sensing techniques and algorithms to study the Earth’s environment from the ionosphere to Earth’s interior.” The announcement says NASA is seeking to emphasize the use of reflected GNSS signals for the characterization of the Earth’s surface and mitigation of natural hazards.
Notices of Intent are requested by January 20, 2015, and the due date for proposals is March 20, 2015.
NASA solicits research through the release of various research announcements in a wide range of science and technology disciplines. NASA uses a peer review process to evaluate and select research proposals submitted in response to these research announcements. NASA says that researchers can help achieve national research objectives by submitting research proposals and conducting awarded research. Visit the announcement page for details.
A Look at High-Latitude and Equatorial Ionospheric Disturbances of GPS Signals
By Yu Jiao, Yu (Jade) Morton, Steve Taylor, and Wouter Pelgrum
INNOVATION INSIGHTS by Richard Langley
THE EARTH’S IONOSPHERE. It’s both a blessing and a curse. Together with the magnetosphere, it helps to protect life on our planet from the damaging outpour of particle and electromagnetic radiation from the sun. In particular, it absorbs a lot of the extreme-ultraviolet (EUV) radiation arriving at the Earth. In fact, that is primarily how the ionosphere is formed. The EUV energy strips off the outer electrons of atmospheric gases producing a plasma of free electrons and ions.
The ionosphere has another beneficial role in that it permits long distance radio communication using high-frequency (HF) or shortwave signals. Although its use is in decline since the advent of the Internet, HF is still in use by some broadcasters and military organizations and is indispensible during natural disasters when electricity grids and network links go down.
But the ionosphere can be a pain, too, particularly for GNSS users. The signals from GNSS satellites must travel though the ionosphere on their way to receivers on or near the Earth’s surface. The signals are perturbed by the presence of the free electrons causing an advance in the phase of a signal’s carrier and a delay in the arrival of the pseudorandom noise code modulation (due to the refractive index being frequency dependent or dispersive) and so there is a contribution to carrier-phase and pseudorange (code) measurements, which must be accounted for when determining positions, velocities, and time (PVT) from the measurements.
Again, since the ionosphere is a dispersive medium, by linearly combining simultaneous measurements (either pseudoranges or carrier phases) on two frequencies such as the GPS L1 and L2 frequencies, an observable virtually free of ionospheric effects can be constructed and used for PVT determinations. This approach does require, however, a dual- or multi-frequency receiver. Single-frequency receivers (or the post-processing of single-frequency data) require the use of a model to account for the ionospheric biases as much as possible. The GPS navigation message, for example, includes values of the parameters of a simple ionospheric model. But, on average, its accuracy is only around 50%. More accurate ionospheric corrections can be acquired from elsewhere, even in real time, such as those from satellite-based augmentation systems.
But there is another ionospheric effect that can play havoc with GNSS signals: scintillations. These are rapid fluctuations in the amplitude and phase of the signals caused by small-scale irregularities in the ionosphere. When sufficiently strong, scintillations can result in the strength of a received signal dropping below the threshold required for acquisition and tracking or in causing problems for the receiver’s phase lock loop resulting in many cycle slips.
The occurrence of scintillations depends on many factors including solar and geomagnetic activity, time of year, time of day, and geographical location. In particular, scintillations are most prevalent in equatorial and polar (Arctic and Antarctic) regions. And the processes involved are not fully understood, hindering our ability to model and predict scintillations.
In an effort to help improve the monitoring, mapping, and modeling of scintillations, a team of researchers led by Prof. Jade Morton is monitoring high-latitude and equatorial scintillations and they discuss some of their preliminary results in this month’s column.
“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. Write to him at lang @ unb.ca.
Among other effects of the Earth’s ionosphere on GPS and other GNSS signals, scintillation is potentially the most problematic. Ionospheric scintillation refers to the random amplitude and phase fluctuations of radio signals after propagating through plasma irregularities. These irregularities occur more frequently in high-latitude and equatorial regions, especially during solar maxima. Occurrence of scintillation is difficult to predict and model because of the complexity of the ionosphere’s internal mechanisms and solar activities that are the driving forces of space weather phenomena. GNSS signals are particularly vulnerable to scintillation, as strong scintillation can severely impact the acquisition and tracking processes in GNSS receivers, causing degradation in positioning accuracy and even loss-of-lock. With the increasing reliance on GNSS applications, understanding the characteristics of ionospheric scintillation and its effects on GNSS signals and receivers has become an important topic and has gained worldwide attention from both ionospheric scientists and GNSS engineers.
Since 2009, our research group has established several ionospheric scintillation monitoring and data collection systems located in high-latitude and equatorial regions. The results presented here are based on data collected from a specialized commercial dual-frequency GPS ionospheric monitoring receiver at Gakona, Alaska (62.4°N, 145.2°W), and a commercial multi-system, multi-frequency GNSS ionospheric monitoring receiver located at Jicamarca, Peru (11.9°S, 76.9°W).
Measurements are filtered to remove slowly varying trends caused by satellite-receiver dynamics, receiver oscillator errors, the background ionosphere and troposphere gradient, and other potential contributions from multipath and man-made interferences. Scintillation events above preset threshold levels from the filter outputs are extracted for analysis. The threshold levels are set based on two commonly used scintillation indices, the S4 index and σφ , which are defined as the standard deviations of the detrended signal amplitude and carrier phase to represent the magnitude of signal intensity and phase fluctuation, respectively. In the study discussed in this article, the thresholds for S4 and σφ are 0.15 and 15°, respectively for high-latitude measurements. For low-latitude data, the threshold for S4 is raised to 0.2 to accommodate stronger amplitude scintillation, while the threshold for σφ remains 15°.
From data collected at Gakona, between August 2010 and March 2013, we extracted 655 amplitude and 2,355 phase-scintillation events from 657 equivalent days of data, while from data collected at Jicamarca, we extracted about 830 amplitude and 1,100 phase-scintillation events from 190 days of data collected from November 2012 to June 2013. Based on these events, we established a number of amplitude and phase scintillation distributions, which include scintillation-index-magnitude distributions, event-duration distributions, and event-occurrence frequency distributions. These results show very different characteristics of scintillation observed at low latitudes and high latitudes, indicating that there must be different mechanisms contributing to the formation and evolution of ionosphere plasma irregularities in the two regions. These characteristics are useful for scintillation-event prediction and modeling in the future.
Data Collection System and Event Thresholds
FIGURE 1 illustrates the general architecture of the event-driven GNSS data collection system. The system hardware consists of a multi-band GNSS antenna, a commercial ionospheric scintillation monitor (ISM) receiver, an array of reconfigurable software-defined radio (SDR) radio-frequency (RF) front-end devices capable of sampling intermediate-frequency (IF) signals, one or multiple data collection servers, a data storage array, timing signal distribution hardware to ensure both time and frequency consistency across all RF front ends and receivers, and network/communication devices that allow remote access of the receivers and servers to monitor the status of the hardware, to query recorded data, and reset and reconfigure the data collection system.
FIGURE 1. General architecture of the event-driven GNSS data collection system deployed at several high-latitude and equatorial sites since 2009.
Custom-designed space weather event monitoring and trigger software resides on the data collection and control server. The ISM receiver operates continuously to produce and record routine measurements such as I and Q channel accumulator outputs, pseudorange, carrier phase, Doppler frequency, C/N0, and scintillation indices, while the SDR RF front ends only temporarily store the latest one-minute worth of IF samples in each device’s circular buffer. Scintillation event thresholds are pre-determined based on analysis of baseline data collected at the same local site using the same hardware. The real-time event trigger software compares ISM receiver measurements with the pre-set event threshold. If the measurements exceed the thresholds, the contents of the circular buffers will be written to the data storage array until after the event subsides. These raw IF samples are then further post-processed using a wide range of receiver processing algorithms for analysis of scintillation features and robust receiver algorithm development.
The high-latitude GNSS receiver array at Gakona, was initially established in 2009 and has been continuously evolving into a four-antenna array capable of collecting GPS L1, L2C, and L5 and GLONASS L1 and L2 signal data until its recent relocation to and upgrade at Poker Flat Research Range, north of Fairbanks. Several publications have discussed the system setup, receiver signal processing of data collected by the system, and characterization of high-latitude scintillations based on analysis of the array outputs (see Further Reading). In this article, only the data collected using the commercial ISM receiver are discussed because this is the longest operating receiver at this site. The receiver outputs L1C/A signal intensity and carrier-phase measurements at a rate of 50 Hz and semi-codeless tracking results of L2P(Y) at 1 Hz.
Since 2011, several GNSS data collection systems have been deployed at low-latitude locations, including Hong Kong, Singapore, Peru, Ascension Island, and Puerto Rico. In this article, we use results from the ISM receiver at Jicamarca, Peru, close to the geomagnetic equator. FIGURE 2 shows the data-collection-system-setup block diagram at Jicamarca. The ISM receiver used in this location generates 100-Hz carrier-phase measurements and I/Q channel correlator outputs; the latter are further processed to generate 50-Hz signal-intensity measurements for GPS L1C/A, L2C, and L5 signals and GLONASS, Galileo, and BeiDou open signals. Seven SDR front ends driven by the same oven-controlled crystal oscillator (OCXO) signal from the ISM receiver sample GPS, GLONASS, Galileo, and BeiDou open signals. Preliminary results obtained from these and other low-latitude SDR data have been presented in several papers in the archived literature (see Further Reading).
FIGURE 2. Current multi-GNSS data collection system configuration at Jicamarca Radio Observatory in Peru. (GLO = GLONASS, BDS = BeiDou System, VPN = virtual private network, ISMET = ionospheric scintillation monitoring event triggering, RAID = redundant array of independent disks)
The raw carrier-phase and signal-intensity measurements obtained from the two ISM receivers at Gakona and Jicamarca were detrended, from which the two scintillation indices S4 and σφ were computed using Equations (1) and (2). In the two equations, I and φ stand for detrended signal intensity and carrier phase, respectively, and <·> represents the expected value that is essentially the average value over the interval of interest. In this study, the interval of interest was set to 10 seconds to most effectively highlight scintillation features based on evaluations of several different time intervals between 10 and 60 seconds.
(1)
(2)
As we mentioned earlier, the characterization of scintillation was carried out on the basis of scintillation events extracted from the raw data. After the evaluation of non-scintillation events and baseline indicators, a set of criteria has been established to extract interesting events through a semi-automated process from a large amount of data while keeping the number of selected events caused by non-scintillation factors (such as multipath and interference) low. A brief summary and explanations of the criteria are listed as follows:
The elevation angle mask is 30° to reduce multipath effects.
The thresholds for S4 and σφ are 0.15 and 15° respectively for data collected at Gakona.
For Jicamarca data, the thresholds are 0.2 and 15° respectively.
To exclude interference cases, the index value has to remain above the threshold value for a minimum of 30 seconds to qualify as a scintillation event.
An event detected within 5 minutes of the end of another event is combined as one event with the previous one.
Scintillations experienced by multiple satellite signals simultaneously are treated separately, and events experienced simultaneously for all visible satellites are further analyzed to ensure that they are not caused by interferences.
Carrier cycle slip/loss-of-lock detection and repair procedures are implemented to determine whether these cases are caused by scintillation or other factors.
It is important to note that the above criteria and procedures contain some degrees of arbitration, especially the last two, as they were applied based on visual inspections. These artificially imposed rules nevertheless are necessary for statistical analysis and comparison of scintillation observations.
Results and Discussion
In this section, we discuss the data sets we have collected and analyzed.
Available Dataset from Alaska and Peru. The ISM receiver at Gakona, started recording effective GPS data in August 2010. Environmental issues and human factors lead to a few intermittent data gaps during the more than three and a half years of data recording.
TABLE 1 lists monthly normal operation days and the percentage of time when data were collected. In all, the results presented in this article are based on approximately 3,000 scintillation events extracted from 657 days’ worth of data that was collected in a time span of 32 months.
Similarly, the number and percentage of days of effective data from Jicamarca, are summarized in Table 2. The dataset from this location runs from November 2012 until June 2013. Roughly 2,000 scintillation events have been extracted to enable statistical comparison of characteristics of scintillation observed in high- and low-latitude regions.
Scintillation Indicator Distributions. The magnitudes of the two scintillation indices, S4 and σφ , are often used to indicate the intensity of ionospheric scintillation, as their values directly reflect the disturbance rate of received power and carrier-phase measurements. Although there have been discussions regarding the suitability of σφ as a phase scintillation indicator, it is, nevertheless, a measure of the magnitude of carrier variations in a certain spectral range that are related to scintillation activities. In the absence of a commonly accepted new indicator for phase scintillation, we will use σφ in this study simply as a means to measure the phase fluctuations. FIGURE 3 compares the intensity distributions of amplitude and phase scintillation observed at the Alaska (square markers) and Peru (triangle markers) sites. MaxS4/σφ in the figures is the peak S4 or σφ value during an amplitude or phase scintillation event, which is a more practical indicator of scintillation impact on GNSS receivers.
FIGURE 3. Maximum S4 and σφ distributions of (a) amplitude and (b) phase scintillation observed at Gakona, Alaska, and Jicamarca, Peru.
Figure 3a shows that amplitude scintillation events observed at Jicamarca are generally more intense than those observed at Gakona. This is consistent with most previous studies, which concluded that scintillation is the most intense in the equatorial region. Figure 3b, on the other hand, shows that the intensity of phase scintillation at Jicamarca is slightly lower than that at Gakona. Nevertheless, this result does not necessarily reflect scintillation intensity observed in other parts of the equatorial region, as Jicamarca is not located close to the equatorial anomaly crest where scintillation activity is the strongest.
The duration of a scintillation event is another indicator of scintillation’s negative impact on the acquisition and tracking processes in receivers. FIGURE 4 plots the amplitude and phase event duration probability distributions, with the mean event durations at each site shown in the plots. The results show that at Gakona (square markers), phase scintillation lasts much longer than amplitude scintillation. At Jicamarca (triangle markers), amplitude scintillation events last slightly longer than the phase ones on average, and both types have much longer durations than those at high latitudes.
FIGURE 4. Duration distributions of (a) amplitude and (b) phase scintillation events observed at Gakona, Alaska, and Jicamarca, Peru.
Ionospheric scintillation of combined high intensity and long duration is usually considered a big threat to signal processing in GNSS receivers. Unfortunately, these two aspects are often correlated, especially at low latitudes. Moderate correlation coefficient values have been observed between scintillation durations and the magnitudes of scintillation indicators at Jicamarca (FIGURE 5b). The correlations, however, are much smaller at Gakona (FIGURE 5a), especially for amplitude scintillation events. These results further confirm that scintillation is a more severe issue in the equatorial region.
FIGURE 5. Scintillation duration vs. intensity at (a) Gakona, Alaska, and (b) Jicamarca, Peru.
Scintillation Occurrence Frequency and Relating Factors. We define the scintillation occurrence frequency as the number of scintillation events recorded during a certain time interval, which can be an hour, a day, a month, a season, and so on. The occurrence frequency is an important indicator in scintillation monitoring and forecasting, as it helps to identify the periods when scintillation events are most likely to occur.
FIGURE 6 illustrates scintillation hourly occurrence probabilities at the two sites with respect to Coordinated Universal Time (UTC) (upper) and hours post sunset (lower). Also consistent with numerous previous research findings, scintillation at high latitudes was more frequent during nighttime than at other times. Scintillation observed at Jicamarca occurred more frequently at night as well, but was greatly concentrated between one and two hours post sunset and midnight. Statistics show that 98% of Jicamarca’s scintillation events were observed from one to six hours after local sunset.
FIGURE 6. Scintillation occurrence frequency with respect to UTC hours and hours after sunset at (a) Gakona, Alaska, and (b) Jicamarca, Peru.
As demonstrated in Figure 6, scintillation occurrence frequency is largely influenced by solar inputs, which are the main driving force in atmospheric ionization and ionospheric irregularity formation. Scintillation occurrence can also be affected by geomagnetic activities. FIGURE 7 shows how scintillation occurrence frequency was affected by solar activity and seasons. The four seasons are defined as: spring (SP) – March to May; summer (SU) — June to August; fall (FA) — September to November; and winter (WI) – December to February. The intensity of solar activity is indicated by the smoothed average sunspot numbers, which are marked as black dots in the plot.
FIGURE 7. Seasonal scintillation occurrence frequency and smoothed sunspot number.
Several phenomena can be observed in Figure 7. At Gakona, scintillation occurrence frequency is clearly influenced by solar activity. The occurrence frequency is also modulated by season, with equinoxes generally more active than adjacent solstices. In contrast to the half-a-year cycle at high latitudes, scintillation occurrence frequency at Jicamarca more closely follows a one-year cycle as described in previous research, and decreases largely in the summer.
Our analysis also shows that the level of geomagnetic field activity also directly impacts scintillation occurrence frequency. FIGURE 8 shows the correlations between scintillation daily occurrence frequencies and Ap index values at the two sites. Ap is a widely used index that linearly reflects the daily average level of global geomagnetic field activity. Ap can be converted to the conventional Kp index using a quasi-logarithmic conversion table. The result in Figure 8a was obtained using data collected during seven months at Gakona: March and November 2011; March, July, October, and November 2012; and March 2013. During these months, scintillation activity was generally high. Figure 8b was generated using all the data listed in Table 2. Clearly shown in the plots, scintillation occurrence frequency at high latitudes is strongly correlated with geomagnetic field activities, while at Jicamarca such correlations do not exist. This result also confirms many previous research findings.
FIGURE 8. Daily scintillation occurrence frequency with respect to Ap index value at (a) Gakona, Alaska, and (b) Jicamarca, Peru.
Summary and Conclusions
This article presented comparative work on ionospheric scintillation characterization using data collected at Gakona, Alaska, and Jicamarca, Peru, during the current solar maximum to investigate the different natures of scintillation at high latitude and in equatorial regions. Scintillation intensity, duration, and occurrence frequency distributions were analyzed to demonstrate the differences at the two locations.
Scintillation in the equatorial region is typically more severe with deeper and faster signal power fadings and longer durations. Also, low-latitude scintillation with stronger intensity usually lasts longer, which further contributes to its negative impact on receivers. At high latitudes, phase fluctuations overwhelmed amplitude scintillation by the number of occurrences and their duration.
Scintillation is more frequent during nighttime, and almost all low-latitude scintillation events occur within six hours after local sunset. The overall occurrence frequency of scintillation not only increases with high solar activity, but also follows certain seasonal patterns. In general, scintillation is more active around the equinoxes. Additionally, high-latitude scintillation is also closely correlated to geomagnetic field activity, while the relationship is not obvious in the equatorial region.
Lastly, we would like to point out that the results presented here are preliminary and may be restricted to local effects, especially at low latitudes. As more data become available from Jicamarca and other equatorial sites where SDR data collection systems ensure quality inputs during strong scintillation events, a more comprehensive analysis and comparison can be made to facilitate global scintillation monitoring, mapping, and modeling.
Acknowledgments
The data collection and analysis project discussed in this article was supported by the U.S. Air Force Office of Scientific Research and Air Force Research Laboratory grants. The authors appreciate the support of High Frequency Active Auroral Research Program (HAARP) staff and the University of Alaska Fairbanks Geophysical Institute for organizing and sponsoring the HAARP campaign and HAARP staff support of the GNSS receiver data collection system setup. The authors would also like to acknowledge Jicamarca Radio Observatory for hosting the GNSS equipment. The Jicamarca Radio Observatory is a facility of the Instituto Geofisico del Peru, operated with support from the U.S. National Science Foundation through Cornell University. This article is based, in part, on the paper “Comparative Studies of High-latitude and Equatorial Ionospheric Scintillation Characteristics of GPS Signals” presented at PLANS 2014, the Institute of Electrical and Electronics Engineers / Institute of Navigation Position, Location and Navigation Symposium held in Monterey, California, May 5–8, 2014.
Manufacturers
The commercial ISM receivers used at Gakona and Jicamarca were a GPS Silicon Valley — now NovAtel Inc. — GSV4004B and a Septentrio N.V. PolaRxS Pro, respectively.
YU JIAO is a Ph.D. candidate at the Colorado State University (CSU), Fort Collins, Colorado. She received her master’s degree in computational science and engineering from Miami University, Oxford, Ohio, in 2013 and her bachelor’s degree in electronic and information engineering from Beihang University (previously known as the Beijing University of Aeronautics and Astronautics), Beijing, China, in 2011. Her research interests are in GNSS signal processing and ionosphere effects on GNSS in both high-latitude and equatorial regions.
YU (JADE) MORTON is an electrical engineering professor at CSU. She received a Ph.D. in electrical engineering from Pennsylvania State University (Penn State), State College, Pennsylvania, and was a post-doctoral research fellow in the Space Physics Research Laboratory of the University of Michigan, Ann Arbor, Michigan. Prior to joining CSU, she was a professor in the Department of Electrical and Computer Engineering at Miami University. Her research interests are advanced GNSS receiver algorithms for accurate and reliable operations in challenging environments, studies of the atmosphere using radar and satellite signals, and development of new applications using satellite navigation technologies.
STEVE TAYLOR is a graduate student in the Department of Electrical and Computer Engineering at Miami University. He received his B.S. in computer science from Miami University in 2011. Taylor developed software systems for ionosphere space weather monitoring and has been involved in deployment of Dr. Morton’s research team’s GNSS data collection system in Alaska, Peru, Hong Kong, Ascension Island, and Puerto Rico.
WOUTER PELGRUM is an assistant professor of electrical engineering at Ohio University, where he conducts research in and teaches about topics in electronic navigation, such as GNSS, Distance Measuring Equipment or DME, and time and frequency transfer. Before joining Ohio University in 2009, he worked in private industry, where he contributed to the development of an integrated GPS-eLoran receiver and antenna. From 2006 until 2008 he operated his own company, specializing in navigation-related research and consulting.
FURTHER READING
• Authors’ Conference Paper
“Comparative Studies of High-latitude and Equatorial Ionospheric Scintillation Characteristics of GPS Signals” by Y. Jiao, Y. Morton, and S. Taylor in Proceedings of PLANS 2014, the Institute of Electrical and Electronics Engineers / Institute of Navigation Position, Location and Navigation Symposium, Monterey, California, May 5–8, 2014, pp. 37–42, doi: 10.1109/PLANS.2014.6851355.
• Introduction to Ionospheric Scintillation and GNSS
“Limitations in GPS Receiver Tracking Performance Under Ionospheric Scintillation Conditions” by S. Skone, K. Knudsen, and M. de Jong in Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, Vol. 26, No. 6-8, 2001, pp. 613–621, doi: 10.1016/S1464-1895(01)00110-7.
“Radio Wave Scintillations in the Ionosphere” — a review paper by C.K. Yeh and C.-H. Liu in Proceedings of the IEEE, Vol. 70, No. 4, 1982, pp. 324–360, doi: 10.1109/PROC.1982.12313.
High-Latitude Scintillations
“Characterization of High Latitude Ionospheric Scintillation of GPS Signals” by Y. Jiao, Y. Morton, S. Taylor, and W. Pelgrum in Radio Science, Vol. 48, 2013, pp. 698–708, doi: 10.1002/2013RS005259.
Equatorial Scintillations
“Statistics of GPS Scintillations over South America at Three Levels of Solar Activity” by A.O. Akala, P.H. Doherty, C.E. Valladares, C.S. Carrano, and R. Sheehan in Radio Science, Vol. 46, No. 5, October 2011, doi: 10.1029/2011RS004678.
“Measuring Ionospheric Scintillation in the Equatorial Region over Africa, Including Measurements from SBAS Geostationary Satellite Signals” by A.J. Van Dierendonck and B. Arbesser-Rastburg in Proceedings of ION GNSS 2004, the 17th International Technical Meeting of the Satellite Division of The Institute of Navigation, Long Beach, California, September 21–24, 2004, pp. 316–324.
“An Improved Ionosphere Scintillation Event Detection and Automatic Trigger for GNSS Data Collection Systems” by S. Taylor, Y. Morton, Y. Jiao, J. Triplett, and W. Pelgrum in Proceedings of ION ITM 2012, The Institute of Navigation 2012 International Technical Meeting, Newport Beach, California, January 30 – February 1, 2012, pp. 1563–1569.
Software Defined Radio Processing of GPS Scintillation Data
“Triple Frequency GPS Signal Tracking During Strong Ionospheric Scintillations over Ascension Island” by M. Carroll, Y.J. Morton, and E. Vinande in Proceedings of PLANS 2014, the Institute of Electrical and Electronics Engineers / Institute of Navigation Position, Location and Navigation Symposium, Monterey, California, May 5–8, 2014, pp. 43–49, doi: 10.1109/PLANS.2014.6851356.
Forecasting Scintillations
“A Forecasting Ionospheric Real-time Scintillation Tool (FIRST)” by R.J. Redmon, D. Anderson, R. Caton, and T. Bullett in Space Weather, Vol. 8, No. 12, December 2010, doi: 10.1029/2010SW000582.
“Specification and Forecasting of Scintillations in Communication/Navigation Links: Current Status and Future Plans” by S. Basu, K.M. Groves, Su. Basu, and P.J. Sultan in Journal of Atmospheric and Solar-Terrestrial Physics, Vol. 64, 2002, pp. 1745–1754, doi: 10.1016/S1364-6826(02)00124-4.
Alternative Scintillation Indices
“Improved Amplitude- and Phase-scintillation Indices Derived from Wavelet Detrended High-latitude GPS Data” by S.C. Mushini, P.T. Jayachandran, R.B. Langley, J.W. MacDougall, and D. Pokhotelov in GPS Solutions, Vol. 16, No. 3, July 2012, pp. 363–373, doi: 10.1007/s10291-011-0238-4
“Perils of the GPS Phase Scintillation Index (sf)” by T.L. Beach in Radio Science, Vol. 41, RS5S31, 2006, doi: 10.1029/2005RS003356.
“Problems in Data Treatment for Ionospheric Scintillation Measurements” by B. Forte and S.M. Radicella in Radio Science, Vol. 37, No. 6, 1096, 2002, pp. 8-1–8.5, doi: 10.1029/2001RS002508.
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
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. Write to him at lang @ unb.ca.
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).
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:
(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.
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:
(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: (3)
where LI represents the linear combination between signals at frequencies f1 and f2; is the ionospheric delay in meters of LI; and BI is composed of several terms: station and satellite phase inter-frequency biases ( and respectively), LI phase ambiguity (λ1N1j – λ2N2j), 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: (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. 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: (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 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 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.
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 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 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.
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 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 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 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.
“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 ofPLANS 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
By Wei Zhang, Attila Komjathy, Simon Banville, and Richard B. Langley
INNOVATION INSIGHTS by Richard Langley
MAY YOU LIVE IN INTERESTING TIMES. So goes the purported Chinese proverb and curse. When it comes to the ionosphere, an interesting time might indeed be a curse for most users of GPS. The ionosphere – that region of the upper atmosphere where free electrons exist in sufficient numbers to affect the propagation of radio waves – owes its existence primarily to the extreme ultraviolet (EUV) and x-ray photons emitted by the sun. They ionize atoms and molecules in the upper atmosphere, freeing the outer electrons. Mostly the ionosphere is well behaved but it can get quite interesting when it is disturbed by space weather events such as solar flares or coronal mass ejections.
The signals from the GPS satellites are perturbed as they transit the ionosphere. Pseudorange measurements are increased in value (an additional delay) and carrier-phase measurements are decreased (a phase advance). If not fully modeled or otherwise accounted for, the perturbations can decrease the accuracy of GPS positioning, navigation, and timing (PNT). For highest PNT accuracies, observations are made at the two frequencies transmitted by all GPS satellites and because the ionosphere’s effect on radio signals is dispersive, a linear combination of the measurements removes almost all of the ionospheric perturbations. On the other hand, the ionosphere’s effect on single frequency observations must be corrected using a model. Most commonly, the model assumes that all of the electrons in the ionosphere can be compressed into a thin shell at a certain height above the receiver. This permits the computation of an estimate of the vertical ionospheric delay. Then, a mapping function is used to predict the slant delay, the delay contributing to a GPS measurement. The approach works reasonably well, particularly if near-real-time values of vertical delay can be provided to users as is done by the Wide Area Augmentation System and other satellite-based augmentation systems. However, this two-dimensional approach ignores the fact that the electron content of the ionosphere is actually spread out in the vertical direction and so has certain inaccuracies, which can increase when the ionosphere is disturbed.
In an effort to improve ionosphere modeling with potential application to single-frequency GNSS users, a couple of my current graduate students together with a former student, have investigated a three-dimensional approach to ionospheric modeling using empirical orthogonal functions or EOFs to describe the vertical structure of the ionosphere. EOFs reduce the dimensionality of a data set or an empirical model consisting of a large number of interrelated variables, while retaining as much of the variance present in the data set as possible. This is achieved by transforming to a new set of variables, the orthogonal functions, which are uncorrelated (orthogonal), and which are ordered so that the first few retain most of the variation present in all of the original variables. Only three functions are required to account for more than 99 percent of the variability in the International Reference Ionosphere – 2007, for example.
In this month’s column we look at the performance of this 3D approach to modeling the ionosphere including times when the ionosphere is particularly interesting.
“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.
Ionospheric modeling plays an important role in improving the accuracies of positioning and navigation, especially for current civil aircraft navigation and mass-market single-frequency users. Measurement-driven models are considered to be among the best candidates for real-time single-frequency positioning owing to their real-time applicability and relatively higher accuracy compared to empirical models, such as the GPS broadcast (also known as Klobuchar) and NeQuick models. A good example of a real-time positioning application is satellite-based augmentation systems (SBAS), including the Wide Area Augmentation System (WAAS), the European Geostationary Navigation Overlay Service (EGNOS), the Japanese MSTAT Satellite-based Augmentation System (MSAS), and the Indian GPS Aided Geo Augmented Navigation system (GAGAN). Because the ionosphere can be the largest error source in single-frequency positioning, the accuracy of ionospheric modeling is critical for single-frequency applications.
Several organizations have been routinely providing ionospheric products to correct errors caused by the ionosphere in the form of ionospheric maps — that is, vertical total electron content (vTEC) at grid points (including regional and global products), such as those from WAAS and the International GNSS Service (IGS), with various processing time delays ranging from near real time to a couple of weeks. Among the earliest works of ionosphere modeling, the University of New Brunswick-Ionospheric Modeling Technique (UNB-IMT) was developed in the mid-1990s. This technique was demonstrated to effectively derive both regional and global total electron content (TEC) maps. However, most of the models, including the current version of UNB-IMT, approximate the ionosphere using a single thin-shell approach with an altitude set at, for example 350 km, which may introduce additional modeling errors up to several TEC units (1 TECU = 1016 electrons/m2), corresponding to meter-level errors of measurement delay or advance at the GPS L1 frequency.
To overcome any downside of such models, three-dimensional (3D) ionospheric tomographic modeling methods have been proposed and implemented by several groups since the late 1990s. Different from the two-dimensional (2D) single thin-shell ionospheric models, where the parameters to be estimated are associated with TEC, the modeled variables in the tomographic model are related to electron density functions. Therefore, we may expect more complex structures of electron densities (such as those observed during ionospheric storms or in the highly variable equatorial anomaly) to be revealed by the models. A commonly accepted modeling approach is to describe the ionospheric horizontal (longitudinal and latitudinal) variability by a spherical harmonic (SH) expansion up to a specific degree and its vertical dimension modeled by empirical orthogonal functions (EOFs).
However, SH models are not ideal for capturing local variability in the ionosphere because each basis function of spherical harmonics exists over the entire geographic region of interest, such as the entire globe in the case of global modeling. In other words, localized measurements will have influence on the estimated state across the whole globe. As alternative approaches, wavelet, finite element (meshes/pixels), and local-basis-function models have been proposed and implemented to capture the localized information content in the measurements and pass this information on to the end user. On the other hand, the inversion process can occasionally become singular as many of the parameters to be estimated tend to be ineffective and less meaningful. This is especially the case when our goal is to obtain better accuracies with higher order wavelet bases or smaller meshes/pixels. Due to the potential computing and transmitting burden, the two modeling techniques may have more difficulties associated with real-time applications, such as real-time single-frequency positioning, although they have advantages for capturing localized structures in the ionosphere.
Aiming for potential real-time applications of 3D tomographic models, we have extended the UNB-IMT from 2D to 3D by modeling the vertical dimension of the ionosphere using EOFs. In this article, we discuss our approach and report on some initial tests including comparing its performance with the 3D SH approach.
The 2D UNB-IMT was demonstrated to work with various network sizes: regional, baseline-by-baseline, and even single standalone stations. Therefore, it is expected that this technique will help in capturing localized ionospheric structures above small regional networks or above a single standalone station. Additional benefits may be expected for disturbed ionospheric conditions. For assessing the two modeling techniques, a small regional network was chosen to perform station-by-station and batch processes. The performance of both methods with the two processing scenarios has been compared by analyzing the post-fit residuals and vTECs of the state estimation process, as well as the repeatability of estimates of differential code biases (DCBs) for both quiet and disturbed ionospheric conditions.
3D UNB-IMT
Because of the limited number of ionospheric parameters to be estimated, the 2D UNB-IMT was considered suitable for real-time applications, such as real-time single-frequency precise point positioning (PPP) and SBASs. In fact, it can be proven that the modeling method of the current 2D UNB-IMT is identical to the original planar fit of WAAS in nature if the locations of reference stations tend to collocate with WAAS ionospheric grid points (IGPs). Although additional parameters are involved, we believe the 3D UNB-IMT approach with its potential for improved modeling accuracy is still suitable for real-time applications. In this section, we will introduce the 3D UNB-IMT modeling strategy and demonstrate its applicability with a regional network and single standalone stations.
Model Description. In order to clearly present the technique demonstrated in our recent work, we first briefly review the 2D UNB-IMT. Linear polynomial functions were initially proposed for describing the spatial variability of the ionosphere. We model the observed slant TEC (sTEC) between a satellite and a receiver from carrier-phase and pseudorange (code) observations at some epoch as the product of a bilinear polynomial representing the vTEC at the thin-shell ionospheric pierce point (IPP) of the signal raypath and a mapping function that projects the vTEC to sTEC plus receiver and satellite instrumental biases (DCBs). The input variables are the geographic longitude of the IPP referenced to the solar-geomagnetic coordinate system (in other words, the difference between the longitude of the IPP and the longitude of the mean sun) and the difference between the geomagnetic latitude of the IPP and the geomagnetic latitude of the station. We consequently have three polynomial coefficients to estimate for each station: a constant term, one to describe the longitude variations, and one for the latitude variations.
The mapping function used in the model is the standard geometric mapping function, which computes the secant of the zenith angle of the signal geometric ray path at the IPP at a specified shell height. Because of the dependence of the ionosphere on solar radiation and the geomagnetic field, the solar-geomagnetic reference frame is used to compute the TEC over each station in this technique. Since the ionosphere changes more slowly in the sun-fixed reference frame than in the Earth-fixed one, such a reference frame is ideal for producing more accurate TEC estimates.
The initial version of UNB-IMT ignored the non-linear spatial variation of the ionosphere. Non-linear terms are expected to be able to absorb more complex variability of the ionosphere and thus more properly describe the ionosphere in disturbed conditions. Regarding this issue, the drawbacks of some modeling methods based on linear models have been reported: for example, the highly variable ionosphere might be absorbed by the estimated DCBs, making the repeatability of the estimated DCBs (day-to-day variability) correlated with the variability of the ionosphere. To enhance the performance of UNB-IMT, especially under disturbed ionospheric conditions, UNB researchers extended the linear version of UNB-IMT to a quadratic one and assessed it by using a wide-area regional network in North America. This modified approach reduced the post-fit residuals significantly by better modeling the ionospheric variations with the help of the additional second order (non-linear) terms.
To better use a priori information in the development of 3D UNB-IMT, we separate the TEC into a background reference or “known” part and a perturbation or to-be-modeled part. The background reference part of TEC could be calculated from an a priori source of electron density, such as any kind of ionospheric model, including empirical and theoretical ionospheric models. The density, as a function of latitude, longitude, height, and time, is integrated along the raypath between the receiver and a satellite.
Then, the perturbation part of the electron density is modeled by the inner product of EOFs and polynomial functions with associated estimated coefficients to depict the variability of the ionosphere in the vertical and horizontal directions respectively. And this part is similarly integrated along the raypath and added to the reference part along with the DCBs.
Empirical Orthogonal Functions. The EOF method is a method of choice for analyzing the variability of a single field (with only one scalar variable). Variability of the ionosphere with respect to height is needed for the 3D models. The method finds the spatial patterns of variability based on historical data sets (as reflected in empirical or theoretical models). In other words, the modes of variability decomposed by the method are primarily “data modes,” and not necessarily physical or actual real-time models. Due to its noted ability in describing the background ionosphere, the data sets output from the empirical Ionospheric Reference Ionosphere 2007, were utilized to form the EOFs in our technique.
Thus, the data sets of electron densities are realized by uniform sampling at the following variant time scale intervals and specific geographic locations:
Solar cycle: [1998:1:2008] (year)
Season of year: [Dec., Mar., Jun., Sep.] (month)
Time of day: [1:1:24] (hour)
Day of month: [1:9:28] (day of month)
Geographic latitude: [30:5:60] (degree)
Geographic longitude: [280:5:300] (degree),
where the numbers separated by colons correspond to minimum:increment:maximum. The data sets cover the whole spatial area of interest. The data sets of a whole solar cycle in typical equinox and solstice months are used to ensure that the EOFs span the range of profile variations that include the variation in solar EUV and x-ray output. Each electron density profile with respect to height at these locations and time points is sampled in the vertical dimension at [100:2:2000] (km). Figure 1 shows the first three third-order normalized EOFs based on the data sets. The first three eigenvalues account for 92.22, 6.69, and 0.78 percent of the total respectively. Provided the solution is nonsingular, the choice of the highest order of EOFs is a trade off between processing time and modeling accuracy as to the specific network and capability of computer(s). In our current work, the highest order of three was chosen. In this case, the neglected vertical variation of the ionosphere corresponding to higher order EOFs is 0.31 percent.
FIGURE 1. The normalized first three dominant EOFs extracted from the IRI-2007 empirical model.
Once the modeling approach has been constructed, the following task is to estimate the coefficients. Considering the potential real-time applications, a Kalman filter is employed to solve the TEC observation equation. To be specific, the following settings are used. The correlation time is set to five minutes, which correspond to the WAAS update interval for ionospheric grid points. The uncertainty of the dynamic model, 0.008 TECU2/second, is chosen to characterize the potential rapid change of the ionosphere.
Finally, the estimated coefficients provided by the Kalman filter are then used to reconstruct the electron density field.
Testing the Approach
In this section, we report on tests of the 3D UNB-IMT and compare its performance with that of the 3D SH approach. Because of the advantages of sensitivity of 2D UNB-IMT, especially with the single-station processing strategy, it is expected that this technique will help in better capturing localized ionospheric structures above small regional networks or above a single standalone station compared to the 3D SH approach. Additional benefits may be expected for disturbed ionospheric conditions.
For assessing the two modeling techniques, a small regional network of four IGS reference stations located from geographic latitude 39.0° N to 48.1° N and longitude 66.7° W to 77.6° W was chosen to perform single-station and multi-station (network) processing. The stations are GODZ in Greenbelt, Maryland; UNBJ and FRDN in Fredericton, New Brunswick; and VALD in Val d’Or, Quebec. Figure 2 shows the locations of the reference stations chosen for the modeling. The dual-frequency GPS data used for the tests was obtained from October 13–25 (day of year (doy) 286–298) in 2011 with the sampling time interval of 30 seconds. The corresponding values of the interplanetary magnetic field Bz component; the planetary geomagnetic index, Kp; the auroral electrojet index, AE; and the disturbance storm-time index, Dst on these days are shown in FIGURE 3. It is seen that a severe ionospheric storm triggered by a coronal mass ejection from the sun occurred late on October 24 (doy 297), 2011, and continued through the entire day of October 25 (doy 298), 2011. The other days seem relatively quiet. Thus, we chose October 16, 2011, as a typical day with quiet ionospheric conditions and October 25, 2011, as a typical day with disturbed ionospheric conditions in the following tests. The performance of both methods (3D UNB-IMT and SH model) with the two processing scenarios will be compared by analyzing the post-fit residuals and TEC of the state estimation process for both quiet and disturbed ionospheric conditions.
FIGURE 2. The network of the four stations used in the evaluation procedures.
All four reference stations in the small network have the ability to provide both C/A- and P-code pseudorange measurements. In our tests, the P-code observable is used to extract TEC through leveling the corresponding carrier-phase measurements. We used a 15°-elevation-angle cut-off in our study.
Single Station Experiment. The estimated parameters of 2D and 3D UNB-IMT have different physical meanings due to the different modeling strategies. In theory, the 3D UNB-IMT can reproduce the electron densities for any location (horizontal and vertical) at any epoch. Figure 4 shows an example of the electron density profile produced by the linear 3D UNB-IMT in the zenith direction of station FRDN at 12:00 UT on October 16 (doy 289), 2011. Therefore, we will have to integrate electron densities into TEC for the 3D UNB-IMT modeling results if we want to compare how the two approaches have modeled the ionosphere side by side. For the purpose of sensitivity comparison, the results from 2D and 3D UNB-IMT are compared in terms of post-fit residuals as well as time series of estimated vTEC in the single-station processing scenario. As discussed above, we use the GPS data from station FRDN only for October 16 and 25, 2011, in this subsection. The post-fit residuals are calculated as the difference between the measured and estimated biased sTEC.
FIGURE 4. The electron density profile produced by linear 3D UNB-IMT overhead FRDN at 12:00 (UT) on October 16 (doy 289) in 2011.
From the top to bottom panels, Figure 5 shows the estimated vTEC in the zenith direction over the station, post-fit residuals, estimated satellite and receiver DCBs, and unbiased sTEC with respect to local mean solar time series obtained with linear 2D (left-hand panels) and 3D (right-hand panels) UNB-IMT approaches respectively. We use a different color for each satellite to see individual improvement of satellites in terms of post-fit residuals, estimated DCB, and unbiased sTEC. As for the potential improvement of 3D UNB-IMT, we supposed, if the 2D model with single-shell assumption does not depict the variability of the ionosphere quite well (especially the vertical variability of the ionosphere), we should expect to see an improvement from the 3D model in terms of post-fit residuals. As seen in this figure, the 3D UNB-IMT improves the results in terms of post-fit residuals. The means and standard deviations of the residuals with the 2D and 3D UNB-IMT are shown in Table 1.
FIGURE 5. Sensitivity test (the panels from the top to the bottom correspond to: estimated vertical TEC, post-fit residuals, satellite and receiver DCB, slant TEC with respect to local time) between linear 2D (the left-hand panels) and 3D (the right-hand panels) models at FRDN on October 16 (doy 289) in 2011.TABLE 1. The means and standard deviations of the residuals under the quiet (Q, October 16, 2011) and disturbed or storm (S, October 25, 2011) ionospheric conditions with linear (L) and quadratic (Q) modeling approaches. Units = TECU.
The 3D UNB-IMT with three times as many parameters is allowed to “accommodate” more (vertical) variations of the ionosphere. The benefits are also manifest in the improvement of the estimated vTEC and estimated satellite and receiver DCBs. In terms of estimated vTEC, the smooth variation of TEC may be expected at mid-latitudes during quiet ionospheric conditions without any ionospheric anomaly. The unmodeled variation of TEC in 2D UNB-IMT seen in the post-fit residuals is also manifest as “artificial small jumps” in the vTEC panel. In other words, the 3D UNB-IMT is able to better represent the measurements from low-elevation-angle satellites owing to the EOFs replacing the mapping function. It is the typical case when a satellite comes into or goes out of view of the receiver. The estimated DCBs are relatively constant over the entire day. But it is also found from the estimated DCBs that the results from 2D UNB-IMT have slightly more variability. Both effects seem to be related to the unmodeled errors. The post-fit residuals in the 3D UNB-IMT are closer to the zero mean Gaussian distribution.
Then, we further evaluated the performance of 2D and 3D UNB-IMT under significantly disturbed conditions. Figure 6 shows the results with the same modeling strategies as demonstrated in Figure 5 but on October 25, 2011. Similar conclusions can be drawn from Figure 6, where better results in terms of post-fit residuals are obtained with 3D UNB-IMT (Table 1). In terms of estimated vTEC, the results from both strategies under the disturbed conditions look more irregular than those under the quiet conditions and deviate a little from the sine-wave-like daily variation. Some actual variation of the ionosphere during disturbed conditions may be captured and correctly illustrated as the bumps for both approaches. Furthermore, the unmodeled errors may also be explained as artificial small jumps/bumps in vTEC curves (revealed by the magnitude of post-fit residuals). It is seen that 3D linear UNB-IMT explains more variation of the ionosphere than 2D linear UNB-IMT. However, some residual unmodeled errors may still exist with the 3D model.
FIGURE 6. Sensitivity test (the panels from the top to the bottom correspond to: estimated vertical TEC, residuals, satellite and receiver DCB, slant TEC with respect to local time) between linear 2D (the left-hand panels) and 3D (the right-hand panels) models at FRDN on October 25 (doy 298) in 2011.
As concluded by other investigators, a higher order model could explain more spatial (non-linear) variations of the ionosphere, especially for geomagnetic storm conditions. The results with 2D and 3D quadratic UNB-IMT approaches are shown in Figure 7. In the post-fit residual panels, it can be seen that the residuals with 3D quadratic UNB-IMT are mostly within ±2 TECU except for several small spikes that happened between 0:00 and 4:00 local mean solar time and reflect that not all the electron density variations had been correctly represented by the model used. But it is clear that the 3D quadratic UNB-IMT can significantly improve the modeling precision compared to the 2D quadratic/linear UNB-IMT and 3D linear UNB-IMT. The magnitude of the post-fit residuals shown in this panel is even comparable with the results for the quiet condition shown in Figure 5. In terms of vTEC, a few spurious spikes are occasionally found when processing the data from the four stations with the 3D quadratic model and single-station processing strategy. Other data sources, such as data from incoherent backscatter measurements, may be needed to confirm if the spikes are caused by the instability of the model or actual ionospheric structures. Still, the vTEC curves with 3D quadratic UNB-IMT look smoother than 2D UNB-IMT. In terms of estimated DCBs, it is found that the results with 3D quadratic UNB-IMT approach exhibit relatively fewer perturbations than the other three approaches tested.
FIGURE 7. Sensitivity test (the panels from the top to the bottom correspond to: estimated vertical TEC, residuals, satellite and receiver DCB, slant TEC with respect to local time) between quadratic 2D (the left-hand panels) and 3D (the right-hand panels) models at FRDN on October 25 (doy 298) in 2011.
As we found for the 2D modeling approaches, the single thin-shell assumption with a fixed ionospheric shell height may introduce additional modeling errors. That is mainly because the layer with highest electron density (F2 layer) is not always located at a fixed height. Especially in disturbed ionospheric conditions, such as the case shown in Figures 6 and 7, the layer height would change significantly. Some methods have been proposed and tested with the help of more reliable “true” heights from other resources, such as ionosondes. However, due to the limited number of the instruments deployed and limited information provided (only information from overhead), the applications with these methods would have to be limited to the specific area covered by stations or networks equipped with the instruments. In addition, as to real-time application, the data processing time delay of ionosondes might be another technical issue these methods have to face. Compared with these methods, one benefit of the 3D UNB-IMT is its potential for real-time application for any size of network. Another benefit is its vertical modeling capability to depict vertical variation of electron density so the improved results would also be expected for disturbed ionospheric conditions. It is clearly seen from Figures 6 and 7 that the lowest vTECs around 4:00 LT reach down to 0 TECU with the 2D linear/quatratic UNB-IMT, which are considered as unphysical results. It is confirmed that small biases still exist in the results with the 2D model likely due to the improper shell height chosen (fixed at 350 km for the results shown in this article).
Multi-Station Experiment. When using the modeling scheme for a network solution, we will generally have two possible processing scenarios. One is processing the data of all the stations as a batch, and the other is processing station by station (or baseline by baseline).
The advantages and disadvantages of the batch process can be summarized as follows. It has more redundancies in the Kalman filter to estimate a more stable and reliable set of satellite and receiver DCBs. Due to more measurements as an input (state) of the Kalman filter, the convergence time would be shorter in terms of the estimated DCBs. It would be of benefit for real-time applications if we have limited a priori information about the estimated ionospheric parameters and/or DCBs. However, the batch solution seems to be less sensitive to localized information content than the station-by-station solution. The overall effect of the batch solution is smoothing over the network, reducing the size of some small perturbations. Theoretically, localized measurements should not have significant influence on the estimated state across an extended area or even the entire globe. In other words, the batch solution may be beneficial for relatively small local-area networks, but may not be ideally suited for networks as large as wide-area ones. Another straightforward disadvantage of the batch process is its relatively longer processing time, which might be a downside if it is used for real-time applications.
In the multi-station experiment, we tested the 3D UNB- IMT with a small regional network of four IGS reference stations (Figure 2) to investigate its performance with localized ionospheric variations. We performed tests with two scenarios: batch and station-by-station. Due to space restrictions, we cannot thoroughly report the results we obtained here. Please see the conference paper listed in Further Reading for the full details. Overall, the results we obtained in terms of post-processing residuals were similar to those in the single station experiment. We also found that the 3D UNB-IMT with EOFs seems to be able to better model the measurements with low elevation angles than the 2D UNB-IMT with a mapping function.
Comparing 3D UNB-IMT with SH Model. We have compared the results using the batch processing strategy with those from the SH model. The reason for this approach is that we intended to compare the results of the two processing strategies (UNB-IMT and SH) with identical conditions. That is, both methods processed the data using a batch scheme and estimated both ionospheric parameters and DCBs simultaneously, instead of using some other source or processed results. Therefore, in this case, we can compare the results side by side and evaluate the effectiveness of the estimated ionospheric parameters.
Based on the data from the network of the four stations, the sensitivity of the SH models is lower than that of 3D UNB-IMT, although the number of ionospheric parameters of the SH models is comparable or even larger than that of 3D UNB-IMT. In other words, the ionospheric parameters in 3D UNB-IMT to describe the variability of the ionosphere are more effective and meaningful to such a network scale than those in the 3D SH model.
Given the nature of its basis functions, the SH model is an excellent tool for global modeling, but it has some shortcomings for localized variability modeling. As to larger regional networks with longer baselines, such as those used for WAAS, which covers North America, the difference of the sensitivities between the batch and the station-by-station solutions should be larger than the results we have obtained. However, we cannot conclude that the sensitivity of 3D UNB-IMT is better than that of the 3D SH model with the batch processing strategy for such large regional networks before more tests are conducted. Still, it is clearly seen in our tests that the 3D SH model is not always ideal for regional networks in terms of sensitivity.
We reached similar conclusions for October 25, 2011, where the residuals spread more widely compared with quiet-condition residuals. In the storm conditions, the residuals of the quadratic 3D UNB-IMT spread relatively less than those of other modeling strategies. This is especially the case for the several hours at the beginning of the day, which corresponds to the peak of the Dst and Kp indices shown in Figure 3. The quadratic 3D UNB-IMT seems to have the capacity to handle the ionospheric spatial and temporal variation even during severe storm conditions.
FIGURE 3. Interplanetary magnetic field Bz component, Kp index, AE index, and Dst index during October 13–25 (doy 286–298) in 2011; nT = nanoteslas (Data from World Data Center for Geomagnetism, Kyoto and Goddard Space Flight Center Space Physics Data Facility).
Repeatability of Estimated DCBs. The DCBs not only have influence on the quality (accuracy) of the vTEC estimation, but their repeatability can also provide information to evaluate ionospheric models. This implies that the ionospheric models that have the capability to estimate/eliminate more accurate DCBs, independent of ionospheric variability, are preferable. We carried out a number of tests to evaluate the repeatability of estimated DCB values using the 2D and 3D UNB-IMT approaches as well as the 3D SH technique under both quiet and disturbed ionospheric conditions. For quiet ionospheric conditions, the performance of all the tested models looks comparable, although the quadratic 3D UNB-IMT performs slightly better than the others. As to the disturbed conditions, the quadratic 2D/3D UNB-IMT seems be able to provide more stable DCBs than the other models. However, the improvement of the extension from 2D to 3D is slight for the quadratic models, although it is significant for the linear models. The performance of the 3D SH model looks fairly poor compared to 3D UNB-IMT for regional modeling. Consult the conference paper for further details.
Conclusions and Future Research
In the work described in this article, we extended the UNB-IMT from 2D to 3D and compared the performance between them in station-by-station and batch processing scenarios for both quiet and storm ionospheric conditions. We used the data from a small regional network of dual-frequency GPS receivers. The DCBs and ionospheric delays were estimated at the same time by a Kalman filter. The newly developed approach was evaluated by analyzing the post-fit residuals, TEC of the state estimation process, and the repeatability of estimates of DCBs.
In the single-station processing, the improvement of 3D UNB-IMT has been demonstrated in both quiet and disturbed ionospheric conditions in terms of post-fit residuals. The 3D UNB-IMT with more parameters allows the depiction of more complex (vertical) variability of the ionosphere. The 3D UNB-IMT is able to better deal with the measurements from low-elevation-angle satellites owing to EOFs replacing the mapping function. The artificial jumps with 2D UNB-IMT when satellites come into or go out of view of the receiver have been properly handled by the 3D UNB-IMT. In addition, the time series of estimated DCBs with 3D UNB-IMT exhibit less perturbation than the results with 2D UNB-IMT.
As to the multi-station (network) processing, it is confirmed that the station-by-station solution is more sensitive to localized information than the batch solution. Based on the results from our research, station-by-station processing with 3D UNB-IMT is suggested to increase chances to catch localized ionospheric structures.
The repeatability of estimated DCBs was investigated as another indicator to evaluate the viability ofionospheric models.
Before the 3D UNB-IMT is tested in the positioning domain for single-frequency positioning, it is worth validating the model with other data sources. In addition, the potential benefits of 3D UNB-IMT during extremely disturbed ionospheric conditions is worth investigating further.
Acknowledgments
We would like to thank the IGS and the Crustal Dynamics Data Information System for providing the GPS data, and we acknowledge the financial contribution of the Natural Sciences and Engineering Research Council of Canada for supporting the first and last authors. This article is based on the paper “Eliminating Potential Errors Caused by the Thin Shell Assumption: An Extended 3D UNB Ionospheric Modelling Technique” presented at the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, September 16–20, 2013.
WEI ZHANG received his M.Sc. degree in space science in 2009 from the School of Earth and Space Science of Peking University, China. He is currently an M.Sc.E. student in the Department of Geodesy and Geomatics Engineering at University of New Brunswick (UNB) under the supervision of Dr. Richard B. Langley.
ATTILA KOMJATHY is a principal investigator at the California Institute of Technology Jet Propulsion Laboratory and an adjunct professor at UNB, specializing in remote sensing techniques using GPS. He received his Ph.D. from the Department of Geodesy and Geomatics Engineering of UNB in 1997.
SIMON BANVILLE works for the Geodetic Survey Division of Natural Resources Canada on real-time precise point positioning (PPP) using global navigation satellite systems. He is also in the process of completing his Ph.D. degree at UNB under the supervision of Dr. Langley.
FURTHER READING
• Authors’ Conference Paper
“Eliminating Potential Errors Caused by the Thin Shell Approximation: An Extended 3D UNB Ionospheric Modelling Technique” by W. Zhang, R.B. Langley, A. Komjathy, and S. Banville in Proceedings of ION GNSS+ 2013, the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, September 16–20, 2013, pp. 2447–2462.
• 2D Ionosphere Modeling
“SBAS Ionospheric Modeling with the Quadratic Approach: Reducing the Risks” by H. Rho, R. Langley, and A. Komjathy in Proceedings of ION GNSS 2005, the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation, Long Beach, California, September 13–16, 2005, pp. 723–734.
“Improvement of a Global Ionospheric Model to Provide Ionospheric Range Error Corrections for Single-frequency GPS Users” by A. Komjathy and R. Langley in Proceedings of the 52nd Annual Meeting of The Institute of Navigation, Cambridge, Massachusetts, January 22–24, 1996, pp. 557–566.
• 3D (4D) Ionosphere Modeling
“Comparison of 4D Tomographic Mapping Versus Thin-shell Approximation for Ionospheric Delay Corrections for Single-frequency GPS Receivers over North America” by D.J. Allain and C.N. Mitchell in GPS Solutions, Vol. 14, No. 3, 2009, pp. 279–291, doi: 10.1007/s10291-009-0153-0.
“Regional 4-D modeling of the Ionospheric Electron Density” by M. Schmidt, D. Bilitza, C. Shum, and C. Zeilhofer in Advances in Space Research, Vol. 42, No. 4, 2008, pp. 782–790, doi: 10.1016/j.asr.2007.02.050.
“History, Current State, and Future Directions of Ionospheric Imaging” by G.S. Bust and C.N. Mitchell in Reviews of Geophysics, Vol. 46, No. 1, RG1003, March 2008, doi: 10.1029/2006RG000212.
“Development of the Global Assimilative Ionospheric Model” by C. Wang, G. Hajj, X. Pi, I.G. Rosen, and B. Wilson in Radio Science, Vol. 39, No. 1, RS1S06, February 2004, doi: 10.1029/2002RS002854.
Contributions to the 3D Ionospheric Sounding with GPS Data by M. García-Fernández, Ph.D. dissertation, Research Group of Astronomy and Geomatics, Universitat Politècnica de Catalunya, Barcelona, Spain, 2004. Available online in three parts:
“The NeQuick Model Genesis, Uses and Evolution” by S.M. Radicella in Annals of Geophysics, Vol. 52, No. 3/4, June/August 2009, pp. 417–422, doi: 10.4401/ag-4597.
“International Reference Ionosphere 2007: Improvements and New Parameters” by D. Bilitza and B. Reinisch in Advances in Space Research, Vol. 42, No. 4, 2008, pp. 599–609, doi: 10.1016/j.asr.2007.07.048.
“Empirical Orthogonal Functions and Related Techniques in Atmospheric Science: A Review” by A. Hannachi, I.T. Jolliffe, and D.B. Stephenson in International Journal of Climatology, Vol. 27, No. 9, July 2007, pp. 1119–1152, doi: 10.1002/joc.1499.
“Empirical Orthogonal Functions: The Medium is the Message” by A.H. Monahan, J.C. Fyfe, M.H.P. Ambaum, D.B. Stephenson, and G.R. North in Journal of Climate, Vol. 22, No. 24, December 2009, pp. 6501–6514, doi: 10.1175/2009JCLI3062.1.
A Manual for EOF and SVD Analyses of Climatic Data by H. Bjornsson and S. Venegas, Report No. 97-1, Department of Atmospheric and Oceanic Sciences and Centre for Climate and Global Change Research, McGill University, Montreal, February 1997.
After a two-week delay, a rocket carrying a GPS instrument designed by University of New Brunswick scientists was launched into space aboard the SpaceX Falcon 9 rocket on September 29. The rocket left Vandenberg Air Force base in California as part of the CASSIOPE (Cascade Smallsat and Ionospheric Polar Explorer) mission.
Dr. Richard Langley, GPS World Innovation editor and professor in geodesy and geomatics engineering at the University of New Brunswick, is a principal investigator behind the scientific portion of the CASSIOPE mission. Langley and his colleagues will monitor data from the GPS instrument, which is part of the Enhanced Polar Outflow Probe (e-POP) payload aboard the spacecraft.
E-POP will continue the sequence of Canada’s orbiting space environment sensors, which began with Canada’s first satellite, Alouette 1, launched in 1962 to study the ionosphere. e-POP is, perhaps, the most extensive suite of sensors for studying the ionosphere/magnetosphere/thermosphere yet to be launched, and will provide Canadian and other scientists with the opportunity to better understand the impact and variability the sun has on the space environment — what we call “space weather.”
A static fire retested the Falcon 9 rocket after several problems cropped up during a hotfire of the launcher’s engines during preparation for the original launch date September 15. The launch was then delayed because the U.S. Air Force Western Range, which controls a network of tracking and communications assets based at Vandenberg, was busy with Minuteman ballistic missile testing.
The small hybrid satellite blasted off on board a Falcon 9 rocket developed by SpaceX, a commercial space company. The Canadian Space Agency became one of SpaceX’s first customers when the agency decided years ago to use the private U.S. rocket to deliver the satellite at a reduced cost of $10 million. It cost the space agency $63 million to develop the satellite.
The Falcon 9 rocket, with CASSIOPE inside its fairing, on the way to the launch pad at Vandenberg Air Force Base. (Photo credit: SpaceX).The research satellite CASSIOPE on a test platform at the Canadian Space Agency’s David Florida Laboratory. CASSIOPE hosts the GPS Attitude, Positioning, and Profiling instrument designed by GGE researchers. The four white antennas on the left-facing side of the spacecraft will be used to determine the position, velocity, and attitude of the spacecraft while the antenna on the upper side will be used to profile the ionosphere’s electron density. (Photograph courtesy of MacDonald, Dettwiler and Associates Ltd.)
Update: Elon Musk, SpaceX’s CEO and chief designer, has posted an update on the status of the upcoming Falcon 9 launch on his Twitter account. “Will do another static fire of rocket to make sure all is good & AF [[Air Force]] needs to test ICBMs, so probable launch Sept 29/30,” Musk tweeted.
“The static fire is scheduled for later this week, perhaps Wednesday, sources said. It will retest the Falcon 9 rocket after several problems cropped up during a hotfire of the launcher’s engines Thursday at Vandenberg Air Force Base, Calif.
“The U.S. Air Force Western Range, which controls a network of tracking and communications assets based at Vandenberg, is busy for the next few weeks due to Minuteman ballistic missile testing.”
The Falcon 9 rocket, with CASSIOPE inside its fairing, on the way to the launch pad at Vandenberg Air Force Base. (Photo credit: SpaceX).
A GPS instrument designed by University of New Brunswick scientists is scheduled to be launched into space aboard the SpaceX Falcon 9 rocket on September 15. The rocket will depart Vandenberg Air Force base in California as part of the CASSIOPE (Cascade Smallsat and Ionospheric Polar Explorer) mission.
Dr. Richard Langley, GPS World Innovation editor and professor in geodesy and geomatics engineering at the University of New Brunswick, is a principal investigator behind the scientific portion of the CASSIOPE mission. Langley and his colleagues will monitor data from the GPS instrument, which is part of the Enhanced Polar Outflow Probe (e-POP) payload aboard the spacecraft.
E-POP will continue the sequence of Canada’s orbiting space environment sensors, which began with Canada’s first satellite, Alouette 1, launched in 1962 to study the ionosphere. e-POP is, perhaps, the most extensive suite of sensors for studying the ionosphere/magnetosphere/thermosphere yet to be launched, and will provide Canadian and other scientists with the opportunity to better understand the impact and variability the sun has on the space environment — what we call “space weather.”
The research satellite CASSIOPE on a test platform at the Canadian Space Agency’s David Florida Laboratory. CASSIOPE hosts the GPS Attitude, Positioning, and Profiling instrument designed by GGE researchers. The four white antennas on the left-facing side of the spacecraft will be used to determine the position, velocity, and attitude of the spacecraft while the antenna on the upper side will be used to profile the ionosphere’s electron density. (Photograph courtesy of MacDonald, Dettwiler and Associates Ltd.)
Monitoring the Ionosphere with Integer-Leveled GPS Measurements
By Simon Banville, Wei Zhang, and Richard B. Langley
INNOVATION INSIGHTS by Richard Langley
IT’S NOT JUST FOR POSITIONING, NAVIGATION, AND TIMING. Many people do not realize that GPS is being used in a variety of ways in addition to those of its primary mandate, which is to provide accurate position, velocity, and time information.
The radio signals from the GPS satellites must traverse the Earth’s atmosphere on their way to receivers on or near the Earth’s surface. The signals interact with the atoms, molecules, and charged particles that make up the atmosphere, and the process slightly modifies the signals. It is these modified or perturbed signals that a receiver actually processes. And should a signal be reflected or diffracted by some object in the vicinity of the receiver’s antenna, the signal is further perturbed — a phenomenon we call multipath.
Now, these perturbations are a bit of a nuisance for conventional users of GPS. The atmospheric effects, if uncorrected, reduce the accuracy of the positions, velocities, and time information derived from the signals. However, GPS receivers have correction algorithms in their microprocessor firmware that attempt to correct for the effects. Multipath, on the other hand, is difficult to model although the use of sophisticated antennas and advanced receiver technologies can minimize its effect.
But there are some GPS users who welcome the multipath or atmospheric effects in the signals. By analyzing the fluctuations in signal-to-noise-ratio due to multipath, the characteristics of the reflector can be deduced. If the reflector is the ground, then the amount of moisture in the soil can be measured. And, in wintery climes, changes in snow depth can be tracked from the multipath in GPS signals.
The atmospheric effects perturbing GPS signals can be separated into those that are generated in the lower part of the atmosphere, mostly in the troposphere, and those generated in the upper, ionized part of the atmosphere — the ionosphere. Meteorologists are able to extract information on water vapor content in the troposphere and stratosphere from the measurements made by GPS receivers and regularly use the data from networks of ground-based continuously operating receivers and those operating on some Earth-orbiting satellites to improve weather forecasts.
And, thanks to its dispersive nature, the ionosphere can be studied by suitably combining the measurements made on the two legacy frequencies transmitted by all GPS satellites. Ground-based receiver networks can be used to map the electron content of the ionosphere, while Earth-orbiting receivers can profile electron density. Even small variations in the distribution of ionospheric electrons caused by earthquakes; tsunamis; and volcanic, meteorite, and nuclear explosions can be detected using GPS.
In this month’s column, I am joined by two of my graduate students, who report on an advance in the signal processing procedure for better monitoring of the ionosphere, potentially allowing scientists to get an even better handle on what’s going on above our heads.
Representation and forecast of the electron content within the ionosphere is now routinely accomplished using GPS measurements. The global distribution of permanent ground-based GPS tracking stations can effectively monitor the evolution of electron structures within the ionosphere, serving a multitude of purposes including satellite-based communication and navigation.
It has been recognized early on that GPS measurements could provide an accurate estimate of the total electron content (TEC) along a satellite-receiver path. However, because of their inherent nature, phase observations are biased by an unknown integer number of cycles and do not provide an absolute value of TEC. Code measurements (pseudoranges), although they are not ambiguous, also contain frequency-dependent biases, which again prevent a direct determination of TEC. The main advantage of code over phase is that the biases are satellite- and receiver-dependent, rather than arc-dependent. For this reason, the GPS community initially adopted, as a common practice, fitting the accurate TEC variation provided by phase measurements to the noisy code measurements, therefore removing the arc-dependent biases. Several variations of this process were developed over the years, such as phase leveling, code smoothing, and weighted carrier-phase leveling (see Further Reading for background literature).
The main challenge at this point is to separate the code inter-frequency biases (IFBs) from the line-of-sight TEC. Since both terms are linearly dependent, a mathematical representation of the TEC is usually required to obtain an estimate of each quantity. Misspecifications in the model and mapping functions were found to contribute significantly to errors in the IFB estimation, suggesting that this process would be better performed during nighttime when few ionospheric gradients are present. IFB estimation has been an ongoing research topic for the past two decades are still remains an issue for accurate TEC determination.
A particular concern with IFBs is the common assumption regarding their stability. It is often assumed that receiver IFBs are constant during the course of a day and that satellite IFBs are constant for a duration of a month or more. Studies have clearly demonstrated that intra-day variations of receiver instrumental biases exist, which could possibly be related to temperature effects. This assumption was shown to possibly introduce errors exceeding 5 TEC units (TECU) in the leveling process, where 1 TECU corresponds to 0.162 meters of code delay or carrier advance at the GPS L1 frequency (1575.42 MHz).
To overcome this limitation, one could look into using solely phase measurements in the TEC estimation process, and explicitly deal with the arc-dependent ambiguities. The main advantage of such a strategy is to avoid code-induced errors, but a larger number of parameters needs to be estimated, thereby weakening the strength of the adjustment. A comparison of the phase-only (arc-dependent) and phase-leveled (satellite-dependent) models showed that no model performs consistently better. It was found that the satellite-dependent model performs better at low-latitudes since the additional ambiguity parameters in the arc-dependent model can absorb some ionospheric features (such as gradients). On the other hand, when the mathematical representation of the ionosphere is realistic, the leveling errors may more significantly impact the accuracy of the approach.
The advent of precise point positioning (PPP) opened the door to new possibilities for slant TEC (STEC) determination. Indeed, PPP can be used to estimate undifferenced carrier-phase ambiguity parameters on L1 and L2, which can then be used to remove the ambiguous characteristics of the carrier-phase observations. To obtain undifferenced ambiguities free from ionospheric effects, researchers have either used the widelane/ionosphere-free (IF) combinations, or the Group and Phase Ionospheric Calibration (GRAPHIC) combinations. One critical problem with such approaches is that code biases propagate into the estimated ambiguity parameters. Therefore, the resulting TEC estimates are still biased by unknown quantities, and might suffer from the unstable datum provided by the IFBs.
The recent emergence of ambiguity resolution in PPP presented sophisticated means of handling instrumental biases to estimate integer ambiguity parameters. One such technique is the decoupled-clock method, which considers different clock parameters for the carrier-phase and code measurements. In this article, we present an “integer-leveling” method, based on the decoupled-clock model, which uses integer carrier-phase ambiguities obtained through PPP to level the carrier-phase observations.
Standard Leveling Procedure
This section briefly reviews the basic GPS functional model, as well as the observables usually used in ionospheric studies. A common leveling procedure is also presented, since it will serve as a basis for assessing the performance of our new method.
Ionospheric Observables. The standard GPS functional model of dual-frequency carrier-phase and code observations can be expressed as:
(1)
(2)
(3)
(4)
where Φijis the carrier-phase measurement to satellite j on the Li link and, similarly, Pijis the code measurement on Li. The term is the biased ionosphere-free range between the satellite and receiver, which can be decomposed as:
(5)
The instantaneous geometric range between the satellite and receiver antenna phase centers is ρ j. The receiver and satellite clock errors, respectively expressed as dT and dtj, are expressed here in units of meters. The term Tj stands for the tropospheric delay, while the ionospheric delay on L1 is represented by I j and is scaled by the frequency-dependent constant μ for L2, where . The biased carrier-phase ambiguities are symbolized by and are scaled by their respective wavelengths (λi). The ambiguities can be explicitly written as:
(6)
where Ni jis the integer ambiguity, bi is a receiver-dependent bias, and bi j is a satellite-dependent bias. Similarly, Bi and Bi j are instrumental biases associated with code measurements. Finally, ε contains unmodeled quantities such as noise and multipath, specific to the observable. The overbar symbol indicates biased quantities.
In ionospheric studies, the geometry-free (GF) signal combinations are formed to virtually eliminate non-dispersive terms and thus provide a better handle on the quantity of interest:
(7)
(8)
where IFBr and IFB j represent the code inter-frequency biases for the receiver and satellite, respectively. They are also commonly referred to as differential code biases (DCBs). Note that the noise terms (ε) are neglected in these equations for the sake of simplicity.
Weighted-Leveling Procedure. As pointed out in the introduction, the ionospheric observables of Equations (7) and (8) do not provide an absolute level of ionospheric delay due to instrumental biases contained in the measurements. Assuming that these biases do not vary significantly in time, the difference between the phase and code observations for a particular satellite pass should be a constant value (provided that no cycle slip occurred in the phase measurements). The leveling process consists of removing this constant from each geometry-free phase observation in a satellite-receiver arc:
(9)
where the summation is performed for all observations forming the arc. An elevation-angle-dependent weight (w) can also be applied to minimize the noise and multipath contribution for measurements made at low elevation angles. The double-bar symbol indicates leveled observations.
Integer-Leveling Procedure
The procedure of fitting a carrier-phase arc to code observations might introduce errors caused by code noise, multipath, or intra-day code-bias variations. Hence, developing a leveling approach that relies solely on carrier-phase observations is highly desirable. Such an approach is now possible with the recent developments in PPP, allowing for ambiguity resolution on undifferenced observations. This procedure has gained significant momentum in the past few years, with several organizations generating “integer clocks” or fractional offset corrections for recovering the integer nature of the undifferenced ambiguities. Among those organizations are, in alphabetical order, the Centre National d’Études Spatiale; GeoForschungsZentrum; GPS Solutions, Inc.; Jet Propulsion Laboratory; Natural Resources Canada (NRCan); and Trimble Navigation. With ongoing research to improve convergence time, it would be no surprise if PPP with ambiguity resolution would become the de facto methodology for processing data on a station-by-station basis. The results presented in this article are based on the products generated at NRCan, referred to as “decoupled clocks.”
The idea behind integer leveling is to introduce integer ambiguity parameters on L1 and L2, obtained through PPP processing, into the geometry-free linear combination of Equation (7). The resulting integer-leveled observations, in units of meters, can then be expressed as: (10)
where and are the ambiguities obtained from the PPP solution, which should be, preferably, integer values. Since those ambiguities are obtained with respect to a somewhat arbitrary ambiguity datum, they do not allow instant recovery of an unbiased slant ionospheric delay. This fact was highlighted in Equation (10), which indicates that, even though the arc-dependency was removed from the geometry-free combination, there are still receiver- and satellite-dependent biases (br and b j, respectively) remaining in the integer-leveled observations. The latter are thus very similar in nature to the standard-leveled observations, in the sense that the biases br and b jreplace the well-known IFBs. As a consequence, integer-leveled observations can be used with any existing software used for the generation of TEC maps. The motivation behind using integer-leveled observations is the mitigation of leveling errors, as explained in the next sections.
Slant TEC Evaluation
As a first step towards assessing the performance of integer-leveled observations, STEC values are derived on a station-by-station basis. The slant ionospheric delays are then compared for a pair of co-located receivers, as well as with global ionospheric maps (GIMs) produced by the International GNSS Service (IGS).
Leveling Error Analysis. Relative leveling errors between two co-located stations can be obtained by computing between-station differences of leveled observations:
(11)
where subscripts A and B identify the stations involved, and εl is the leveling error. Since the distance between stations is short (within 100 meters, say), the ionospheric delays will cancel, and so will the satellite biases (b j) which are observed at both stations. The remaining quantities will be the (presumably constant) receiver biases and any leveling errors. Since there are no satellite-dependent quantities in Equation (11), the differenced observations obtained should be identical for all satellites observed, provided that there are no leveling errors. The same principles apply to observations leveled using other techniques discussed in the introduction. Hence, Equation (11) allows comparison of the performance of various leveling approaches.
This methodology has been applied to a baseline of approximately a couple of meters in length between stations WTZJ and WTZZ, in Wettzell, Germany. The observations of both stations from March 2, 2008, were leveled using a standard leveling approach, as well as the method described in this article. Relative leveling errors computed using Equation (11) are displayed in Figure 1, where each color represents a different satellite. It is clear that code noise and multipath do not necessarily average out over the course of an arc, leading to leveling errors sometimes exceeding a couple of TECU for the standard leveling approach (see panel (a)). On the other hand, integer-leveled observations agree fairly well between stations, where leveling errors were mostly eliminated. In one instance, at the beginning of the session, ambiguity resolution failed at both stations for satellite PRN 18, leading to a relative error of 1.5 TECU, more or less. Still, the advantages associated with integer leveling should be obvious since the relative error of the standard approach is in the vicinity of -6 TECU for this satellite.
FIGURE 1. Relative leveling errors between stations WTZJ and WTZZ on March 2, 2008: (a) standard-leveled observations and (b) integer-leveled observations.
The magnitude of the leveling errors obtained for the standard approach agrees fairly well with previous studies (see Further Reading). In the event that intra-day variations of the receiver IFBs are observed, even more significant biases were found to contaminate standard-leveled observations. Since the decoupled-clock model used for ambiguity resolution explicitly accounts for possible variations of any equipment delays, the estimated ambiguities are not affected by such effects, leading to improved leveled observations.
STEC Comparisons. Once leveled observations are available, the next step consists of separating STEC from instrumental delays. This task can be accomplished on a station-by-station basis using, for example, the single-layer ionospheric model. Replacing the slant ionospheric delays (I j) in Equation (10) by a bilinear polynomial expansion of VTEC leads to:
(12)
where M(e) is the single-layer mapping function (or obliquity factor) depending on the elevation angle (e) of the satellite. The time-dependent coefficients a0, a1, and a2 determine the mathematical representation of the VTEC above the station. Gradients are modeled using Δλ, the difference between the longitude of the ionospheric pierce point and the longitude of the mean sun, and Δϕ, the difference between the geomagnetic latitude of the ionospheric pierce point and the geomagnetic latitude of the station. The estimation procedure described by Attila Komjathy (see Further Reading) is followed in all subsequent tests. An elevation angle cutoff of 10 degrees was applied and the shell height used was 450 kilometers. Since it is not possible to obtain absolute values for the satellite and receiver biases, the sum of all satellite biases was constrained to a value of zero. As a consequence, all estimated biases will contain a common (unknown) offset. STEC values, in TECU, can then be computed as:
(13)
where the hat symbol denotes estimated quantities, and is equal to zero (that is, it is not estimated) when biases are obtained on a station-by-station basis. The frequency, f1, is expressed in Hz. The numerical constant 40.3, determined from values of fundamental physical constants, is sufficiently precise for our purposes, but is a rounding of the more precise value of 40.308.
While integer-leveled observations from co-located stations show good agreement, an external TEC source is required to make sure that both stations are not affected by common errors. For this purpose, Figure 2 compares STEC values computed from GIMs produced by the IGS and STEC values derived from station WTZJ using both standard- and integer-leveled observations. The IGS claims root-mean-square errors on the order of 2-8 TECU for vertical TEC, although the ionosphere was quiet on the day selected, meaning that errors at the low-end of that range are expected. Errors associated with the mapping function will further contribute to differences in STEC values. As apparent from Figure 2, no significant bias can be identified in integer-leveled observations. On the other hand, negative STEC values (not displayed in Figure 2) were obtained during nighttimes when using standard-leveled observations, a clear indication that leveling errors contaminated the observations.
FIGURE 2. Comparison between STEC values obtained from a global ionospheric map and those from station WTZJ using standard- and integer-leveled observations.
STEC Evaluation in the Positioning Domain. Validation of slant ionospheric delays can also be performed in the positioning domain. For this purpose, a station’s coordinates from processing the observations in static mode (that is, one set of coordinates estimated per session) are estimated using (unsmoothed) single-frequency code observations with precise orbit and clock corrections from the IGS and various ionosphere-correction sources. Figure 3 illustrates the convergence of the 3D position error for station WTZZ, using STEC corrections from the three sources introduced previously, namely: 1) GIMs from the IGS, 2) STEC values from station WTZJ derived from standard leveling, and 3) STEC values from station WTZJ derived from integer leveling. The reference coordinates were obtained from static processing based on dual-frequency carrier-phase and code observations. The benefits of the integer-leveled corrections are obvious, with the solution converging to better than 10 centimeters. Even though the distance between the stations is short, using standard-leveled observations from WTZJ leads to a biased solution as a result of arc-dependent leveling errors. Using a TEC map from the IGS provides a decent solution considering that it is a global model, although the solution is again biased.
FIGURE 3. Single-frequency code-based positioning results for station WTZZ (in static mode) using different ionosphere-correction sources: GIM and STEC values from station WTZJ using standard- and integer-leveled observations.
This station-level analysis allowed us to confirm that integer-leveled observations can seemingly eliminate leveling errors, provided that carrier-phase ambiguities are fixed to proper integer values. Furthermore, it is possible to retrieve unbiased STEC values from those observations by using common techniques for isolating instrumental delays. The next step consisted of examining the impacts of reducing leveling errors on VTEC.
VTEC Evaluation
When using the single-layer ionospheric model, vertical TEC values can be derived from the STEC values of Equation (13) using:
(14)
Dividing STEC by the mapping function will also reduce any bias caused by the leveling procedure. Hence, measures of VTEC made from a satellite at a low elevation angle will be less impacted by leveling errors. When the satellite reaches the zenith, then any bias in the observation will fully propagate into the computed VTEC values. On the other hand, the uncertainty of the mapping function is larger at low-elevation angles, which should be kept in mind when analyzing the results.
Using data from a small regional network allows us to assess the compatibility of the VTEC quantities between stations. For this purpose, GPS data collected as a part of the Western Canada Deformation Array (WCDA) network, still from March 2, 2008, was used. The stations of this network, located on and near Vancouver Island in Canada, are indicated in Figure 4. Following the model of Equation (12), all stations were integrated into a single adjustment to estimate receiver and satellite biases as well as a triplet of time-varying coefficients for each station. STEC values were then computed using Equation (13), and VTEC values were finally derived from Equation (14). This procedure was again implemented for both standard- and integer-leveled observations.
FIGURE 4. Network of stations used in the VTEC evaluation procedures.
To facilitate the comparison of VTEC values spanning a whole day and to account for ionospheric gradients, differences with respect to the IGS GIM were computed. The results, plotted by elevation angle, are displayed in Figure 5 for all seven stations processed (all satellite arcs from the same station are plotted using the same color). The overall agreement between the global model and the station-derived VTECs is fairly good, with a bias of about 1 TECU. Still, the top panel demonstrates that, at high elevation angles, discrepancies between VTEC values derived from standard-leveled observations and the ones obtained from the model have a spread of nearly 6 TECU. With integer-leveled observations (see bottom panel), this spread is reduced to approximately 2 TECU. It is important to realize that the dispersion can be explained by several factors, such as remaining leveling errors, the inexact receiver and satellite bias estimates, and inaccuracies of the global model. It is nonetheless expected that leveling errors account for the most significant part of this error for standard-leveled observations.
For satellites observed at a lower elevation angle, the spread between arcs is similar for both methods (except for station UCLU in panel (a) for which the estimated station IFB parameter looks significantly biased). As stated previously, the reason is that leveling errors are reduced when divided by the mapping function. The latter also introduces further errors in the comparisons, which explains why a wider spread should typically be associated with low-elevation-angle satellites. Nevertheless, it should be clear from Figure 5 that integer-leveled observations offer a better consistency than standard-leveled observations.
FIGURE 5. VTEC differences, with respect to the IGS GIM, for all satellite arcs as a function of the elevation angle of the satellite, using (a) standard-leveled observations and (b) integer-leveled observations.
Conclusion
The technique of integer leveling consists of introducing (preferably) integer ambiguity parameters obtained from PPP into the geometry-free combination of observations. This process removes the arc dependency of the signals, and allows integer-leveled observations to be used with any existing TEC estimation software. While leveling errors of a few TECU exist with current procedures, this type of error can be eliminated through use of our procedure, provided that carrier-phase ambiguities are fixed to the proper integer values. As a consequence, STEC values derived from nearby stations are typically more consistent with each other. Unfortunately, subsequent steps involved in generating VTEC maps, such as transforming STEC to VTEC and interpolating VTEC values between stations, attenuate the benefits of using integer-leveled observations.
There are still ongoing challenges associated with the GIM-generation process, particularly in terms of latency and three-dimensional modeling. Since ambiguity resolution in PPP can be achieved in real time, we believe that integer-leveled observations could benefit near-real-time ionosphere monitoring. Since ambiguity parameters are constant for a satellite pass (provided that there are no cycle slips), integer ambiguity values (that is, the leveling information) can be carried over from one map generation process to the next. Therefore, this methodology could reduce leveling errors associated with short arcs, for instance.
Another prospective benefit of integer-leveled observations is the reduction of leveling errors contaminating data from low-Earth-orbit (LEO) satellites, which is of particular importance for three-dimensional TEC modeling. Due to their low orbits, LEO satellites typically track a GPS satellite for a short period of time. As a consequence, those short arcs do not allow code noise and multipath to average out, potentially leading to important leveling errors. On the other hand, undifferenced ambiguity fixing for LEO satellites already has been demonstrated, and could be a viable solution to this problem.
Evidently, more research needs to be conducted to fully assess the benefits of integer-leveled observations. Still, we think that the results shown herein are encouraging and offer potential solutions to current challenges associated with ionosphere monitoring.
Acknowledgments
We would like to acknowledge the help of Paul Collins from NRCan in producing Figure 4 and the financial contribution of the Natural Sciences and Engineering Research Council of Canada in supporting the second and third authors. This article is based on two conference papers: “Defining the Basis of an ‘Integer-Levelling’ Procedure for Estimating Slant Total Electron Content” presented at ION GNSS 2011 and “Ionospheric Monitoring Using ‘Integer-Levelled’ Observations” presented at ION GNSS 2012. ION GNSS 2011 and 2012 were the 24th and 25th International Technical Meetings of the Satellite Division of The Institute of Navigation, respectively. ION GNSS 2011 was held in Portland, Oregon, September 19–23, 2011, while ION GNSS 2012 was held in Nashville, Tennessee, September 17–21, 2012.
SIMON BANVILLE is a Ph.D. candidate in the Department of Geodesy and Geomatics Engineering at the University of New Brunswick (UNB) under the supervision of Dr. Richard B. Langley. His research topic is the detection and correction of cycle slips in GNSS observations. He also works for Natural Resources Canada on real-time precise point positioning and ambiguity resolution.
WEI ZHANG received his M.Sc. degree (2009) in space science from the School of Earth and Space Science of Peking University, China. He is currently an M.Sc.E. student in the Department of Geodesy and Geomatics Engineering at UNB under the supervision of Dr. Langley. His research topic is the assessment of three-dimensional regional ionosphere tomographic models using GNSS measurements.
FURTHER READING
• Authors’ Conference Papers
“Defining the Basis of an ‘Integer-Levelling’ Procedure for Estimating Slant Total Electron Content” by S. Banville and R.B. Langley in Proceedings of ION GNSS 2011, the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 19–23, 2011, pp. 2542–2551.
“Ionospheric Monitoring Using ‘Integer-Levelled’ Observations” by S. Banville, W. Zhang, R. Ghoddousi-Fard, and R.B. Langley in Proceedings of ION GNSS 2012, the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, September 17–21, 2012, pp. 3753–3761.
• Errors in GPS-Derived Slant Total Electron Content
“GPS Slant Total Electron Content Accuracy Using the Single Layer Model Under Different Geomagnetic Regions and Ionospheric Conditions” by C. Brunini, and F.J. Azpilicueta in Journal of Geodesy, Vol. 84, No. 5, pp. 293–304, 2010, doi: 10.1007/s00190-010-0367-5.
“Calibration Errors on Experimental Slant Total Electron Content (TEC) Determined with GPS” by L. Ciraolo, F. Azpilicueta, C. Brunini, A. Meza, and S.M. Radicella in Journal of Geodesy, Vol. 81, No. 2, pp. 111–120, 2007, doi: 10.1007/s00190-006-0093-1.
• Global Ionospheric Maps
“The IGS VTEC Maps: A Reliable Source of Ionospheric Information Since 1998” by M. Hernández-Pajares, J.M. Juan, J. Sanz, R. Orus, A. Garcia-Rigo, J. Feltens, A. Komjathy, S.C. Schaer, and A. Krankowski in Journal of Geodesy, Vol. 83, No. 3–4, 2009, pp. 263–275, doi: 10.1007/s00190-008-0266-1.
“Undifferenced GPS Ambiguity Resolution Using the Decoupled Clock Model and Ambiguity Datum Fixing” by P. Collins, S. Bisnath, F. Lahaye, and P. Héroux in Navigation: Journal of The Institute of Navigation, Vol. 57, No. 2, Summer 2010, pp. 123–135.
The GSA has just published a new document on the NeQuick Ionospheric Model to compensate for ionospheric errors on Galileo and other GNSS signals. The document, “European GNSS (Galileo) Open Service Ionospheric Correction Algorithm for Galileo Single Frequency Users,” contains detailed description and results from years of research. NeQuick improves accuracy levels globally when using single-frequency services, even during hyperactive periods of the 11-year solar cycle, according to the GSA. This document gets further discussion in my April GNSS Design & Test e-newsletter column.
