Ever since it came on-line in February 2022, the website GPSJam.org has shown what appears to be regular interference with GPS signals in Texas near San Antonio and Del Rio, and locations north and south of Oklahoma City, Oklahoma.
Only on normal workdays, however. Not on weekends or holidays. Furthermore, whatever was happening also took time off between the Christmas and New Year holidays GPSJam.org also shows similar, though less regular, activity in New Mexico. Experts say this is easily explained as White Sands Missile Range is often the site of electronic warfare training and tests. These are always announced in advance in FAA Notices to Air Missions (NOTAMs) when any interference with GPS reception is anticipated.
The regular patterns observed in Texas and Oklahoma and the lack of NOTAMs led some experts to speculate the source could be inadvertent interference from a commercial or government activity. Said one former official, “It’s just the kind of pattern you see from large organizations. They are off every weekend, federal holidays, and around Christmas.”
Aerobatic-capable Military Training aircraft reporting low NIC values (Image: Stanford University)
GPSJam.org is the brainchild of aviation analyst John Wiseman. The site uses crowdsourced ADS-B reports gathered by the ADS-B Exchange and displays it on a world map. Areas in yellow indicate that between two and ten percent of ADS-B reports for the day had low navigation accuracy. Areas in red had ten percent or more.
Information from the site has proved useful in identifying patterns of regular GPS jamming and spoofing in Russia and other conflict areas around the globe.
The workday patterns in Texas and Oklahoma have appeared on GPSJam.org displays since the site went live in February 2022.
GPS Interference and Aviation
Minor interference with GPS signals is fairly common. GPS jamming devices, while illegal to use, are inexpensive and easy to obtain from vendors on the internet.
Truck drivers wanting to defeat their company’s fleet tracking system, people concerned about being tracked by the government or others, even ministers trying to keep parishioners from texting during sermons – all have been known to use such devices.
Most GPS interference is unintentional. A two-year European Union study found hundreds of thousands of potentially harmful signals, but judged only about ten percent to be intentional. The rest were the inadvertent byproduct of poorly tuned electrical and electronic equipment.
ADS-B tracks of training aircraft performing aerobatics. Red indicates low NIC value reported. (Image: Stanford University)
While most GPS interference is unintentional and localized, spurious signals powerful enough to noticeably impact airborne operations are not unknown.
In two separate incidents last year strong interference near the Denver and Dallas airports impacted air traffic, each for more than a day. The Denver incident lasted for 33 hours before authorities found the source and shut it down. Air traffic was disrupted at Dallas for 44 hours according to government sources, though researchers found the actual interference only lasted for 24 hours. The source of the disruption was never identified.
In 2019 a passenger aircraft was almost lost due to GPS interference while on approach to Sun Valley, Idaho’s Friedman Memorial Airport. As the aircraft flew a GPS-based approach in smoke and haze, the interfering signal was just strong enough to lure it off course and toward a mountain. Fortunately, a sharp-eyed radar controller hundreds of miles away spotted the problem and intervened in time. The source of the interference was never identified.
As a result of the Sun Valley incident and input from numerous aviation groups, the International Civil Aviation Organization told its members there was an “urgent need to address harmful interferences” to satnav signals.
Texas and Oklahoma Mystery Solved
A researcher at Stanford University finally solved the puzzle of the strange recurring sequence of reports from Texas and Oklahoma.
While investigating last October’s GPS interference event near the Dallas airport, PhD candidate Zixi Liu noticed aircraft outside the main area of effect also reporting low Navigation Integrity Category (NIC) values. This began before and continued after complaints from commercial airlines about GPS not being available at Dallas-Fort Worth. These aircraft were in the same general area of Texas, but far enough away that there were large areas between them and Dallas that did not contain any reports with low NIC values.
Low navigation accuracy reports displayed at GPSJam.org. in New Mexico reports were due to GPS interference from military testing. In Texas and Oklahoma, military aerobatics training likely caused reports of low navigation accuracy. (Image: GPSJam.org)
At the same time MS Liu was also investigating anomalous ADS-B reports near San Antonio and Del Rio, Texas. She discovered in all three cases the reports of low NIC values were coming from military training aircraft regularly used for aerobatics. Other aircraft nearby reported good NIC values and showed no evidence interference.
In a recent presentation to the Institute of Navigation, she postulated that Interference with GPS signals was not the cause of the low navigation integrity reports. Rather, the rapid maneuvers and unusual aircraft attitudes of aerobatics caused the airplanes’ navigation receivers to intermittently lose lock on signals from GPS satellites. This caused their ADS-B equipment to report low navigation integrity.
Having solved that mystery, Ms. Liu continues to work on her original question – identifying the source of October’s 24-hour GPS disruption near the Dallas-Fort Worth airport.
Mr. Dana A. Goward is the President of the Resilient Navigation and Timing Foundation and a former US Coast Guard helicopter pilot.
AS CAT STEVENS (yes, he’s back to using his old name) famously sang on “Wild World”:
“… take good care Hope you make a lot of nice friends out there But just remember there’s a lot of bad and beware Beware.”
While he was talking about a girlfriend leaving him, the warning can just as well apply to GNSS users — especially those relying on GNSS for safety-of-life navigation and the maintenance of critical public infrastructure systems.
GNSS signals are relatively weak and they are susceptible to unintentional and intentional jamming that can make reception of the signals difficult or impossible. The jamming of radio signals to hinder reception is nothing new. It’s been used by those wanting to interfere with the use of the radio spectrum ever since radio became an important tool for communication and navigation in the early 20th century. Jamming has been used in hot wars to try to defeat military communication as well as in cold wars to try to prevent a perceived enemy from broadcasting to a particular country’s citizens. Notably, the shortwave radio broadcasts from Western countries were jammed by the former Soviet Union. And even today, broadcasts directed at China, Cuba and some other countries are regularly jammed.
GNSS is also being intentionally jammed on a regular basis in some parts of the world for various purposes including the protection of politicians and civilian infrastructure and to foil GNSS-guided munitions. But while directed at supposed threats, the jamming affects all GNSS receivers in a certain radius of the jammer. Such jamming activities are being reported in the popular press with an increasing frequency.
While GNSS jamming is receiving increased attention in our troubled world, even more pernicious is GNSS spoofing. Spoofing is the attempt to mimic GNSS signals to try to trick a receiver into tracking them and thereby compute a wrong position and/or time at the receiver. This can have disastrous consequences if not detected immediately and the use of GNSS deactivated.
So, how do you detect GNSS signal jamming and spoofing? We have discussed this issue in several columns over the years, but in this month’s column, a team of researchers from Stanford University and the University of Colorado describe how they are using relatively inexpensive equipment and sophisticated software and analyses to detect and warn of GNSS jamming and spoofing. Clearly, they are heeding Cat Stevens’ warning.
By Leila Taleghani, Fabian Rothmaier, Yu-Hsuan Chen, Sherman Lo, Todd Walter, Dennis Akos and Benon Granite Gattis
GNSS signals are extremely low power by the time they reach users on Earth and are easily overwhelmed by nearby terrestrial signals. Such signals can interfere with a user’s ability to receive the desired GNSS signals or, even worse, replace them with simulated signals that cause the user to obtain the wrong position or time estimate. Two major types of radio-frequency interference (RFI) threats have been identified: jamming and spoofing. Jamming results from emissions that do not mimic GNSS signals, but interfere with the receiver’s ability to acquire and track GNSS signals. Spoofing is the emission of GNSS-like signals that may be acquired and tracked in combination with, or instead of, the intended signals.
Both threats have been studied at length by researchers, and their presence around the globe has been reported even in the popular press. Some research has been done into the prevalence of spoofing. Even so, there is no well-developed understanding of how widespread these threats are.
Terrestrial interfering signals may be fairly weak and only effective in a limited area. Complex environments with buildings or terrain may further limit their effective area of influence and hinder the ability of external interference detection. To create a better understanding of the presence and characteristics of jamming and even spoofing, we are developing a low-cost RFI detector based on a commercial, off-the-shelf GNSS receiver: the u-blox F9. We are pairing this receiver with a Raspberry Pi computer and are developing custom software to monitor the receiver outputs and store data surrounding interesting events.
We are developing a toolset in MATLAB and C/C++ with the intention of processing and analyzing the u-blox data. The toolset includes functionality to decode selected u-blox messages that contain parameters of interest. These metrics include automatic gain control (AGC), carrier-to-noise-density ratio (C/N0) and spectral power. They also include raw pseudoranges from multiple constellations and internal u-blox interference metrics. With the volume of data that can be gathered from continuous monitoring, we have begun characterizing nominal performance and developing approaches to spoofing and jamming detection. The publicly available code can be accessed through our Git Repository at https://github.com/stanford-gps-lab/navsu.
With the raw pseudoranges and downloaded broadcast ephemeris data, we compute navigation solutions using different combinations of constellations and frequencies. When the individual and multi-constellation position solutions are compared to each other, discrepancies can be flagged and investigated for possible interference. We have begun characterizing nominal power metrics such as AGC and C/N0. With the quantity of data that we can get from the RFI monitor, we are working to characterize other receiver-specific parameters such as the u-blox continuous wave (CW) jamming indicator. We leverage data collected under nominal and jammed conditions to understand and identify a threshold for what can be considered interference.
Many different methods have been proposed for GNSS interference detection and mitigation with large-scale data at multiple locations. In this article, we present our data-selection process, our development of thresholds for determining interference, and results from three u-blox receivers set up at different locations in the United States to glean information about nominal (non-spoofed) conditions. We inform our thresholds and analysis tools using datasets from nominal conditions, and then compare their performance to a dataset containing RFI events from a government-sanctioned jamming and spoofing test. Our results display how we leverage simple and powerful metrics informed by a low-cost receiver to understand nominal noise environments and successfully identify jamming and spoofing events.
Data and Metrics
We collect and analyze a variety of data types and metrics to help identify and characterize jamming and spoofing occurrences. The receiver model we started with, u-blox ZED-F9P-02B, can monitor two different RF bands and many signals, including GPS L1C/A, L2C; GLONASS L1OF, L2OF; Galileo E1B/C, E5b; BeiDou B1I, B2I; QZSS L1C/A, L1S, L2C; and SBAS L1C/A. It has 184 channels, which can be configured to sweep through an array of signals to be monitored. We are also developing monitors based on the recently released ZED-F9T-10B, which is capable of L1 and L5 signal reception. TABLE 1 describes which version of the u-blox receivers each dataset comes from.
TABLE 1. Locations of u-blox monitor for nominal noise environment characterization and jam/spoof test. (Data: Authors)
L1 and L5 are the primary frequencies used for aviation, hence a monitor for these frequencies would be more useful for protecting aviation than the F9P, which is only capable of L1 and L2 reception. The available data includes raw measurements such as code and carrier phase, position estimates, power level estimates including C/N0, AGC and spectral power. It also has active CW interference detection. These metrics are all necessary for the consistency checks and power monitoring methods we summarize in this article. Consult our conference proceedings paper for details (see Acknowledgments). By examining all of these signals and measurements, we can observe changes in the RF environment and detect inconsistencies in the received signals.
Data Logging. The u-blox receiver logs messages in a specific format. The message types important to log are selected based on the desired data. Due to limited bandwidth, we prioritized messages that efficiently include all desired parameters for the interference detection methods we describe in this article. We have used both the u-blox F9P and the u-blox F9T.
To characterize nominal noise environments, u-blox receivers were set up at three locations: Stanford University, the University of Colorado (CU) in Boulder, and at the Colorado Springs airport. All measurements from satellites below an elevation angle of 5 degrees were ignored. The results from these locations are summarized below. Results from a jamming/spoofing test sanctioned by the U.S. Department of Homeland Security are presented and labeled with the acronym “GET-CI” (GPS Testing for Critical Infrastructures) in the subsequent discussion. Table 1 describes the parameters of the u-blox receiver at each location.
Positioning Metrics Development.The nominal error of the single- and multi-constellation position solutions is made by noting the difference between the computed position and the known truth. The inter-constellation consistency check is defined as the difference between the positions computed from two constellations, with no reference to a known truth position. To analyze the nominal differences in the north, east and down (NED) directions, we use the position covariance matrix, R, computed in the least-squares solver, to set a covariance-bound threshold. The covariance for each constellation is assumed independent. We present our results using this threshold in our results sections.
Our results in FIGURE 1 show that the Galileo position solution variance is higher than the dual-constellation and GPS-only solution. This is attributed in part to the fact that Galileo, while operational, has not filled out all planned satellite slots and therefore has fewer satellites and worse geometry than GPS.
FIGURE 1a. Map visualization of the comparison among position solutions computed using only GPS, only Galileo and a combined GPS plus Galileo dual-constellation solution at Colorado Springs. (Image: Authors)FIGURE 1b. Map visualization of the comparison among position solutions computed using only GPS, only Galileo and a combined GPS plus Galileo dual-constellation solution at CU Boulder. (Image: Authors)FIGURE 1c. Map visualization of the comparison among position solutions computed using only GPS, only Galileo and a combined GPS plus Galileo dual-constellation solution at Stanford. (Image: Authors)
Nominal Noise Results
Here are some of our positioning and power monitoring results under nominal reception conditions.
Positioning. Based on the methods described earlier, we present a selection of our results from the positioning consistency checks. We present several informative visualizations of the error between the computed position solution and the known truth of each u-blox receiver and use the covariance threshold to bound the raw error. The error for dual-constellation, single-constellation and inter-constellation consistency checks are all displayed and compared to one another. The pseudorange residuals and their accompanying chi-squared (χ2) statistic are also evaluated and compared for the GPS and Galileo single-constellation position solutions.
Positioning Consistency Comparison Maps. From the maps in Figure 1, we observe that Galileo has the highest error, followed by GPS, and then the dual-constellation solution. The map also serves as a method to spatially visualize the tails of the error distribution.
NED Time Histories. We compare the time history of the dual-constellation, GPS and Galileo position solution error to the three sigma (3σ) covariance bound computed at each epoch (see FIGURE 2). We also compare the GPS vs. Galileo inter-constellation difference to the 3σ covariance bound. The covariance bound is never crossed, indicating that 3σ threshold is conservative for both the error and the inter-constellation difference between GPS and Galileo.
FIGURE 2a. Dual-constellation north-east-down error vs. known truth, bounded by a 3σ threshold, at Colorado Springs. (Image: Authors)FIGURE 2b. Dual-constellation north-east-down error vs. known truth, bounded by a 3σ threshold, at CU Boulder. (Image: Authors)FIGURE 2c. Dual-constellation north-east-down error vs. known truth, bounded by a 3σ threshold, at Stanford. (Image: Authors)
Pseudorange Residuals and χ2 Statistic Threshold. Pseudorange residuals have a long history of being used as a consistency check between range measurements. As an example, the pseudorange residuals for the GPS position solutions are shown in FIGURE 3, and their corresponding χ2 statistic is shown in FIGURE 4.
FIGURE 3a. GPS pseudorange residuals at Colorado Springs. (Image: Authors)FIGURE 3b. GPS pseudorange residuals at CU Boulder. (Image: Authors)FIGURE 3c. GPS pseudorange residuals at Stanford. (Image: Authors)FIGURE 4a. GPS χ2 and probability of false alert (PFA) threshold for the nominal noise environments at Colorado Springs. (Image: Authors)FIGURE 4b. GPS χ2 and probability of false alert (PFA) threshold for the nominal noise environments at CU Boulder. (Image: Authors)FIGURE 4c. GPS χ2 and probability of false alert (PFA) threshold for the nominal noise environments at Stanford. (Image: Authors)
The χ2 statistic is computed using the finite pseudorange residuals at each epoch, where the degrees of freedom are n − 4, where n is the number of satellites used at that epoch and 4 is the number of variables solved for (x, y, z, and the receiver time offset) when using a single constellation. A p-value is computed using the cumulative distribution function (CDF) of the χ2 statistic, and indicates the probability that the χ2 statistic at each epoch would be greater than the observed value. The statistic is compared to a theoretical 10−9 probability of false alert (PFA) based on the theoretical χ2 and the actual degrees of freedom of each epoch. Very low values for the χ2 statistic, such as those obtained with Galileo, are attributed to regions where very few satellites are in view, thus decreasing the degrees of freedom. Any spikes in the pseudorange residuals are also reflected with a higher χ2 statistic and low p-value, though those residuals are de-weighted in the position solution and ultimately do not trigger the 10−9PFA threshold or the 3σ threshold, thus indicating that a 10−9PFA is a conservative threshold.
Power Monitoring. For each nominal location with a u-blox receiver, we analyze results from the power-monitoring metrics mentioned earlier. We also observe results from the internal u-blox jamming indicators in a region where a possible RFI event was observed.
For power monitoring, we analyze spectral power and programmable gain amplifier (PGA) results.
For the nominal noise environments, the spectral power, PGA and corresponding C/N0 results indicated no significant anomalies.
Threshold and Metric Validation Results
An examination of thresholds and other metrics are important for characterizing RFI.
GPS Testing for Critical Infrastructure. From a DHS-sanctioned RFI testing event, we identify five regions of interference or spoofing. To identify the interference, we use a combination of the power and positioning metrics as well as the thresholds we developed through the characterization of the nominal noise environments described in the previous sections of this article.
We use the thresholds and tests we’ve developed to identify regions of spoofing and RFI events (labeled C I1–C I5) in the GET-CI dataset. For ease of comparison, all regions are labeled on plots that display the full 5.5 hours of data collection. All details as to the truth location and time of the test have been removed. C I1 is identified through the power metrics. C I2–C I5 are identified as regions that the NED difference between GPS and Galileo clearly crossed the 3σ threshold in all three directions, as visualized in FIGURE 5.
FIGURE 5a. Map view of solutions using GPS, Galileo and GPS plus Galileo for the DHS-sanctioned RFI testing event (identifying coordinates and physical features removed). (Image: Authors)FIGURE 5b. Corresponding log-scale visualization of the GPS vs. Galileo position solution difference in the north-east-down directions. (Image: Authors)
From our pseudorange residuals, it appears as though the most significant interference events happened on the GPS constellation, as indicated by the high pseudorange residuals that fall into the C I2 and C I5 regions. Using the GPS χ2 statistic and p-value computations, we determined that the regions that crossed the 10−9 PFA threshold line are consistent with the regions of interference identified in Figure 5. The Galileo χ2 statistic, p-values and pseudorange residuals all show signs of possible interference. These regions are explored more in the power monitoring discussion below.
Since the GPS pseudorange residuals and χ2 statistic results show more signs of spoofing than the Galileo ones, we explore the Galileo-only position solution. Because the truth position is unknown, we take a point during the non-C I regions and define this as the “truth,” that is, a point in the position solution we believe has not been subject to spoofing. Any references to a truth position are from a position recognized as “truth” through post-processing rather than from a pre-determined and known location.
The p-values dip in each of the C I regions, but are lowest in regions C I5. Combined with the fact that the pseudorange residuals and NED error are the highest in C I5, we identify this as the region that likely experienced a significant spoofing event. We determined from an outlier at the beginning of the C I5 region (see Figure 5) that even the Galileo constellation is not immune to the spoofing in this scenario.
To further check the accuracy of our determination that GPS was spoofed, we evaluated the histograms of the Galileo error. With the biggest outlier in C I5 removed, we saw that the error appears relatively Gaussian, with some outliers and possible multi-modal behavior that were also seen in the nominal locations. The variance was higher than was observed at nominal locations, which could be attributed both to the presence of known RFI events, the fact that the nominal noise environment at the RFI event test has not been characterized (that is, it is possible there is a noisier nominal environment at this location), and that the “truth” position was not a known truth but obtained through post-processing of a dataset with increased RFI. Normalized error indicates that the error does not cross the 3σ threshold in any NED direction, further supporting the assertion that 3σ is a conservative threshold.
Important to note is that the major outlier around T+3.5 hours is visible in the NED plot (Figure 5), but the corresponding histograms do not contain that outlier. This indicates that the covariance also increases at that point. It dictates a need to monitor the covariance bound itself, as well as the positioning error. The NED time history plot and the raw error histograms serve this purpose, since it is clear that if we were to be only looking at the error normalized by 3σ, we would not have found significant evidence of the outlier, since the normalized error barely passes the 3σ threshold. This further supports our methods of combining multiple metrics, thresholds and visualizations rather than relying on a single metric to identify jamming and spoofing.
From the Galileo solution analysis, we increase our confidence that we have identified the regions with interference. We removed those areas and looked at the GPS vs. Galileo inter-constellation consistency difference. The normalized differences were now mostly within the 3σ threshold, and the raw error displayed some Gaussian behavior and is no longer on the order of the 105-meter error we were seeing in Figure 5. While these regions still have a higher error than nominal conditions and thus still display signs of interference, we are able to use our spoofing analysis to identify epochs in which we should not trust the GNSS. Using times outside those regions, we are able to figure out a reasonable truth position within 20 meters rather than 200 kilometers.
Positioning analysis using the inter-constellation consistency check is a powerful tool for determining the reliability of a position solution, even when the truth location is unknown. With the power metrics, we can further corroborate the positioning results, as well as find events indicating interference that the positioning metrics were unable to track.
FIGURE 6a. GPS pseudo range residuals for position solutions computed using only the GPS constellation. (Image: Authors)FIGURE 6b. Galileo pseudorange residuals for position solutions computed using only the Galileo constellation for the DHS-sanctioned RFI testing event. (Image: Authors)
Next Steps and Summary
Leveraging the raw data collected by u-blox receivers in multiple locations with different nominal noise environments, we have developed the toolsets to do inter- and intra-constellation consistency checks to monitor for jamming and spoofing. Many further observables usable for RFI detection are being recorded by the u-blox receivers. Several power monitoring metrics have been evaluated in a preliminary analysis. The next step is to further characterize metrics such as C/N0, AGC and u-blox internal jamming metrics under nominal conditions.
In summary, the tools we have developed so far show that the u-blox receiver will allow for many different consistency checks on a variety of parameters to be running simultaneously. It would be difficult for a spoofer to interfere with all the dimensions we have covered in our detector. Continuously monitoring a wide variety of parameters will increase the chance that we are able to detect interference, thus lowering the chance that a spoofer is able to evade detection.
Acknowledgments
We gratefully acknowledge the support of both the FAA Satellite Navigation Team and The Aerospace Corporation under their university partnership program. We especially wish to thank Steve Lewis of Aerospace for his support and guidance throughout the development of this project. This article is based on the paper “Low Cost RFI Monitor for Continuous Observation and Characterization of Localized Interference Sources” presented at ION ITM 2022, the 2022 International Technical Meeting of the Institute of Navigation, Jan. 25–27, 2022.
LEILA TALEGHANI recently graduated with her MS degree from Stanford University in aeronautics and astronautics and is now a navigation engineer at Trimble.
FABIAN ROTHMAIER is a navigation research and development engineer at Airbus Defence and Space in Munich, Germany, and a former a Ph.D. student at the Stanford GPS Laboratory.
YU-HSUAN CHEN is a research associate at the Stanford GPS Laboratory.
SHERMAN LO is a senior research engineer at the Stanford GPS Laboratory.
TODD WALTER is a research professor in the Department of Aeronautics and Astronautics at Stanford University.
DENNIS AKOS is a professor with the Aerospace Engineering Sciences Department at the University of Colorado, Boulder.
BENON GRANITE GATTIS is a laboratory assistant and undergraduate student in the Aerospace Engineering Sciences Department at the University of Colorado, Boulder.
“Seen & Heard” is a monthly feature of GPS World magazine, traveling the world to capture interesting and unusual news stories involving the GNSS/PNT industry.
Photo: IBM
Sailing new school
An autonomous ship designed to recreate the Mayflower’s historic journey across the Atlantic 400 years ago returned to the UK after developing a mechanical problem. IBM’s Mayflower Autonomous Ship (MAS) set sail on June 15 on its 3,500-mile journey from Plymouth in the UK to Massachusetts in the United States. The voyage is expected to take about three weeks, and includes collections of data on marine life and sampling for plastic waste. The 50-foot long, solar-powered trimaran is capable of speeds of up to 10 knots (18 km/h) and is being navigated by on-board artificial intelligence (AI) with information from six cameras and 50 sensors. Project leaders say the AI worked perfectly. The ship navigates with precision GNSS, inertial measurement units, radar, weather station, SATCOM and the automatic identification system.
Photo: Lt.j.g. Alexander Fairbanks/U.S. Navy
Sailing old school
U.S. Navy sailors aboard mine-countermeasures ship USS Patriot used celestial navigation to navigate an 1,100-mile voyage back to port on the western coast of Japan in July 2020. The voyage allowed the crew to improve their mariner skills as they used sextants to find their latitude and longitude and compasses to determine their heading. The exercise wasn’t entirely old school. The sailors entered the celestial measurements into a computer to pinpoint their position using the System to Estimate Latitude and Longitude Astronomically (STELLA). The combination of repeatedly inputting sextant measurements, the course and speed of the ship, and time into STELLA, provided an accurate fix of the ship’s position. For backup, Combat Information Center (CIC) watch standers followed the ship’s course with GPS. Training in celestial navigation returned to the Navy as a core competency in 2016, 17 years after the U.S. Naval Academy stopped requiring midshipmen to learn the technique.
Photo: Lt.j.g. Alexander Fairbanks/U.S. Navy
Linear clock shows sunrise, sunset
A creative technologist spent his COVID-19 downtime creating a device that uses a GNSS receiver to compute time relative to sunrise and sunset. “Since it derives time from the satellite signal, it never needs to be set, or ever adjusted for daylight saving time,” explains creator James Wilson on his webpage. The device uses satellite navigation and astronomy to show time as a progress bar measuring the percentage of the day elapsed since sunrise. A second indicator marks the time to sunset in blue.
Tracking Iran’s nuclear site
A team with Stanford University’s Center for International Security and Cooperation (CISAC) is keeping tabs on activity at Iran’s Natanz nuclear facility using BlackSky’s geospatial imagery and burst collection technology. BlackSky’s satellites provide intraday revisit capabilities, allowing CISAC’s research team to receive multiple images a day, throughout the day, rather than just one image collected at roughly the same time each day. The satellites also can capture a sequence of 20 images within minutes (burst collection) and splice them together to generate a moving sequence of activity. With BlackSky’s assistance, the research team was able to witness trucks emerging from the facility’s underground tunnels.
PUB QUIZ QUESTION:Who was Jean-Baptiste Alphonse Karr? He was a 19th-century French critic, journalist and novelist. He was at one time the editor of Le Figaro, the French daily newspaper. But he is most commonly known for the quotations from his works including the aphorism plus ça change, plus c’est la mêmechose commonly translated as “the more things change, the more they stay the same.” But what has this to do with GNSS you might ask?
One of the major sources of error in GNSS positioning is the ionosphere. As I have written in the Springer Handbook of GNSS, “[t]he ionosphere is that region of the Earth’s atmosphere in which ionizing radiation (principally from solar extreme ultraviolet (EUV) and x-ray emissions) cause electrons to exist in sufficient quantities to affect the propagation of radio waves. It extends from about 50 to 1000 km or more, above which we have the plasmasphere (also known as the protonosphere).” While GNSS technology has advanced over the years, Mother Nature stays pretty constant in the long term (global warming notwithstanding). And so the ionosphere is still a factor controlling the accuracy of single-frequency GNSS positioning as it has been for the past 40 years or more. The GPS navigation message includes values of the parameters of a simple ionospheric model known as the broadcast or Klobuchar model, named after its developer Jack Klobuchar. This model permits an estimate of the zenith ionospheric delay to be computed at a receiver’s location at a particular time of day and is driven by recent solar conditions as interpreted by the GPS control segment. The other GNSS use similar approaches in an attempt to reduce the positioning error of single-frequency positioning.
But the ionosphere is also an issue for dual- or multi-frequency positioning. Yes, the ionosphere is a dispersive medium so that 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 position determinations. And high-accuracy positioning, particularly with carrier-phase observations, is possible with a relatively short period of observations using relative or differential positioning. However, the technique of precise point positioning or PPP requires tens of minutes or more of continuous carrier-phase observations to approach an accuracy level of a few centimeters — the well-known convergence problem of PPP. Back in 2014, Simon Banville, one of my former Ph.D. students, demonstrated that ionospheric corrections could be used to reduce the convergence time of PPP to 10-cm horizontal accuracies from about 30 minutes to a few minutes. This approach has drawn the attention of the positioning industry, which is looking into several aspects of its use including questions about the level of accuracy that can be achieved depending on the state of the ionosphere, the latency of corrections supplied in real-time PPP, as well as the location and coverage of the network of stations required to determine the corrections.
In this month’s article, researchers at Stanford University and Hexagon Positioning Intelligence team up to help answer these questions.
By Todd Walter, Juan Blanch, Lance de Groot and Laura Norman
Figure 1. The three station locations. (Image: Authors)
Hexagon is investigating the utility of applying ionospheric corrections to decrease the overall convergence time of the precise point positioning (PPP) filter. Stanford University has conducted several analyses on the accuracy of these ionospheric corrections over the course of the past two years. Stanford has created MATLAB tools to process data from multiple days and locations as well as to investigate intervals with larger disagreements between the raw ionospheric measurements and the provided corrections. In addition, the tool can apply varying magnitudes of latency to examine its effect on correction accuracy and error bounding.
The current study was performed using data from April 12–May 9, 2020. These days exhibit typical ionospheric behavior for a solar minimum period. Hexagon provided 1-Hz correction data for three International GNSS Service (IGS) sites to evaluate its accuracy:
Stanford University (IGS 4-letter identifier: STFU), 1-Hz data
Vandenberg Space Force Base (VNDP) in southern California, measurements at every 15 seconds
Priddis, Alberta, Canada (PRDS), measurements every 30 seconds.
These sites were chosen because they tend to have high volumes of good quality data and are covered by the ionospheric correction service.
The provided corrections were specifically calculated for the three selected reference sites. They include corrections for both GPS and GLONASS satellites. We downloaded RINEX data for the three sites for all 28 days from IGS. FIGURE 1 shows the locations of the three sites.
PROCESSING METHODOLOGY
The residual errors were determined by comparing the measured ionosphere to the corrections for all satellites. These differences contain a common mode effect due to the changing inter-frequency biases that are part of the corrections. We formed double differences for all satellite pairs (within each constellation) that have measurements and corrections present at the same time. For each such pair, the continuous tracks are determined, and a constant offset for each continuous track is subtracted to obtain the final residual error. This process is illustrated in the flowchart shown in FIGURE 2 as well as in the following example.
Figure 2. The processing flowchart. (Image: Authors)
FIGURE 3 shows the raw ionospheric measurements for GPS satellites with pseudorandom noise codes (PRNs) 3 and 31. The blue plus signs use the L2-frequency minus L1-frequency code-measurement difference divided by (γ–1) where γ is the square of the ratio of the L1 and L2 carrier frequencies (𝑓12/𝑓22≅1.65). The green circles are the L1 code minus the L1 carrier divided by two, and the red dots are the L1 minus L2 carrier measurement difference divided by (γ–1). The different measurements are formed to help identify erroneous measurements that might corrupt the evaluation. Fortunately, the vast majority of the measurement data is well behaved. The traces shown in Figure 3 are all self-consistent and indicative of valid measurement data. The carrier-phase difference measurements are then used in the remainder of the processing, as these have the least amount of measurement noise.
Figure 3 Raw ionospheric measurements for GPS PRNs 03 (left) and 31 (right). (Image: Authors)
On the left side of FIGURE 4, we present the carrier phase ionospheric delay measurements of PRNs 3 and 31 alongside their corresponding corrections. The middle section of the figure shows the differences between measured and estimated correction values for each satellite. Notice that there are common mode drifts that span ~50 centimeters for this example. The right side of Figure 4 shows the difference between the two curves in the middle portion. This double difference is the difference between these two corrected satellites for the periods of time that they are simultaneously observed by each reference station. For each continuous double-difference track (that is, it has no detected bias break), we subtract the mean value (provided that the track spans at least four minutes). We examine this residual error in meters and the normalized residual error where we divide by the root-sum-square of the provided correction 1σ values. The process begins by comparing PRNs 1 and 2, then comparing PRNs 1 and 3 and so on until PRN 31 has been compared to PRN 32. We then repeat the same process for the GLONASS PRNs.
Figure 4. Ionospheric measurements and corrections for GPS PRNs 3 and 31 (left), differences between the measurements and corrections (middle) and double differences between the satellite pair (right). (Image: Authors)
These values are put into histograms, and the 95%, 99.9% and 99.999% quantiles are determined for each metric. These are calculated on a daily basis across all satellite pairs as well as aggregated over multiple days and stations. By comparing different quantile behaviors, we can see whether the full distributions are close to Gaussian (well behaved) or if they have outliers that create large tail values (poorly behaved). FIGURE 5 shows the histograms of data for the Stanford University station for the first day analyzed.
Figure 5. Histogram of double-differenced residual error at Stanford (left) and normalized error (right). (Image: Authors)
As can be seen, the data is very well behaved (the histograms are plotted on a semi-log scale to emphasize the performance of the tails). If the data strictly followed a Gaussian distribution, we would expect that about 95% of the values would fall within 2σ, 99.9% within 3.29σ, and 99.999% within 4.42σ where σ is the standard deviation of the distribution. Often, similar data would have much wider tails and include many outliers; however, this data has only slightly wider tails than would be expected for a Gaussian distribution. The double difference includes the noise from two sets of measurements and two different corrections. The values in the right side of Figure 5 should be divided by the square root of 2 to assess the magnitude of error affecting just one satellite. The values on the left histogram use the square root of the sum of the variances associated with the corrections, so no similar adjustment is required there.
FIGURE 6 shows the results of evaluating the Stanford station over all 28 days. Here the 95%, 99.9%, 99.999% and maximum values are shown for each individual day. The 95% values are fairly consistent over the 28-day period, but there is more variability in the tails of these distributions. The same data was analyzed for Vandenberg and for Priddis. The errors are largest for Vandenberg, which is situated near the edge of coverage for the corrections, with a maximum value above 35 centimeters. Priddis has the smallest errors with a maximum value below 20 centimeters, likely due to good network coverage and smaller ionospheric delays nearer to the Earth’s polar regions.
Figure 6. Ionospheric corrections accuracy quantiles for GPS and GLONASS at Stanford April 12–May 9, 2020. Ionospheric delay double-differenced residuals (left) and normalized values (right). (Image: Authors)
FIGURE 7 shows the aggregate histograms for all of the data across the three stations for the full 28 days. Note that the84-days reference in the figure headers refers to station-days (28 × 3). The accuracy of these corrections for the vast majority of the data remains quite impressive; the 95% value indicates a 1σ accuracy of ~1 centimeters (3 centimeters/(2√2)). The higher quantiles indicate slightly larger values due to the wider tails of the distribution with the 99.9% indicating a 1σ of ~1.7 centimeters (8 centimeters/(3.29√2)) and the 99.999% indicating a 1σ of ~2.9 centimeters (18 centimeters/(4.42√2)). The provided error bounds are conservative for most of the data. For 95% they are four times larger than necessary, and for 99.9% two times larger. However, by 99.999%, they are only 10% larger than strictly necessary and are insufficient for even smaller probabilities. This highlights the larger tail behavior and that the error bounds, which are currently only a function of elevation angle, should be updated to reflect more information about the transformation of the reference measurements into the estimate of ionospheric delay. Corrections near to the edge of coverage or that make use of fewer or less accurate measurements would be expected to have larger error bounds.
Figure 7. Ionospheric correction histograms for GPS and GLONASS at all three sites April 12–May 9, 2020. Ionospheric delay double-differenced residuals (left) and normalized values (right). (Image: Authors)
KLOBUCHAR CORRECTIONS
We are currently at a solar minimum period, and the ionospheric delays are both smaller and smoother than are typically experienced during other phases of the ionospheric solar cycle. To demonstrate that the corrections are accurately following the ionospheric behavior, and that the demonstrated accuracy is not merely a reflection of an extremely smooth ionosphere, we repeated the same process using the single-frequency global ionospheric model broadcast by the GPS satellites. This model is commonly referred to as the Klobuchar model after its developer. FIGURE 8 uses the same measurement data as Figure 7, but now the corrections are replaced with the Klobuchar model from each day and the error bound is set to a constant 1 meter 1σ value. As can be seen, the error magnitude is significantly increased to values of 50–60 centimeters 1σ. Thus, the provided corrections are accurately following the ionospheric behavior to within a few centimeters, and the actual variations in the ionosphere are more than an order of magnitude larger.
Figure 8. Klobuchar correction histograms for GPS and GLONASS at all three sites April 12–May 9, 2020. Ionospheric delay double-differenced residuals (left) and normalized values (right). (Image: Authors)
To examine the changes in ionospheric variability over the solar cycle, we examined four eastern stations during a significant ionospheric disturbance on Oct. 29, 2003. These stations are in Bermuda; Greenbelt, Maryland; Santiago de Cuba, Cuba; and Washington, D.C. They experienced very large ionospheric gradients during that event. FIGURE 9 shows similar data for the four stations from that day. Note that, again, the figure headers refer to station-days and the x-axis for each graph had to be expanded to include all the errors. Here the errors are between 2.8 and 7.4 meters 1σ.
Figure 9. Klobuchar correction histograms for GPS and GLONASS at four sites on Oct. 29, 2003. Ionospheric delay double-differenced residuals (left) and normalized values (right). (Image: Authors)Ionospheric delay double-differenced residuals (left) and normalized values (right).
EFFECTS OF LATENCY
We are able to configure the tool to implement different levels of latency for the corrections. This is configured as a minimum age for the corrections before they can be applied to the measurements. In all cases, the maximum age of the data beyond the initial latency value was set to 30 seconds. For example, when set to 60 seconds of latency, corrections had to be at least 60 seconds old to apply to the current epoch. If no correction existed that was between 60 and 90 seconds old, then the measurement would not be corrected.
FIGURES 10 and 11 show results for this latency study. The top row of each corresponds to 0, 30 and 60 seconds from left to right. There was surprisingly little effect for this range of latencies, most likely due to the benign ionosphere during the current solar minimum period. The accuracy quantiles increased only by less than half of a centimeter over this period. The normalized errors saw somewhat larger growth, but the sigma values are still appropriately bounding the errors. The bottom rows correspond to 120, 240 and 360 seconds of latency, from left to right. Here we begin to see more effect from latency; the residual error is doubled by 360 seconds. Between 240 and 360 seconds, the 99.999% normalized residual error exceeds 4.42, which corresponds to the expected Gaussian value. We can also see more outliers beyond 6σ.
Figure 10. Histograms showing the double-difference residual accuracy for differing amounts of latency. (From left) Top row: 0, 30 and 60 seconds. Bottom row: 120, 240 and 360 seconds.Figure 11. Histograms showing the normalized double-difference residual accuracy for differing amounts of latency. (From left) Top row: 0, 30 and 60 seconds. Bottom row: 120, 240 and 360 seconds.Bottom row: 120, 240 and 360 seconds. (Image: Authors)
We fit the quantiles vs. the latency times and found a strong quadratic dependence. TABLE 1 shows the resulting growth rates for the overall error and the 1σ values for each quantile. For the observed level of ionospheric activity, we recommend adding an increase to the 1σ confidence value as a function of the age of the correction. We recommend an added value of 4.5 × 10-5 centimeters/second2; thus, after 200 seconds, the 1σ value should be increased by 1.8 centimeters. However, for solar maximum periods and during significant ionospheric disturbances, we feel that this error bound will need to be increased, perhaps significantly. This error-bound term should be linked to the state of the ionosphere.
The correction accuracy is generally quite good, with 95% daily values almost always below 4 centimeters and below 6.25 centimeters overall. There are, however, outliers that affect the daily 99.9% and 99.999% percentiles, particularly at Vandenberg, which is toward the edge of the correction coverage region. The provided error bounds are mostly conservative, but there were still some occasional outliers. These error bounds should be more than simply functions of elevation angles. They should include real-time updates on the state of the ionosphere and quality of the correction based on the input measurements.
We evaluated the effects of latency and found that during this solar minimum period, fairly long latency times (up to 120 seconds) showed little impact on performance. It was not until more than 240 seconds that the sigma values stopped adequately bounding the tails and the overall accuracy degraded appreciably. We advocate including a quadratic term to the error bound to account for the age of the correction. During solar minimum time, we observed that this term can be quite small (4.5 × 10-5 centimeters/second2), but anticipate it needing to be significantly larger during times of ionospheric disturbance.
ACKNOWLEDGMENT
This article is based on the paper “Assessment of Ionospheric Correction Behavior for Use with Precise Point Positioning (PPP)” presented at the virtual 2021 International Technical Meeting of The Institute of Navigation, Jan. 25–28, 2021.
TODD WALTER is a research professor in the Department of Aeronautics and Astronautics at Stanford University. He received his Ph.D. in applied physics from Stanford in 1993.
JUAN BLANCH is a senior research engineer at Stanford University, where he works on integrity monitoring algorithms for radionavigation. He received a Ph.D. in aeronautics and astronautics from Stanford in 2003.
LANCE DE GROOT works for Hexagon Positioning Intelligence, Calgary, Alberta, Canada, in the Safety Critical Systems Group. He holds a B.Sc. and an M.Sc. in geomatics engineering from the University of Calgary.
LAURA NORMAN works for Hexagon Positioning Intelligence in the Safety Critical Systems Group. She obtained her B.Sc. and M.Sc. in geomatics engineering from the University of Calgary.
A team with Stanford University’s Center for International Security and Cooperation (CISAC) used BlackSky’s geospatial imagery and burst collection technology to track and monitor activity at a secretive Iranian nuclear facility in a new intelligence study. The study tracks and monitors activity at the Natanz nuclear facility in Iran.
Screenshot: Janes.com video/BlueSky
“The BlackSky/CISAC research team demonstrated the power of combining rapid revisit satellite imagery, human domain expertise and AI/ML (artificial intelligence/machine learning) techniques to identify and understand activity at Natanz, which was previously unknown to much of the world,” said Patrick O’Neil, chief data scientist at BlackSky. “Observations that provide real-time, activities-based insights have the potential to change the world.”
BlackSky’s high-revisit satellite imagery enabled researchers at Stanford University’s Center for International Security and Cooperation (CISAC) to monitor the pattern of life at the Natanz nuclear facility and gain a better understanding of activity and events at the site.
BlackSky’s satellites provide high, intraday revisit capabilities, allowing CISAC’s research team to receive multiple images a day, throughout the day, rather than just one image collected at roughly the same time each day.
BlackSky satellites are also capable of capturing a sequence of up to 20 images within a matter of minutes, known as a burst collection, and then splicing them together. Instead of a single picture, burst collections are geospatially normalized and joined together to generate a moving sequence of activity. With BlackSky’s assistance, the research team was able to witness trucks emerging from the facility’s underground tunnels.
Allison Puccioni, a renowned imagery analyst and BlackSky consultant, assembled a research team at Stanford University, with help from Rose Gottemoeller, diplomat, former NATO deputy secretary, and visiting professor at Stanford. The pair enlisted two principal research assistants in geospatial science to develop a sophisticated situational-intelligence program to monitor the Natanz nuclear facility.
Natanz is Iran’s primary facility for advanced uranium enrichment and is an active political and military location driven by concerns about the country’s nuclear operations.
By R. Eric Phelts, Kazuma Gunning, Juan Blanch and Todd Walter
Innovation Insights with Richard Langley
AS WE NOTED IN THE LAST INNOVATION COLUMN, integrity — at least from a safety viewpoint — is the most important characteristic of a navigation system. Yes, accuracy, availability and continuity are also required but, without integrity, the advertised accuracy of a system might become meaningless and perhaps misleading. While GPS and user receivers are highly reliable, we cannot presume that there will never be an erroneous signal transmitted by a GPS satellite that would result in a receiver outputting a hazardously misleading position solution. While “supervisory” systems such as satellite-based augmentation systems monitor GPS signals and can alert users about defective satellites within a very short period of time, it is advantageous for a user receiver to autonomously detect problematic satellites and quarantine them so that they do not perturb the position solution.
It is for this reason that receiver autonomous integrity monitoring (RAIM) techniques were developed. As we know, a receiver needs signals from a minimum of four satellites simultaneously to determine its 3D position and its clock offset. However, typically there are more than four satellites in view, and so multiple solutions using subsets of four satellites are possible. If five satellites are visible, then it is possible to determine that one of them is faulty, but not which one (geometry plays a role here). This is called fault detection (FD). And if six satellites are visible, the faulty satellite can be determined and then excluded from the position solution (fault detection and exclusion, or FDE). This is the basic principle of RAIM.
Advanced RAIM (ARAIM) extends RAIM to other constellations beyond GPS. ARAIM enables the use of the newer GNSS constellations to provide better levels of performance than RAIM with GPS alone. It also uses dual-frequency measurements for enhanced vertical positioning reliability.
Central to positioning techniques providing a safety-of-life service is the notion that the uncertainty of a provided position must be conservatively estimated and provide for both nominal uncertainty and the uncertainty of a faulted solution such as that detected using RAIM. These conservative estimates are known as the horizontal and vertical protection levels. The horizontal protection level (HPL) is the radius of a circle in the horizontal plane with its center at the true position, which describes the region that is assured to contain or bound the provided horizontal position to a very high probability. The vertical protection level is half the length of a segment in the vertical direction with its center at the true position, which describes the region that is assured to contain or bound the provided vertical position to a very high probability. The probability levels are typically taken to be 99.9999998 and 99.99999% for HPL and VPL, respectively.
The usual approach for RAIM and ARAIM is to use the so-called “snapshot” approach, where measurements are assumed to be uncorrelated epoch to epoch. In this month’s column, a team of authors from Stanford University discusses a superior approach for ARAIM using the technique of precise point positioning.
Advanced Receiver Autonomous Integrity Monitoring (ARAIM) is implemented using solution separation in positioning and navigation software. Solution separation computations presume one or more GNSS satellites may be faulty, and they iteratively compute multiple position solutions comprised of subsets of the n satellites in view (n, n-1, n-2, and so on) to ensure that at least one of the solutions is fault-free. Using assumptions on the nominal and faulted uncertainty of the solutions, the software can compute conservative horizontal and vertical protection levels (PLs) by bounding the uncertainty from all the solutions. This assures (to a targeted level of probability) that the user position is contained within these limits.
Traditional solution separation techniques generally operate as a “snapshot.” The basic measurements are dual-frequency, carrier-smoothed pseudorange (code), and errors are generally assumed to be uncorrelated from epoch to epoch. This procedure requires that errors at each time step are conservatively bounded with large uncertainties (sigmas) designed to protect the user against the worst-case error. These assumptions minimize the complexity and computational cost of the solution by providing a robust, provably safe bound. However, the PLs computed are relatively large. In addition, they can change suddenly from one epoch to the next due to changes in available satellites or platform dynamics. This can make meeting performance goals (such as continuity) for aircraft approaches more challenging.
Solution separation procedures using techniques based on precise point positioning (PPP) implement an extended Kalman filter (EKF) to filter measurements over time. In this case, the basic measurements are dual-frequency code and carrier phase, and errors are assumed to have some correlation between each time step to the next. Accordingly, these techniques leverage higher quality measurements (that is, carrier-phase-based as opposed to code-based) to smooth and reduce large sigmas and to estimate (and calibrate) errors over time. The complexity associated with defining and characterizing the decorrelation models for the errors, so that the nominal covariance produced by the EKF conservatively describes the actual error, is significant. Also, the computational cost of estimating the error states may be substantially higher than with the traditional snapshot approach. However, the computed protection levels provide integrity and are often significantly smaller. In addition, the filtering makes them more robust to platform dynamics, which makes them well-suited for aircraft in flight.
Flight Data: Outages and Cycle Slips. ARAIM performance may be significantly affected by aircraft dynamics. Specifically, banking can induce satellite outages and cycle slips. Outages weaken the constellation geometry and can cause sudden changes in the protection level. Frequent cycle slips prevent code measurements from being smoothed, potentially inflating protection levels of carrier-phase-smoothed code measurements for extended periods of time.
When the outages and cycle slips are computed as a rate, a trend can be seen. Both increase notably as the relative elevation angle to the satellites decrease. FIGURE 1 shows an example of outages as a function of the apparent elevation angle of the satellites (relative to the aircraft). Cycle slips on GPS L1-L5 and Galileo El-E5a are plotted in FIGURES 2 (a) and (b), respectively.
FIGURE 1. Outages as a function of body frame or apparent elevation angle during aircraft banking. (Image: Authors)FIGURE 2a. Cycle-slip rate (per satellite-second) for GPS L1-L5. (Image: Authors)FIGURE 2b. Cycle-slip rate (per satellite-second) for E1-E5a. (Image: Authors)
For this article, we have used the flight data from one of our earlier papers on the effect of aircraft banking on ARAIM performance (see Further Reading). With this data, we show that significant advantages of PPP can be retained even during aircraft maneuvers when outages and cycle slips threaten ARAIM continuity and availability the most.
MODEL ASSUMPTIONS
The traditional snapshot solution separation approach is well-established and was implemented according to the standards established by a working group operating under the U.S.-European Union Agreement on GPS-Galileo Cooperation, which has been extended to all constellations (see Further Reading). For this article, we limited the constellations to GPS and Galileo, and the prior probabilities assumed for satellite and constellation faults were as follows:
Psat = 10-5, Pconst,GPS = 10-8 and Pconst,GAL = 10-4
We implemented the PPP algorithm with solution separation using an EKF using dual-frequency code and carrier-phase measurements (from GPS and Galileo) with estimated parameters comprising the receiver position and velocity, clock biases for each constellation in use, a residual tropospheric delay, carrier-phase float ambiguities for each tracked carrier, multipath error, receiver differential code bias, and broadcast orbit and clock error. Modeled (not estimated) effects include solid Earth tide modeling, ocean loading, an initial tropospheric delay and relativistic effects. Many of the details of the implementation can be found in our paper “Design and Evaluation of Integrity Algorithms for PPP in Kinematic Applications” (see Further Reading).
PPP techniques typically utilize precise ephemeris information obtained from a global network of ground reference stations such as those operating in the network coordinated by the International GNSS Service. Snapshot solution separation techniques, however, use only ephemeris information broadcast from the satellites themselves. For a proper comparison of the protection levels computed by each technique, the PPP filter was constrained to use this broadcast information.
The model we have applied is mostly typical of a traditional PPP implementation with one significant exception — the state tracking the error contribution of the broadcast orbit and clock on each line-of-sight signal. The error contributed by the broadcast orbit and clock is handled by the filter leveraging a characterization of the rate of change of the error, then including it as an estimation state for each line of sight and only adding enough process noise to capture the slowly changing error. We have previously characterized the rate of change of the error in the broadcast orbit and clock and process noise (for GPS). Complete tables of initial state uncertainties and additional settings for process and measurement noise were provided in our earlier work (see Further Reading).
RESULTS
Flight data collected over a period of approximately one year was used to evaluate ARAIM performance through momentary outages and cycle slips due to aircraft dynamics. A multi-constellation, multi-frequency receiver tracked GPS (L1 C/A and L5) and Galileo (E1 and E5a) satellites. This receiver is installed in a Global 5000 jet owned and operated by the FAA William J. Hughes Technical Center. It records and stores GNSS measurements whenever flights are taken. The data we used for this article included data recorded over approximately 35 flights from September 2017 to April 2018.
FIGURE 3 shows the trajectory and altitude information corresponding to a single flight (Flight #6) taken on Sept. 20, 2017, and FIGURE 4 compares the corresponding horizontal and vertical protection levels computed using snapshot and “broadcast” PPP techniques. For an additional reference, we also computed protection levels using PPP with precise orbits and clocks (we call this precise PPP despite the terminology redundancy) and plotted these in Figure 4, too.
FIGURE 3b. Altitude information for Flight #6 (Sept. 20, 2017). (Image: Authors)FIGURE 4a. Horizontal protection levels for Flight #6 (Sept. 20, 2017); red circles indicate a satellite being dropped or reentering the solution. (Image: Authors)FIGURE 4b. Vertical protection levels for Flight #6 (Sept. 20, 2017); red circles indicate a satellite being dropped or reentering the solution. (Image: Authors)
Several things are readily apparent from these comparisons. First, after the initial time required for convergence, there is a substantial reduction in the PLs using the broadcast-PPP-based approach. The precise PPP PLs, as expected, produce the largest reduction, but use additional information not available to the snapshot method. In addition, the snapshot solution separation PLs vary significantly due to cycle slips and momentary satellite outages. FIGURE 5 shows the number of satellites tracked by the receiver during this flight; red circles plotted on the snapshot protection-level line indicate when satellites are coming into and out of view. Despite numerous abrupt changes in number of measurements and measurement quality, the EKF of the PPP techniques produces PLs that are relatively smooth and continuous.
FIGURE 5. Number of satellites tracked for Flight #6 (Sept. 20, 2017). (Image: Authors)
FIGURE 6 shows the trajectory and altitude information corresponding to Flight #4 taken on Sept. 15, 2017.
FIGURE 6a. Flight path for Flight #4 (Sept. 20, 2017). (Image: Authors)FIGURE 6b. Altitude information for Flight #4 (Sept. 20, 2017). (Image: Authors)
FIGURE 7 compares the horizontal and vertical PLs for snapshot solution separation and the PPP-based techniques.
FIGURE 7. Horizontal protection levels for Flight #4 (Sept. 15, 2017); red circles indicate a satellite being dropped or reentering the solution. (Image: Authors)FIGURE 7b. Vertical protection levels for Flight #4 (Sept. 15, 2017); red circles indicate a satellite being dropped or reentering the solution.
As in the case shown in Figure 4, the PLs in Figure 7 reveal a substantial reduction in the mean PLs computed using the PPP-based approach. And the snapshot solution separation approach displays even more variations due to momentary satellite outages. Some of the cycle slips affected enough satellites to introduce brief spikes in the PPP solution as well. These reconverge quickly, but they suggest that some tuning of the EKF can still be done to mitigate these interruptions. Still, the filtered approach produces PLs that are more robust to the outages and are substantially smaller than with the snapshot method.
FIGURE 8 compares the horizontal and vertical PLs computed using snapshot solution separation and PPP techniques for Flight #20 — where the airplane remained stationary on the runway. In the absence of flight dynamics, the levels for all the approaches were relatively smooth. However, a few discontinuities can still be observed for the snapshot case. Also note, in the case of the broadcast PPP, the convergence time is noticeably longer. This is likely because the integer ambiguity resolution in the solution took longer to converge without platform motion.
FIGURE 8a. Horizonta protection levels for a stationary aircraft (Flight #20, Dec. 4, 2017); red circles indicate a satellite being dropped or reentering the solution. (Image: Authors)FIGURE 8b. Vertical protection levels for a stationary aircraft (Flight #20, Dec. 4, 2017); red circles indicate a satellite being dropped or reentering the solution. (Image: Authors)
The mean horizontal and vertical PLs for both techniques are summarized in FIGURE 9. (There were issues with the data from Flight #14 and it was not processed.) The PPP approach consistently produces protection levels anywhere from 30 to 75% smaller than those computed using the snapshot approach. The mean PLs for the PPP techniques were always below those computed with the snapshot method.
FIGURE 9a. Comparison of mean horizontal PLs for “snapshot” vs. a PPP-based technique. (Image: Authors)FIGURE 9b. Comparison of mean vertical PLs for “snapshot” vs. a PPP-based technique. (Image: Authors)
CONCLUSIONS
Data from 35 flights was used to compare ARAIM protection levels computed by the traditional “snapshot” solution separation versus a PPP-based approach during both in-flight and several static scenarios. We observed that the filtering of PPP methods yields mean PLs approximately 30 to 75% of those computed using traditional methods in all cases. This improvement can be attributed to exploiting — through filtering and estimation — carrier-phase-based measurements and a time-correlation of the errors. In addition, the EKF employed by the PPP approach demonstrated improved robustness to outages and cycle slips induced by aircraft dynamics. Despite the increased complexity and computational cost, we believe that PPP approaches hold promise for significantly improving ARAIM performance.
ACKNOWLEDGMENT
This article is based on the paper “Evaluating the Application of PPP Techniques to ARAIM Using Flight Data” presented at ION ITM 2020, the 2020 International Technical Meeting of The Institute of Navigation, San Diego, California, Jan. 21–25, 2020.
MANUFACTURER
The flight data was recorded using a Trimble BX935-INS receiver fed by an Antcom Avionic II GNSS antenna.
R. ERIC PHELTS is a research associate in the Department of Aeronautics and Astronautics at Stanford University, California. He received a Ph.D. in mechanical engineering from Stanford University in 2001. His research involves signal deformation monitoring for SBAS and flight-data analyses for ARAIM.
KAZUMA (KAZ) GUNNING is a Ph.D. candidate in the GPS Laboratory at Stanford University working under the guidance of Todd Walter. He is also the navigation algorithms and architecture lead at Xona Space Systems in San Mateo, California. His research interests are in precise point positioning and integrity.
JUAN BLANCH is a senior research engineer at Stanford University, where he works on integrity monitoring algorithms for radionavigation. He received a Ph.D. in aeronautics and astronautics from Stanford University in 2003. He has received The Institute of Navigation (ION) Parkinson and Early Achievement awards.
TODD WALTER is a research professor in the Department of Aeronautics and Astronautics at Stanford University. He received his Ph.D. in applied physics from Stanford University in 1993. His research focuses on implementing high-integrity air navigation systems. He has received the ION Thurlow and Johannes Kepler awards. Walter is also a Fellow of the ION and has served as its president.
“A Baseline RAIM Scheme and a Note on the Equivalence of Three RAIM Methods” by R.G. Brown in Navigation, Vol. 39, No. 3, Fall 1992, pp. 301–316.
Advanced Receiver Autonomous Integrity Monitoring
“SBAS Corrections for PPP Integrity with Solution Separation” by K. Gunning, J. Blanch and T. in Proceedings of ITM 2019, the 2019 International Technical Meeting of The Institute of Navigation, Reston, Virginia, Jan. 28–31, 2019, pp. 707–719.
“Design and Evaluation of Integrity Algorithms for PPP in Kinematic Applications” by K. Gunning, J. Blanch, T. Walter, L. de Groot and L. Norman in Proceedings of ION GNSS+ 2018, the 31st International Technical Meeting of the Satellite Division of The Institute of Navigation, Miami, Florida, Sept. 24–28, 2018, pp. 1910–1939.
“Effect of Aircraft Banking on ARAIM Performance” by R.E. Phelts, J. Blanch, K. Gunning, T. Walter and P. Enge in Proceedings of ION GNSS+ 2018, the 31st International Technical Meeting of the Satellite Division of The Institute of Navigation, Miami, Florida, Sept. 24–28, 2018, pp. 2632–2641.
“Precise Point Positioning” by J. Kouba, F. Lahaye and P. Tétreault, Chapter 25 in Springer Handbook of Global Navigation Satellite Systems, edited by P.J.G. Teunissen and O. Montenbruck, published by Springer International Publishing AG, Cham, Switzerland, 2017.
The Railway High-Integrity Navigation Overlay System (RHINOS) work program explores candidate concepts for provision of the high integrity required for train positioning within a train-control system. GPS and Galileo plus satellite-based augmentation systems constitute the global reference infrastructure. In addition, local augmentation elements, advanced receiver autonomous integrity monitoring, and other trainboard sensors on can mitigate hazards due to environmental effects governing rail applications. RHINOS will be developed in cooperation with Stanford University researchers experienced in high-integrity aviation applications. The goal is moving beyond regional applications towards a global solution in the fast-growing train signalling market. RHINOS is financed by the European GNSS Agency and led by the Italian consortium RadioLabs, with partners Stanford University, Sogei, German Aerospace Center, University of Nottingham and University of Pardubice.
