It’s been a tough couple of weeks for SBAS (Satellite-Based Augmentation System), namely the USA’s WAAS program and India’s GAGAN program. WAAS and GAGAN have taken big hits recently that threaten the integrity of the programs. Both events were totally unexpected and are causing disruptions of GPS correction services.
Let’s Start with WAAS
First of all, consider the following infrastructure graphic describing WAAS.
WAAS Infrastructure (note: GEO satellites positioning not geographically correct in graphic)
At the moment, WAAS uses two geostationary satellites (referred to as GEOs) to broadcast GPS corrections throughout the WAAS service area, which covers the U.S., Mexico, and most of Canada. The user’s GPS receiver must be able to “see” at least one of the WAAS GEOs in order to receive the GPS corrections. Currently, one WAAS GEO (PRN 135) is located at 133°W longitude and one (PRN 138) is located at 107°W longitude. They are positioned, for the most part, to provide “dual coverage” in case one fails as the following graphic illustrates. The solid line represents the visibility above the horizon of PRN 138 (107°W). The dashed line represents the visibility above the horizon of PRN 135 (133°W). In New York, for example, PRN 138 is visible at 30°+ above the horizon while PRN 135 is visible at ~15° above the horizon.
The Federal Aviation Administration (FAA) is the WAAS steward. WAAS (and SBAS) was designed for aviation use and paid for by the FAA. The fact that surveying and mapping users benefit from WAAS is a by-product. The FAA owns and controls most of the WAAS infrastructure, such as the 38 WAAS reference stations located throughout the U.S., Canada, and Mexico. About the only thing they don’t own are the WAAS GEO satellites, and this has been the source of most of the problems with WAAS in the past few years.
Lease vs. Buy
It would be prohibitively expensive for the FAA to own GEO satellites that were exclusively used by WAAS. Instead, the agency leases bandwidth from owners of commercial satellites. These are the same commercial satellite owners who lease bandwidth to media (e.g., television) customers. It’s not unlike a utility pole you see along the road with many different wires and devices attached to the pole from different companies who pay to lease space on the pole, except it’s a very expensive pole orbiting in space.
If you’ve been using WAAS for a number of years, you’ll remember back in 2006 there was a hiccup with the WAAS GEOs at that time. The FAA was leasing space on two Inmarsat satellites (AOR-W and POR). They began transitioning to the current WAAS GEOs but before the transition was complete, Inmarsat began moving AOR-W. This was a headache for some WAAS users and really showed the vulnerability of WAAS.
Losing Control
The vulnerability reared its ugly head again last week when one of the commercial satellite operators (Intelsat) that the FAA leases space from announced it had lost contact with its Galaxy 15 (G-15) satellite, which is the GEO that WAAS PRN 135 is broadcast from. Intelsat reported it had lost the ability to send commands to G-15. Without the ability to control the satellite, it will slowly drift out of orbit until it becomes unusable. The FAA estimates this will occur in one to three weeks.
Solutions?
Intelsat’s answer was to bring in an older generation backup satellite (G-12), which was in a backup orbit at 122°W. It arrived at 133°W around April 14. Intelsat said that G-12 has virtually an identical C-band package as the G-15 and they could transfer C-band customers to the G-12. The problem is that there is no L-band package (which WAAS needs) on the G-12, so the FAA was out of luck.
Since Intelsat’s G-12 backup won’t help WAAS, the FAA is looking at other alternatives:
Contract with Inmarsat to bring back POR (178°E). The FAA says that will take 12-18 months. Personally, I don’t think it’s a good solution. It’s too far to the east to help much at all. Its coverage footprint barely covers the western U.S.
Speed up the testing on the new PRN 133 (98°W) and bring it into service more quickly than the original December 2010 schedule. The FAA says it can accelerate testing by one to two months. This is good and I see the benefit, but it still doesn’t help Alaskan users.
The replacement backup satellite being moved to 122°W to backup G-12 may be a solution. It will be a few weeks before it is known what is possible. That would be the best scenario from a coverage footprint standpoint. The question is how long it would take to bring it into service.
On another note, the FAA stated that with the money they are saving with G-15 going out of service, they will be able to accelerate the acquisition of another WAAS GEO. I have no doubt that this has put a new level of fear into the FAA folks, and they have to realize that they can’t be running thin on WAAS GEOs. If you weren’t aware, the future of aviation navigation is based on GPS, WAAS, LAAS, etc. These sorts of hiccups would be an absolute nightmare if the National Airspace System (NAS) was already dependent on GPS.
GAGAN
GAGAN (GPS-Aided Geo Augmentation Navigation) is India’s SBAS. It has been under development for many years and is quite far along in development. It is funded through implementation by the Airport Authority of India with the Indian Space Research Organization. In 2008, GAGAN was broadcasting a test signal from an Inmarsat GEO with reasonable results.
India’s intent was to launch its new GSAT-4 communication satellite with part of its purpose being a GAGAN GEO satellite. GSAT-4 was to be India’s first rocket with an Indian-designed and built cryogenic-fueled third stage. Apparently it is a very difficult technology to master as it reportedly took India 16 years to develop.
Last week, after much anticipation, the rocket with GSAT-4 onboard was brought to the launch pad. Liftoff was reportedly flawless. At 8:25 minutes into flight, the rocket failed and the entire rocket, GSAT-4 and all, ended up splashing into the Bay of Bengal. It’s a crushing blow to India’s GAGAN SBAS program, which has suffered a number of delays.
P.S. Veeraraghavan, director of the Vikram Sarabhai Space Centre in Thiruvananthapuram, said “Our target is to fly a GSLV with our indigenous cryogenic engine within one year. But it will be tough.”
Following is a video report from an India news organization describing the event:
Webinar Tomorrow
If you don’t receive this too late (or you can access the archive if you do miss it), you might want to catch my 60-minute webinar “GPS, GLONASS and SBAS Constellation Updates.” It’s free and full of the latest information. I’ll also be answering a number of questions from people who registered. I hope to see you there!
After reviewing current performance of WAAS, EGNOS, and MSAS, the authors present expected future performance, including the benefits of GPS L5. They evaluate the impact of the Indian GAGAN and Russian SDCM systems on global coverage and examine southward expansions for the original three SBASs. Finally, a look at the impact of a second constellation of navigation satellites and the performance for a user taking advantage of two core constellations.
By Todd Walter, Juan Blanch, and Per Enge, Stanford University
The Wide Area Augmentation System (WAAS) monitors GPS and provides both differential corrections to improve accuracy and associated confidence bounds to assure integrity. The first satellite-based augmentation system (SBAS), it was commissioned for service in 2003. Japan’s MTSAT-based Satellite Augmentation System (MSAS) was commissioned in 2007, and the European Geostationary Navigation Overlay Service (EGNOS) was declared operational in 2009, with safety-of-life service commissioning expected in mid-2010. Two other SBASs are in the developmental stage: India’s GPS Aided Geo Augmented Navigation (GAGAN) and Russia’s System for Differential Corrections and Monitoring (SDCM) have fielded equipment and plan to become operational in the next few years.
Coming improvements will expand SBAS coverage areas and strengthen their performance. In the near term, these include more monitoring stations and algorithmic enhancements, with incorporation of a second civil signal in a protected aeronautical band and new GNSS constellations in the long term.
An SBAS utilizes a network of precisely surveyed reference receivers, located throughout its coverage region. The information gathered from these reference stations monitors the GNSS satellites and their propagation environment in real time. Availability of SBAS service is a function of two quantities: the arrangement of the pseudorange measurements used to determine the user’s position, referred to as geometry; and the quality of each individual measurement, referred to as the confidence bound. Although very small confidence bounds can make up for poor geometries, and strong geometries can overcome large confidence bounds, both values are generally required to be good to obtain high availability.
Geometry is determined purely by the locations of the ranging satellites relative to the user. Currently the basic geometry is provided by the GPS constellation. Historically it has exceeded commitments, and there are currently 29 healthy satellites in orbit when only 21 are nominally guaranteed. However, as satellites are taken off-line in critical orbital slots, the quality of the geometry can degrade significantly. There could be short duration losses of service daily at some locations. Since the goal is to provide service more than 99.9 percent of the time, these outages can have a dramatic impact. WAAS currently mitigates this concern by adding geostationary satellites with a ranging function virtually identical to the GPS satellites. These satellites are always in view and improve the overall geometry, although they do not eliminate the problem completely.
The confidence bounds relate to the expected error sources on the range measurements. Currently three error sources are corrected via broadcast to the user: satellite clock error, satellite ephemeris error, and delay error due to propagation through the ionosphere. These error sources are described by two confidence bound terms: the user differential range error (UDRE) for the satellite errors, and the grid ionospheric vertical error (GIVE) for the ionospheric errors.
For single-frequency SBAS, this last error source is the most significant. Users may sample the ionosphere anywhere in the service volume, but the SBAS only has measurements from its reference station locations. Thus, there is always the possibility of undetected ionospheric disturbances. This leads to larger confidence bounding terms and lower availability.
The combination of geometry and confidence bounds yields the protection levels (PL). PLs are the real-time confidence bound on the user’s position error. To match aviation requirements these are broken into a vertical protection level (VPL) and a horizontal protection level (HPL). Each SBAS guarantees that the user’s actual position error will be smaller than these values 99.99999 percent of the time. The PLs are calculated in real-time using stored and broadcast information. They must be compared to the maximum allowed value for a desired operation. The upper bounds are called alert limits (AL) and they are fixed numbers whose values depend on the operation.
In this article we are interested in the localizer performance with vertical guidance (LPV)-200 approach with a VAL of 35 meters and HAL of 40 meters. Currently, LPV aviation approaches can only be accomplished with a WAAS GPS receiver. Performance of an LPV approach allows minimums as low as 200 feet above ground level before a missed approach must be executed. As of January 2010, there were 1,930 published WAAS LPVs, with plans to add 300 per year in the United States.
Because GPS and SBAS generally perform better at horizontal positioning than vertical, the requirement that the VPL be below the VAL is nearly always the limiting constraint for these operations.
Methodology
To determine the global availability and the effect of potential improvements, we used our Matlab Algorithm Availability Simulation Tool (MAAST). This tool uses almanac data to calculate the position of the satellites for each specified epoch. The almanac chosen for this study corresponds to the GPS almanac broadcast on April 8, 2009, when there were 30 healthy satellites. However, PRNs 25 and 32 were removed to simulate a condition with 28 healthy satellites. MAAST also implements the WAAS integrity algorithms to calculate the corresponding UDRE and GIVE values. Finally, it uses these values to implement the airborne algorithms specified in the minimum operational performance standards (MOPS) for SBAS. The MOPS specifies user algorithms for determining the protection levels. For these simulations, the VPL and HPL are calculated about every 5 minutes and every two and a half degrees across the globe.
MAAST does a good job of predicting WAAS behavior. It is less accurate when predicting other systems’ performance. EGNOS has developed its own monitoring receivers and integrity algorithms and has different criteria for assigning a satellite a particular UDRE value and assigning each ionospheric grid point’s (IGP’s) GIVE value. Nevertheless, both systems are designed to meet ICAO requirements for integrity, and their performance should be somewhat similar. In observing EGNOS coverage plots and comparing them to MAAST predictions, we do see differences. However, the size of the coverage region and approximate boundaries are reasonably close and provide an idea of performance if not an exact map.
The MSAS algorithms are based upon the same algorithms used in earlier versions of WAAS. Therefore, MAAST should be slightly more accurate in modeling its performance. GAGAN uses the same prime contractor as WAAS and therefore similar algorithms may be expected. Less is known about the intended SDCM algorithms and therefore the modeling of this system faces the largest uncertainty. Again, the MAAST predictions should be viewed as indicative rather than precise. Individual availability maps will not be completely correct, but relative performance improvements should be properly indicated.
Current Systems Status
Currently WAAS is in its full LPV-200 performance (FLP) phase. It consists of 20 WAAS reference stations (WRS) in the conterminous United States (CONUS), in addition to seven in Alaska, one in Hawaii, one in Puerto Rico, four in Canada, and five in Mexico for a total of 38. The station locations are shown as blue circles in Figure 1. There are three WAAS master stations (WMS) and two geostationary satellites (GEOs). The GEOs are the Intelsat Galaxy XV satellite
at 1338 W and the Telesat ANIK F1R satellite at 1078 W.
FIGURE 1. Existing SBAS reference networks, consisting of 38 reference stations for WAAS, 34 for EGNOS, and 8 for MSAS.FIGURE 2. Simulation results from MAAST for availability of LPV-200 provided by current systems.
As can be seen in Figure 2, availability of LPV-200 service is very high for most of North America. In general, this performance meets the goals for the system. However, in some regions performance is lower than the 99 percent minimum target. The West Coast, Alaska, and Southern Mexico all suffer from reduced availability.
MSAS is in its initial operating phase. It consists of six ground monitoring stations (GMSs) on the Japanese Islands, one in Australia, and one in Hawaii (magenta triangles in Figure 1). There are two master control stations (MCSs) and two Multifunction Transport Satellite (MTSAT) geostationary satellites at 1408 E and 1458 E.
Because of the limited network size, the GEO UDREs for MSAS are set to 50 meters and therefore do not benefit vertical guidance. Further, the limited ionospheric observations offer little availability of LPV-200 service as can be seen in Figure 2. As a result, vertically guided operations have not yet been authorized based upon MSAS. The Japanese Civil Aviation Bureau (JCAB) has studied performance improvements that could allow it to provide LPV-200 operations. Until then, MSAS provides only lateral navigation.
EGNOS is also in its initial operations phase. It consists of 28 ranging and integrity monitoring stations (RIMS) in Europe, one in Turkey, three in Africa, one in North America, and one in South America (green squares in Figure 1). There are four master control centers (MCCs) and two GEOs, the INMARSAT Atlantic Ocean Region-East (AOR-E) satellite at 15.58 W and the ARTEMIS satellite at 21.58 E.
For a variety of reasons, EGNOS has chosen to implement its GEO satellites without a ranging capability. Thus, for our simulations we have set them as data-links only and do not model a ranging capability. EGNOS also currently implements Message Type 27 (MT-27) rather than Message Type 28 (MT-28) as do WAAS and MSAS. MT-27 restricts the use of low UDRE values to a box centered on the European region. Its borders can be discerned in Figure 2. Currently it has little impact on LPV-200 service, but if EGNOS is to expand its coverage, it may become a limiting factor. Availability of LPV-200 service is very high for most of Europe. However, there is a desire to expand coverage to more reliably cover Iceland, Scandinavia, Eastern Europe, and the Mediterranean and South Atlantic regions.
Near-Term Improvements
EGNOS is fielding additional reference stations in the Canary Islands, Northern Africa, and the Middle East. In the longer term, MT-28 is being considered as a replacement for MT-27. In our modeling we added seven new RIMS, shown in Figure 3, and implemented MT-28. We also improved the ionospheric mask by including additional IGPs. We did not update GEO locations nor did we model ranging capability that could further enhance performance. By comparing
FIGURE 3. Improved SBAS networks. The newly added reference stations are marked by yellow filled squares for EGNOS and yellow filled triangles for MSAS.
Figure 4 to Figure 2 improvements can be seen, in particular expanded LPV-200 operation to the south.
FIGURE 4. Improved single frequency SBAS coverage for the original three SBAS.
The future of MSAS improvements is less certain, with no firm commitments for major service enhancements. We have chosen to model fairly aggressive enhancements based upon studies made by the Electronic Navigation Research Institute in Japan. We have added 10 new reference stations in Japan and made the ionospheric threat model less conservative, in line with current WAAS algorithms. Together, these improvements offer good vertical guidance coverage over Japan.
These improvements extend coverage in the vicinity of the reference station networks, but are unable to push availability much beyond. This is primarily due to the limitations of the ionospheric corrections. Because strong gradients can exist outside of the viewing area of the network, tight confidences cannot be provided to those regions.
SBASs model the ionosphere as a thin 2-dimensional shell 350 kilometers above Earth. This works well for quiet mid-latitude and polar ionosphere. However, equatorial ionosphere often has significant vertical structure that is not well replicated by the SBAS message. The resulting confidence bounds are then too large to reliably provide LPV-200 capability. No certified algorithm capable of bounding the equatorial ionosphere is known to the authors. Instead, it is recommended that SBASs in equatorial areas wait for the forthcoming L5 signal to provide vertical guidance in their regions.
GPS L5
The next GPS satellite to be launched will contain a new civil signal, L5, centered at 1176.45 MHz and in a protected aviation band. As such, it will be approved for use on aircraft. When the L5 signal is used in combination with L1, the ionospheric delay for each line-of-sight can be directly estimated. This will dramatically lower the uncertainty of the pseudorange measurement. Thus, if the SBAS is upgraded to provide corrections appropriate for an L1/L5 user and the user similarly upgrades his or her avionics, SBAS service can be dramatically improved.
Another important advantage of the second civil frequency is its relative immunity to ionospheric storms. Because the users are now directly eliminating the amount of delay they actually experience, they are no longer affected by shortcomings in the MOPS ionospheric model. The weaker effect of scintillation may have some impact; however, we do not expect to lose vertical guidance altogether. Furthermore, the availability of two civil frequencies offers protection against unintentional interference. If either L1 or L5 is jammed, the user still has access to guidance on the available frequency.
At the moment there is no MOPS for an L1/L5 user, so any ground or user algorithms will have to be speculative. We propose basing future L1/L5 algorithms on the existing L1-only algorithms. Instead of using L1-only pseudorange measurements, the user forms the ionosphere-free combination. For the confidence term representing the total pseudorange error on a line-of-sight, the ionospheric correction terms and airborne multipath terms are replaced with a single value representing airborne noise and multipath for the ionosphere-free combination.
For a single frequency user, each line-of-sight has four confidence terms that are summed together to obtain the total confidence. These terms correspond to: the satellite clock and ephemeris corrections (σflt), the ionospheric correction (σUIRE), the airborne code noise and multipath (σair), and the troposphere (σtrop). The total one-sigma confidence bound for a particular line-of-sight is the root sum square (RSS) of these four terms:
(1)
When a user has access to two civil frequencies, they can remove the ionospheric effects by forming the iono-free combination of the two pseudoranges:
(2)
where f1 and f5 are the L1 and L5 frequencies (1575.42 MHz and 1176.45 MHz) respectively. If σ1 and σ5 are comparable then the iono-free combination has roughly three times as much noise as either single frequency term, but is substantially smaller than σUIRE . Furthermore, satellites do not need a grid correction to be used, thus satellites farther from the network and IGP mask can be incorporated into the position solution. The dual-frequency confidence bound for a single satellite is then given by
(3)
where σair is used in place of σ1 and σ5 in (2).
For the VPL we propose adding nominal bias terms to handle observed signal biases and non-Gaussian behavior of the underlying error terms. By including these terms it is possible to reduce the net impact of these biases on the user. Further, we propose tailoring the VPL equation to the most significant remaining threat to the user: single satellite fault modes. The L1-only VPL equation is appropriate for threats that affect many signals simultaneously as may happen with the ionosphere or troposphere. However, with the user directly eliminating ionospheric effects, the most significant threats come from satellite fault modes. As these faults are rare, they are unlikely to affect more than one ranging measurement at a time. Therefore, a VPL can be constructed to explicitly account for such a threat. We recommend that the dual frequency VPL take the following form:
(4)
where KHMI and σ5 is the Gaussian tail factor corresponding to the probability of Hazardously Misleading Information, s3,i is the projection of the pseudorange error onto the vertical position estimate, sff is the fault free overbounding sigma, biasnomis the nominal bias bound, Kfault is the Gaussian tail factor accounting for the probability of fault, and biasfault is a bound on the magnitude of all satellite faults. The H0 condition corresponds to the most likely condition of no faults present. The H1 condition corresponds to the unlikely event of a fault on the dominant satellite. The final VPL is the maximum across both conditions.
Because the faulted bias term covers the satellite faults the fault-free sigma term, σff, can be much smaller than the current total value (1), or the dual frequency version (3). Further, since the probability of fault is small, Kfault can be much smaller than KHMI . The net result is that the proposed VPL is smaller than the existing VPL for the same conditions. To model L1/L5 availability we chose the following parameters:
KHMI = 5.33
Kfault = 2.33
σ 2ff = (σflt / 3 ) 2 + σ 2iono_free + σ 2trop
biasnom = 0.5 m
biasfault = 5.333 x σflt
Other values follow the single frequency MOPS specifications as normally implemented by MAAST.
Given these parameters, the H1 hypothesis nearly always dominates the VPL calculation. We have used a nominal weighting scheme to optimize for accuracy. It is possible to deweight the dominant satellite to improve availability. We will be looking at practical methods for determining more optimal weighting for the VPL given in (4). However, there is a concern that such optimizations could harm accuracy. The potential benefits vs. risks will be studied.
The improvement in performance for a dual-frequency user can be seen in Figure 5. The coverage is significantly expanded. Now each region is robustly covered with large margins surrounding their intended service regions. However, coverage is still limited to the areas around these first three SBASs.
FIGURE 5. Potential dual frequency coverage of the first three SBASs including network improvements.
GAGAN and SDCM
Two additional SBASs are currently under development that will extend coverage to more regions. India is developing GAGAN. Currently it has eight Indian reference stations (INRES) all in India (blue diamonds in Figure 6). There is one Indian master control center (INMCC), and plans to use the GSAT-4 as its initial GEO. The GSAT-4 is planned for launch in 2010 and will be located near 82° E. The geomagnetic equator passes through India and it therefore faces the full impact of equatorial ionosphere. The advent of L5 will allow GAGAN to obtain high LPV-200 availability that is unlikely to be achievable for single-frequency users.
FIGURE 6. The networks of five SBAS systems are shown. In addition to the reference stations from Figure 3, the 8 Indian stations are shown as blue diamonds and the 19 Russian stations are shown as red stars.
Russia is developing SDCM. It now has nine operational measuring points (MPs) and has plans for at least 10 more locations, all in Russia (red stars in Figure 6). There are also plans to use three GEOs: Luch-5a planned for launch in 2010 and to be located near 16° W, Luch-5b planned for launch in 2011 and to be located near 95° E, and Luch-4 planned for launch in 2013 and to be located near 167° E.
Figure 7 shows the combined dual-frequency coverage of all five systems, WAAS, EGNOS, MSAS, GAGAN, and SDCM.
FIGURE 7. The combined dual frequency availability of the five SBASs is shown.
The vast majority of land masses in the northern hemisphere are now well covered by at least one of the SBASs. Figures 6 and 7 clearly highlight that the majority of development has occurred in the northern hemisphere. In fact, only two reference stations have been placed below the Equator.
Southern Hemisphere
If SBAS is to provide a global solution, its coverage must extend into the southern hemisphere. There have been many discussions with representatives of countries in the southern hemisphere. Further, the United States has had testbed receivers in South America for nearly 15 years. Europe has fielded receivers in Africa. Australia investigated its own variant of SBAS called the Ground-based Regional Augmentation System (GRAS). However, we are not aware of concrete plans for development in this hemisphere.
We anticipate that discussions will eventually evolve into firm plans and that either independent SBASs will be developed in these regions or existing SBASs will expand their networks southward. We have chosen to assume that WAAS, EGNOS, and MSAS will expand their networks to extend LPV-200 coverage to the southern portion of their GEO footprints. This is but one of many possible scenarios. The pr
oposed expansion shown in Figure 8 is not based on any plans, but is based on the notion that civil aviation authorities will want to obtain global coverage. The assumed new southern reference stations are shown as yellow-filled circles for WAAS in South America, yellow-filled squares for EGNOS in southern Africa, and yellow-filled triangles for MSAS in and around Australia. Advantages of dual frequency allow us to have much less dense networks for the expansions, in addition to allowing LPV-200 capability to be obtained in equatorial areas.
FIGURE 8. The networks of the five SBAS systems including hypothetical expansions into the southern hemisphere
Figure 9 shows the combined dual-frequency coverage for these SBASs with the expanded network. Now nearly all land masses have good LPV-200 coverage. Note that we have not attempted to optimize these networks to assure coverage to all land masses, not have we tried to find the minimum number of stations that offer this capability.
FIGURE 9. The combined dual frequency availability of the SBASs with the southern hemisphere stations is shown.
Added Core Constellations
Galileo is envisioned as compatible with GPS in that each satellite provides ranging using signals covering the L1 and L5 frequencies with similar modulations. Although the final specifications are not yet set, it is envisioned that Galileo satellites will provide a service that is fully interoperable with the GPS civil signals. Thus, we can approximately model Galileo satellites as being equivalent to GPS satellites in different orbits. In parallel, China is developing the COMPASS system whose signals are also planned to be compatible with GPS.
The Russian GLONASS system has been operational for many years. However, its current signal structure makes it less suited for incorporation into avionics. There are modernization plans to broadcast L1 signals that are more in alignment with the other constellations. Thus it, too, may one day be incorporated into SBAS. We believe that SBASs will someday broadcast satellite clock and ephemeris corrections for GPS and one or more other core constellations. These corrections will remove any difference in the reference times or coordinate frames between the two systems, allowing the corrected signals to be considered fully interchangeable.
Adding 24 or more extra ranging sources will have tremendous benefit for all civil GNSS users. The user’s geometry would be very robust to the loss of one or two satellites. Adding one or more core constellations has the potential to significantly improve SBAS coverage. We chose to model the addition of one constellation, by combining the almanac we used for GPS with one that had been proposed for Galileo. For these scenarios, MAAST is modeling 55 medium earth orbiting navigation satellites in addition to the GEOS used by each SBAS. Because the orbital repeat period is approximately 10 sidereal days for Galileo, the simulated time step and total run time were each increased by a factor of ten.
Figure 10 shows the improved coverage when the reference stations shown in Figure 6 are used. The additional satellites fill in many potential coverage gaps and now, compared to Figure 7, the SBASs all have even more reliable coverage well beyond their reference networks. Indeed, the Northern Hemisphere is now essentially fully covered. Figure 11 shows the results when the expanded networks of Figure 8 are incorporated. Compared to Figure 9, the southern hemisphere is much more reliably covered. The remaining gaps could easily be filled in with just a few more reference stations if full global coverage were desired.
FIGURE 10. The combined dual-frequency, LPV-200 coverage of the five SBAS systems with both GPS and Galileo.FIGURE 11. Combined dual-frequency LPV-200 coverage, SBASs with GPS and Galileo and the southern hemisphere stations.
Conclusions
For single-frequency SBAS the coverage is limited to areas very close to the monitoring station network. However, each region can obtain very good LPV-200 coverage within their desired service area. The addition of GPS L5 makes vertical guidance largely immune to ionospheric disturbances, and permits SBAS coverage to extend into equatorial areas. Independence from the ionospheric grid also allows service to extend farther away from the core network regions. When new Indian and Russian systems are commissioned, a very large fraction of the northern hemisphere will have LPV-200 coverage.
With dual frequency, LPV-200 coverage can be established with comparatively sparse networks in South America, Africa, and around Australia. Additional dual-frequency core constellations such as Galileo, Compass, or GLONASS could greatly expand coverage to well outside the original reference network regions. As GNSS capability is improved and expanded, we anticipate that SBAS coverage may one day provide nearly global LPV-200 or better service capability.
Acknowledgments
The authors acknowledge support of the FAA Satellite Product Office. However, the opinions and potential future scenarios reflect those of the authors and are not necessarily representative of the FAA.
Todd Walter is a senior research engineer at Stanford University. He has been active in the development of the Wide Area Augmentation System and related systems around the globe. His focus is on the provision of certified integrity for aviation applications.
Juan Blanch is a research associate at Stanford University, where he works on integrity algorithms for GNSS. He holds a Ph.D. in aeronautics and astronautics from Stanford.
Per Enge is professor of aeronautics and astronautics at Stanford, where he directs the Stanford GPS Research Laboratory. He has a Ph.D. from the University of Illinois.
Deterministic risk modeling, the basis of the Efficient Market Hypothesis (EMH) at the core of modern quantitative finance, is known to be fundamentally flawed, but its elegance and convenience has blinded researchers to growing evidence of its weaknesses. The near-complete acceptance of the EMH led to models that dramatically accentuate its flaws, which in turn led to absurd but eagerly accepted conclusions for loan-default risk. These models proved dramatically vulnerable to changes in the housing market in 2007–2008 and led directly to the ensuing crash.
The gross inattention to potential anomalies and violations of nominal behavior that characterize quantitative finance fortunately do not apply to satellite navigation integrity assurance. Similar techniques and probability distributions are used, but understanding what can go wrong leads to detailed emphasis on modeling and mitigating rare events. Where significant uncertainty exists, conservative assumptions try to be robust to it. Thus, certification of satellite- and ground-based augmentation systems (SBAS and GBAS) likely demonstrates that these systems meet their integrity risk requirements with substantial margin.
Despite this, the predominant use of deterministic models for risk assessment is dangerous because it purports to provide guaranteed bounds on uncertainty that do not apply in practice. The conservative nature of satellite navigation risk assessment greatly reduces but cannot eliminate the underlying integrity risk, while it leads to performance losses with potentially unmeasured safety impacts. Given the uncertainty that is present, probabilistic models are much better suited to providing “illusion-free” risk assessments that enable realistic system-level design trade-offs.
Economics. Decades of financial theory are based upon the assumption that the normal (Gaussian) distribution applies to financial markets. In spite of common-sense arguments to the contrary, assuming that it does is too convenient to give up, and the theories it gives rise to are so useful that it was thought better to force-fit the model to financial processes. Academic and professional preference for tractable, analytical, easy-to-use models trumped the search for truth.
The simplification of correlation into a single parameter made it easier to fit historical data on mortgage default risk correlation to a tractable model. Despite this, the relative rarity of defaults prior to 2000 made any correlation model based on historical default data highly uncertain. An EMH-based market-driven model for default risk correlation became instantly popular, enabling the creation of complicated mortgage-backed derivatives without in-depth analysis.
The simplicity of the Value-at-Risk output that encouraged its widespread use in corporte risk assessment allowed managers to forget that it was only useful to, at most, the 99th percentile. It quickly became thought of as an actual worst-case bound on losses and treated as such in portfolio optimization. Loss reserves throughout the economy fell far short of what was needed. In retrospect, such approaches that oversimplify risk to the point where managers think they fully understand it are worse than useless, as they are so likely to be abused. Experts should understand risk in all its complexity and communicate that risk to decision-makers as fully as possible.
Mathematics. This financial experience suggests that, as Albert Einstein said, “As long as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
Deterministic models provide precise quantification of uncertainty whose accuracy and precision are illusory because they depend wholly on the assumptions used to generate the results. Probabilistic models also produce imprecise outputs, but the imprecision is real, and the goal of these models is to identify this lack of precision, rather than cover it up.
Because the probabilistic approach is so philosophically different from the deterministic one, it is likely that more traditional deterministic risk models will remain dominant. These require multiple assumptions regarding uncertain behavior and simplifications to make the resulting model tractable and useful for analysis. Danger lies in forgetting how these models were created and growing to believe in them too strongly while ignoring all contrary data, as happened with the EMH.
To avoid this, assumptions and simplifications on which deterministic risk models are based should be highlighted not only during the modeling process but also when results are presented. If these shaky foundations are consistently emphasized, fewer people will be tempted to willfully or accidentally misinterpret the results, and researchers will be less likely to extrapolate from one flawed model to another.
Lessons for SatNav Integrity
We must first recognize that integrity or safety assurance for satellite navigation is a unique application of risk assessment in which the aim is to protect passengers from the consequences of very rare but potentially hazardous threats. As in the financial world, the Gaussian probability distribution is used extensively to model nominal error behavior and to compute position-domain protection levels intended to bound worst-case user position errors at the integrity-risk probabilities required for user safety. The Gaussian model is a convenient, efficient means to communicate ground-system errors to SBAS and GBAS users in a single parameter: the standard deviation (or sigma) of range-domain errors.
Great care is taken in using the tails of the Gaussian assumption to bound rare-event errors under nominal conditions (so-called rare-normal errors). Extensive studies of GPS, SBAS, and GBAS data show that, while the Gaussian distribution approximately holds in many cases and is usually a good model within the 99th percentile of errors, it is not a good description of rare-event behavior. In particular, rare-event tails of actual data often considerably exceed what is predicted by the Gaussian distribution. Several reasons exist, but the dominant one is the phenomenon of mixing of errors with different underlying actual distributions. This makes sense: rare-normal errors are not really normal but are instead combinations of off-nominal conditions that have different causes.
Because use of the Gaussian distribution is built into the SBAS and GBAS standards, the primary defense against its inapplicability at low probabilities is to inflate the sigmas broadcast by SBAS or GBAS (or assumed in user equipment) such that the assumed distribution overbounds the actual, unknown (and likely very complex) error distribution at the probabilities that matter for user safety. This is a difficult problem. No matter what approach to deriving bounding inflation factors from collected data is used, no means of proving rare-event error bounding by Gaussian distributions exists or can exist, given that the required assumptions cannot be proven. Despite this, conservatism and common sense in deriving inflation factors (and then applying additional margin for “unknown unknowns”) should sufficiently cover the underlying uncertainty.
Even after inflation has been applied, reliance on Gaussian error models becomes much more critical when they are extrapolated to derive distributions for squares of errors, as is done in receiver autonomous integrity monitoring (RAIM) and in real-time monitoring of the broadcast sigma parameters. Errors in the Gaussian error model are greatly magnified when squared and then assumed to follow a chi-square distribution.
History. Using GPS performance to build models of failure probabilities and anomaly behaviors suffers from a lack of data since GPS was not fully commissioned until 1995. Estimating the prior probability of sudden, unpredictable failures in GPS satellites is mostly based upon the observed failure history of GPS satellites in orbit — but such failures are quite rare and are not consistent across all satellites. They occur more frequently as satellites approach end-of-life, and they change as different satellite blocks deploy over time. There is no guarantee that future satellite or Operational Control Segment performance will correspond to that observed in the past. It is risky to estimate one failure rate across all satellites.
For SBAS and GBAS, conservatism and common sense must again be applied to limit the impact of these uncertainties. Failure-rate estimates are made from data where different satellites are combined, but significant margin is applied to account for differences among satellites. The resulting prior probabilities for failures are conservative for all fault types and extremely conservative for faults where limited or no data exists. The problems of relying on limited historical data are even more severe when threat models are created to represent possible system behaviors when a particular fault or anomaly (for example, satellite signal deformation, ionospheric storms) occurs. In the case of satellite signal deformation, deterministic threat models have been extrapolated from a single observed event, the fault on SVN19 discovered in 1993.
Errors and Failures. The problem of modeling uncertain and potentially time-changing correlations breaks down into error correlation and anomaly correlation. Correlation among nominal errors is relatively easy to deal with because significant data exists; one does not have to wait for anomalous conditions. However, even when truly uncorrelated data is present, the statistical noise inherent in correlation coefficients estimated from data is almost always non-zero. Since the designer cannot tell whether real correlation exists or not, the resulting error sigmas must conservatively allow for significant non-zero correlations.
In GBAS, ground-system reference-receiver antennas are sited far enough apart (100–200 meters) that diffuse multipath (and most specular multipath) should be statistically independent from receiver to receiver. However, this cannot be guaranteed, and even if it is true at a given site, statistical correlation estimates will be non-zero. Therefore, the assumption that nominal error sigmas in the resulting pseudo-range corrections are reduced by a factor of two when averaging measurements across four reference receivers is not strictly valid. Conservative handling of the estimated correlation at a given site can properly de-weight the assumed credit given for averaging, or the designer can choose to take no averaging credit at all.
On the other hand, modeling correlations among rare-event anomalies is very difficult. GNSS satellite failure correlations are hard to foresee because of our limited understanding of their causes. The temptation to ignore correlations and to treat all failures as statistically independent is very high, as this allows the use of simplified probability models and produces probabilities of multiple failures that are usually small enough to be ignored.
This dangerous trap can lead to neglecting important sources of integrity risk. Avoiding it requires assuming some non-zero degree of failure correlation, but without detailed failure cause-and-effect information, it is very difficult to know how much correlation is sufficiently conservative in a deterministic risk model. Here, probabilistic models are far superior, as our degree of uncertainty regarding actual failure correlations can be handled directly by representing different correlation scenarios, or possible states of reality, and assigning probability weights (themselves random variables) to each.
Worst Case. Since the uncertainty inherent in the development of deterministic failure models is well understood, the resulting threat models are usually applied in terms of the worst-case fault within the bounds of the threat model. Once one agrees to ignore the possibility of faults exceeding the threat-model bounds, this worst-case-fault assumption is the most conservative one possible. The worst-case fault is judged from the user’s point of view rather than that of the GNSS or service provider. For example, the worst-case C/A-code signal-deformation on a GPS satellite depends upon the design of the reference receiver providing differential corrections (if any) and the design of the user receiver. SBAS and GBAS users are allowed a pre-specified receiver design space. Given the reference receiver chosen by a given SBAS or GBAS installation, finding the worst-case signal-deformation fault requires error maximization over all possible deformations in the threat model and all possible user receiver design parameters.
Another class of anomalies, large ionospheric spatial gradients, can be used to illustrate this procedure. Figure 1 shows a simplified, linear model of a large, wedge-shaped ionospheric spatial gradient affecting a GBAS installation, and Figure 2 shows a graphical summary of the parameter bounds of the associated threat model developed for the FAA LAAS based on CONUS data. The geometry assumed in Figure 1 is a simplification of reality and cannot be assumed to hold precisely, even though the threat model assumes that it does. Fortunately, the resulting risk assessment is not very sensitive to small deviations from a perfectly linear front slope. This kind of sensitivity analysis is required to test our vulnerability to violations of deterministic models whose underlying assumptions cannot be verified.
FIGURE 1. Geometry of GBAS (LAAS) ionospheric threat model
The parameter bounds in Figure 2 cover the worst validated ionospheric gradients observed since 1999. They cannot be guaranteed to cover future anomalies; thus, ongoing monitoring of ionospheric anomalies is required to see if these bounds need updating in the future. However, the outer bounds of the existing threat model appear to be very conservative because they are driven by a single ionospheric storm on a single day (20 November 2003) in a small region (northern Ohio). This storm appears much worse than the other observations shown in Figure 2. The vast majority of anomalous gradients discovered, most of which are not shown in Figure 2, have slopes under 200 millimeters/kilometer (mm/km) and are generally not threatening to GBAS users.
FIGURE 2. Parameter bounds on GBAS (LAAS) ionospheric threat model for continental United States (CONUS
Therefore, in a probabilistic model, the vast majority of the weighting (given that an anomaly condition exists) would go toward non-threatening gradients with tolerable slopes, a small fraction would go to the 200–300 mm/km slope range, a much smaller fraction to the 300–425 mm/km range, and then a very small but non-zero fraction to gradients above 425 mm/km (the upper bound in Figure 2) that have not been observed to date but cannot be ruled out.
Given this uncertainty within a deterministic model, the worst-case gradient of 425 mm/km (for high-elevation satellites) is assumed to be present at all times, and its hypothetical presence is simulated, with the worst possible approach geometry and timing relative to a single approaching aircraft, on all pairs of satellites otherwise approved by a LAAS ground facility (LGF). The largest resulting vertical position error over all potential user satellite geometries represents the maximum ionospheric error in vertical position (MIEV) that must be protected against. Before mitigation by LGF geometry screening, this worst-case error can be as large as 40–45 meters.
Figure 3 illustrates the potential magnitude of vertical errors under near-worst-cas
e ionospheric anomaly conditions based on a limited probabilistic model that varies front slope (above 350 mm/km), speed, satellites impacted, and approach direction relative to that of the aircraft for a user approaching the LAAS facility at Memphis International Airport with the SPS-standard 24-satellite GPS constellation (only subset geometries with two or fewer satellites removed are considered). The worst-case position error, or MIEV, prior to LGF geometry screening is about 41 meters, but the relative likelihood of this result is very low. Much more common are errors in the 5–15 meter range. This figure does not show the majority of cases where the LGF detects the anomaly before any error occurs. LGF geometry screening acts to remove potential subset geometries (make them unavailable by inflating the broadcast parameters) whose worst-case error exceeds 28.8 meters, but the price of this is substantially lower availability for CAT I precision approaches.
FIGURE 3. Near-worst-case ionosphere-induced vertical position errors at Memphis
Figure 3 shows the extreme level of conservatism that typically results from deterministic worst-case threat model impact analysis. This level of conservatism is so great that it is hard to imagine that the actual user integrity risk is somehow worse than what is modeled in this manner. However, “hard to imagine” does not equate to “is guaranteed not to happen.” The goal of worst-case analysis is to eliminate uncertainty (by assuming the worst possible outcome of the uncertain variables) and thus prove that a given probabilistic integrity risk requirement is met. However, the limited knowledge upon which threat models are based means that such proof is illusory at best and dangerously misleading at worst. Meanwhile, a great deal of performance (in terms of user availability and continuity) is sacrificed. As shown by the example in Figure 3, probabilistic analysis makes it possible to trade off risk reduction and performance benefit in a coordinated manner. The illusion of guaranteed bounds on risk is abandoned, but as the financial crisis illustrates, it is just that — an illusion.
SAM PULLEN is a senior research engineer at Stanford University, where he is the director of the Local Area Augmentation System (LAAS) research effort. He has a Ph.D. from Stanford in aeronautics and astronautics. This article passes quickly over economic details included in his ION-GNSS 2009 paper, “Providing Integrity for Satellite Navigation: Leassons Learned (thus far) from the Financial Collapse.”
Few precise-positioning users have employed Loran in a professional sense, although maybe you have in your personal life if you’re a airplane pilot or a mariner. Then again, if you’ve flown as an airline passenger or cruised onboard a ship, you’ve benefited from the back-up to GPS that Loran provides. Similarly, if you’ve used a mobile phone recently; you don’t see it, but the wireless carriers all use Loran as a back-up. That back-up is about to go away.
Loran was developed initially for marine navigation and then adopted for aviation navigation. I used Loran-C for aviation navigation in the early 90’s after I earned my private pilot’s license. It was much easier than triangulating off of VORs and NDBs. Yes, GPS receivers for aviation were starting to emerge at that time but flying is expensive so a hand-held GPS was an out-of-reach luxury for a newlywed who just bought his first house and was preparing to start a family.
Loran is a terrestrial (ground-based) system of broadcasting towers, somewhat synonymous with NDGPS. You can read details about the system in the link I provided, but essentially it’s a line-of-sight system in which the Loran receiver antenna needs a direct path to the tower to utilize the signal. Coverage depends on the density of the broadcasting towers. Some regions are covered better than others and when I was using it, there were many areas that were not covered. Accuracy is always an ambiguous subject with respect to navigation technologies, so I’ll go out on a limb and say that Loran-C accuracy is repeatable to about 20 meters. A proposal was floated to upgrade Loran to a system called e-Loran which is reportedly accurate to about 9 meters.
Anyway, over the past several years there’s been a discussion about what to do with the Loran system because it’s clear that GPS has supplanted Loran as the primary navigation system for marine and aviation. Several articles have been published in GPS World by industry experts with most being in favor of maintaining Loran. The primary argument is that we need a back-up system for GPS, not only for navigation, but for the many invisible ways that GPS supports the national infrastructure (financial networks, wireless communications, transportation).
Here are several relevant articles, from most recent to further back:
The Case for eLoran In addition to these articles , the U.S. government publishes the Federal Radionavigation Plan (FRP) roughly on a biennial basis. There was one published in 2001, then 2005 and the last one was published in 2008/early 2009. It is the official policy document in which all US navigation systems are planned. According to the FRP, it is prepared jointly by the Department of Defense, Department of Homeland Security, the Department of Transportation and a number of other contributing government agencies.
If you don’t have time to read the 2008 FRP, following is a telling statement from the document:
“In March 2007, the DOT Pos/Nav Executive Committee and the DHS Geospatial/PNT Executive Committee accepted the findings of the Institute for Defense Analysis’ Independent Assessment Team and approved to pursue the designation of Enhanced-Loran, commonly referred as eLoran, as a national PNT backup for the U.S. homeland.
At its March 2007 meeting, the National Space-based PNT ExComm supported this approach and tasked DOT and DHS to complete an action plan that includes identifying an executive agent, developing a transition plan to address funding and operations and requesting the approval by the DOT and DHS Secretaries resulting in a final decision. DoD has not approved eLoran as a GPS backup for military applications.
In March 2008, the National Space-based PNT ExComm endorsed the DOT/DHS decision to transition the LORAN system to eLoran.
With respect to transportation to include aviation, commercial maritime, rail, and highway, the DOT has determined that sufficient alternative navigation aids currently exist in the event of a loss of GPS-based services, and therefore Loran currently is not needed as a back-up navigation aid for transportation safety-of-life users. However, many transportation safety-of-life applications depend on commercial communication systems and DOT recognizes the importance of the Loran system as a backup to GPS for critical infrastructure applications requiring precise time and frequency.
Currently, DHS is determining whether alternative backups or contingency plans exist across the critical infrastructure and key resource sectors identified in the National Infrastructure Protection Plan in the event of a loss of GPS-based services. An initial survey of the Federal critical infrastructure partners indicates wide variance in backup system requirements. Therefore, DHS is working with Federal partners to clarify the operational requirements.”
By the way, that Independent Assessment Team mentioned in the first paragraph was led by Brad Parkinson, who knows someting about GPS. Further, the government read the report behind closed doors but refused to release it, until forced to do so nearly two years later, by public information access filings.
There still aren’t any answers to the question about a real back-up to GPS. No doubt it’s a vulnerable system. But that’s a subject for another day.
What’s Loran got to do with us?
The reason I’m writing about this is because as support for Loran wanes, attention (resources and focus) shifts away from Loran, it comes to bear more intensely on GPS navigation and its augmentations for marine and aviation; specifically DGPS and SBAS (WAAS/EGNOS/MSAS).
With a significant policy shift such as this (albeit it has been in the cards), manufacturers stop allocating engineering development resources to the products/technologies with a dim future and shift those resources to products/technologies with a bright future. True, DGPS has been around for better than a decade and SBAS for about half that time so there’s been plenty of time for manufacturer’s to exploit those technologies, but there is still a lot that can be done.
Engineers are experimenting with and implementing technologies in some interesting areas.
HA-NDGPS. High accuracy NDGPS. Currently with a high performance DGPS receive
r, one can attain about meter-level accuracy. Testing with HA-NDGPS, using a dual frequency GPS receiver shows that accuracies in the 10cm (95%) horizontal and 20cm (95%) vertical range are achievable within a 100 mile baseline according to the US DOT Federal Highway Administration Turner-Fairbank Research Center. Test broadcasts are being sent from a site in Hagerstown, MD.
Broadcasting DGPS/SBAS corrections via NTRIP. The emergence of RTK Networks has spurred the popularity of using the internet to deliver GPS corrections. NTRIP has become a commonly used method of accomplishing this. One of the weak points of DGPS technology has been the reliability and expense of broadcasting DGPS corrections via the 283-325kHz band. Of course, with NTRIP one must have internet access somehow and that typically happens via WiFi or GSM/CDMA mobile phone network. But it’s not that complicated. I’ve been with a GPS user who has pulled the SIM card from their iPhone, plugged it into a GPS receiver, and begin receiving DGPS corrections immediately.
During my last webinar, someone had posed the question if receiving SBAS corrections is possible via the internet in order to bypass the requirement to maintain visibility of the SBAS geostationary satellite. Streaming SBAS corrections via the internet is already happening in Europe. Users can access EGNOS corrections and bypass the EGNOS geostationary satellites by using SISNeT. A similar type of system could be implemented for any SBAS and not necessarily by the SBAS service provider. It could be a commercial entity.
I think the internet and GSM/CDMA mobile phone networks are really going to transform the way we transport data from reference stations to our receivers in the field. We’ve been fighting this battle of delivering GPS corrections for better than a decade. In the past, we’ve experimented with FM pagers and landline modems and now we’ve settled on low frequency radiobeacon, VHF/UHF/Spread spectrum and geostationary satellites but none are close to the perfect solution. GSM/CDMA mobile phone networks may be the final solution as the networks continue to build-out towards complete geographic coverage. Of course, we are helped immensely by the mobile phone industry whose focus on data for the many new social networking applications will drive the price of data plans downward.
By the way, almost all wireless carriers use Loran as a back-up technology; highly precise timing is a key aspect of how wireless communication works. The carriers use GPS for that, but if GPS goes down — as it did in San Diego during a memorable jamming episode a few years ago — so do all cell phones, if the carriers don’t have a timing back-up. In San Diego, they didn’t. Just something to think about, if you are using your mobile phone network to transport data or receive corrections.
