Abstract:
Systems, methods, devices and subassemblies for creating and delivering a GNSS augmentation service include one or more reference stations for receiving signals transmitted by navigation beacons and an augmentation server coupled to the reference stations. At least one of the reference stations is able to receive at least one of the signals from a low earth orbit satellite. Each of the reference stations determines first navigation observables based on the received signals and transmit information associated with the first navigation observables to the augmentation server. The augmentation server is configured to determine and distribute augmentation information to a receiver. The augmentation information is based on the received information associated with the first navigation observables, locations of the reference stations, and computational models. The distributed augmentation information is usable by the receiver to determine a high-precision position, velocity, and time solution for the receiver based on second navigation observables associated with the receiver.

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     The present application claims priority of U.S. provisional application 61/735,798, filed Dec. 11, 2012, entitled “Systems And Methods For GNSS Augmentation, Ionospheric Modeling And Observables, Communications And/Or Navigation Device Updates.” The entirety of the foregoing application is incorporated by reference herein. 
    
    
     BACKGROUND 
     Field of the Invention 
     The present invention relates to the determination and generation of models and/or other augmentation information that may be used to support high-precision position, velocity, and/or timing (PVT) solutions based on signals received from overhead assets such as satellites and, in particular, to techniques suitable for providing rapid acquisition access to such PVT solutions without resort to a generally proximate, terrestrial ground station with a fixed and precisely known position. 
     Description of the Related Art 
     Radio signals have been used as an aid to navigation and to obtain position estimates for decades. In much the same way that sailors could navigate near land using two or more light houses, the earliest systems used a directional antenna that determined a bearing to two or more radio transmitters. As long as line of sight could be maintained between the receiver and the two or more radio transmitters, a location of the receiver could be determined by triangulating the known locations of the two or more radio transmitters and the bearings to each of those radio transmitters. And although this approach may generally provide just a horizontal location (latitude and longitude) of the receiver, this may be adequate for localized navigation, such as the landing of aircraft or the navigation of ships around nearby navigational hazards. 
     Limiting radio navigation systems to local two-dimensional positioning, however, does not address many interesting positioning problems. For example, surveyors often desire to know the height/altitude of a location as well as its latitude and longitude, and pilots of aircraft often desire to know their altitude. To address these desires, more complex and longer distance radio navigation systems are typically utilized. Many of these radio navigation systems rely on the basic principle that radio waves generally propagate through the air at a known speed. By measuring the length of time it takes for a radio wave to propagate between a transmitter and a receiver, a distance between the transmitter and the receiver may be determined. By using the distance between the receiver and several transmitters with known locations, it is possible to determine the position of the transmitter by trilateration. For example, by using three transmitters, it is possible to determine the latitude, longitude, and altitude of the receiver. As additional transmitters are used and detected by the receiver, additional variables may be removed from the solution. For example, by adding time information to the radio signals, a fourth transmitter may be used to solve for the current time at the receiver. 
     Global Positioning Satellite (GPS) navigation, and more broadly Global Navigation Satellite System (GNSS) navigation, has become the standard for most military and civilian radio navigation applications. There exist in both military and civil sectors hundreds of millions of GPS or GNSS receivers that are used daily to provide real-time positioning and navigation. The GPS system is based on a constellation of approximately 24 to 32 middle-earth orbit (MEO) satellites that broadcast continuous carrier wave signals. A GPS receiver typically relies on the ability to receive signals from four or more satellites allowing the receiver to determine latitude, longitude, altitude, and time error at the receiver. For a typical GPS receiver, accuracy in location to within about 10 meters may be rapidly obtained. 
     To obtain higher precision PVT solutions for a GNSS receiver typically requires an augmentation to the general GNSS infrastructure. Traditional augmentation approaches for satellite navigation techniques include real time kinematic (RTK) and differential GPS (DGPS) precise point positioning (PPP) techniques that are commonly used in surveying and high accuracy timing applications. In a typical RTK system, a base station is installed in a fixed and known location. Once the base station is able to obtain a PVT solution from the satellite transmissions, it is able to transmit any differences between its known location and the PVT solution as a correction signal to a nearby mobile or roving unit. RTK systems are typically fairly expensive, require time to set-up the base station, and the base station and mobile unit need to stay within a close proximity to each other. In a typical PPP system, a network of fixed reference stations receive the satellite signals and generate correction information that is distributed to the GNSS receiver using satellites or other terrestrial-based wireless technology, such as a cellular network. While less expensive than RTK systems, a GNSS receiver in a PPP system generally takes up to 30 minutes to converge on a high precision PVT solution and provides poor coverage at high latitudes or in challenging environments such as cities, steep terrain, and heavily wooded areas. 
     Improved techniques are desired. 
     SUMMARY 
     It has been discovered that position, velocity, and/or timing (PVT) solutions may be provided with levels of precision that have previously and conventionally been associated with RTK and PPP systems without many of the drawbacks. Using the augmentation techniques described herein, high-precision PVT solutions may be provided without resort to a generally proximate, terrestrial ground station having a fixed and precisely known position. Instead, techniques described herein utilize a series of reference stations that track one or more combinations of traditional GNSS satellites that are in MEO, geostationary satellites, geosynchronous satellites, terrestrial beacons, low earth orbiting (LEO) satellites, and/or the like. The LEO satellites may include one or more satellites in the Iridium constellation. The use of the shorter orbital period LEO satellites significantly improves the time to achieve geometric diversity, reducing convergence time from 30 minutes down to as little as 1 or 2. In addition, the use of the orbital diversity of some LEO satellites also provides better high-precision PVT coverage at high latitudes and in challenging environments, thus providing higher deployment flexibility. 
     Using the developed techniques, a GNSS augmentation service uses a series of terrestrially-based reference stations to track one or more combinations of MEO satellites, geostationary satellites, geosynchronous satellites, terrestrial beacons, LEO satellites, and/or the like, such as combinations of the GPS satellites, and LEO satellites, such as the Iridium satellites. Using the tracking information from both the navigation beacons and/or LEO satellites, the augmentation service generates modeling and other correction (augmentation) information that is then distributed to GNSS receivers using satellite, cellular, wireless, and/or wired techniques. The GNSS receivers use the augmentation information to correct their own observation of the navigation beacon and/or LEO signals to arrive at a high-precision PVT solution with initial convergence times of as little as one to two minutes or less. 
     In some embodiments, a method of augmented GNSS positioning includes receiving at one or more reference stations first signals transmitted by one or more navigation beacons, determining by the reference stations first navigation observables based on the received first signals, receiving at an augmentation server information associated with the first navigation observables, determining by the augmentation server augmentation information, transmitting the augmentation information to a receiver using a distribution network, receiving by the receiver the augmentation information, receiving by the receiver second signals transmitted by the one or more navigation beacons, determining by the receiver second navigation observables based on the received second signals, and determining by the receiver a high-precision position, velocity, and time (PVT) solution for the receiver based on the received augmentation information and the second navigation observables. At least one of the reference stations receives at least one of the first signals from a low earth orbit (LEO) satellite. The augmentation information is based on at least the received information associated with the first navigation observables, known or computed locations of the reference stations, and computational models. 
     In some embodiments, a GNSS augmentation system includes one or more reference stations configured to receive first signals transmitted by one or more navigation beacons and an augmentation server coupled to the reference stations. At least one of the reference stations receiving at least one of the first signals from a low earth orbit (LEO) satellite. Each of the reference stations is configured to determine first navigation observables based on the received signals and transmit information associated with the first navigation observables to the augmentation server. The augmentation server is configured to determine augmentation information and distribute the augmentation information to a receiver using a distribution network. The augmentation information is based on at least the received information associated with the first navigation observables, known or computed locations of the reference stations, and computational models. The distributed augmentation information is usable by the receiver to determine a high-precision position, velocity, and time (PVT) solution for the receiver based on second navigation observables associated with the receiver. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a simplified diagram of an augmented radio navigation system according to some embodiments. 
         FIG. 2  is a simplified diagram of perturbation effects and corresponding models that may be used by the augmentation server of  FIG. 1  according to some embodiments. 
         FIG. 3  is a simplified diagram of an augmented radio navigation system according to some embodiments. 
         FIG. 4  is a simplified diagram of a method of providing GNSS augmentation information according to some embodiments. 
         FIG. 5  is a simplified diagram of tropospheric modeling according to some embodiments. 
     
    
    
     The present invention may be better understood, and its numerous objects, features, and advantages made apparent to those skilled in the art by referencing the accompanying drawings. Further details are provided in Appendix A, which forms an integral portion of the present disclosure. 
     DETAILED DESCRIPTION 
       FIG. 1  is a simplified diagram of an augmented radio navigation system  100  according to some embodiments. As shown in  FIG. 1 , augmented radio navigation system  100  includes one or more navigation beacons  110  and one or more LEO satellites  120 . In some embodiments, the navigation beacons  110  may include MEO satellites, geostationary satellites, geosynchronous satellites, terrestrial beacons, and/or the like. In some examples, the LEO satellites  120  may also be referred to as navigation beacons. In some examples, the MEO satellites may be GPS satellites and/or the LEO satellites  120  may be Iridium satellites. Each of the navigation beacons  110  and the LEO satellites  120  transmit one or more signals that may become navigation and LEO observables, respectively, when they are received by one or more reference stations  130 . Depending upon the locations of the navigation beacons  110 , the LEO satellites  120 , and the reference stations  130 , each of the reference stations  130  may observe navigation and/or LEO observables from different combinations of the navigation beacons  110  and/or the LEO satellites  120 . In some examples, some of the reference stations  130  may not receive any LEO observables. In some examples, some of the reference stations  130  may not receive any navigation observables. Reference stations  130  are typically terrestrially-based and have a known or computed location. In some embodiments, the reference stations  130  may be distributed throughout an area for which augmentation services are desired. In some examples, the number of references stations  130  that are used to receive LEO observables is typically quite small, with approximately 15 reference stations  130  with this capability being capable of supporting a worldwide augmented radio navigation system with an accuracy of at least ten centimeters, 95% of the time. In some examples, the accuracy may be as precise as two or three centimeters or less. Each of the references stations  130  shares information about the received navigation and LEO observables with an augmentation server  140  using a network or other communication system. In some embodiments, the references stations  130  may also provide additional information to the augmentation server, including such information as local weather conditions. 
     In some embodiments, the augmentation server  140  may be a standalone workstation, a cluster, a production server, within a virtual machine, a plurality of computer servers using distributed processing, and/or the like. In some examples, augmentation server  140  may be implemented using a cloud-based computing infrastructure. In some examples, augmentation server  140  may include one or more processors coupled to memory. In some examples, the one or more processors may control operation and/or execution of hardware and/or software on augmentation server  140 . In some examples, each of the one or more processors may be a CPU, a multi-core processor, a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), a virtual processor, and/or the like. The memory may include one or more types of machine readable media. Some common forms of machine readable media may include floppy disk, flexible disk, hard disk, magnetic tape, any other magnetic medium, CD-ROM, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, RAM, PROM, EPROM, FLASH-EPROM, any other memory chip or cartridge, and/or any other medium from which a processor or computer is adapted to read. 
     Using the information about the navigation and/or LEO observables and the locations of the reference stations  130 , the augmentation server  140  uses one or more models to develop augmentation information that may be used to account for various perturbations in the navigation and/or LEO observables that commonly affect radio signals transmitted over long distances through the atmosphere. In some examples, the augmentation server  140  may also compute the locations of the reference stations  130  based on the navigation and/or LEO observables. 
       FIG. 2  is a simplified diagram of perturbation effects and corresponding models that may be used by augmentation server  140  according to some embodiments. As shown in  FIG. 2 , the perturbations may include effects due to gravitation, solar activity, tides, relativity, tectonic motion, the ionosphere, and/or the troposphere. Each of these perturbations may be addressed using one or more known and/or improved models as noted in  FIG. 2 . Some embodiments may also include other sources of perturbations such as space vehicle thrust maneuvers, exogenous perturbing forces, ocean and atmospheric tides, tidal loading effects, multipath and/or signal reflection models, reference station and/or receiver antenna models, and/or the like. These, and the perturbations noted in  FIG. 2 , may be modeled, for example, via coefficients and/or known information, and/or may be estimated as part of the augmentation and/or correction information. In some embodiments, one or more perturbations may be ignored. 
     Referring back to  FIG. 1 , based on the modeling of the navigation and/or LEO observables as affected by the various perturbations of  FIG. 2 , the augmentation server  140  determines augmentation and/or correction information to account for errors in positions and/or clocks of the navigation beacons  110  and/or the LEO satellites  120  as well as other atmospheric effects due to the troposphere and the ionosphere. The determined augmentation information is sufficiently broad in geographic and/or temporal scope that it may account not only for the errors and/or perturbations in the navigation and/or LEO observables received at the reference stations  130 , but also account for expected errors and/or perturbations that are anticipated at radio navigation receivers, such as receiver  160 , that may be located at significant distances from any of the reference stations  130 . More specifically, computational techniques that are described in greater detail in an Algorithm Description included with Appendix A, may be used by augmentation server  140  to model and/or determine the augmentation information. 
     The augmentation information is made available to receiver  160  using one or more distribution systems  150 . In some embodiments, distribution system  150  may include one or more networks including local area networks (LANs), such as Ethernets, and/or wide area networks (WANs), such as the internet. In some examples, one or more of the networks may be proprietary to prevent sharing of the augmentation information with recipients other than authorized users. In some examples, at least the last segment of the one or more networks in distribution system  150  is wireless in nature so that receiver  160  is not tethered via a cable to distribution system  150 . In some examples, the last segment may be implemented using any wireless technology including wireless hot spots, cellular networks, satellite transmissions, and/or the like. In some examples, distribution system  150  may forward the augmentation information to an uplink station for the navigation beacons  110  and/or the LEO satellites  120  so that the augmentation information may be distributed by the navigation beacons  110  and/or the LEO satellites  120 . In some examples, the augmentation information may be transmitted as data embedded in the signals transmitted by the navigation beacons and/or the LEO satellites. 
     In some embodiments, the augmentation information distributed by augmentation server  140  to receiver  160  may be less than all of the augmentation information available to augmentation server  140 . Full worldwide augmentation information may be several megabytes or larger in size and may be sufficiently dynamic to require regular updates. Thus, it may not be practical and/or possible to distribute this much augmentation information throughout the augmented radio navigation system  100 . 
     In some embodiments, the augmentation server  140  may reduce the amount of augmentation information distributed to receiver  160  based on geographic information associated with receiver  160  and/or the last segment in distribution system  150  to receiver  160 . In some examples, when the last segment in distribution system  150  is only capable of reaching receivers  160  in a limited geographic area, the augmentation information may be limited to the augmentation information associated with that limited geographic area. For example, the limited geographic area may be defined by a transmission range for a wireless hot spot/network, a cellular tower/network, a satellite spot beam, and/or the like. In some examples, this may include distributing satellite clock and/or orbit correction information associated with only the satellites from which observables may be received at the respective receiver  160 . For example, a receiver  160  located in North America does not generally have to receive augmentation information associated with a satellite currently over Australia. In some examples, this may include distributing ionospheric, tropospheric, and/or multipath correction information associated with the limited geographic area. For example, a receiver  160  located in North America does not generally have to receive augmentation information associated with the ionosphere, atmosphere, and/or multipath environment in Australia. 
     In some embodiments, the augmentation server  140  may reduce the amount of augmentation information distributed to receiver  160  based on temporal information associated with receiver  160  and/or the last segment in distribution system  150 . In some examples, one or more users of receiver  160  may desire to limit reception of the augmentation information only during periods when receiver  160  is active, during periods of subscription, and/or the like. In some examples, when no receivers  160  within a limited geographic area associated with a last segment in distribution system  150 , it may be possible to temporarily suspend distribution of the augmentation information in that limited geographic area. 
     In some embodiments, the augmentation server  140  may also distribute augmentation information that varies in geometric scope, temporal scope, resolution, and/or the like from already modeled augmentation information. In some examples, the augmentation server  140  may use one or more numerical interpolation and/or extrapolation methods to generate the augmentation information for distribution. 
     In some embodiments, the augmented information may include modeling information that receiver  160  may use to determine a high-precision PVT solution for receiver  160 . In some examples, the modeling information may include modeling data for ionospheric effects, tropospheric effects, corrected ephemerides for the navigation beacons  110  and/or LEO  120  satellites, clock drift and/or frequency errors in the navigation beacons  110  and/or LEO  120  satellites, modeling data for multipath effects and/or signal reflections, modeling data for specific receiver antenna types, and/or the like. 
     In some embodiments, receiver  160  may be an augmented and/or enhanced version of a conventional GNSS or GPS receiver. In some examples, receiver  160  may be enhanced to receive not only the navigation observables from the navigation beacons  110 , but also the LEO observables from the LEO satellites  120 . In some examples, receiver  160  may be further enhanced to receive the augmentation information from augmentation server  140  and use the augmentation information to correct the navigation and/or LEO observables to obtain a high-precision PVT solution for receiver  160 . In some examples, the use of the LEO observables in determining the augmentation information and reception of the LEO observables by receiver  160  may allow receiver  160  to converge on the high-precision PVT solution in ten minutes or less. In some examples, the convergence may occur in two minutes or less. 
     In some embodiments, receiver  160  may be associated with a mobile phone or other portable device. A custom application may be made available to the portable device that may be used to receive the augmentation information from augmentation server  140  and to use the received augmentation information to improve the accuracy and/or precision of the PVT solutions computed for the mobile device. 
       FIG. 3  is a simplified diagram of an augmented radio navigation system  300  according to some embodiments. As shown in  FIG. 3 , the augmented radio navigation system  300  is one possible implementation of the augmented radio navigation system  100  using GPS satellites as the navigation beacons  110  and the Iridium satellites as the LEO satellites  120 . The augmented radio navigation system  300  further uses the Iridium communication system for at least a portion of the distribution system  150  including the last segment to the receiver. 
       FIG. 4  is a simplified diagram of a method  400  of providing GNSS augmentation information according to some embodiments. In some embodiments, one or more of the processes  410 - 440  of method  400  may be implemented, at least in part, in the form of executable code stored on non-transient, tangible, machine readable media that when run by one or more processors (e.g., the one or more processors associated with augmentation server  140 ) may cause the one or more processors to perform one or more of the processes  410 - 440 . 
     At a process  410 , information associated with navigation observables is received from one or more reference stations. One or more references stations in an augmented radio navigation system receive signals transmitted by one or more navigation beacons and generate observables associated with the received signals. In some embodiments, the reference stations may be the reference stations  130  and/or the reference stations of  FIG. 3 . In some embodiments, the augmented radio navigation system may be the augmented radio navigation system  100  and/or  300 . In some embodiments, the navigation beacons may be the navigation beacons  110 , the LEO satellites  120 , the GPS satellites in  FIG. 3 , and/or the Iridium satellites in  FIG. 3 . In some embodiments, the navigation observables are associated with one or more MEO satellites and one or more LEO satellites. In some embodiments, the information associated with the navigation observables may include errors between the known or computed locations of the reference stations and the observed location of the reference stations. In some embodiments, additional information may be received from the reference stations, such as local weather information. 
     At a process  420 , augmentation information is determined based on at least the received observable information, locations of the one or more reference stations, and/or various models. In some examples, the locations of the reference stations may be known or computed based on the received observable information. In some examples, the various models may include one or more of the models in  FIG. 2  to account for various perturbations that may affect the observables received by the reference stations. Some embodiments may also include other sources of perturbations, such as space vehicle thrust maneuvers, exogenous perturbing forces, ocean and/or atmospheric tides, tidal loading effects, multipath and/or signal reflection models, reference station and/or receiver antenna models, and/or the like. These, and the perturbations noted in  FIG. 2 , may be modeled, for example, via coefficients and/or known information, and/or may be estimated as part of the augmentation and/or correction information. In some embodiments, one or more perturbations may be ignored. In some embodiments, the augmented information may include modeling information that a receiver, such as receiver  160 , may use to determine a high-precision PVT solution for the receiver. In some examples, the modeling information may include modeling data for ionospheric effects, tropospheric effects, corrected ephemerides for the satellites associated with the satellite observables, clock drift and/or frequency errors in the satellites, modeling data for multipath effects and/or signal reflections, modeling data for specific receiver antenna types, and/or the like. In some embodiments, depending on the desired scope and/or resolution of the augmentation information, determination of the augmentation information may include using one or more numerical methods for interpolation and/or extrapolation. 
     At an optional process  430 , the augmentation information may be limited based on geographic and/or temporal information. To limit the amount of augmentation information that may be distributed to receivers, the augmentation information may be limited in scope based on geographic and/or temporal information associated with the receivers. 
     In some embodiments, the amount of augmentation information distributed to the receivers may be limited based on geographic information associated with the respective receivers and/or the last segment in a distribution system used to provide the augmentation information to the receivers. In some examples, when the last segment in the distribution system is only capable of reaching receivers in a limited geographic area, the augmentation information may be limited to the augmentation information associated with that limited geographic area. For example, the limited geographic area may be defined by a transmission range for a wireless hot spot/network, a cellular tower/network, a satellite spot beam, and/or the like. In some examples, this may include distributing navigation beacon clock and/or orbit correction information associated with only the navigation beacons from which observables may be received at receivers in the limited geographic area. In some examples, this may include distributing ionospheric, tropospheric, and/or multipath correction information associated with the limited geographic area. 
     In some embodiments, the amount of augmentation information distributed to the receivers may be limited based on temporal information associated with receivers and/or the last segment in the distribution system. In some examples, one or more users of the respective receivers may desire to limit reception of the augmentation information only during periods when the respective receivers are active, during periods of subscription, and/or the like. In some examples, when there are no receivers within a limited geographic area associated with a last segment in the distribution system, it may be possible to temporarily suspend distribution of the augmentation information in that limited geographic area. 
     At a process  440 , the augmentation information may be distributed to one or more receivers. The augmentation information determined during process  420  and/or optionally limited during process  430  is distributed to one or more receivers so that the receivers may use the augmentation information to develop a high-precision PVT solution based on the navigation observables detected by the respective receivers. In some embodiments, the augmentation information may be distributed using a distribution system similar to distribution system  150 . In some examples, the distribution system may include one or more networks including local area networks (LANs), such as Ethernets, and/or wide area networks (WANs), such as the internet. In some examples, one or more of the networks may be proprietary to prevent sharing of the augmentation information with recipients other than authorized users. In some examples, at least the last segment of the one or more networks in the distribution system is wireless in nature so that the receivers are not tethered via a cable to the distribution system. In some examples, the last segment may be implemented using any wireless technology including wireless hot spots, cellular networks, satellite transmissions, and/or the like. In some examples, the distribution system may forward the augmentation information to an uplink station associated with one or more satellites so that the augmentation information may be distributed by the satellites. In some examples, the augmentation information may be transmitted as data embedded in the signals that form the navigation observables received by the reference stations and/or the receivers. 
       FIG. 5  is a simplified diagram of tropospheric modeling according to some embodiments. As shown in  FIG. 5 , the effect that the ionosphere has on navigation observables depends on where the satellite is located relative to the ionosphere. The ionosphere extends from about 90 km to 1600 km above the surface of the earth and is composed of plasma containing free electrons and ions. This plasma affects electromagnetic waves in very predictable ways that should be accounted for in augmented radio navigation systems  100  and/or  300 . The speed of propagation of radio signals through the ionosphere depends on the number of free electrons in the path of the radio signal. During night time hours the number of free electrons in the ionosphere maintains a relatively low and stable value, but during the day solar radiation and/or solar flares significantly increase the level of free electrons in the ionosphere and thus the impact the ionosphere may have on the navigation observables. 
     Many models exist for determining the impact of the ionosphere on the navigation observables for satellites located above the ionosphere, such as a MEO satellite  510  as shown in  FIG. 5 . Some models are empirical in nature and others are based on first principles, such as those based on measurements made at two different nominal carrier frequencies broadcast from the same transmitter. In some systems, the effect of the ionosphere may be modeled using the Klobuchar Model. The Klobuchar Model is based on a four-parameter zenith model of the effect the ionosphere has on a radio signal traveling vertically between a transmitter and receiver that are respectively above and below the ionosphere. The Klobuchar Model is shown in Equation 1. 
     
       
         
           
             
               
                 
                   
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     The four parameters, A 1 -A 4 , which vary by the frequency of the signal being transmitted by satellite  510 , may be provided to the receivers, such as receiver  520  located on the surface of the earth  530 , as part of the augmentation information distributed by an augmentation server. In some embodiments, the effect of the ionosphere from Equation 1 may also be adjusted to account for the increased distance the received signal travels through the ionosphere when, for example, the transmitter is not located directly above the receiver  520  as is the case for satellite  510 . This adjustment may be determined by knowing the line of sight unit vector û, determined using the positions of satellite  510  and receiver  520 . In some examples, the position of satellite  510  may be included in or may derivable from the augmentation information and the position of receiver  520  may be estimated from a recent PVT solution for receiver  520 . In some embodiments, Ĩ may be multiplied by the obliquity factor OF of Equation 2 to make this adjustment, where ζ is the angle of the satellite from the zenith and is derivable from the line of sight unit vector û, R E  is the average radius of the earth, and h I  is the mean ionospheric height, which typically ranges from 300 to 400 km. 
     
       
         
           
             
               
                 
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     The Klobuchar Model of Equation 1, even when adjusted by the obliquity factor of Equation 2, does not provide a very complete model of the effects of the ionosphere on the satellite observables when, as in the case of a LEO satellite  540 , the LEO satellite  540  is located within the ionosphere. The Klobuchar Model of Equation 1 and other ionosphere models, typically model the total electron count (TEC) and/or a similar quantity for the entire ionosphere as if the ionosphere were a thin shell between the satellite, such as satellite  510 , and the receiver  520 . As the location of the LEO satellite  540  demonstrates, the ionosphere is not a thin shell and a more complex ionospheric model, such as a tomographic model should be used that accounts for the location of satellite  540  within the ionosphere. In some examples, this tomographic model uses a non-uniform model of the ionosphere to account for free electron densities that vary depending on the location and altitude within the ionosphere. Distribution of the tomographic model of the ionosphere with the augmentation information would permit receiver  520  to remove the effects due to the portion of the ionosphere located above satellite  540  when processing and analyzing observables from satellite  540 . In some examples, this would improve the accuracy and precision of the PVT solution determined for receiver  540 . 
     Some embodiments of the augmentation server  140  may include non-transient, tangible, machine readable media that include executable code that when run by one or more processors may cause the one or more processors to perform the processes of method  400  as described above. Some common forms of machine readable media that may include the processes of method  400  are, for example, floppy disk, flexible disk, hard disk, magnetic tape, any other magnetic medium, CD-ROM, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, RAM, PROM, EPROM, FLASH-EPROM, any other memory chip or cartridge, and/or any other medium from which a processor or computer is adapted to read. 
     Although illustrative embodiments have been shown and described, a wide range of modification, change and substitution is contemplated in the foregoing disclosure and in some instances, some features of the embodiments may be employed without a corresponding use of other features. One of ordinary skill in the art would recognize many variations, alternatives, and modifications. Thus, the scope of the invention should be limited only by the following claims, and it is appropriate that the claims be construed broadly and in a manner consistent with the scope of the embodiments disclosed herein.