Magnetic-inertial global positioning system

One example includes a magnetic-inertial global positioning system mounted on a platform. The system includes an inertial system configured to determine an approximate latitude associated with an approximate global position of the global positioning system. The system also includes a magnetometer system configured to determine an ambient magnetic field at the approximate global position. The system further includes a location processor configured to compare the ambient magnetic field with a predetermined magnetic field profile to determine an approximate longitude along the determined approximate latitude to determine the approximate global position of the platform.

TECHNICAL FIELD

The present disclosure relates generally to sensor systems, and specifically to a global positioning system.

BACKGROUND

Location detection has been an important aspect of navigation for centuries. Nautical voyages dating back to ancient times utilized time and/or celestial features to plot approximate locations for navigating across seas and oceans to be able to arrive at intended destinations with relative certainty. In more modern times, location detection is implemented through a variety of technological means. As one example, Global Navigation Satellite Systems (GNSS) such as Global Positioning Satellite (GPS) systems can provide location information based on receiving signals transmitted from satellites having known orbital positions relative to each other. However, because GNSS systems rely on relatively low-level satellite transmissions, it may be difficult to receive the signals based on the location of the vehicle or intervening obstacles. While an initial location of most vehicles can be easily identified (typically by the operator or user), some vehicles, such as autonomous vehicles, may be activated in an unknown location, known as the “kidnapped robot problem”, making it more difficult for the vehicle to determine its location.

SUMMARY

One example includes a magnetic-inertial global positioning system mounted on a platform. The system includes an inertial system configured to determine an approximate latitude associated with an approximate global position of the platform. The system also includes a magnetometer system configured to determine an ambient magnetic field at the approximate global position. The system further includes a location processor configured to compare the ambient magnetic field with a predetermined magnetic field profile to determine an approximate longitude along the determined approximate latitude to determine the approximate global position of the platform.

Another example includes a method for determining a global position of a platform. The method includes determining an approximate latitude associated with an approximate global position of the platform via an inertial system associated with the platform. The method also includes determining an ambient magnetic field at the approximate global position via a magnetometer system associated with the platform. The method also includes accessing a predetermined magnetic field profile from a memory associated with the platform. The method further includes comparing the ambient magnetic field with the predetermined magnetic field profile to determine an approximate longitude along the determined approximate latitude to determine the approximate global position of the platform.

Another example includes a magnetic-inertial global positioning system mounted on a vehicular platform. The magnetic-inertial global positioning system includes an inertial system. The inertial system includes a plurality of accelerometers associated with each of three orthogonal axes that are configured to collectively determine a down vector associated with a gravity center of a celestial body and track a down vector direction along a motion trajectory between an initial location and a second location of motion of the vehicular platform. The inertial system also includes a plurality of gyroscopes associated with each of three orthogonal axes that are configured to collectively determine a net rotation of the vehicular platform about a spin axis of the celestial body and to track a spin axis direction between the initial location and the second location of motion of the vehicular platform. The inertial system can be configured to determine an approximate latitude of the vehicular platform in response to the down vector and the net rotation of the vehicular platform between the initial location and the second location. The system also includes a magnetometer system configured to track an ambient magnetic field during the motion along a motion trajectory. The system further includes a location processor configured to compare the ambient magnetic field with a predetermined magnetic field profile to determine an approximate longitude along the determined approximate latitude to determine the approximate global position of the vehicular platform at the initial and to continue to compare the ambient magnetic field with the predetermined magnetic field profile along the motion trajectory to refine the determination of the approximate global position at the second location.

DETAILED DESCRIPTION

The present disclosure relates generally to sensor systems, and specifically to a magnetic-inertial global positioning system. The magnetic-inertial global positioning system can be mounted on a platform, such as a vehicle platform. As an example, the vehicle platform can be an aerial vehicle (e.g., an unmanned aerial vehicle (UAV)), or can be any of a variety of other platforms (mobile or immobile, manned or unmanned). The magnetic-inertial global positioning system can be configured to determine an approximate global position of the platform (e.g., of the associated vehicle) agnostically as to an initial location and time. For example, the magnetic-inertial global positioning system can determine the approximate global position and an approximate present time upon a power-up condition in any location on a celestial body. As a result, the magnetic-inertial global positioning system addresses the “kidnapped robot problem”, such that the magnetic-inertial global positioning system is configured to determine the approximate location and approximate present time in a manner that is completely agnostic as to initial location and time, and without the assistance of a Global Navigation Satellite Systems (GNSS) such as Global Positioning Satellite (GPS) systems. The celestial body is described hereinafter as corresponding to Earth. However, it is to be understood that the principles of operation of the magnetic-inertial global positioning system are equally applicable to any solid celestial body (e.g., the Moon, Mars, or another planet) for which global position is desired to be known.

The magnetic-inertial global positioning system includes an inertial system, such as the inertial navigation system (INS) of the associated vehicle that can be configured to determine an approximate latitude associated with the approximate global position of the platform. For example, the inertial system can include an accelerometer configured to determine a down vector associated with a gravity center of Earth, and can also include a gyroscope system configured to determine a net rotation of the platform about a spin axis of Earth. Therefore, the platform can be arranged initially stationary at a first location and can collect inertial data that includes the acceleration and rotation data to determine the approximate latitude. The magnetic-inertial global positioning system also includes a magnetometer system that is configured to measure an ambient magnetic field (e.g., a net magnetic field that includes magnetic fields in each of three orthogonal axes).

Upon collecting the inertial data to determine the approximate latitude, a location processor can implement a matching algorithm to compare the measured ambient magnetic field with a predetermined magnetic field profile to determine an approximate longitude of the platform. For example, the predetermined magnetic field profile can be part of a global magnetic field model, and can correspond to a predetermined latitude magnetic field profile associated with a predetermined magnetic field about the 360° of longitude at the INS predetermined latitude, such that the location processor can determine an approximate match of the net magnetic field along the circle of longitude at the predetermined latitude. For example, the magnetic field profile can be associated with a global magnetic field anomaly map that can be accessed at initialization of the platform and in response to the measured ambient magnetic field. Accordingly, the location on the latitude of the predetermined magnetic field profile that approximately matches the determined net magnetic field can correspond to the approximate longitude, and thus the approximate global position of the platform.

As an example, the determination of the latitude and longitude can be an initial estimate within an uncertainty region that can be refined. For example, in response to determining an initial estimate of the latitude and longitude, the magnetic-inertial global positioning system can move to gather additional inertial and magnetic field data. As described previously, the magnetic-inertial global positioning system can be vehicle-mounted, such that the vehicle can move to collect additional data that can be implemented to ascertain the global position of the platform. While the platform is in motion, the global positioning system can track the motion of the platform via the inertial system (e.g., via the INS) to determine precise directional data of the motion of the platform. Additionally, the magnetic-inertial global positioning system can continuously collect magnetic field data during the motion of the platform. As a result, the location processor can continue to implement the matching algorithm to continuously compare the magnetic field data that is collected during the motion with the predetermined magnetic field profile. As a result, the magnetic-inertial global positioning system can refine the approximate global position (e.g., approximate latitude and approximate longitude) to determine a more precise global position.

Furthermore, as an example, the magnetic-inertial global positioning system can further include a celestial tracking system (e.g., including one or more celestial (e.g., star)-trackers). The celestial tracking system can be implemented to provide an initial celestial observation (e.g., during the initial stationary position of the global positioning system) to calculate an approximate time based on the approximate global position. For example, in response to determining the initial approximate global position, the magnetic-inertial global positioning system can implement the celestial tracking system to determine an initial approximate present time, which can be based on an initial clock system (e.g., a free-running clock). The magnetic-inertial global positioning system can thus use the approximate present time to further refine the approximate global position, and upon determining the refined global position (e.g., after motion of the platform), the celestial tracking system can further refine the determination of time based on the initial celestial observation. As another example, the celestial tracking system can again provide a celestial observation in response to the determination of the refined global position, which can thus further refine the present time. Accordingly, the magnetic-inertial global positioning system can implement the celestial tracking system to refine the determination of the global position of the magnetic-inertial global positioning system and/or to calculate a precise present time of operation of the magnetic-inertial global positioning system.

FIG. 1illustrates an example of a magnetic-inertial global positioning system10. The magnetic-inertial global positioning system10can be implemented in any of a variety of navigation or location-service applications to provide an approximate global position of a platform (not shown) on which the magnetic-inertial global positioning system10is mounted or located. As an example, the platform can be a vehicle, such that the magnetic-inertial global positioning system10can provide an approximate global position of the vehicle. As described herein, the magnetic-inertial global positioning system10can provide the approximate global position of the platform in a manner that is agnostic with respect to an initial location of the platform, such as at power-up of the magnetic-inertial global positioning system10(e.g., the “kidnapped robot problem”). Additionally, the magnetic-inertial global positioning system10can provide the approximate global position of the platform without the assistance of Global Navigation Satellite Systems (GNSS) such as Global Positioning Satellite (GPS) systems.

The magnetic-inertial global positioning system10includes an inertial system12that is configured to collect inertial data associated with the platform. As an example, the inertial system12can correspond to an inertial navigation system (INS) of the associated vehicle or a vehicle-mounted platform. In the example ofFIG. 1, the inertial system12includes a gyroscope system14and an accelerometer system16. The gyroscope system14includes at least one gyroscope18that is configured to monitor rotation of the platform about a respective at least one sensitive axis. For example, the gyroscope(s)18can include three gyroscopes that have respective orthogonal sensitive axes to be able to determine rotation of the platform about X, Y, and Z axes in three-dimensional space. Similarly, the accelerometer system16includes at least one accelerometer20that is configured to monitor an acceleration of the platform along at least one input axis. For example, the accelerometer(s)20can include three accelerometers that have respective orthogonal input axes to be able to determine acceleration of the platform along the X, Y, and Z axes in three-dimensional space.

The magnetic-inertial global positioning system10also includes a magnetometer system22that is configured to generate magnetic field data that is associated with an ambient magnetic field at the location of the platform. In the example ofFIG. 1, the magnetometer system22includes at least one magnetometer24that is configured to collect magnetic field measurements. For example, the magnetometer(s)24can collect scalar measurements of the ambient magnetic field and vector magnetic field measurements in each of three orthogonal axes. As described herein, the magnetic-inertial global positioning system10is configured to determine the approximate global position based on a combination of inertial measurements, as provided by the inertial system12, and magnetic field measurements, as provided by the magnetometer system22.

The inertial system12provides rotation data ROT that is collected by the gyroscope system14and acceleration data ACL that is collected by the accelerometer system16to a location processor26. Additionally, the magnetometer system22provides magnetic field data MF that is collected by the magnetometer(s)24to the location processor26. The location processor26is configured to determine the approximate global position of the platform, as described in greater detail herein, based on the combination of the rotation data ROT, the acceleration data ACL, and the magnetic field data MF.

During an initial operation of the magnetic-inertial global positioning system10, such as at power-up, the magnetic-inertial global positioning system10may have no knowledge of a current location, and is thus agnostic as to an initial global position and time (e.g., the “kidnapped robot problem”). As an example, the platform on which the magnetic-inertial global positioning system10is mounted may not have a GNSS system, or may have a GNSS system that is disabled or inoperable, such as based on occlusion of the signals provided by the associated GNSS satellites. Therefore, the magnetic-inertial global positioning system10can determine the approximate global position of the platform based solely on the rotation data ROT, the acceleration data ACL, and the magnetic field data MF. Thus, during the initial operation of the magnetic-inertial global positioning system10, the magnetic-inertial global positioning system10can remain stationary in a first fixed location to determine an approximate latitude associated with the approximate global position of the platform.

As an example, in the first fixed location, the inertial system12can collect inertial data associated with the Earth. For example, the accelerometer(s)20of the accelerometer system16can determine an acceleration acting upon the platform, such as gravity, to determine a down vector that is directed toward the gravity center of Earth. In addition, the gyroscope(s)18of the gyroscope system14can determine a rotation of the platform, such as about the three orthogonal axes, that is based on the rotation of Earth about the Earth spin-axis. Therefore, based on the combination of the down vector directed toward the gravity center of Earth and based on the known orientation of the platform relative to the Earth spin-axis, the location processor26can calculate an angle between the down vector and a vector orthogonal to the Earth spin-axis. As a result, the location processor26can determine an approximate latitude of Earth on which the approximate global position of the platform resides.

FIG. 2illustrates an example diagram50of Earth. The diagram50demonstrates an approximate location52of where the magnetic-inertial global positioning system10can be powered up in a manner that is agnostic with respect to the initial position. In the example ofFIG. 2, the approximate location52is demonstrated as approximately in Arlington, Va., United States, continent of North America, in the Northern and Western Hemispheres. Upon power-up, the global positioning system10can be completely unaware of where the platform is located. Additionally, as described in greater detail herein, the global positioning system10can also be completely unaware of a present time at which the global positioning system10was activated (powered-on).

FIG. 3illustrates an example diagram100of determining latitude on Earth. The diagram100is demonstrated as an outline of Earth that also includes the approximate location52of the activated platform. As described previously, during an initial operation of the magnetic-inertial global positioning system10at power-up, the magnetic-inertial global positioning system10has no knowledge of a current location and is thus agnostic as to an initial global position and time. Therefore, in the first fixed location, the inertial system12collects inertial data associated with the Earth. In the example ofFIG. 3, the accelerometer(s)20of the accelerometer system16determine a down vector102that is directed toward the gravity center of Earth based on gravity acceleration acting upon the platform. For example, the down vector102can be directed along the local net gravity field, approximately toward the gravity center of Earth. In addition, the gyroscope(s)18of the gyroscope system14determine a rotation of the platform, such as about the three orthogonal axes, that is based on the rotation of Earth about the Earth spin-axis104. The rotation of the platform about three axes based on rotation of the platform associated with the Earth spin-axis104can thus be determinative of a vector106that is orthogonal to the Earth spin-axis104. Therefore, an angle θ can be measured between the vector106and the down vector102, which corresponds to an equal angle θ between the equatorial plane of Earth and the down vector102. Accordingly, the location processor26can calculate an approximate latitude108on which the approximate location52resides. As an example, the approximate latitude108can correspond to an approximate latitude, such that the approximate latitude108can be determined by the location processor26to include an uncertainty region (e.g., of meters to hundreds of kilometers).

In response to determining the approximate latitude108, the magnetic-inertial global positioning system10can be configured to determine an approximate longitude110on which the approximate location52resides. As an example, the global positioning system10can collect ambient magnetic field measurements via the magnetometer(s)24of the magnetometer system22while at the approximate location52of the platform (e.g., while stationary at a first fixed location). The ambient magnetic field measurements can include a magnetic field associated with the Earth polar magnetic field112that is off-axis from the Earth spin-axis104. Because the Earth polar magnetic field112is off-axis from the Earth spin-axis104, the ambient magnetic field can vary greatly about the entire 360° around a given latitude of Earth, including the approximate latitude108. Therefore, the ambient magnetic field can provide information associated with a given longitude that intersects the given latitude. In addition, the ambient magnetic field can include measurements of fixed Earth-based magnetic field anomalies, such as associated with metallic compositions of the Earth's crust. Such Earth-based magnetic field anomalies can be predetermined (e.g., through geological measurements), such that the ambient magnetic field can include components of both the Earth polar magnetic field112and the Earth-based magnetic field anomalies.

Referring back to the example ofFIG. 1, the magnetic-inertial global positioning system10further includes a magnetic model database28that is configured to store a predetermined magnetic field model of Earth. As an example, the predetermined magnetic field model of Earth can be generated based on geological data associated with magnetic field measurements from across the surface of Earth, such that the predetermined magnetic field model of Earth can include a predetermined magnetic field profile across substantially the entire surface of Earth. Therefore, in response to collecting the ambient magnetic field measurements at the approximate location52of the platform, the magnetometer system22can provide the magnetic field measurements MF to the location processor26. As an example, the magnetic field measurements MF can include a scalar amplitude of the ambient magnetic field and/or each of three orthogonal vector measurements of the ambient magnetic field. In response, the location processor26can implement the magnetic field measurements MF and the approximate latitude108, as ascertained via the inertial system12, as described previously to determine the approximate longitude110. For example, the location processor26can access the magnetic model database28to obtain a predetermined latitude magnetic field profile that is associated with the determined approximate latitude108, and can implement a matching algorithm with respect to the predetermined latitude magnetic field profile to mitigate errors in the determined latitude to further refine the approximate latitude, as well as to determine the approximate longitude110.

FIG. 4illustrates another example diagram150of Earth. The diagram150of Earth demonstrates a distorted view of a map of the entirety of Earth, and thus an approximate 360° representation of the latitudes of Earth. The diagram150also demonstrates an approximate latitude152that can correspond to the approximate latitude108demonstrated in the example ofFIG. 3. The diagram150also demonstrates a predetermined latitude magnetic field profile154that can correspond to the entire 360° of the approximate latitude152(e.g., the latitude 38.878° N of the approximate location52in the Arlington, Va.). The predetermined latitude magnetic field profile154can thus be stored in the magnetic model database28as part of the predetermined magnetic field model of Earth. Therefore, the location processor26can implement a matching algorithm of the magnetic field measurements MF with respect to the predetermined latitude magnetic field profile154. The matching algorithm can thus determine the approximate longitude110in response to determining an approximate match of the ambient magnetic field, as provided by the magnetic field measurements MF, with a given magnetic field along the predetermined latitude magnetic field profile154. Accordingly, the match of the ambient magnetic field along the predetermined latitude magnetic field profile can be indicative of an approximate longitude156intersecting the approximate latitude152, and thus an approximate global position158of the platform.

In the example ofFIG. 5, the predetermined latitude magnetic field profile200is demonstrated as spanning 360° of latitude about the Earth spin-axis104, and demonstrates four separate magnetic field profiles. Particularly, the predetermined latitude magnetic field profile200includes a total scalar magnetic field amplitude202, an X-axis magnetic field204, a Y-axis magnetic field206, and a Z-axis magnetic field208. The total scalar magnetic field amplitude202can thus correspond to a vector sum (e.g., a Root of the Sum of the Squares) of the X, Y, and Z-axis magnetic fields204,206, and208. The magnetic field amplitudes202,204,206, and208can thus represent a given predetermined magnetic field in each of a scalar amplitude and three-axis orthogonal amplitudes, respectively, at a given longitude on the specific latitude represented by the predetermined latitude magnetic field profile200. As an example, the magnetic field amplitudes202,204,206, and208can be predetermined, such as via geographic measurements, and can represent one latitude of a plurality of latitudes of a magnetic field model that substantially covers the surface of the Earth.

As described previously, in response to collecting the ambient magnetic field measurements at the approximate location52of the platform, the magnetometer system22can provide the magnetic field measurements MF to the location processor26. As an example, the magnetic field measurements MF can include a scalar amplitude of the ambient magnetic field and each of the three orthogonal vector measurements of the ambient magnetic field. In response, the location processor26can implement the matching algorithm with respect to the predetermined latitude magnetic field profile200to determine the approximate longitude110. As an example, the matching algorithm can evaluate the relative measurements of the ambient magnetic field, such as with respect to the scalar measurement and the three orthogonal measurements, with respect to the magnetic field amplitudes202,204,206, and208. The matching algorithm can thus determine a given longitude that provides a closest match of the measured ambient magnetic field with respect to the magnetic field amplitudes202,204,206, and208. In the example ofFIG. 5, the closest match is demonstrated at approximately 77° W, which may have provided the closest match with of the measured ambient magnetic field with respect to the magnetic field amplitudes202,204,206, and208, and thus which corresponds to the approximate global position in Arlington, Va.

As described previously, the approximate latitude152can be a latitude that is within a region of uncertainty. The approximate longitude156can likewise be a longitude that is within a region of uncertainty. Thus, the approximate latitude152and approximate longitude156can be associated with the approximate global position158that is within a global position region of uncertainty (e.g., accurate to within meters to hundreds of kilometers). For example, the global positioning system10can be located at an approximate global position in which the local magnetic anomaly is stronger than the Earth polar magnetic field112, or is located at one of a plurality of similar magnetic fields along the predetermined latitude magnetic field profile. As described previously, the approximate global position158can be ascertained by the platform on which the global positioning system10is mounted being stationary at a fixed first location. As described in greater detail herein, the platform can begin to move from the fixed first location to a second location to refine the approximate global position to a much more precise determination (e.g., to within meters of uncertainty).

FIG. 6illustrates an example diagram250of refining an approximate global position. The diagram250demonstrates an aircraft252corresponding to the platform on which the global positioning system10can be mounted. While the diagram250demonstrates an aircraft, it is to be understood that the vehicle is not limited to the aircraft252, but could instead be any of a variety of vehicles. In the example ofFIG. 6, the aircraft252is demonstrated as moving from a first fixed location254to a second fixed location256. While the aircraft252is moving, the inertial system12of the global positioning system10can be configured to substantially continuously collect inertial data, and thus to substantially continuously collect acceleration data ACL and rotation data ROT via the respective accelerometer system16and gyroscope system14. As a result, the inertial system12, and thus the location processor26can monitor a continuous and precise change in location of the aircraft252from the first fixed location254to the second fixed location256. As a result, the location processor26can very precisely identify the difference in distance and location of the second fixed location256relative to the first fixed location254.

In addition, the magnetometer system25can continuously collect ambient magnetic field data MF along the path between the first fixed location254and the second fixed location256. The ambient magnetic field data MF can thus be implemented for refining the approximate location of the aircraft252. For example, because the location processor26can precisely identify a change in location of the aircraft252from the first fixed location254to the second fixed location256, the location processor26can access the magnetic model database28to determine changes in the collected ambient magnetic field that can correspond to an associated change in the magnetic field model stored in the magnetic model database28. For example, the location processor26can implement the matching algorithm to determine a match of changes in the ambient magnetic field along the path from the first fixed location254to the second fixed location256to a corresponding change in predetermined magnetic field data along an approximately identical path (e.g., angle and distance) in the magnetic field model stored in the magnetic model database28. The location processor26can therefore, determine a significantly more precise approximate global position of the aircraft252at the second fixed location256(e.g., which could be an instantaneous location mid-flight) based on the changes in magnetic field measurements MF along the path from the first fixed location254to the second fixed location256relative to the magnetic field model in the magnetic model database28.

In addition to determining an approximate global position of the platform, the magnetic-inertial global positioning system10can be configured to determine an approximate present time (e.g., real time) upon powering-up, and thus in a manner that is agnostic with respect to an initial time of powering-up. Referring back to the example ofFIG. 1, the magnetic-inertial global positioning system10further includes a celestial tracking system30that includes one or more celestial trackers (e.g., star trackers)32. As an example, the celestial tracking system30can provide an approximate present time of operation of the magnetic-inertial global positioning system10in response to determining the approximate global position of the platform based on performing one or more celestial observations. For example, typical celestial trackers can be configured to perform celestial observations to determine location information of a platform to assist in navigation based on predetermined celestial location information at a given known time. The celestial tracking system30can instead be implemented by the magnetic-inertial global positioning system10to operate in the reverse to determine a present time based on a known approximate location of the platform.

For example, the celestial tracking system30can be configured to obtain a celestial observation while the platform is initially stationary (e.g., at the first fixed location254in the example ofFIG. 6) via the celestial tracker(s)32and to provide celestial observation data CO to the location processor26. Upon determining the approximate global position of the platform at the initial stationary location (e.g., based on determining the initial approximate latitude108and the initial approximate longitude110), the location processor26can determine an initial approximate present time based on the celestial observation data CO and based on the approximate global position. Given that the planets of the solar system repeat relative positioning with respect to each other once every approximately 5126 years, the location processor26can determine the approximate present time based on the assumption that less than half of the planetary alignment cycle time has passed since the magnetic-inertial global positioning system10was powered-off (e.g., less than 2,563 years).

As another example, a single celestial observation while the platform is at the first fixed location upon determining the approximate global position of the platform at the initial stationary location can provide a present time that is within a range of uncertainty (e.g., within a few seconds to a few minutes). Such a range of uncertainty can be based on the uncertainty of the determined approximate global position, and can be based on the celestial observation being singular. Therefore, the global positioning system10can be configured to refine the present time based on performing multiple celestial observations via the celestial tracking system30at various times. For example, as described previously, the platform configured as aircraft252can move from the first fixed location254to the second fixed location256. Therefore, the celestial tracking system30can perform multiple celestial observations, such as a first celestial observation at the first fixed position254and a second celestial observation at the second fixed position256(e.g., and/or including multiple additional celestial observations therebetween). Therefore, based on the difference between the celestial observations between the first fixed position254and the second fixed position256, and based on the refined determination of the approximate global position, the magnetic-inertial global positioning system10can determine the present time in a much more precise manner (e.g., to within milliseconds of accuracy).

As another example, the global positioning system10can include a local time reference (e.g., internal clock), such as a crystal oscillator-based clock. As an example, a typical crystal clock can operate for years on a very small battery, and can be reasonably stable over a small range of temperatures. However, after a year or more of operation at extreme ends of temperature range, the local time reference can still provide time with an uncertainty below approximately twelve hours. However, such a baseline present time after power-up can provide a time reference that can be refined based on the celestial observation(s) provided by the celestial tracking system30. The baseline time reference can thus refine the present time determination down to the limit of the position uncertainty. Such a determination of the present time can thus be performed much more quickly. For example, if the determination of time becomes sufficiently refined, then it could be possible to implement observations of signals from pulsars/magnetars with known frequency and timing to further refine the determination of time, such as to sub-millisecond levels.

Therefore, as described herein, the determination of the approximate global position can be implemented by the magnetic-inertial global positioning system10to refine the determination of the approximate present time. In addition, the determination of the approximate present time can be implemented by the magnetic-inertial global positioning system10to refine the determination of the approximate global position. Accordingly, the global positioning system10can implement both the approximate present time and the approximate global position in a feedback manner with respect to each other to refine the approximate present time and approximate global position.

In view of the foregoing structural and functional features described above, a methodology in accordance with various aspects of the present disclosure will be better appreciated with reference toFIG. 7. While, for purposes of simplicity of explanation, the methodology ofFIG. 7is shown and described as executing serially, it is to be understood and appreciated that the present disclosure is not limited by the illustrated orders, as some aspects could, in accordance with the examples herein, occur in different orders and/or concurrently with other aspects from that shown and described herein. Moreover, not all illustrated features may be required to implement the methodology in accordance with an aspect of the present disclosure.

FIG. 7illustrates an example of a method for determining an approximate global position of a platform (e.g., the vehicular platform252). At302, an approximate latitude associated with an approximate global position of the platform is determined via an inertial system (e.g., the inertial system12) associated with the platform. At304, an ambient magnetic field is determined at the approximate global position via a magnetometer system (e.g., the magnetometer system22) associated with the platform. At306, a predetermined magnetic field profile (e.g., the magnetic field profile200) is accessed from a memory (e.g., the magnetic field model database28) associated with the platform. At308, the ambient magnetic field is compared with the predetermined magnetic field profile to determine an approximate longitude along the determined approximate latitude to determine the approximate global position of the platform.

What have been described above are examples of the disclosure. It is, of course, not possible to describe every conceivable combination of components or method for purposes of describing the disclosure, but one of ordinary skill in the art will recognize that many further combinations and permutations of the disclosure are possible. Accordingly, the disclosure is intended to embrace all such alterations, modifications, and variations that fall within the scope of this application, including the appended claims.