The present disclosure gee rally relates to accurately guiding projectiles and more particularly to guiding projectiles in GPS-denied or GPS-limited environments using, at least partially, radio frequency (RF)/orthogonal interferometry (OI) techniques.
The dominant approach currently used for guiding a weapon, projectile, UAV, or other similar asset is the global positioning system (GPS). The weapon, projectile, UAV, or the like measures its earth position in latitude, longitude, and altitude, to calculate and execute a trajectory towards a GPS located target. This approach has been in use for many years but is now becoming vulnerable to GPS jamming, both denied and spoofing. Other techniques to extend the GPS approach involve pseudolites, or pseudo-satellites, which are devices that are placed along the path to the target and which utilizes GPS-like transmissions to aid the navigation of the asset. One issue with this approach is the delivery/placement of the pseudolites along the path to the target. The risk to the installer is high given these pseudolites are typically in hostile regions and they are also susceptible to jamming since they are analogous to systems using GPS waveforms. Other pseudolite deployments utilize air platforms, which complicate the engagement logistically.
Wherefore it is an object of the present disclosure to overcome the above-mentioned shortcomings and drawbacks associated with conventional projectile guidance systems especially in GPS-denied and GPS-limited environments.
It has been recognized that there is a need to replace GPS navigation with a new, jam resistant navigation system for success in today's tactical environment. One aspect of the present disclosure is a navigation method within a GPS-denied or a GPS-limited environment that utilizes a local domain RF illuminator for weapon, projectile, UAV, or other asset guidance that can be deployed away from the engagement area. In certain embodiments, the RF system provides GPS navigation-like performance, but is resistant to jamming.
One innovation on this present disclosure is the employment of the Orthogonal Interferometer (OI) principle to achieve a GPS denied guidance and navigation capability by capturing the object measurements using the RF based OI configuration (
One aspect of the present disclosure is a flight navigation system directing at least one projectile to a target area, comprising: a radio frequency orthogonal interferometry array providing a reference frame, via a projected grid, in the direction of the target area; the reference frame providing azimuth and elevation information for use in guidance of the at least one projectile from a distance from the target to a hand-off point; the flight navigation system deriving location or orientation information using a projectile state estimator and not an inertial measuring unit; and a short range guidance system configured to accept hand-off from the radio frequency orthogonal interferometry array and begin guidance of the at least one projectile from the hand-off point to the target area.
One embodiment of the flight navigation system directing at least o projectile to a target area is wherein the radio frequency orthogonal interferometry array is aligned via a north finding device. In some cases, the distance from the target is about 100 km. In certain embodiments, the radio frequency orthogonal interferometry array accuracy is about ±5 m in range and about ±100 m in azimuth and elevation. In some embodiments, the hand-off point is less than about 10 km.
Another embodiment of the flight navigation system directing at least one projectile to a target area is wherein a CEP-50 is about 30 m. In some cases, the short range guidance system is a semi-active laser seeker having a hand off error of less than 0.1 degree. In certain embodiments, the short range guidance system is an image automatic target recognition system having a hand-off error of less than 2 m.
Yet another embodiment of the flight navigation system directing at least one projectile to a target area is wherein the at least one projectile is two or more projectile and each projectile receives unique target and guidance information.
Still yet another embodiment is wherein each of the at least one projectile comprise an RF receiver, an on-board processor, a communication module, and at least one other detector for use in short range guidance.
Another aspect of the present disclosure is a munition flight navigation method comprising: initiating a fire command via a fire control system; loading and firing at least one munition; powering up the at least one munition after launch; powering up a radio frequency orthogonal interferometry (RF/OI) array, wherein the radio frequency orthogonal interferometry array provides a reference frame, via a projected grid, in the direction of a target area; receiving target location and waveform mission code information, at the at least one munition; collecting, via a RF detector on the at least one munition, unique waveform data from the radio frequency orthogonal interferometry array; determining via a processor on the at least one munition, azimuth, elevation and range data for the at least one munition via the RF detector, the munition flight navigation system deriving munition location information using a projectile state estimator and not an inertial measuring unit; powering up a short range guidance system located on each of the at least one munition; designating a target via each short range guidance system; calculating target navigation waypoints for respective short range hand-off for each of the at least one munition; handing off guidance from the RF/OI array to a respective short range guidance system for each of the at least one munition; guiding the at least one munition to the target via the respective short range guidance system; and signaling the detonation of the at least one munition.
The present disclosure offers a GPS-denied navigation solution without explicitly requiring an onboard Inertial Measurement Unit (IMU) while providing the Guidance and Autopilot the ability to guide and intercept a designated target (of interest.)
These aspects of the disclosure are not meant to be exclusive and other features, aspects, and advantages of the present disclosure will be readily apparent to those of ordinary skill in the art when read in conjunction with the following description, appended claims, and accompanying drawings.
The foregoing and other objects, features, and advantages of the disclosure will be apparent from the following description of particular embodiments of the disclosure, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the disclosure.
In one embodiment of the system of the present disclosure, an Orthogonal Interferometry (OI) RF illuminator is located behind the weapon system (e.g., at 0 to 100 km) and an RF/OI receiver is mounted on an asset and receives the OI waveforms (distinguishable waveforms referenced to respective phase centers) to determine azimuth and elevation and range information to guide the asset to a target. In some embodiments, the azimuth and elevation information has an accuracy of about 100 to 300 μrads depending on the transmitter configuration. In some cases, the system range information has an accuracy of about +/−20 to 40 meters depending on various system operating parameters. In certain embodiments, the asset is given the target's location prior launch or via RF communications link after launch within the RF/OI frame of reference. The asset then calculates the trajectory for the target intercept using on-board guidance laws on an on-board processor.
The approach to local domain guidance control of the present disclosure allows the user to deploy an RF/OI illumination system anywhere in the world given the portability of the system (e.g., it fits on a small utility trailer), the system's range >100 km, and the system's accuracy. This system's performance is similar to GPS systems, but has the added benefit of inherent Jam resistance due to the use of custom coding of the RF/OI waveform, the illuminator's signal strength, the deployment geometry, and the antenna configurations. Unlike the GPS navigation waveforms which are published, the RF/OI illumination system would be classified or otherwise held secret. The system operator could select frequency, Pulse Repetition Interval (PRI) and pulse duration. Assuming a 100 nanosecond pulse, frequency hopping with varying PRI could be utilized in a code format loaded just prior to launch or during flight. In addition the rearward looking antenna on the projectile provides receiver isolation from the Jammers forward or below the projectile. The combination waveform control and antenna spatial selectivity provides inherent counter measure immunity. Ground based jammers have the additional burden of being direct line of sight of the RF/OI illuminator, thereby making detecting its presents difficult due to the curvature of the earth.
Referring to
Still referring to
In some embodiments, the RF array 108 guides (and tracks if equipped with fire control system) the one or more assets along the trajectory 106 with accuracy of about ±5 m range and ±10 m azimuth and elevation 112. In certain embodiments, the RF array uses orthogonal interferometry (OI) methods to project a reference frame, or a projected grid, in the air, which is analogous to a polar coordinate azimuth and elevation. The polar coordinates can be mapped to a standard grid coordinates utilizing latitude and longitude. In some cases, the RF/OI system 108 produces a reference frame that is aligned using a north finding gyro, or the like, such that the one or more projectiles or assets do not require separate north finding capabilities. This also tempers the need for precise alignment of the assets—center mass aiming—and thus, minimizes operator workload. In certain embodiments, the RF/OI system can provide 10°, 20°, or 30° fields of engagement. In some embodiments, the system provides for adjustable accuracy/guidance precision based, in part, on the RF/OI transmit power, antenna spacing, and deployment angle, where the cross range accuracy is equal to angular resolution times range.
Additionally, the system of the present disclosure eliminates the varying energetics and the cross wind impact of each of the one or more projectiles by maintaining the desired trajectory using the RF/OI system array for long range tracking and guiding. This technique reduces the complexity and the cost of the control actuator system (CAS) by simplifying the components needed on the projectiles. In some cases, an RF receiver and RF apertures are present on each round. In some cases, by using the RF/OI system, no azimuth aiming is required and minimal elevation adjustment is needed for each projectile, thus allowing the flight navigation system to make the course corrections accounting for the range differential due to energetics and aiming errors.
In one embodiment of the system of the present disclosure, the RF/OI system 108 “hands off” the tracking and guidance of the one or more projectiles at a certain hand-off point 114. Hand off refers to a transition from the use of the RF/OI guidance to a secondary form for guidance, to increase the accuracy of the projectile. In some cases, the hand-off point 114 is about six km to about ten km from the target along the flight path. In some cases, the hand-off point 114 is located a distance above a plane 116 on which the target is located. In some cases the distance 116 is about two km to about three km above the plane. In some cases, the target is on land. In some other cases the target is on the surface of water. The hand-off can be accomplished as a timed event starting from launch or the hand-off can be event driven. In certain embodiments, an event driven hand-off may be when a short range guidance system (e.g., a semi-active laser or image seeker) detects the target and initiates terminal guidance. In other cases, the hand-off point can be the point where LOS limitation for the RF/OI system effect the accuracy of terminal guidance.
The navigation approach of the present disclosure can be adapted for airborne targets, such as UAV but a tracking subsystem on the ground providing target location updates to the airframe would be needed. The fire control system would track the UAV, providing azimuth, elevation and range information in the RF/OI reference frame and then this information would be uplinked to the guided projectile/weapon to complete the guidance loop. The uplink can be accomplished by an EO/IR or RF modality, or the like.
In certain embodiments, the hand-off is from the RF/OI array to a semi-active laser (SAL) seeker. In some cases, each of the one or more projectiles has a unique SAL hand-off associated with it. In certain cases, the hand-off error is less than 0.1 degree. In some embodiments of the present disclosure, a SAL seeker is located on the front of the asset and the asset is guided by a designator (laser) coming from a forward observer on the ground, a UAV, or an aircraft. The use of coding technology in the SAL seeker mitigates false locks onto a second target where multiple designators are in the same engagement space or counter countermeasures (CCM) are being employed to defeat the weapons accuracy. In some cases, the SAL seeker is capable of detection at ten km with a one mrad target angle error. In some embodiments, the SAL seeker has a field of view (FOV) ranging from about 40 to about 70 degrees.
In other embodiments, the hand-off include projectile state estimation used in the last four to five seconds prior to detonation. In certain embodiments, the RF/OI illuminator provides sufficient guidance control even when guidance is ended at two to three meters above a target. The use of projectile state estimation, as known in the art, can adequately provide the orientation and/or location approximation needed to accurately deploy the projectile.
In still other embodiments, the hand-off is to an image-based homing and navigation system. In certain embodiments, a library of images exists for a given target area. The library is available to the one or more assets for guidance purposes and when one or more images in the library are matched to images from the field as view of the asset, once the asset is within a certain distance, the munition may be detonated. In some cases, automatic target recognition (ATR) is used. Generally, image-based methods work best for fixed targets, such as buildings, and the like. Wind and the energetics of launch can affect the trajectory of a munition but the RF/OI system is used, in part, to keep the correct steering for the munition until a short range guidance system takes over.
As seen in
Still referring to
The LOS prevents the weapon from seeing the RF/OI illuminator below the horizon. In addition, the RF/OI receiver's wave form is controlled to mitigate multipath due to the earth and influencing the accuracy of the position measurement. Waveforms allow multipath mitigation and allow the receiver to post process the impact of multipath out of the position results. These techniques yield a safe zone of navigation that corresponds to a slant angle of about one degree 126 from a transmitter (e.g., a tank) to the projectile at point 124 from the RF/OI illuminator or a height restriction 116 which is range dependent.
As depicted the CI case 200 has a common transmit path 214 and distinct receive paths 216a, 216b while the OI case 202 has distinct transmit and receive paths 218a, 218b at each receiver 212a, 212b. Decoding OI has achieved a double path length dependency, which provides twice the target angle 210 sensitivity as compared to CI with an equivalent SNR. The phase difference relationship of an interferometry is defined as
where D is the interferometer baseline (array phase center separation) 224, λ is the nominal operating wavelength), and Kϕ represents the phase gain factor that depends on path length. This expression highlights the physical advantage of a system with an electrically large baseline
in that yields a greater Δϕ for the same target offset θ; the geometric “gain” of the larger interferometric baseline yields a larger Δϕ relative to SNR dependent phase estimation noise σΔϕ2 and provides a more precise measurement of θ. In many signal processing applications the localized performance of an estimator can be bounded by the Cramer-Rao Lower Bound (CRLB). This bound on the θ estimation error for a CI radar or an OI radar is:
Note that for the same interferometer baseline (D) and same SNR the OI angle accuracy is a factor of two better than the CI angle accuracy.
This increase in the local precision of the angular estimate of θ due to an increased
comes at the cost of an increased chance of an ambiguous θ estimate. Angle ambiguity is a fundamental tradeoff that must be resolved for the potential of this increased estimator precision to have a real world benefit. There are a range of techniques used to suppress interferometer ambiguity. Depending on the particular application a combination of these techniques (discussed briefly herein) can provide effective angle disambiguation.
For interferometer baselines with D>>λ, Δϕ can greatly exceed 2π so the determination of angle-of-arrival using phase difference
will be ambiguous by N 2π wraps where N is the ambiguity number.
lobes within the main lobe—all reflecting the same Δϕ (modulo 2π measurement). Two important points should be taken from the “zoom” portion shown in
lobe 234 trace is much finer than the physical beam pattern. Trying to disambiguate these closely spaced lobes based on a model of the amplitude difference from the main lobe's much broader response will require very high SNR and a highly consistent signal model that is unlikely to be available in a tactical system.
Still referring to
Another approach to ambiguity mitigation for the OI-tracer application would exploit the high prior information on the projectile trajectory, which provides the opportunity to incorporate accurate kinematic models. In this case, the 236 trace can be interpreted as a prior estimate in a non-linear estimation/tracking formulation where a specific
lobe's probability is updated via a Bayesian recursion and the local covariance is update via a Kalman Filter. A physical example of exploiting prior information would involve an OI radar with
or 1 meter at 100 m range which is still extremely coarse as compared to the “close-in” CEP of the projectile.
For a projectile guidance application, where all the projectiles are cooperative, and there are well timed targets, this approach would be naturally integrated into a tracking filter that can be incorporated the aero-ballistic modeling. A final approach to ambiguity suppression involves multiple measurements at distinct λ/D values forming multiple interferometric baselines. For each available λ/D baseline, the relationship among feasible ambiguity numbers scales (by λ/D) but since the true target angle θ is independent of
the unwrapped 0th lobe experiences no shift.
measurements.
This lobe-wise product will only admit an θ ambiguity where the two lobe spaces overlap closely; in the combination of
238 and of
240 or the 125/100 case, the first significant overlap 242 occurs at the 5th lobe
and the 4th
lobe. Hence, there is another ambiguity suppression approach that involves the projectile priors and the interferometer design. In sum, achieving very high precision angle and trajectory estimates via large baseline interferometry incurs the additional complexity of angle ambiguity. Successful mitigation of the ambiguity challenge in an operational system requires substantial integration of the interferometer, array, and aero-ballistic modeling—the details each depending on the particular system configuration under consideration.
In certain embodiments of the system of the present disclosure, the RF system via an orthogonal interferometry (OI) reference frame operates at a frequency of about 5-10 GHz and has a signal-to-noise ratio (SNR) of about 20 dB. In some embodiments, the antenna gain is about 15-20 dB. In some cases, the baseline is about 1.5 m with an angular precision of less than 1 mrad. In some cases, the angular accuracy is about 0.45 mrad. This accuracy is in contrast to conventional radar systems that have angular accuracy of about one to two degrees. Conventional radar systems are also limited by bandwidth. Additionally, radar has cross range accuracy at 100 km of about 2.5 km (1.5° beam width) as compared to a 45 m cross range accuracy for the RF/OI system disclosed herein. At 50 km, the present system has 22 m accuracy, or hand-off error. This accuracy provides for accurate hand-off positioning. The present system provides actual location within GPS norms. In contrast, conventional radar systems produce a beam that is too broad to implement an angle transfer as described herein.
In some cases, the power requirement for the system ranges from about 100-200 W. The power needed is much lower than for a conventional radar system (e.g. 100 kW). Additionally, the RF/OI system is preferred due to inherent jamming resistance as compared to radar systems. In some embodiments, the projectiles have rear looking antennas for use with the RF/OI system. In some cases, the RF/OI illuminator can control multiple weapon batteries or UAV against multiple targets. The RF/OI reference frame is analogous to the localized GPS where several weapons platforms, air vehicles, and weapons can use the same RF/OI reference frame for navigation. In some cases, the pulse width for the system of the present disclosure is about 1.7 μsec which encapsulates the RF/OI waveform.
The RF/OI reference frame is analogous to GPS, the spatial extent of the illuminator provides elevation and azimuth bearings from the OI illuminator Like GPS, knowing where the satellites are in GPS constellation you can determine your position with the RF/OI illuminator; knowing it's latitude and longitude position and the zero phase line direction relative to true north. In the multiple weapons scenario, the weapons can be preprogrammed the information prior to launch and then guided using the RF/OI as a reference. This information can also be programmed after launch via a communications link.
Referring to
Referring to
In some embodiments, multiple rounds are coordinated in one RF/OI reference frame. In some cases a full battery of Howitzers, or the like, are used and each round has customized trajectories for the particular target type or for masking the round's location. In some cases this is limited to the weapons control authority and its ability to fly an azimuth arc from the point of launch thereby disguising it's launch point from enemy counter fire radar.
In certain embodiments, the RF/OI reference frame is extended to about 100 km and provides location to within about 100 m. In some cases the reference frame is extended to about 50 km and provides location to within about 50 m. The system utilizes one way illumination with rear-looking antennas on the projectiles. The system of the present disclosure provides for RF jam hardening.
In some cases the round may be programmable during the initial flight path, which can reduce the time to fire. By equipping the RF/OI reference frame with a high quality north seeker, the system allows for “on the go” alignment for all of the rounds. No azimuth aiming is required with the RF/OI reference frame, and only minimal elevation adjustment is needed to account for a range differential. The RF/OI can be designed to cover various fields of engagement. In some cases, the field of engagement may be 10, 20 or 30 degrees.
Still referring to
In some cases, the RF/OI illuminator's guidance of a munition is handed off to a SAL seeker, or the like. There, the round is equipped with laser detection ROIC or the like. In some cases, the short range guidance system is small, e.g., about 1 in3, including the optics. In one embodiment, the SAL seeker is capable of detection at 10 km with 1 mrad target angle error with a FOV ranging from 40 to 70 degrees. In certain embodiments, a SAL seeker located on the front of the asset is guided by a designator (laser) coming from a forward observer on the ground, a UAV, or an aircraft. In some cases, the short range guidance system utilizes full counter countermeasure (CCM) filtering with spatial and temporal filtering and/or full pulse repetition frequency (PRF) and pulse interval modulation (PIM) decoding with multiple designators within the FOV.
In some cases, the RF/OI illuminator's guidance of a munition is handed off to an image based homing and navigation system. In certain embodiments, the short range guidance system utilizes image ATR (automatic target recognition). ATR is generally better suited for fixed targets, including, but not limited to buildings or structures. A series of images are stored in a database and either loaded onto a round or accessible by a round. The images are for areas of interest and/or for particular types of assets. When a round is within a certain range, the round can “recognize” the target form the images stored in the library. In some cases the library of images comprises items viewed at a distance of 1000 to 3000 meters. The processed imagery for stationary targets would need to factor in the attack angle for both elevation and azimuth direction of flight relative to the target; i.e. building or fortification. Moving targets (missile launcher) would need to also consider various poses; missiles in firing stowage or launch position would represent two exemplary different images or poses.
In some cases, the RF/OI illuminator's guidance of a munition is handed off to an IMU during the final four to five seconds, or the terminal phase. The IMU would be the primary means of navigating to the target in the last few seconds when the RF/OI illuminator in hindered by the LOS of the system. In some cases, this method is utilized in a grid pattern for area bombing.
Referring to
Referring again to
A short range guidance section 540 is used when the projectile reaches a hand-off point near the terminal end of the trajectory near the target area. The short range guidance section 540 in one example is a SAL seeker that receives a signal such as reflected laser signal from the target. Another example is an imaging section that uses a camera to view the target area and compares the captured image to stored images to identify the target and guide the projectile to the target. The processing includes having a state estimator to provide orientation information without relying upon GPS or an IMU. In one example, after the RF/OI communications is no longer available, the projected waypoints provide estimated target locations. By using the short range guidance systems such as imaging electronics, the orientation can be determined and used to continue along the trajectory with the proper orientation. The short range guidance systems may also enable highly accurate target location information to help guide the projectile and maintain orientation.
It will be appreciated from the above that portions of the invention may be implemented as computer software, which may be supplied on a storage medium or via a transmission medium. It is to be further understood that, because some of the constituent system components and method steps depicted in the accompanying Figures can be implemented in software, the actual connections between the systems components (or the process steps) may differ depending upon the manner in which the present invention is programmed. Given the teachings of the present system provided herein, one of ordinary skill in the related art will be able to contemplate these and similar implementations or configurations of the present invention.
It is to be understood that the present invention can be implemented in various forms of hardware, software, firmware, special purpose processes, or a combination thereof. In one embodiment, the present invention can be implemented in software as an application program tangible embodied on a computer readable program storage device. The application program can be uploaded to, and executed by, a machine comprising any suitable architecture. The computer readable medium as described herein can be a data storage device, or unit such as a magnetic disk, magneto-optical disk, an optical disk, or a flash drive. Further, it will be appreciated that the term “memory” herein is intended to include various types of suitable data storage media, whether permanent or temporary, such as transitory electronic memories, non-transitory computer-readable medium and/or computer-writable medium.
While various embodiments of the present invention have been described in detail, it is apparent that various modifications and alterations of those embodiments will occur to and be readily apparent to those skilled in the art. However, it is to be expressly understood that such modifications and alterations are within the scope and spirit of the present invention, as set forth in the appended claims. Further, the invention(s) described herein is capable of other embodiments and of being practiced or of being carried out in various other related ways. In addition, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having,” and variations thereof herein, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items while only the terms “consisting of” and “consisting only of” are to be construed in a limitative sense.
The foregoing description of the embodiments of the present disclosure has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the present disclosure to the precise form disclosed. Many modifications and variations are possible in light of this disclosure. It is intended that the scope of the present disclosure be limited not by this detailed description, but rather by the claims appended hereto.
A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made without departing from the scope of the disclosure. Although operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results.
While the principles of the disclosure have been described herein, it is to be understood by those skilled in the art that this description is made only by way of example and not as a limitation as to the scope of the disclosure. Other embodiments are contemplated within the scope of the present disclosure in addition to the exemplary embodiments shown and described herein. Modifications and substitutions by one of ordinary skill in the art are considered to be within the scope of the present disclosure.
This application claims priority to U.S. Provisional Patent Application No. 62/738,059, filed Sep. 28, 2018, the content of which is incorporated by reference herein its entirety.
Number | Name | Date | Kind |
---|---|---|---|
6255992 | Madden | Jul 2001 | B1 |
8120526 | Holder | Feb 2012 | B2 |
8854252 | Holder | Oct 2014 | B2 |
9401741 | Holder et al. | Jul 2016 | B2 |
9696418 | Holder | Jul 2017 | B2 |
20170314892 | Holder | Nov 2017 | A1 |
Number | Date | Country |
---|---|---|
2007016098 | Feb 2007 | WO |
Entry |
---|
“Heterodyne”, https://en.wikipedia.org/wiki/Heterodyne, known of at least since Apr. 24, 2019. |
“Interferometry”, https://en.wikipedia.org/wiki/lnterferometry, known of at least since Apr. 24, 2019. |
Monopulse radar, https://en.wikipedia.org/wiki/Monopulse radar, known of at least since Apr. 24, 2019. |
“Pulse-Doppler signal processing”, https://en.wikipedia.org/wiki/Pulse-Doppler_signal_processing, known of at least since Apr. 24, 2019. |
“Undersampling”, https://en.wikipedia.org/wiki/Undersampling, known of at least since Apr. 24, 2019. |
Armin W. Doerry, “SAR Processing with Stepped Chirps and Phased Array Antennas”, Sandia Report, Sandia National Laboratories, Printed Sep. 2006, Albuquerque, NM. |
M. Mallick et al., “Angle-only filtering in 3D using Modified Spherical and Log Spherical Coordinates”, 14th International conference on Information Fusion, Chicago, Illinois; pp. 1905-1912, Jul. 5-8, 2011. |
K. Radhakrishnan et al., “Bearing only Tracking of Maneuvering Targets using a Single Coordinated Turn Model”, International Journal of Computer Applications (0975-8887) vol. 1—No. 1, pp. 25-33; 2010. |
Number | Date | Country | |
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62738059 | Sep 2018 | US |