UNITED STATES PROVISIONAL APPLICATION FOR PATENT

FOR

SYSTEM AND METHOD FOR SENSING AIRCRAFT AND OTHER OBJECTS

INVENTOR: JED MARGOLIN

SYSTEM AND METHOD FOR SENSING AIRCRAFT AND OTHER OBJECTS

BACKGROUND OF THE INVENTION - Field of Invention

[001] This invention relates to the field of sensing aircraft and other objects and is part of the See and Avoid (SAA) function for manned aircraft and the Detect, Sense and Avoid (DSA) function for remotely piloted vehicles (RPVs) and unmanned aerial vehicles (UAVs). RPV is an older term for UAV. “UCAV” shall mean “Unmanned Combat Aerial Vehicle.” UCAV is also sometimes defined as an “Uninhabited Combat Aerial Vehicle.” UCAV is a UAV that is intended for use in combat. UAS means “Unmanned Aerial System.” UCAS means “Unmanned Combat Air System.” The characteristics all these vehicles have in common is that there is no human pilot onboard, and although they may be operated autonomously they can also be controlled by a remotely located operator or pilot. The term UAV shall be used as a generic term for such vehicles. Detect, Sense, and Avoid (DSA) is also commonly called Sense and Avoid (SAA) since “Detect” and “Sense” mostly mean the same thing. This invention is directed to the “See” in “See and Avoid” and the “Sense” in “Sense and Avoid.”

BACKGROUND OF THE INVENTION – Prior Art

[002] In an aircraft with the pilot onboard, Sense and Avoid is called See and Avoid. FAA Regulations do not give much guidance for seeing other aircraft.

Right-of-way rules: Except water operations 14 CFR § 91.113(b) [Ref. 1]:

(b) General. When weather conditions permit, regardless of whether an operation is conducted under instrument flight rules or visual flight rules, vigilance shall be maintained by each person operating an aircraft so as to see and avoid other aircraft. When a rule of this section gives another aircraft the right-of-way, the pilot shall give way to that aircraft and may not pass over, under, or ahead of it unless well clear.

Right-of-way rules: Water operations 14 CFR § 91.115(a) [Ref. 2]

(a) General. Each person operating an aircraft on the water shall, insofar as possible, keep clear of all vessels and avoid impeding their navigation, and shall give way to any vessel or other aircraft that is given the right-of-way by any rule of this section.

When operating under Visual Flight Rules the idea is to look out small windows providing a limited field of view and hope you see any nearby aircraft in time to avoid a collision. This is made more difficult because of the wide range of aircraft sizes and speeds. (Is it a large aircraft far away or a small aircraft much closer?) This is even more difficult under instrument flight rules where there may be no visibility.

[003] Radar can be used to sense aircraft. Ground-based Radar allows Air Traffic Control (ATC) to direct aircraft in controlled airspace and keep aircraft safely apart. Military aircraft are generally equipped with onboard radar.

[004] One type of collision avoidance system uses Secondary Surveillance Radar (SSR) where the Primary Surveillance Radar (PSR) used in air traffic control (ATC) detects and measures the position of aircraft and a secondary signal is transmitted that triggers a transponder in an aircraft that requests additional information from the aircraft itself such as its identity and altitude. Unlike Primary Surveillance Radar systems, which measure only the range and bearing of targets by detecting reflected radio signals, Secondary Surveillance Radar relies on its targets being equipped with a transponder which replies to each interrogation signal by transmitting its own response containing encoded data. U.S. Patent 4,782,450 Method and apparatus for passive airborne collision avoidance and navigation issued November 1, 1988 to Flax teaches that an aircraft can be equipped with a system that monitors the signals from the Secondary Surveillance Radar and the signals produced by each aircraft’s transponders to produce its own onboard display of the locations of aircraft in the area. [Ref. 3]

[005] The Traffic alert and Collision Avoidance System (TCAS) is an aircraft collision avoidance system designed to reduce the incidence of mid-air collisions between aircraft. It monitors the airspace around an aircraft by interrogating the transponders of other TCAS-equipped aircraft via the 1030 MHz frequency. It then uses the received transponder signals (via the 1090 MHz. frequency) to compute distance, bearing and altitude relative to its own aircraft. This interrogation-and-response cycle may occur several times per second. From the FAA’s Introduction to TCAS II Version 7 [Ref. 4]

The TCAS Computer Unit, or TCAS Processor, performs airspace surveillance, intruder tracking, its own aircraft altitude tracking, threat detection, RA maneuver determination and selection, and generation of advisories. The TCAS Processor uses pressure altitude, radar altitude, and discrete aircraft status inputs from its own aircraft to control the collision avoidance logic parameters that determine the protection volume around the TCAS aircraft. If a tracked aircraft is a collision threat, the processor selects an avoidance maneuver that will provide adequate vertical miss distance from the intruder while minimizing the perturbations to the existing flight path. If the threat aircraft is also equipped with TCAS II, the avoidance maneuver will be coordinated with the threat aircraft.

Where TCAS is relied upon to prevent mid-air collisions, an aircraft that does not have the equipment installed (or TCAS is broken or has been deliberately turned off) is a hazard to itself and other aircraft in the vicinity.

[006] The system by which an aircraft periodically transmits its identification, location, altitude, and heading is taught by U.S. Patent 5,153,836 Universal dynamic navigation, surveillance, emergency location, and collision avoidance system and method issued October 10, 1992 to Fraughton et al. [Ref. 5] and was materially adopted by the FAA as Automatic Dependent Surveillance-Broadcast (ADS-B). According to the article Gulf of Mexico Helo Ops Ready for ADS-B in Aviation Week & Space Technology (02/26/2007, page 56) [Ref. 6]:

By the end of 2010, FAA expects to have the ADS-B system tested and operationally acceptable for the NAS, with Houston Center providing services in the Gulf region. By 2013, all of the U.S. is scheduled to be covered with ground infrastructure.

As with TCAS, where ADS-B is relied upon to prevent mid-air collisions, an aircraft that does not have the equipment installed (or ADS-B is broken or has been deliberately turned off) is a hazard to itself and other aircraft in the vicinity. ADS-B also comes with the risk that terrorists can use it to identify and track targets.

[007] A passive radar system is taught by U. S. Patent 5,187,485 Passive ranging through global positioning system issued February 16, 1993 to Tsui, et al. [Ref. 7] The patent teaches a method for determining the distance from a target to an observation station, using four GPS satellites as radiation sources, and a GPS receiver at the observation station to form a bistatic radar system, wherein an angle of arrival (AOA) of the target to the observation station has been measured first. Because the signal level from the GPS satellites is already low, the signal reflected from various objects is very low, requiring the use of a large antenna or more-powerful GPS satellites. See Test Results from a Novel Passive Bistatic GPS Radar Using a Phased Sensor Array by Alison Brown and Ben Mathews, NAVSYS Corporation. [Ref. 8]

[008] There are other types of radar that attempt to keep the presence and location of the emitter from being detected. Examples are Spread Spectrum, Frequency Hopping, Ultra Wideband, and Noise Radar. Although there are differences between them, what they have in common is that they are designed to transmit a signal that cannot be detected except by the originating entity. As a result, target echoes also cannot be detected except by the originating entity. They generally do this by using a much wider bandwidth than a standard radar.

Spread Spectrum will be used here as an example. An example of Spread Spectrum Radar is taught by U.S. Patent 5,724,041 Spread spectrum radar device using pseudorandom noise signal for detection of an object issued March 3, 1998 to Inoue, et al. [Ref. 9].

Abstract

A radar device transmits by a transmitting part a wave whose band is spread by a PN code from a PN generator, receives at a receiving part a reflected wave from an object based on the wave and detects the object by detecting correlation between the received signal and the PN code. In this radar device, the received signal which is spread to a wide range is converted to a low-frequency band which is easy to be measured by a down converter so that a signal is generated when correlation is made by a delay of the PN code from a delay circuit, and generates a pulse signal through waveform shaping of the signal to detect the object and to measure its relative speed and distance at a processing part according to the pulse signal and the delay time.

Note that “PN” means Pseudo-Random Number. A pseudo-random number is produced by an algorithm so it is not truly random. However, it has the advantage that sequences of pseudo-random numbers can be reproduced. An example of a method of producing pseudo-random numbers is the Linear Feedback Shift Register. A simple Linear Feedback Shift Register can be used to produce white noise for testing audio equipment as taught in the article Shift Register With Feedback Generates White Noise by Marc Damashek in the May 27, 1976 issue of Electronics magazine. [Ref. 10] It has also been used in U.S. Patent 4,159,293 Random dot generator for raster scan video displays issued March 25, 1980 to Margolin (the current inventor). [Ref. 11]

Abstract

A Linear-Feeback-Shift-Register produces a pseudorandom sequence of bits that are used to produce a stationary random pattern of dots on a standard raster scan video display. The density of dots is adjustable as is their intensity. This dot pattern may be combined with other video sources and thus may serve as a background for the playing of TV video games, especially those of the "space war" variety. The dot pattern may also be moved as a whole under player control and thus form the basis for a novel type of video game to be described.

[009] Linear-Feedback-Shift-Registers (LFSRs) have also been used to produce pseudo-random sequences of binary signals for use as test signals for transmission paths (U.S. Patent 3,986,168 Multichannel error signal generator issued October 12, 1976 Anderson) [Ref. 12], and as code sequences for encoding information (U.S. Patent 3,515,805 Data scrambler issued June 2, 1970 to Fracassi et al.). [Ref. 13] The theory of Linear-Feedback-Shift-Registers (LFSRs) is covered extensively in "Shift Register Sequences" by Solomon Golomb (Holden-Day Inc., San Francisco, 1967, and Aegean Park Press, 1982) [Ref. 14].

A very good description of spread spectrum is The ABCs of Spread Spectrum - A Tutorial by Randy Roberts, Director of RF/Spread Spectrum Consulting. [Ref. 15]

[010] The problem with spread spectrum radar is that it might not be undetectable. See Undetectable Radar? (Probably Not) by Erik Hundman, Defensetech.org, August 3, 2006. [Ref. 16]

[011] Any entity that radiates an electromagnetic signal stands a good chance of being detected, even if spread spectrum signals are used. The use of bistatic radar avoids this problem. In bistatic radar the transmitter and the receiver are physically separated by some distance so the location of the receiver cannot be detected by tracking the transmission. Bistatic radar is commonly called passive radar and is the basis for U. S. Patent 5,187,485 previously mentioned which uses the signals from the GPS system as the radiators. Other systems have been proposed using what are called “unintentional radiators.” That doesn’t mean the transmitters are unintentionally radiating, only that they are not radiating for the purpose of providing a signal to be used for bistatic radar. Examples are FM broadcast stations, TV broadcast stations, and cell phone base stations. See From a Different Perspective: Principles, Practice, and Potential of Bistatic Radar by H.D. Griffiths. [Ref. 17]. The problems with these radiators are that:

1. There might not be one where you need it.

2. They cannot be relied upon to always be transmitting.

3. In a combat zone they are prime targets for anti-radiation missiles and other attacks.

[012] UAVs have special problems sensing other aircraft.

1. If the UAV is flown manually by a remote pilot looking at the video produced by a camera mounted in the nose of the aircraft the field of view will be too limited to see other aircraft other than those directly ahead.

2. If the UAV is flown autonomously there is no human pilot. If the flight is supervised by a human operator the problem remains that the field of view from a camera mounted in the nose of the aircraft will be too limited.

3. Military UAVs might not want to use TCAS, ADS-B, or onboard radar because it would allow other aircraft and ground facilities to detect and track them. They want to sense without being sensed.

BACKGROUND OF THE INVENTION – Current Practice in Flying UAVs

[013] The current practice in flying UAVs in civilian airspace is typified by the report Sensing Requirements for Unmanned Air Vehicles by AFRL's Air Vehicles Directorate, Control Sciences Division, Systems Development Branch, Wright-Patterson AFB OH, June 2004, which relies on computer-intelligence to use sensors to sense and avoid other aircraft. [Ref. 18]

[014] According to the presentation entitled Developing Sense & Avoid Requirements for Meeting an Equivalent Level of Safety given by Russ Wolfe, Technology IPT Lead, Access 5 Project at UVS Tech 2006 this had not changed as of January 18, 2006. [Ref. 19] Access 5 was a national project sponsored by NASA and Industry with participation by the FAA and DOD to introduce high altitude long endurance (HALE) remotely operated aircraft (ROA) to routine flights in the National Airspace System (NAS). Access 5 started in May 2004 but when NASA withdrew its support (and funding) the Industry members decided not to spend their own money and Access 5 was dissolved at the end of 2005.

[015] The presentation Integration into the National Airspace System (NAS) given by John Timmerman of the FAA’s Air Traffic Organization (July 12, 2005) essentially says that under current UAS Operations in the NAS UAVs should not harm other aircraft or the public. (Page 3: “While ensuring ‘no harm’ to other NAS customers and public”) [Ref. 20]

[016] The article Zone Ready for Drone, April 7, 2006, on the web site for the FAA’s Air Traffic Organization Employees states that [Ref. 21],

Since March 29, a temporary flight restriction … has limited access to the airspace along almost 350 miles of the border, expanding an earlier TFR near Nogales. The restriction is in effect nightly from 6 p.m. to 9 a.m., although that time can be expanded by issuance of a Notice to Airmen. Aircraft wishing to fly in the TFR when it is active must receive authorization from air traffic control prior to entry. Once in, pilots are required to maintain two-way communication with ATC and transmit a discrete transponder code.

The reason for the TFR is to enable Predator UAVs to patrol the border. The article quotes Stephen Glowacki, a Systems Safety and Procedures specialist with the FAA’s Air Traffic Organization as saying:

This is an extreme situation that has been presented to us,” states Stephen Glowacki, a Systems Safety and Procedures specialist with the FAA’s Air Traffic Organization, stressing the nation’s security. “We have been working with U.S. Customs and Border Protection to try and answer this situation.”

Inserting UASs into the National Airspace System is not a simple feat. According to Glowacki, the technology and certification that will permit unmanned aircraft to “see and avoid” other air traffic is still eight to ten years away. In the mean time, a carefully controlled environment is needed.

[017] From Quadrennial Roles and Missions Review Report, Department of Defense, January 2009, page 29 [Ref. 22]:

U.S. Joint Forces Command Joint UAS Center of Excellence has identified three areas necessary to ensure access to applicable classes of the National Airspace System: (1) Airworthiness Certification; (2) establishment of standardized basic UAS qualifications consistent with Federal Aviation Administration guidelines for each class of airspace; and (3) development of sense and avoid technology. Working with the Services, the U.S. Joint Forces Command Joint UAS Center of Excellence will ensure these areas are addressed during UAS development.

(Emphasis added.)

OBJECTIVES

[018] Therefore, an objective of the present invention is to improve TCAS so that aircraft equipped with TCAS can detect aircraft not equipped with it (or TCAS is broken or has been deliberately turned off).

Another objective of the invention is to improve ADS-B so that aircraft equipped with ADS-B can detect aircraft not equipped with it (or ADS-B is broken or has been deliberately turned off).

Another objective of the invention is to detect and locate aircraft which are using spread spectrum radar in an attempt to be undetected.

Another objective of the invention is a system to detect and locate aircraft and other objects without itself being detected or located.

A further objective of the invention is an integrated bistatic spread spectrum radar system using a satellite constellation for the radar function as well as for communications.

SUMMARY OF THE INVENTION

[019] TCAS can be improved by using the interrogation signal transmitted from a TCAS unit as a radar transmitter with a receiver to receive reflections. In a first preferred embodiment the standard TCAS antennas are used to receive the reflections of the TCAS signal. Although one of the TCAS antennas is a directional antenna, its directionality is currently limited to 90 degree quadrants. The time delays between the transmitted signal and the reflections are used to determine the range of other aircraft and are used to match the range and number of targets to the TCAS transponder signals normally received. Doppler analysis can be used to confirm the speeds of the targets. In a second preferred embodiment a separate directional receiving antenna is used to give both the range and bearing of aircraft and other objects in the vicinity of the user’s aircraft even when other aircraft are not equipped with TCAS.

[020] ADS-B can be improved by using the signal transmitted from an ADS-B unit as a radar transmitter with the ADS-B receiver used to receive reflections. In a third preferred embodiment a standard omni-directional antenna is used to receive the reflections of the ADS-B signal. The time delays between the transmitted signal and the reflections are used to determine the range of other aircraft and match the range and number of targets to the ADS-B signals normally received. Doppler analysis can be used to confirm the speeds of the targets. In a fourth preferred embodiment a directional receive antenna is used to give both the range and bearing of aircraft and other objects in the vicinity of the user’s aircraft even when other aircraft are not equipped with ADS-B.

[021] Aircraft using spread spectrum radar can be detected by using two separate receiving systems, each with its own antenna and receiver. Each receiving system is configured to have the same frequency range and bandwidth. The output of each receiver system is digitized to have the same number of samples in a frame of data. A cross-correlation is then performed between the two data frames. The noise produced by each receiver system is completely independent of each other so the internally generated noise is uncorrelated. If there is a correlation between the data frames from two receiver systems it can only have come from an external source, such as a spread spectrum signal.

[022] In a fifth preferred embodiment each receiving system uses an omni-directional antenna, the two receiving systems are spatially separated, and the phase term (time delay) in the cross-correlation function is used to determine the bearing to the target. However, this produces the “Hemisphere Problem” as it is known in the field of Radio Direction Finding (RDF). A target on either side of the line between the two antennas produces the same time delay, and therefore the same angle. One method to determine which side of the line the target is on is to use a third antenna that is not collinear with the first two antennas. The receiving system from the third antenna produces a signal that is cross-correlated with the signal from one of the first two antennas. The other method is to use Doppler from the target to determine the target’s velocity along with the change in the User’s position. This is used for triangulation of the target. A good place to put the first two antennas are at the ends of the wings, especially in winglets made of non-conducting composites with one antenna in each winglet. The third antenna may be placed either in the nose or the tail. Alternatively, the first two antennas may be placed in the nose and in the tail with the third antenna placed at the end of either wing.

[023] A sixth preferred embodiment adds a second pair of receiving systems using omni-directional antennas. The pair of antennas in the first receiving system are located physically apart from each other and from the first pair of receiving antennas. The bearing produced by the second pair of receiving systems is used for performing triangulation with the first pair of receiving systems to determine the range to the target.

[024] In a seventh preferred embodiment, to improve the Probability of Intercept (POI), two co-located directional antennas are used. In this mode the antennas must be pointed in the same direction. However, this improvement in POI comes at the expense of obtaining range information. Bearing information is produced by the direction of the antennas since it is no longer possible to use the phase information term in the cross-correlation function to determine the bearing to the target.

[025] In an eighth preferred embodiment the two directional antennas are spatially separated. Bearing information is produced by the direction of the antennas and triangulation is used to produce range information. Since a correlated signal is produced only when both antennas are pointed at the target the antenna angles must be coordinated.

[026] In a ninth preferred embodiment a second pair of co-located receiving systems is added, spatially separated from the first pair of co-located receiving systems. Triangulation between the first pair of receiving systems and the second pair of receiving systems is used to determine the range to the target. This has the advantage that each pair of receiving systems may independently search for the presence of a target. When a target is detected by one pair of receiving systems the other pair of receiving systems is brought to bear on it for triangulation to determine its range.

[027] The use of directional antennas requires the ability to aim the antennas. This can be done by physically aiming the antennas (such as when the antennas use parabolic dish reflectors) or by using active electronically scanned arrays. Because each area must be separately scanned the time to detect and locate spread spectrum targets is increased according to the directionality of the antennas. The use of directional antennas reduces the noise received that is produced by the Sun, except when the antennas are pointed at the Sun. (The level of the sun's contribution depends on the solar flux.) It also reduces the noise received that is produced by the Earth (about 290K.), except when the antennas are pointed at the Earth.

The technology requirements for performing a reasonably fast digital cross-correlation on two wideband signals are formidable: a fast Analog-to-Digital Converter (ADC) and a fast Digital Signal Processor (DSP). However, fast ADCs are available, such as the AD9481 (8-Bit, 250 MSPS) by Analog Devices Inc. [Ref. 23]. Fast and inexpensive DSPs are available due to their increasing use in consumer products. An example is the C6713B from Texas Instruments. [Ref. 24]

Operating at 300 MHz, the C6713B delivers up to 1800 million floating-point operations per second (MFLOPS), 2400 million instructions per second (MIPS), and with dual fixed-/floating-point multipliers up to 600 million multiply-accumulate operations per second (MMACS).

If additional processing power is required, the cross-correlation function is very amenable to parallel processing.

[028] A system and method for detecting and locating aircraft and other objects without being detected or located will now be described.

As previously discussed, any entity that radiates an electromagnetic signal stands a good chance of being detected and possibly located, even if spread spectrum signals are used. The use of bistatic radar avoids this problem. Systems have been proposed using “unintentional radiators” such as FM broadcast stations, TV broadcast stations, and cell phone base stations. However, these sources cannot be relied upon to always be transmitting, and in a combat zone they are prime targets for anti-radiation missiles and other attacks. Because of the likelihood that any radiator can be detected and probably tracked, the solution is to make the transmitter difficult to attack.

[0029] One or more high-flying aircraft can be used as the transmitting source(s) for a bistatic radar system. One disadvantage of this method is that the technology race between aircraft and anti-aircraft missiles (and directed energy weapons) favors anti-aircraft missiles and directed energy weapons. An example of a directed energy weapon is taught by U.S. Patent 6,377,436 Microwave Transmission Using a Laser-Generated Plasma Beam Waveguide issued April 23, 2002 to Margolin (the present inventor). [Ref. 25] Another disadvantage of using high-flying aircraft is that it requires the close coordination of multiple assets.

[0030] The solution is to go higher and use a permanently orbiting constellation of satellites. It can be called the Global Radar System (GRS). Although this might resemble the method taught in U. S. Patent 5,187,485 Passive ranging through global positioning system the purpose of the satellites is different and can be optimized to the mission.

1. GRS satellites will use higher power than GPS.

2. The precise position of each GRS satellite does not need to be known, only the precise range and bearing to the User. The use of GPS should not be a requirement for the operation of the GRS.

3. The GRS satellites will produce a secured spread-spectrum signal. Although GPS also uses a spread-spectrum signal the details are publicly available so manufacturers can make and sell the GPS receivers to the general public.

4. The GPS constellation is in orbital planes approximately 20,200 km above the Earth (Medium Earth Orbit or MEO). The GRS constellation should be in Low Earth Orbit (LEO) in the range of 160 km - 2,000 km.

One of the reasons for using LEO is that it is desirable to keep the existence of GRS a secret and it would be difficult to secretly launch and operate a constellation of satellites. Therefore, the GRS function should be hidden in a satellite constellation that has a non-secret mission. A prime candidate is a new satellite system for providing communications with UAVs around the world. For various reasons, communications with UAVs should have low latency, and a LEO system will have lower latency than a MEO system. The military’s increasing use of UAVs and need for dedicated low-latency bandwidth justifies a dedicated satellite system using spread spectrum communications. The function of also providing a spread-spectrum signal for bistatic radar does not have to be publicly revealed. The need to have these “communication” satellites always transmitting can be explained as “continuous monitoring of system health.” Indeed, there is value for a User to know that the communications system is working and that a channel is available. It reduces POI by avoiding unnecessary transmissions. POI can also be reduced by using a directional antenna for transmitting and aiming it at an available satellite with the lowest POI. For example, the satellite most directly overhead may have the lowest POI in many situations. This presents the opportunity to provide an integrated bistatic spread spectrum radar system using a satellite constellation for the radar function as well as for communications.

[031] It is desirable to have the capability for GRS satellite-to-satellite communications, preferably using optical links.

[032] The following example is for a 2D system which will be expanded later to a 3D system. A satellite constellation is being used, and each satellite transmits a spread spectrum signal and has its own unique PN code. It is assumed that the User is receiving a signal in straight paths from one or more satellites and that there is a straight path from the satellites to the target and from the target to the User and that the range and bearing from the User to each satellite is known. As a result, the length of the path from each satellite reflected from the target is also known.

[033] The distance from each satellite to the User can be known in several ways. One method is to use GPS for the location of the User and for the satellites to broadcast their GPS positions (regardless of how their positions are determined). Another method is for the User to use GPS, an accurate clock, and an ephemeris that gives the locations of satellites for a period of time in advance. Another method is for the User to have an accurate clock and for the satellites to include the time of transmission in their signals. Another method is for the User to send a signal to the appropriate satellite which responds with a signal that the User can use to get the range and bearing of that satellite. Thereafter, Inertial Navigation may be used. This method has the advantage that it does not use GPS but would be limited to those times when radio silence by the User is not necessary. A further method is to build a simplified form of Global Navigation Satellite System (GNSS) into GRS (and kept secret) as a military backup to GPS. It does not have to be as accurate as GPS because its purpose is to sense other aircraft in order to prevent a collision. It is not necessarily for delivering weapons, which has the opposite goal.

[034] When the User receives a reflected signal from the target a cross correlation is performed using the PN codes for the satellites in order to determine which satellite the reflected signal is coming from. The use of an ephemeris would allow the User to test only for those satellites that are visible.

Where the User determines the position of the satellite using GPS, an accurate clock, and an ephemeris it is not necessary for the User to receive a direct signal from the satellite, only the reflection from the target.

[035] At this point the User knows the total length of the path from a first satellite to the target and then to the User and wants to know the length of the path from the target to himself. The User also knows the length of the path from the first satellite to himself. Mathematically, this is the definition of an ellipse. The User and the first satellite are at the foci and the target is somewhere on the ellipse.

[036] When a second satellite is added, a second ellipse is formed. The User is at one of the foci, the second satellite is at the other. The first ellipse and the second ellipse intersect at only two points, with the target at one of the points.

[037] When a third satellite is added, a third ellipse is formed. Again, the User is at one of the foci and the third satellite is at the other. The three ellipses intersect at only one point. That is where the target is.

[038] A 3D system is more complicated because the geometric figure produced between each satellite and the User is not a 2D planar ellipse. Picture an ellipse rotating around the axis between the User and the satellite. The figure that each Satellite produces is an ellipsoid (a prolate spheroid) that looks remarkably like a football (U.S. or Canadian).

[039] Satellite 1 produces an ellipsoid with the User at one of the foci and the satellite at the other. The target is somewhere on the surface of the ellipsoid.

[040] When a second satellite is added, a second ellipsoid is formed. The User is at one of the foci, the second satellite is at the other. The first ellipsoid and the second ellipsoid intersect and produce an ellipse. The reason for this is because they share a common focus. [Ref. 26]

[041] When a third satellite is added, a third ellipsoid is formed. The User is at one of the foci, the third satellite is at the other. The first and second ellipsoids and the third ellipsoid intersect at two points, with the target at one of the two points.

[042] When a fourth satellite is added, a fourth ellipsoid is formed. The User is at one of the foci, the fourth satellite is at the other. The first three ellipsoids and the fourth ellipsoid intersect at only one point. That is where the target is.

[043] The geometry that has been described might not be obvious to someone versed mainly in GPS geometry. GPS uses only three satellites to determine the User’s position in three dimensions. (A fourth satellite is used for time correction.) The reason for this difference is because instead of using only the signal received directly from the satellite, the User is receiving both the direct signal and a signal reflected from the target. A line from the target meets the line from the User to the satellite at a 90 degree angle and forms the radius of a circle. The target can be anywhere on that circle. That is why the additional satellite is needed to determine the position of the target.

[044] There is something to note. Not all ellipses that share a focus point will intersect. However, in this case they must intersect because the ellipses were created by reflections from the same target, and the target cannot be in more than one place at the same time.

[045] The issue of multiple targets will now be discussed. A single target will produce four reflections, one from each satellite. A second target will produce four more reflections unless the geometry of the User and the targets causes one or more of the reflections to coincide. This is unlikely, but possible. A third target produces four more reflections, and so on. A User receiving system using a single omni-directional antenna will have to sort out all these reflections and perform the calculations looking for a single possible solution. To provide better results, Doppler analysis of each reflection can be performed so that the various reflected signals can be matched together. The Doppler shift of each reflected signal is a result of the velocity of the target, the velocity of the satellite producing the signal that is reflected, and the velocity of the User. Another solution is for the User system to use directional antennas.

[046] The geometry shows that several system configurations are possible.

1. System 0 – It is not necessary to receive any signals directly from any satellites. Only the signals reflected from the target are needed. The User tries all of the PN codes for all the satellites or uses an ephemeris to try only the codes for the satellites that are in view. A signal that is detected is subjected to the various treatments described in the previous section on detecting spread spectrum radar. It may be possible to use the radio frequency emanations from the Sun and not use any satellites, but only during daytime.

2. System 1 – The direct and reflected signal from only one satellite is used. This detects the presence of the target but its position can be anywhere on an ellipsoid, which is better than nothing. A directional antenna is used to scan those areas corresponding to the surface of the ellipsoid.

3. System 2 – The direct and reflected signals from two satellites are used. This detects the presence of the target and locates its position to an ellipse. A directional antenna is used to scan the ellipse.

4. System 3 - The direct and reflected signals from three satellites are used. This detects the presence of the target and narrows its position down to only two positions. A directional antenna is used to determine which position the target is in.

5. System 4 – The direct and reflected signals from four satellites are used to detect the presence and position of the target. Only a single omni-directional antenna is needed.

[047] Although it is anticipated that the system will use microwave frequencies, the use of lower frequencies would make it possible to detect stealth aircraft. There are tradeoffs involving the frequency used, the resolution that can be achieved, and the ability to detect stealth aircraft. The lower the frequency the lower the resolution. A lower frequency requires either a larger antenna or an antenna of reduced efficiency. However, a lower frequency increases the ability to detect stealth aircraft. Stealth aircraft commonly employ reflecting surfaces and/or microwave-absorbing surface material. As the wavelength becomes longer and approaches the dimensions of the aircraft, the reflecting surfaces no longer produce localized reflections. And there is a frequency below which energy-absorbing material becomes ineffective depending on the specifics of the material.

[048] In view of the foregoing, a tenth preferred embodiment for sensing aircraft and other objects uses bistatic radar with a spread spectrum signal transmitted from remotely located sources. In an eleventh preferred embodiment an integrated bistatic spread spectrum radar system uses a satellite constellation for the radar function as well as for communications.

BRIEF DESCRIPTION OF THE DRAWINGS

[049] The invention may best be understood by referring to the following description and accompanying drawings which illustrate the invention. In the drawings:

[050] FIG. 1 is a general illustration showing a TCAS system used as a radar, using standard TCAS antennas.

[051] FIG. 2 is a general illustration showing a TCAS system used as a radar, using a separate directional receiving antenna.

[052] FIG. 3 is a general illustration showing an ADS-B system used as a radar, using omni-directional antennas.

[053] FIG. 4 is a general illustration showing an ADS-B system used as a radar, using a separate directional receiving antenna.

[054] FIG. 5 is a general illustration showing a method for detecting spread spectrum radar and determining its bearing, using two omni-directional antennas.

[055] FIG. 6 is a general illustration showing why there is a “hemisphere problem” in Radio Direction Finding with two omni-directional antennas

[056] FIG. 7 is a general illustration showing the addition of an additional antenna to solve the “hemisphere problem” in Radio Direction Finding.

[057] FIG. 8 is a general illustration showing a method for detecting spread spectrum radar, using two pairs of spatially separated omni-directional antennas.

[058] FIG. 9 is a general illustration showing a method for detecting spread spectrum radar, using two co-located directional antennas.

[059] FIG. 10 is a general illustration showing a method for detecting spread spectrum radar and determining its range and bearing, using two spatially separated directional antennas.

[060] FIG. 11 is a general illustration showing a method for detecting spread spectrum radar and determining its range and bearing, using two spatially separated pairs of co-located directional antennas.

[061] FIG. 12 is a general illustration showing a spread spectrum bistatic radar using a satellite constellation as the radar transmitters.

[062] FIG. 13 is a general illustration showing the User equipment suitable for use in a spread spectrum radar using a satellite constellation as the radar transmitters and an omni-directional receive antenna.

[063] FIG. 14 is a general illustration showing another form of User equipment suitable for use in a spread spectrum radar using a satellite constellation as the radar transmitters and an omni-directional receive antenna.

[064] FIG. 15 is a general illustration showing the User equipment suitable for use in a spread spectrum radar system using a satellite constellation as the radar transmitters, a directional receive antenna, and an omni-directional receive antenna.

[065] FIG. 16 is a general illustration showing another form of User equipment suitable for use in a spread spectrum radar system using a satellite constellation as the radar transmitters, a directional receive antenna, and an omni-directional receive antenna.

[066] FIG. 17 is a general illustration showing an integrated bistatic spread spectrum radar system using a satellite constellation for the radar function as well as for communications.

[067] FIG. 18 is a general illustration showing the geometry of a bistatic radar.

[068] FIG. 19 is a general illustration showing that the geometry of a bistatic radar describes an ellipse.

[069] FIG. 20 is a general illustration showing the geometry of an ellipse.

[070] FIG. 21 is a general illustration further showing the geometry of an ellipse.

[071] FIG. 22 is a general illustration further showing the geometry of an ellipse.

[072] FIG. 23 is a general illustration showing a receiver and a first satellite at the foci of a first ellipse.

[073] FIG. 24 is a general illustration showing a receiver and a first satellite at the foci of a first ellipse and the receiver and a second satellite at the foci of a second ellipse.

[074] FIG. 25 is a general illustration showing a receiver and a first satellite at the foci of a first ellipse, the receiver and a second satellite at the foci of a second ellipse, and the receiver and a third satellite at the foci of a third ellipse.

[075] FIG. 26 is a general illustration showing an ellipse that does not intersect another ellipse even though they share a focus.

[076] FIG. 27 is a general illustration showing an ellipse that intersects another ellipse at only one point even though they share a focus.

[077] FIG. 28 is a general illustration showing an ellipsoid.

[078] FIG. 29 is a general illustration showing a cross section of the longitudinal axis of the ellipsoid shown in Fig. 28.

[079] FIG. 30 is a general illustration also showing two ellipsoids with a common focus, meeting end-to-end.

[080] FIG. 31 is a general illustration of two ellipsoids with a common focus, meeting at a first arbitrary angle.

[081] FIG. 32 is a general illustration of two ellipsoids with a common focus, meeting at a second arbitrary angle.

DETAILED DESCRIPTION

[082] In the following description, numerous specific details are set forth to provide a thorough understanding of the invention. However, it is understood that the invention may be practiced without these specific details. In other instances well-known circuits, structures, and techniques have not been shown in detail in order not to obscure the invention.

[083] Figure 1 is a general illustration showing a TCAS system used as a radar, using standard TCAS antennas. TCAS Interrogation Receiver 106 listens for Interrogation signals from other aircraft. When it receives one, TCAS Transponder Transmitter 107 sends out a signal containing the unique ID number of the aircraft and its altitude. TCAS Interrogation Transmitter 105 periodically (and randomly) sends out an Interrogation signal that other TCAS-equipped aircraft respond to. These transponder responses are received by TCA Transponder Receiver 108. There are at least two antennas: Omni-Directional Antenna 101 and Directional Antenna 102 which is under the control of Antenna Controller 103. Directional Antenna 102 and Antenna Controller 103 may be in the form of several directional antennas which may be selected in turn or used simultaneously. Antenna Diplexer 104 is used to select and/or combine Omni-Directional Antenna 101 and Directional Antenna 102 and route the signals (receiving and transmitting) to the appropriate piece of equipment. The preceding operations are under the control of TCAS Processor 109. The time delay between when the TCAS Interrogation signal is sent out by TCAS Interrogation Transmitter 105 and when a transponder signal from other aircraft is received by TCA Transponder Receiver 108 is used to determine the range to the responding aircraft.

TCAS operation is improved by using the signal produced by TCAS Interrogation Transmitter 105 as a radar with reflected signals received by TCAS Interrogation Receiver 106 under the control of TCAS Processor 109 and Radar Processor 110.

If the number and range of targets reported by radar do not match the number and range of aircraft reported by TCAS then there is an aircraft out there that does not have TCAS or it is broken or has been disabled.

[084] In Figure 2, a separate directional antenna (Antenna 201) is used to receive the reflected signals. The advantage of using a separate antenna for this function is that it can be made to be more directional than the standard Directional Antenna 102 used by TCAS. Directional Antenna 201 is controlled by Antenna Controller 202 under the direction of Radar Processor 210 which also controls the radar function through TCAS Processor 109. Antenna Diplexer 204 is used to select and/or combine Omni-Directional Antenna 101, Directional Antenna 102, and Directional Antenna 201 and route the signals (receiving and transmitting) to the appropriate piece of equipment. Directional Antenna 201 and Antenna Controller 202 may be a system that mechanically aims Directional Antenna 201 or the combination may be an electronically scanned array.

If the number, range, and bearing of targets reported by radar do not match the number, range, and bearing of aircraft reported by TCAS then there is an aircraft out there that does not have TCAS or it is broken or has been disabled.

[085] Figure 3 is a general illustration showing an ADS-B system used as a radar, using omni-directional antennas. ADS-B Transmitter 303 periodically sends out interrogation signals to be received by other aircraft. When these other aircraft are equipped with ADS-B they respond by transmitting messages containing their unique aircraft ID, GPS coordinates, and other data. This signal is received by ADS-B Receiver 304. When ADS-B Receiver 304 receives an interrogation signal from other aircraft ADS-B Transmitter 303 is used to send the present aircraft’s unique ID, GPS coordinates, and other data. Omni-Directional antenna 301 is used for this exchange of ADS-B signals with Antenna Diplexer 302 used to route the signals from Omni-Directional Antenna 301 to ADS-B Transmitter 303 and ADS-B Receiver 304. Omni-Directional Antenna 306 is used with GPS Receiver 307 to provide the GPS coordinates of the present aircraft. All of this is controlled by ADS-B Processor 305.

ADS-B operation is improved by using the signal produced by ADS-B Transmitter 303 as a radar with reflected signals received by ADS-B Receiver 304 under the control of ADS-B Processor 305 and Radar Processor 308.

If the number and range of targets reported by radar do not match the number and range of aircraft reported by ADS-B then there is an aircraft out there that does not have ADS-B or it is broken or has been disabled.

[086] In Figure 4, a separate directional antenna (Antenna 401) is used to receive the reflected signals. The advantage of using a separate antenna for this function is that it is directional, as opposed to Omni-Directional Antenna 301 used by ADS-B. Directional Antenna 401 is controlled by Antenna Controller 402 under the direction of Radar Receiver and Processor 403 which also controls the radar function through ADS-B Processor 305. Directional Antenna 401 and Antenna Controller 402 may be a system that mechanically aims Directional Antenna 401 or the combination may be an electronically scanned array.

If the number, range, and bearing of targets reported by radar do not match the number, range, and bearing of aircraft reported by ADS-B then there is an aircraft out there that does not have ADS-B or it is broken or has been disabled.

[087] Figure 5 is a general illustration showing a method for detecting spread spectrum radar and determining its bearing using two receiving systems with omni-directional antennas. Omni-Directional Antenna 501 and Receiver 502 make up the first receiving system. Omni-Directional Antenna 503 and Receiver 504 make up the second receiving system. The data from Receiver 502 is stored in Data Buffer 505. The data from Receiver 504 is stored in Data Buffer 506. The data in Data Buffer 505 and Data Buffer 506 are used by Cross-Correlator 507 under control of System Controller 508.

The noise produced by each receiver system is completely independent of each other so the internally generated noise is uncorrelated. If there is a correlation between the data frames from two receiver systems it can only have come from an external source, such as a spread spectrum signal. The phase term (time delay) in the cross-correlation function is used to determine the bearing to the target subject to the “Hemisphere Problem” which occurs because a target on either side of the line between the two antennas produces the same time delay, and therefore the same angle. Referring to Figure 6, Antenna 601 and Antenna 602 both receive Signal 603 from a target. Antenna 602 receives Signal 603 later than Antenna 601. Time translates to distance dt 604 which produces Angle 605. However, Antenna 602 could also receive Signal 606 from a target later than Antenna 601 and with the same delay. Distance dt 607 is the same as distance dt 604 so that Angle 608 is the same as Angle 605.

In Figure 7 a third receiving system is added with Antenna 701 that is not collinear with Antenna 601 and Antenna 602. Signal 603 takes longer to arrive at Antenna 701 than does Signal 606 (distance dt 703 versus distance dt 702). The time delay of the signal received by Antenna 701 is compared to the two calculated values based on the geometry of Antennas 601, 602, and 701. Thus, it is determined whether the signal is Signal 603 or Signal 606.

[088] Figure 8 is a general illustration showing a method for detecting spread spectrum radar, using two pairs of receiving systems where the omni-directional antennas used in each receiving system are spatially separated and the two pairs of receiving systems are spatially separated from each other.

In the first pair of the receiving systems Omni-Directional Antenna 801 and Receiver 802 produce a first signal. The output of Receiver 802 is stored in Data Buffer 805. Omni-Directional Antenna 803 and Receiver 804 produce a second signal. The output of Receiver 804 is stored in Data Buffer 806. The data in Data Buffer 805 and Data Buffer 806 are used by Cross-Correlator 807 which performs a cross-correlation of the signals produced by Receiver 802 and Receiver 804. The noise produced by each receiver system is completely independent of each other so the internally generated noise is uncorrelated. If there is a correlation between the data frames from the two receiver systems it can only have come from an external source, such as a spread spectrum signal. The phase term (time delay) in the cross-correlation function is used to determine a first bearing to the target.

In the second pair of the receiving systems Omni-Directional Antenna 808 and Receiver 809 produce a third signal. Omni-Directional Antenna 810 and Receiver 811 produce a fourth signal. The output of Receiver 809 is stored in Data Buffer 812. The output of Receiver 811 is stored in Data Buffer 813. The data in Data Buffer 812 and Data Buffer 813 are used by Cross-Correlator 814 which performs a cross-correlation of the signals produced by Receiver 809 and Receiver 811. The noise produced by each receiver system is completely independent of each other so the internally generated noise is uncorrelated. If there is a correlation between the data frames from the two receiver systems it can only have come from an external source, such as a spread spectrum signal. The phase term (time delay) in the cross-correlation function is used to determine a second bearing to the target.

System Controller 815 controls the operation of Cross-Correlator 807 and Cross-Correlator 814. It may also control the operation of Receivers 802, 804, 809, and 811.

The distance between the first pair of receiving systems and the second pair of receiving systems is known. The first bearing to the target is determined using the first pair of receiving systems. The second bearing to the target is determined using the second pair of receiving systems. The distance and range to the target are determined using triangulation.

[089] Figure 9 is a general illustration showing a method for detecting spread spectrum radar using two co-located directional antennas. Directional Antenna 901 and Receiver 903 make up the first receiving system. The direction of Directional Antenna 901 is controlled by Antenna Controller 902. Directional Antenna 904 and Receiver 906 make up the second receiving system. The direction of Directional Antenna 904 is controlled by Antenna Controller 905. The data output of Receiver 903 is stored in Data Buffer 907. The output of Receiver 906 is stored in Data Buffer 908. The data in Data Buffer 907 and Data Buffer 908 are used by Cross-Correlator 909 under control of System Controller 910 which also controls Antenna Controller 902 and Antenna Controller 905.

Because directional antennas are used, the phase term (time delay) in the cross-correlation function cannot be used to determine the bearing to the target. Directional Antenna 901 and Directional Antenna 904 are controlled so they always point in the same direction. The bearing to the target is determined from the direction the antennas are pointing.

Directional Antenna 901 and Antenna Controller 902 may be a system that mechanically aims Directional Antenna 901 or the combination may be an electronically scanned array.

Likewise, Directional Antenna 904 and Antenna Controller 905 may be a system that mechanically aims Directional Antenna 904 or the combination may be an electronically scanned array.

[090] Figure 10 is a general illustration showing a method for detecting spread spectrum radar and determining its range and bearing using two spatially separated directional antennas.

Directional Antenna 901 and Receiver 903 make up the first receiving system. The direction of Directional Antenna 901 is controlled by Antenna Controller 902. Directional Antenna 904 and Receiver 906 make up the second receiving system. The direction of Directional Antenna 904 is controlled by Antenna Controller 905. The output of Receiver 903 is stored in Data Buffer 907. The output of Receiver 906 is stored in Data Buffer 908. The data in Data Buffer 907 and Data Buffer 908 are used by Cross-Correlator 909 under control of System Controller 1010 which also controls Antenna Controller 902 and Antenna Controller 905.

Because directional antennas are used, the phase term (time delay) in the cross-correlation function cannot be used to determine the bearing to the target. Directional Antenna 901 and Directional Antenna 904 are spatially separate from each other. When a source of correlated noise is found the bearing of Directional Antenna 901 and the bearing of Directional Antenna 904 are used, along with the distance between, to triangulate the position and bearing of the external source of correlated noise, namely the target.

Directional Antenna 901 and Antenna Controller 902 may be a system that mechanically aims Directional Antenna 901 or the combination may be an electronically scanned array.

Likewise, Directional Antenna 904 and Antenna Controller 905 may be a system that mechanically aims Directional Antenna 904 or the combination may be an electronically scanned array.

[091] Figure 11 is a general illustration showing a method for detecting spread spectrum radar and determining its range and bearing, using two spatially separated pairs of co-located directional antennas.

The first pair of co-located directional antennas are Directional Antenna 1101 and Directional Antenna 1104. Directional Antenna 1101 and Receiver 1103 make up the first receiving system of the pair. The output of Receiver 1103 is stored in Data Buffer 1113. The direction of Directional Antenna 1101 is controlled by Antenna Controller 1102. Directional Antenna 1104 and Receiver 1106 make up the second receiving system of the pair. The output of Receiver 1106 is stored in Data Buffer 1114. The direction of Directional Antenna 1104 is controlled by Antenna Controller 1105. The data in Data Buffer 1113 and Data Buffer 1114 are used by Cross-Correlator 1115 under control of System Controller 1119 which also controls Antenna Controller 1102 and Antenna Controller 1105.

Because directional antennas are used, the phase term (time delay) in the cross-correlation function cannot be used to determine the bearing to the target. Directional Antenna 1101 and Directional Antenna 1104 are controlled so they always point in the same direction. The first bearing to the target is determined from the direction the antennas are pointing.

The second pair of co-located directional antennas are Directional Antenna 1107 and Directional Antenna 1110. Directional Antenna 1107 and Receiver 1109 make up the first receiving system of the pair. The output of Receiver 1109 is stored in Data Buffer 1116. The direction of Directional Antenna 1107 is controlled by Antenna Controller 1108. Directional Antenna 1110 and Receiver 1112 make up the second receiving system of the pair. The output of Receiver 1112 is stored in Data Buffer 1117. The direction of Directional Antenna 1110 is controlled by Antenna Controller 1111. The data in Data Buffer 1116 and Data Buffer 1117 are used by Cross-Correlator 1118 under control of System Controller 1119 which also controls Antenna Controller 1108 and Antenna Controller 1111. The noise produced by each receiver system is completely independent of each other so the internally generated noise is uncorrelated. If there is a correlation between the data frames from two receiver systems it can only have come from an external source, such as a spread spectrum signal.

Because directional antennas are used, the phase term (time delay) in the cross-correlation function cannot be used to determine the bearing to the target. Directional Antenna 1107 and Directional Antenna 1110 are controlled so they always point in the same direction. The second bearing to the target is determined from the direction the antennas are pointing.

When a source of correlated noise is found by the first pair of co-located directional antennas the second pair of co-located directional antennas is brought to bear until it also finds the target. The first bearing to the target and the second bearing to the target, along with the distance between the first pair of co-located directional antennas and the second pair of co-located directional antennas, is used to triangulate the position and bearing of the external source of correlated noise, namely the target.

Conversely, when a source of correlated noise is found by the second pair of co-located directional antennas the first pair of co-located directional antennas is brought to bear until it also finds the target. The first bearing to the target and the second bearing to the target, along with the distance between the first pair of co-located directional antennas and the second pair of co-located directional antennas, is used to triangulate the position and bearing of the external source of correlated noise, namely the target.

Directional Antenna 1101 and Antenna Controller 1102 may be a system that mechanically aims Directional Antenna 1101 or the combination may be an electronically scanned array.

Directional Antenna 1104 and Antenna Controller 1105 may be a system that mechanically aims Directional Antenna 1104 or the combination may be an electronically scanned array.

Directional Antenna 1107 and Antenna Controller 1108 may be a system that mechanically aims Directional Antenna 1107 or the combination may be an electronically scanned array.

Directional Antenna 1110 and Antenna Controller 1111 may be a system that mechanically aims Directional Antenna 1110 or the combination may be an electronically scanned array.

[092] Figure 12 is a general illustration showing a spread spectrum bistatic radar using a satellite constellation as the radar transmitters. Satellites 1202, 1203, 1204, and 1205 transmit a spread spectrum signal, each having a unique PN code. The signal from each satellite is received in a direct path by User 1201. The signal from each satellite is also reflected by Target 1206 and received by User 1201. User 1201 determines his own position and the positions of Satellites 1202, 1203, 1204, and 1205. User 1201 determines the length of the direct path to the satellites and the total length of the signal path from each satellite reflected by Target 1206. By performing the appropriate mathematical calculations User 1201 determines the absolute position of Target 1206.

Alternatively, User 1201 determines the positions of Satellites 1202, 1203, 1204, and 1205 relative to himself. User 1201 determines the length of the direct path to the satellites and the total length of each signal path from each satellite reflected by Target 1206. By using the appropriate mathematical calculations User 1201 determines the relative position of Target 1206.

[093] Figure 13 is a general illustration showing the User equipment suitable for use by spread spectrum radar using a satellite constellation as the radar transmitters. Omni-Directional Antenna 1301 receives the signals transmitted directly from Satellites 1202, 1203, 1204, and 1205 (Figure 12) as well as the satellite signals reflected by Target 1206 (also Figure 12). Omni-Directional Antenna 1301 sends these signals to Receiver 1302. The output of Receiver 1302 is stored in Data Buffer 1303. Under the control of System Controller 1306, Correlator 1304 performs correlations between the data stored in Data Buffer 1303 and a list of PN Codes 1305 which correspond to the PN Codes used by the satellites in the satellite constellation. System Controller 1306 also determines the length of the direct path from each satellite, the length of the path from each satellite reflected by Target 1206 (Figure 12) and performs the calculations to determine the range and bearing to Target 1206.

[094] Figure 14 is a general illustration showing another form of User equipment suitable for use by spread spectrum radar using a satellite constellation as the radar transmitters. Omni-Directional Antenna 1301 receives the signals transmitted directly from Satellites 1202, 1203, 1204, and 1205 (Figure 12) as well as the satellite signals reflected by Target 1206 (also Figure 12). Omni-Directional Antenna 1301 sends these signals to Receiver 1302. The output of Receiver 1302 is stored in Data Buffer 1303. Under the control of System Controller 1406, Correlator 1304 performs correlations between the data stored in Data Buffer 1303 and a list of PN Codes 1305 which correspond to the PN Codes used by the satellites in the satellite constellation. System Controller 1406 uses GPS Receiver 1407 to determine the User’s position. System Controller 1406 also determines the length of the direct path from each satellite, the length of the path from each satellite reflected by Target 1206 (Figure 12) and performs the calculations to determine the range and bearing to Target 1206.

[095] Figure 15 is a general illustration showing the User equipment suitable for use by spread spectrum radar using a satellite constellation as the radar transmitters. Directional Antenna 1501 receives the signals reflected by Target 1206 (Figure 12) from Satellites 1202, 1203, 1204, and 1205 (Figure 12). Directional Antenna 1501 sends these signals to Receiver 1503. The output of Receiver 1503 is stored in Data Buffer 1504. Under the control of System Controller 1511, Correlator 1505 performs correlations between the data stored in Data Buffer 1504 and a list of PN Codes 1510 which correspond to the PN Codes used by the satellites in the satellite constellation. System Controller 1511 also controls the direction of Directional Antenna 1501 using Antenna Controller 1502.

Omni-Directional Antenna 1506 receives the signals directly sent by Satellites 1202, 1203, 1204, and 1205 (Figure 12). Omni-Directional Antenna 1506 sends these signals to Receiver 1507. The output of Receiver 1507 is stored in Data Buffer 1508. Under the control of System Controller 1511, Correlator 1509 performs correlations between the data stored in Data Buffer 1508 and a list of PN Codes 1510 which correspond to the PN Codes used by the satellites in the satellite constellation. System Controller 1511 also determines the length of the direct path from each satellite and performs the calculations to determine the range and bearing to Target 1206.

Directional Antenna 1501 and Antenna Controller 1502 may be a system that mechanically aims Directional Antenna 1501 or the combination may be an electronically scanned array.

[096] Figure 16 is a general illustration showing another form of User equipment suitable for use by spread spectrum radar using a satellite constellation as the radar transmitters. Directional Antenna 1501 receives the signals reflected by Target 1206 (Figure 12) from Satellites 1202, 1203, 1204, and 1205 (Figure 12). Directional Antenna 1501 sends these signals to Receiver 1503. The output of Receiver 1503 is stored in Data Buffer 1504. Under the control of System Controller 1611, Correlator 1505 performs correlations between the data stored in Data Buffer 1504 and a list of PN Codes 1510 which correspond to the PN Codes used by the satellites in the satellite constellation. System Controller 1611 also controls the direction of Directional Antenna 1501 using Antenna Controller 1502.

Omni-Directional Antenna 1506 receives the signals directly sent by Satellites 1202, 1203, 1204, and 1205 (Figure 12). Omni-Directional Antenna 1506 sends these signals to Receiver 1507. The output of Receiver 1507 is stored in Data Buffer 1508. Under the control of System Controller 1611, Correlator 1509 performs correlations between the data stored in Data Buffer 1508 and a list of PN Codes 1510 which correspond to the PN Codes used by the satellites in the satellite constellation. System Controller 1611 also uses GPS Receiver 1612 to determine the length of the direct path from each satellite and performs the calculations to determine the range and bearing to Target 1206.

Directional Antenna 1501 and Antenna Controller 1502 may be a system that mechanically aims Directional Antenna 1501 or the combination may be an electronically scanned array.

[097] Figure 17 is a general illustration showing an integrated bistatic spread spectrum radar system using a satellite constellation as the radar as well as for communications. Omni-Directional Antenna 1701 receives the signals transmitted directly from Satellites 1202, 1203, 1204, and 1205 (Figure 12) which contain the communications signals which are also used for bistatic radar. The signals from Omni-Directional Antenna 1701 are sent to Receiver 1702. The output of Receiver 1702 is stored in Data Buffer 1703. Under the control of System Controller 1713, Correlator 1704 performs correlations between the data stored in Data Buffer 1703 and the List of PN Codes 1714 used by the satellites in the satellite constellation shown in Figure 12.

System Controller 1713 uses List of PN Codes 1714 to create a spread spectrum signal and transmits it to the satellites using Transmitter 1707 and Directional Antenna 1705. System Controller 1713 controls the direction of Directional Antenna 1705 using Antenna Controller 1706.

Directional Antenna 1708 is used to receive the satellite signals reflected by Target 1206 (Figure 12). Directional Antenna 1708 sends these signals to Receiver 1710. The output of Receiver 1710 is stored in Data Buffer 1711. Under the control of System Controller 1713, Correlator 1712 performs correlations between the data stored in Data Buffer 1711 and a List of PN Codes 1714 which correspond to the PN Codes used by the satellites in the satellite constellation.

System Controller 1713 determines the length of the direct path from each satellite, the length of the path from each satellite reflected by Target 1206 (Figure 12) and performs the calculations to determine the range and bearing to Target 1206. The use of GPS Receiver 1715 in determining the User’s position is optional. System Controller 1713 controls the direction of Directional Antenna 1708 using Antenna Controller 1709.

Directional Antenna 1705 and Antenna Controller 1706 may be a system that mechanically aims Directional Antenna 1705 or the combination may be an electronically scanned array.

Directional Antenna 1708 and Antenna Controller 1709 may be a system that mechanically aims Directional Antenna 1708 or the combination may be an electronically scanned array.

Geometry

[098] The geometry of a bistatic radar will be discussed, starting with a 2D system which will then be expanded to a 3D system.

Referring to Figure 18, Receiver 1801 receives a signal directly from Transmitter 1802 through Path L 1804. Receiver 1801 also receives a signal from Transmitter 1802 reflected off of Target 1803 through Path r1 1805 and Path r2 1806.

Receiver 1801 only knows the sum of Path r1 1805 and Path r2 1806. The locus of all points of a plane whose distances to two fixed points add to the same constant is an ellipse. As a result, as shown in Figure 19, Receiver 1801 only knows that Target 1803 is somewhere on Ellipse 1907. Receiver 1801 and Transmitter 1802 are located at the two foci of Ellipse 1907.

In the following discussion, the labels are emboldened and omit the drawing figure numbers in order to avoid an unmanageable clutter.

Figure 20 shows an ellipse in standard form. The foci are at f1 and f2. The semi-major axis is a. (The major axis is 2 * a) The semi-minor axis is b. (The minor axis is 2 * b)

The two foci are equidistant from the Y axis, and are separated by distance L.

The sum of r1 and r2 is constant so that Point P traces out the ellipse.

The parametric equation for an ellipse is:

x² y²

— + — = 1

a² b²

Note that if a = b:

x² y²

— + — = 1

a² a²

x² + y²

———— = 1

a²

x² + y²=a²

If we rename a and call it r, most engineers will recognize this as the parametric equation for a circle.

x² + y²= r²

An ellipse is also a simple form of Lissajous Figure where:

x = R * sin(2πt) and y = R * sin(2πt + δ)

For more on Lissajous Figures see Ref. 27.

The ellipse data produced by the present system will be L and the sum of r1 and r2. L is the distance between the foci f1 and f2. Another way of putting it is that f1 = -f2 = L/2. We want to determine the semi-major axis (a) and the semi-minor axis (b).

In Figure 21, Point P has been moved to (a,0). r1 and r2 are not shown because they lie on the X axis.

The distance from f1 to (a,0) and from (a,0) to f2 is the sum of r1 and r2 because that is the definition of an ellipse.

The distance from f1 to f2 is L. The distance from f2 to (a,0) is d. The distance from (a,0) back to f2 is, again, d.

r1 + r2 = L + d + d

2 * d = r1 + r2 – L

d = ( r1 + r2 – L)/2 = (r1 + r2)/2 – L/2

Therefore:

a = L/2 + d

= L/2 + (r1 + r2)/2 – L/2

= (r1 + r2)/2

Now that we have found the semi-major axis a, let’s find the semi-minor axis b. Referring to Figure 22, when P is located at (0,b) the sum of r1 + r2 is divided into two equal parts and forms two right triangles with the Origin (0,0) and the foci. Note that in this case r1 = r2 and the line from P to each focal point is the same length as the semi-major axis (r1 + r2)/2.

Therefore, since the present system measures (r1 + r2) and measures (or calculates) L we can calculate a and b and with that we can calculate any point on the ellipse.

x² y²

— + — = 1

a² b²

where:

a = (r1 + r2)/2

[099] The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by the parametric equation:

x² y² z²

— + — + — = 1

a² b²c²

Note that if a = b = c:

x² y² z²

— + — + — = 1

a² a²a²

x² + y²+ z²

——————— = 1

a²

x² + y²+ z²=a²

If we rename a and call it r, most engineers will recognize this as the parametric equation for a sphere.

x² + y²+ z²=r²

In the current ellipsoid:

x² y² z²

— + — + — = 1

a² b²c²

c = b because the target is on the radius of a circle around the axis formed by the two foci. To be precise, this makes our ellipsoid a spheroid and since it is likely that the target will be much closer than any of the satellites a will be larger than b, making it a prolate spheroid.

In the current ellipsoid:

x² y² z²

— + — + — = 1

a² b²b²

x² y²+ z²

— + ——— = 1

a² b²

[100] When two ellipsoids having a common focus intersect they produce an ellipse. Figure 30 is a general illustration showing two ellipsoids with a common focus, meeting end-to-end, producing a circle seen edge-on. Figure 30, Figure 31, and Figure 32 were produced by a computer program that modeled an ellipsoid as a segmented prolate spheroid, i.e. a number of circles around a major axis. The radii of the circles vary according to the curve of an ellipse. Projection is orthonormal. In Figure 31 the two ellipsoids are meeting at a first arbitrary angle. In Figure 32 the two ellipsoids meet at a second arbitrary angle. By inspection it appears that the smaller the angle between the ellipsoids the larger the intersection ellipse. The implication of this is that the closer together the satellites are, the larger the ellipse of intersection becomes. As the satellites become farther apart, the ellipse of intersection becomes smaller.

[101] Starting with the first satellite in Figure 12 (but in 2D) the User knows the total length of the path from a first satellite to the target and then to the User and wants to know the length of the path from the target to himself. The User also knows the length of the path from the first satellite to himself. Mathematically, this is the definition of an ellipse. The User and the first satellite are at the foci and the target is somewhere on the ellipse. See Figure 23.

[102] When a second satellite is added, a second ellipse is formed. The User is at one of the foci, the second satellite is at the other. The first ellipse and the second ellipse intersect at only two points, with the target at one of the two points. See Figure 24.

[103] When a third satellite is added, a third ellipse is formed. Again, the User is at one of the foci and the third satellite is at the other. The three ellipses intersect at only one point. That is where the target is. See Figure 25.

[104] There is something to note. Not all ellipses that share a focus point will intersect. See Figure 26. However, in the present case they must intersect because the ellipses were created by reflections from the same target, and the target cannot be in more than one place at the same time. It is possible that two ellipses that share a focus point will intersect at only one point, but that is a special case. See Figure 27.

[105] A 3D system is more complicated because the geometric figure produced between each satellite and the User is not a 2D planar ellipse. Picture an ellipse rotating around the axis between the User and the satellite. The figure that each Satellite produces is an ellipsoid, more specifically, a prolate spheroid, that looks remarkably like a football (U.S. or Canadian). See Figure 28. That is because a line from the target meets the line from the User to the satellite at a 90 degree angle and forms the radius of a circle. See Figure 29. The target can be anywhere on that circle which means it can be anywhere on the surface of the ellipsoid.

[106] Referring to Figure 12, Satellite 1202 produces an ellipsoid with the User at one foci and the satellite at the other. The target is somewhere on the surface of the ellipsoid.

[107] When a second satellite (Satellite 1203) is added, a second ellipsoid is formed. The User is at one of the foci, the second satellite is at the other. The first ellipsoid and the second ellipsoid intersect and produce an ellipse. The reason the ellipsoids produce an ellipse is because they share a common focus. [Ref. 26]

[108] When a third satellite (Satellite 1204) is added, a third ellipsoid is formed. The User is at one of the foci, the third satellite is at the other. The first and second ellipsoids and the third ellipsoid intersect with the target at one of two points.

[109] When a fourth satellite (Satellite 1205) is added, a fourth ellipsoid is formed. The User is at one of the foci, the fourth satellite is at the other. The first three ellipsoids and the fourth ellipsoid intersect at only one point. That is where the target is.

[110] The geometry that has been described might not be obvious to someone versed mainly in GPS geometry. GPS uses only three satellites to determine the User’s position in three dimensions. (A fourth satellite is used for time correction.) The reason for this difference is because instead of using only the signal received directly from the satellite, the User is receiving both the direct signal and a signal reflected from the target. A line from the target meets the line from the User to the satellite at a 90 degree angle and forms the radius of a circle. The target can be anywhere on that circle. That is why the additional satellite is needed to determine the position of the target.

[111] The geometry shows that several system configurations are possible.

3. System 2 – The direct and reflected signals from two satellites are used. This detects the presence of the target and locates its position to the area of a planar ellipse. A directional antenna is used to scan those areas corresponding the surface of the ellipse.

5. System 4 – The direct and reflected signals from four satellites are used to detect the presence and position of the target. Only a single omni-directional antenna is needed.

[112] While preferred embodiments of the present invention have been shown, it is to be expressly understood that modifications and changes may be made thereto.

[113] ABSTRACT OF THE DISCLOSURE

The reliability and safety of TCAS and ADS-B are improved by using the signals transmitted from a TCAS or ADS-B unit as a radar transmitter with a receiver used to receive reflections. With a standard omni-directional antenna the reflections can be used to determine the range of other aircraft and match the range and number of targets to the TCAS or ADS-B signals normally received. Doppler analysis can be used to confirm the speeds of the targets. With a directional antenna the TCAS or ADS-B system provides the range and bearing of aircraft and other objects in the vicinity of the user’s aircraft even when other aircraft are not equipped with TCAS or ADS-B. Aircraft and other objects using spread spectrum radar are detected by using two separate receiving systems. Cross-Correlation between the outputs of the two receiving systems reveals whether a noise signal is produced by the receiving systems themselves or is coming from the outside. A system and method for sensing aircraft and other objects uses bistatic radar with spread-spectrum signals transmitted from remotely located sources such as aircraft flying at very high altitudes or from a satellite constellation. Only authorized users will have the encryption key and be able to use the system. A bistatic spread spectrum radar system using a satellite constellation can be integrated with a communications system.

References

Ref. 1: 14 CFR § 91.113(b) Right-of-way rules: Except water operations.

http://ecfr.gpoaccess.gov/cgi/t/text/text-idx?c=ecfr&sid=4f09aa904bfbb808de07eada6cb86e5a&rgn=div8&view=text&node=14:2.0.1.3.10.2.4.7&idno=14

Ref. 2: 14 CFR § 91.115(a) Right-of-way rules: Water operations.

http://ecfr.gpoaccess.gov/cgi/t/text/text-idx?c=ecfr&sid=4f09aa904bfbb808de07eada6cb86e5a&rgn=div8&view=text&node=14:2.0.1.3.10.2.4.8&idno=14

Ref. 3: U.S. Patent 4,782,450 Method and apparatus for passive airborne collision avoidance and navigation issued November 1, 1988 to Flax.

Abstract

A passive method for an aircraft to use its on-board locating apparatus to monitor interrogation signals and ISLS signals transmitted by at least one secondary surveillance radar, and coded reply signals transmitted by at least one fixed ground transponder; to match said transponder reply signals with said ISLS signals, in order to associate said transponder reply signals with interrogations from said radar; to repetitiously compute said aircraft's instantaneous position in space, said computations being based on hyperbolic and linear functions related to said aircraft, said radar, and said associated fixed transponder; and to display said positions for navigational purposes. Furthermore, having said computations, said passive method uses said locating apparatus to monitor coded reply signals from transponders of other aircraft; to match said other-aircraft reply signals with said ISLS signals to determine which other-aircraft transponder reply signals are associated with interrogations from said radar; to repetitiously compute the instantaneous positions of other aircraft in space, said computations being based on elliptic and linear functions related to said locating apparatus' own aircraft, said other aircraft, and said radar; and to display said positions for collision-avoidance purposes.

Ref. 4: Introduction to TCAS II Version 7, United States Department of Transportation, Federal Aviation Administration November 2000.

www.arinc.com/downloads/tcas/tcas.pdf

Page 11:

TCAS Computer Unit

Ref 5: U.S. Patent 5,153,836 Universal dynamic navigation, surveillance, emergency location, and collision avoidance system and method, Fraughton, et al., October 6, 1992.

Abstract

A craft tracking and collision avoidance system is disclosed. The system allows the positions of a plurality of craft, either on land, sea, or air, or space, to be monitored. Each craft determines its own position using an existing position determining system such as LORAN or GPS. Each craft then transmits a radio frequency signal into which position information, preferably identifying information, and other messages, have been encoded. Each craft broadcasts its position, identifying information and other messages on a regular basis without the need for any interrogation signal. The broadcast position and identification information can be received by other craft and, since each craft has determined its own position, can be used to determine the proximity and identity of other craft, and if the craft are on a collision course. Preferably, the position of all the craft within a predetermined range of a craft is represented on a display in order to give the craft operator a visual indication of traffic surrounding his craft.

Ref. 6: Gulf of Mexico Helo Ops Ready for ADS-B, Aviation Week & Space Technology, Francis Fiorino, 02/26/2007, page 56.

Ref. 7: U. S. Patent 5,187,485 Passive ranging through global positioning system, Tsui, et al., February 16, 1993. Assignee: The United States of America as represented by the Secretary of the Air Force.

The patent teaches a method for determining the distance from a target to an observation station, using four GPS satellites as radiation sources, and a GPS receiver at the observation station to form a bistatic radar system, wherein an angle of arrival (AOA) of the target to the observation station has been measured first.

Ref. 8: Test Results from a Novel Passive Bistatic GPS Radar Using a Phased Sensor Array, Alison Brown and Ben Mathews, NAVSYS Corporation, Proceedings of ION NTM 2007, San Diego, CA, January 2007.

www.navsys.com/Papers/07-01-002.pdf

Ref. 9: U.S. Patent 5,724,041 Spread spectrum radar device using pseudorandom noise signal for detection of an object issued March 3, 1998 to Inoue, et al.

Abstract

Ref. 10: Shift Register With Feedback Generates White Noise, Marc Damashek, Electronics magazine, May 27, 1976.

Ref. 11: U.S. Patent 4,195,293 Random dot generator for raster scan video displays issued March 25, 1980 to Margolin.

Ref. 12: U.S. Patent 3,986,168 Multichannel error signal generator issued October 12, 1976 to Anderson.

Ref. 13: U.S. Patent 3,515,805 Data scrambler issued June 2, 1970 to Fracassi et al.)

Ref. 14: Shift Register Sequences, S. Golomb (Holden-Day Inc., San Francisco, 1967, and Aegean Park Press, 1982)

Ref. 15: The ABCs of Spread Spectrum - A Tutorial, Randy Roberts, Director of RF/Spread Spectrum Consulting. http://sss-mag.com/ss.html

Ref. 16: Undetectable Radar? (Probably Not), Erik Hundman, Defensetech.org, August 3, 2006. http://www.defensetech.org/archives/002641.html

Active radar signals, due to those pesky laws of physics, are generally easy to detect. Because a radar system emits a powerful beam of electromagnetic radiation, traditionally in a very narrow frequency band, an adversary equipped with only a passive radiation detector can easily zero in on the platform carrying the radar.

For decades the military has been searching for a less visible (and vulnerable) "low probability of intercept" (LPI) radar. This June, Ohio State University’s ElectroScience Laboratory claimed that its engineers—led by Dr. Eric K. Walton—had succeeded and "invented a radar system that is virtually undetectable."

From what we know now, the "undetectable" claim is something of a stretch, but these radars will almost certainly find uses. They do not interfere with each other or nearby electronics (which are designed to filter out noise), and they can see through walls. If ever used in a military capacity, they would likely force a change in radar detection and seeking technologies. It might cost the Pentagon a pretty penny to detect these new toys, but undetectable radars are probably still a long way off.

Ref. 17: From a Different Perspective: Principles, Practice, and Potential of Bistatic Radar by H.D. Griffiths, Dept. of Electron. & Electr. Eng., Univ. Coll. London, UK; Radar Conference, 2003. Proceedings of the International; Publication Date: 3-5 Sept. 2003; ISBN: 0-7803-7870-9; INSPEC Accession Number: 7892750

Abstract

Bistatic radar systems have been studied and built since the earliest days of radar. They have the advantages that the receivers are passive, and hence undetectable. The receiving systems are also potentially simple and cheap. Bistatic radar may have a counter-stealth capability, since target shaping to reduce monostatic RCS will in general not reduce the bistatic RCS. In spite of those advantages, rather few bistatic radar systems have got past the 'technology demonstrator' phase. It has also been remarked that activity in bistatic radar tends to vary on a period of approximately fifteen years, and that currently we are at a peak of that cycle; there is particular current interest in passive coherent location (PCL) techniques, using broadcast and communications signals as 'illuminators of opportunity'. This paper presents a review of some of the history, and the properties and current developments in the subject, and conjectures whether or not the present interest is just another peak in the cycle.

Ref. 18: Sensing Requirements for Unmanned Air Vehicles, AFRL's Air Vehicles Directorate, Control Sciences Division, Systems Development Branch, Wright-Patterson AFB OH, June 2004, http://www.afrlhorizons.com/Briefs/Jun04/VA0306.html .

Ref. 19: Presentation entitled, Developing Sense & Avoid Requirements for Meeting an Equivalent Level of Safety (6MB | ppt), given by Russ Wolfe, Technology IPT Lead, Access 5 Project at UVS Tech 2006. 18 January 2006.

Ref. 20: Presentation Integration into the National Airspace System (NAS) given by John Timmerman of the FAA’s Air Traffic Organization (July 12, 2005)

Ref. 21: Zone Ready for Drone, April 7, 2006, on the web site for the FAA’s Air Traffic Organization Employees,

http://www.ato.faa.gov/DesktopDefault.aspx?tabindex=4&tabid=17&itemid=937&mid=103

Ref. 22: Quadrennial Roles and Missions Review Report, Department of Defense, January 2009. Page 29 (PDF page 37)

www.defenselink.mil/news/Jan2009/QRMFinalReport_v26Jan.pdf

• U.S. Joint Forces Command Joint UAS Center of Excellence has identified three areas necessary to ensure access to applicable classes of the National Airspace System: (1) Airworthiness Certification; (2) establishment of standardized basic UAS qualifications consistent with Federal Aviation Administration guidelines for each class of airspace; and (3) development of sense and avoid technology. Working with the Services, the U.S. Joint Forces Command Joint UAS Center of Excellence will ensure these areas are addressed during UAS development.

Ref. 23: Analog Devices, Inc. AD9481: 8-Bit, 250 MSPS, 3.3 V A/D Converter

http://www.analog.com/en/analog-to-digital-converters/ad-converters/ad9481/products/product.html

Ref. 24: Texas Instruments C6713B

http://focus.ti.com/docs/prod/folders/print/tms320c6713b.html#features

Ref. 25: U.S. Patent 6,377,436 Microwave Transmission Using a Laser-Generated Plasma Beam Waveguide issued April 23, 2002 to Margolin.

Ref. 26: Simple Solutions for Hyperbolic and Related Position Fixes, Bertrand T. Fang,

The Analytic Sciences Corp.; IEE Transactions on Aerospace and Electronic Systems,
Publication Date: Sep 1990; Volume: 26, Issue: 5; page(s): 748-753; ISSN: 0018-9251

https://svn.v2.nl/andres/Documentation/TDOA/Simple_Solutions_for_TDOA-fang.pdf

From page 751:

DISCUSSION

It is shown in the above that several problems of interest in computing hyperbolic (elliptic) navigation fixes can be reduced to the solution of a quadratic or quartic equation. The solution to a quadratic is trivial. Analytic solution of a quartic is available, although some algebra is involved, but it is a simple matter to program the algorithm on a computer, as has been done by the author. The simplicity of the solutions results from the recognition that the intersection of two hyperboloids (ellipsoids) of revolution with a common focus is a hyperbola or an ellipse symmetrical with respect to the plane of the foci. By exploring the geometrical interpretations the nature of the navigation fixes are clarified. When the navigation position is governed by the quadratic, generally two admissible navigation positions exist and the ambiguity must be resolved from other information such as knowledge of the general whereabouts of the navigator. The quartic may have four distinct real roots corresponding to four possible navigation positions. Frequently some are extraneous roots which can be rejected by showing that they do not produce the correct measurements. If a navigation position exists, it may be one of the real roots of the quadratic or the quartic, as the case may be. The nonexistence of an admissible root indicates a gross measurement error.

The navigation fixes discussed are based on range difference or range sum information, converted from time difference and time sum measurements. For terrestrial navigation systems that rely on ground wave propagation such conversion can be complicated. For line-of-sight wave propagation, or navigation in space, the conversion is straightforward. Very long baseline interferometry (time difference) and bilateration using a remote ground transponder (time-sum) are examples of such space navigation systems [3].

Ref. 27: Lissajous Figures, Jed Margolin, May 2001;

http://www.jmargolin.com/mtest/LJfigs.htm