1. Field of the Invention
This invention relates generally to the location of objects from space via a satellite and, more particularly, to the accurate geolocation of possibly non-cooperative emitters from a single low earth orbit (LEO) satellite utilizing the minimum number of antennas required to derive ambiguous emitter direction of arrival.
2. Description of Related Art
Geolocation as used here refers to the determination of the emitter in both earth-center inertial (ECI) coordinates, and geodetic latitude and longitude. Using satellites to locate ground emitters is an important civilian and military task. Examples are emergency rescue of downed aircraft, determination of inadvertent sources of communications interference and location of malicious jammers disrupting military satellite usage. The transmitters may or may not aid or cooperate in their location.
Cooperative emitter location can take many forms. A common method is to transmit a stable CW narrow band signal. These signals may be continuous, or sent in burst; however, the transmitters always endeavor to be on during ranging. This allows a single LEO satellite to locate the emitter using the signal frequency's Doppler shifts. To provide location to a useable accuracy, a typical transmitter requirement is frequency stability of one part in 10−8 for twenty minutes over a wide range of adverse climatic conditions. Thus the transmitter is specifically designed and built to facilitate its location.
Non cooperative transmitters are not necessarily attempting to avoid geolocation. That is just not their reason for operating. Hence they are not required to have the frequency stability needed for delta-Doppler shift location, nor are they required to transmit for an extended period. However, rapid, accurate location of these non cooperative emitters becomes important when they interfere with satellite communication.
This interference is not necessarily malicious. The Ku band and C band of the electromagnetic spectrum are crowded, and inadvertent interference is commonplace. By contrast, X band activity is generally military, and interference is typically hostile. But whether inadvertent or hostile, the geolocation method used to find non-cooperative interferers must quickly produce emitter latitude and longitude or its equivalent to an accuracy eventually providing unique identification. Multiple satellite solutions have heretofore been favored for this. Using multiple satellites means Doppler shift techniques can still be used, but now it is the shift measured simultaneously between satellite pairs. So the emitter frequency stability requirement is not nearly as stringent as when locating using dwell-to-dwell measurements.
Thus simultaneous intercept of the interfering signals is a strong point of multiple satellite solutions. But it is also a problem since the emitter must lie simultaneously within the field of view of all the satellites, and be simultaneously detected by them.
To minimize the impact of these problems, U.S. Pat. No. 6,417,799, “Method of Locating an Interfering Transmitter for a Satellite Telecommunications System,” Aubain et al., discloses a known two satellite solution. They reduce the number of satellites required to two by using combinations of three measurements: (a) signal time difference of arrival (TDOA) between the two satellites; (b) frequency Doppler difference (FDOP) between the two satellites; and, (c) signal angle of arrival (AOA) using an interferometer on a single satellite. The implementation Aubain et al uses in U.S. '799 to illustrate their method is locating the jammer of a geosynchronous orbit (GEO) telecommunications satellite. A second special “detection” satellite is in a LEO orbit with an interferometer mounted on it. Aubain assumes a linear interferometer as shown in FIG. 1 of subject applicant's set of drawings where a linear interferometer measures phase (φ) 104 and from this obtains the (θ) angle of arrival (AOA) 100 between the baseline vector ({right arrow over (d)}) 101 and normal to the signal wavefront, or direction of arrival (DOA) unit vector ({right arrow over (μ)}) 102.
Thus the linear interferometer determines a cone 103 that the emitter DOA vector lies on. The cone intersects the earth giving a line of position (LOP) for the emitter. The intersection of this cone with a tangent plane at the emitter is a conic section, usually a parabola. This parabolic LOP has a thickness or uncertainty due to the interferometer phase measurement error (ε) 106. The AOA error is reduced by extending the baseline length 101 between the antenna phase centers. It is also reduced at higher emitter frequencies, or shorter signal wavelengths (λ) 107.
Aubain et al. uses the interferometer in two ways. First, frequency and time measurements are performed and the resulting TDOA and FDOP LOP have multiple points of intersection. The AOA parabola then provides an additional measurement picking out the correct intercept. In this application the extent of the AOA error or, equivalently, the thickness of the parabolic LOP is not critical because the TDOA and FDOP lines of position determine the location accuracy. The second way the interferometer is used is with either a TDOA or FDOP measurement. For example, assume TDOA and AOA intercepts determine the emitter position. Then resolving the multiple intersections is accomplished by sequential dwells. As the LEO satellite moves the parabolic and hyperbolic LOP generated at each receiver dwell intersect near the emitter with an uncertainty due to their thickness. So in this case the AOA uncertainty is critical.
Increasing the spacing between the antenna phase centers, i.e., increasing the baseline vector ({right arrow over (d)}) 101 length, proportionally improves the LOP accuracy. However, increasing the baseline length beyond a half wavelength (λ/2) of the signal source generates phase measurement ambiguities 105. Here n 105 is an integer reducing the true phase so the measured phase (φ) 104 lies in the region −π≦φ<π. This means that interferometer phase is measured modulo 2π.
Determining ambiguity integers to recover the true phase requires special processing, an example of which is described by Malloy in a 1983 IEEE ICASSP paper entitled “Analysis and Synthesis of General Planar Interferometer Arrays.” See also U.S. Pat. No. 6,421,008, “Method to Resolve Interferometric Ambiguities” Dybdal and Rousseau, and U.S. Pat. No. 5,572,220, “Technique to Detect Angle of Arrival with Low Ambiguity,” Khiem V. Cai.
These results show eliminating the phase measurement integer ambiguities requires adding additional antennas between the outermost elements. Thus a linear interferometer installed to robustly and fully implement Aubain's method as taught in U.S. '799 may actually resemble FIG. 2 of applicant's drawings, not FIG. 1. In FIG. 2, antennas 203 and 204 are added to determine the integers ni 207 to resolve the phase measurement (φ1) 205, and hence find the angle of arrival (θ) 206 from the true phase resolved phase vector ({right arrow over (φ)}) 211. This resolution is done by processing measurements by an ambiguity resolver 209 across the multiple baselines. An error in determining ni on any baseline invalidates the subsequent relation between the resolved phase vector ({right arrow over (φ)}) and DOA unit vector ({right arrow over (u)}) 212, throwing off the subsequent estimate of AOA 206 by a large amount. Hence it is called a gross error.
In doing the processing as indicated by reference numeral 209 of FIG. 2, Malloy obtains a uniform gross error rate across the frequency band of interest independent of the emitter relative bearing by only allowing antennas placed at relatively prime integer multiples of a fundamental spacing (d0). He calls the discrete set of candidate points the array lattice. FIG. 3 of subject applicant's drawings illustrates a simple linear three antenna array designed according to Malloy's approach. In this FIG. 300 is the array lattice, and the antennas 301 have relative integer spacings 3 and 4 times the lattice spacing (d0) 302. The lattice spacing is determined by the wavelength 304 at the highest frequency and the FOV constraint 303.
The fixed value of the gross error rate across frequency and AOA is a most desirable property. A further significant advantage of using Malloy's placement restrictions and his design method is they result in arrays maximizing the AOA or DOA accuracy while minimizing the gross error rate. Also, critical for satellite applications, his method does this using the minimum possible number of antennas.
Malloy's approach thus produces the best sparse element interferometer, optimal in the sense that, for a given Gaussian phase error vector ({right arrow over (ε)}) as indicated by reference number 214 with covariance matrix R, the quadratic cost L which can be expressed as:
                    L        =                                            (                                                ϕ                  ⇀                                -                                                                            2                      ⁢                      π                                        λ                                    ⁢                  D                  ⁢                                      u                    ⇀                                                  +                                  2                  ⁢                  π                  ⁢                                                                          ⁢                                      m                    ⇀                                                              )                        T                    ⁢                                    R                              -                1                                      ⁡                          (                                                ϕ                  ⇀                                -                                                                            2                      ⁢                      π                                        λ                                    ⁢                  D                  ⁢                                      u                    ⇀                                                  +                                  2                  ⁢                  π                  ⁢                                                                          ⁢                                      m                    ⇀                                                              )                                                          (        1        )            is minimized. D in equation (1) is the matrix of baseline vectors 216 shown in FIG. 2, where ({right arrow over (k)}) 217 is the unit vector along the antenna phase centers and ({right arrow over (u)}) the DOA unit vector 212. For planar arrays as shown in FIG. 5 of this set of drawing figures and discussed hereinafter, (D) is the matrix 506 of baseline vectors ({right arrow over (d)}1) 508 forming the array. Planar arrays are used when DOA rather than AOA is required. Interferometers designed according to Malloy's method are thus ideal for satellite applications.
None the less, utilizing a simple array as shown in FIG. 3 of the set of drawing figures disclosed herein, or an equivalent with four antennas as taught by the satellite telecommunications system of Aubain (U.S. Pat. No. 6,417,799) presumably could be used, especially since in the Aubain approach the detection satellite could be dedicated to the emitter location problem and hence ab initio designed to support an optimal multi-antenna element linear array. But signal jamming is not just a problem for GEO telecommunication satellites. LEO communication satellites are also important. For example, U.S. Pat. No. 5,412,388, “Position Ambiguity Resolution,” Attwood, discloses an LEO communications satellites support radio telecommunications system operating with portable units. Portability requires low power battery operation, and small antennas. Such units can communicate with satellites in LEO orbits, but not GEO satellites 30× farther out.
Aubain's multi-satellite technique does not adapt well to locating LEO jammers. For example, reversing the roles of the low earth orbit and geosynchronous satellites will not work because of the GEO detection difficulty Nor does using two LEO satellites work since simultaneous emitter detection is a significant problem in low earth orbit. It is a problem both because of weak signals, where one of the LEO satellites is far from the transmitter, and because the emitter may not be visible to all antennas in the detection satellite's array.
Coordination is a further major problem. This is a difficulty for any multiple LEO satellite scheme, not just one based on Aubain's approach. Even when all the satellites detect the interfering signal, some central controller and processor must recognize that a jammer was detected, collect data of the same jammer signal from all the satellites, and then derive a geolocation estimate. To satisfy this need Aubain suggests downlinking and processing the data at a ground station. This is a satisfactory solution in Aubain's original scenario because of the presence of a geostationary telecommunications satellite and such a satellite can always have a ground station visible. But with only LEO satellites, it is much too restrictive to assume a ground station with the required processing facilities will be visible to any of the satellites let alone all when the jammer transmits.
Because of these detection and coordination problems, the most robust operational approach to LEO geolocation of interfering emitters is to use a single satellite. Further, that satellite must be the one experiencing jamming, and must be able to autonomously derive the jammer location from onboard measurements. Attwood solved the emitter location problem with a single LEO satellite by making sequential time delay and frequency change measurements, but suggested synchronizing the frequency base and time base used by the satellite and transmitter to achieve the required signal stability. Jammers, however, are not so helpful. Because the jamming transmitter will not generally cooperate by providing signal stability, allowing the use of delta-Doppler, location must be derived solely from angle of arrival (AOA) or direction of arrival (DOA). AOA is adequate in Aubain's approach because it is used with time difference of arrival (TDOA) or frequency Doppler difference (FDOP). But when only angle measurements are available, DOA is far superior to AOA since it results in an actual emitter location estimate at each receiver dwell, rather than just the line-of-position on which the transmitter lies. Also, the transmitter may be on only briefly. Accordingly, using DOA greatly expedites the location process.
Attempts have previously been made to measure DOA with a single antenna, and thus avoid the need for phase measurements across a two dimensional interferometer array. For example, U.S. Pat. No. 6,583,755, “Method and Apparatus for Locating a Terrestrial Transmitter from a Satellite,” Martinerie and Bassaler, discloses the concept of performing single platform LEO geolocation by measuring a plane the emitter's DOA vector lies in, called the propagation vector. However, it uses a single special antenna to make this measurement. The plane intersects the earth, resulting in a circle of position. The DOA plane is derived from measurements of the electromagnetic field's polarization, with the polarization being restricted to linear polarization. Unfortunately the restriction to one special type of electromagnetic wave polarization greatly limits the method's usefulness. Jamming signals are not restricted in their polarization.
Accordingly, there is currently no robust way to perform single satellite geolocation other than by measuring DOA by implementing a multielement antenna array equivalent to a planar interferometer. And in particular, if a conventional planar array is chosen, an approach such as presented by Malloy appears to be the best available. As noted, such an array will generate the best DOA accuracy for the lowest gross error rate utilizing the minimum number of antennas. The antennas may be chosen to cover the frequency band of interest and respond to any transmitted polarization. Such an array, if large enough, could accurately locate emitters in a single receiver dwell by intersecting the DOA vector with the earth's surface. This method is called Az/El geolocation. However, the baselines for such an array are comparatively large and they typically are measured in meters rather than conventional centimeters.
Hence implementing such an array generally requires specifically designing the satellite to support it, possibly using such specialized structures as that described in U.S. Pat. No. 6,016,999, “Spacecraft Platforms” by Simpson, McCaughey and Hall. Therefore, for the widest possible application, especially on existing satellite designs, smaller arrays must be considered. Such arrays, however, do not support Az/El geolocation, but do support locating emitters using some form of triangulation or bearings-only geolocation over several dwells as the satellite moves in its orbit.
An example of such an array using Malloy's design approach is shown in FIG. 4 of this specification. The points 400 of FIG. 4 represent a lattice of antenna spacings for an optimal planar array analogous to the antenna spacings 300 in FIG. 3 for the linear array. The points are now located by two fundamental lattice position vectors ({right arrow over (d)}1) and ({right arrow over (d)}2) shown by reference numeral 40. At least nine (9) antennas 402 are typically required to provide a small gross error rate while providing DOA performance supporting bearings-only geolocation. The optimal array is designed by arranging the nine antennas on the lattice points in different configurations consistent with the relatively prime integer-multiple requirement and computing the quadratic cost (Equation 1) for each arrangement. Just as for the linear array, utilizing these lattice points and prime integer spacings guarantees an array having a gross error rate independent of frequency and signal angle of arrival. The configuration chosen would be one minimizing the cost while giving the required DOA accuracy with the lowest gross error rate. The configuration shown in FIG. 4 is illustrative of how such a final design would look.
The array 500 shown in FIG. 5A is a more pictorial representation showing its implementation with a two channel receiver. By intersecting the AOA cones in a DOA processor 501 across multiple antenna pairs, a unique DOA unit vector ({right arrow over (u)}) 502 is found. The DOA unit vector 502 is also shown relative to the array 500.
Note that because of the phase measurement error vector ({right arrow over (ε)}) 503 the DOA unit vector ({right arrow over (u)}) 502 has an error cone 505 associated with it. This is usually taken to represent a 3σ error deviation, so the true DOA lies within this cone 98.9% of the time. Because of this error the range line 506 shown in FIG. 5B extending the DOA 52 to the earth's surface, thus providing a slant range to the emitter, does not usually intersect the earth at the emitter's true location. Rather a somewhat elliptical boundary 507 is formed by the cone 505, shown in FIG. 5A, and the emitter lies within this boundary all but about 1% of the time.
When the emitter lies near the satellite's suborbital point, the boundary closely approximates an ellipse 600 shown in FIG. 6A. But as emitters approach the satellite's horizon, the boundary becomes more distorted, larger and egg shaped as shown by reference numeral 601. The increase in the area is due to the interaction of the earth's curvature 602 shown in FIG. 6B with the DOA error cone 603. The earth's curvature 603 increases the range uncertainty to the emitter. Thus the slant range error 605 is significantly larger away from the suborbital point 604 compared with the error 606 for transmitters closer in.
The error cone 603, and hence slant range errors 605 and 606 are reduced by extending the outermost interferometer baseline spacings. So accurately locating any emitter within the satellite's field of view, particularly those near its horizon, requires increasing the outer antenna spacing in the array 500 shown in FIG. 5A to the maximum extent possible. But improving DOA accuracy introduces larger phase measurement ambiguities 507, and hence requires more antennas to resolve them. The nine (9) antennas shown in FIG. 5A may thus actually represent a lower bound for the number required in a planar interferometer array supporting LEO bearings-only location for emitters far from the suborbital point.
Hence even implementing an optimal interferometer with the minimal number of elements to solve the LEO location problem still generates what is derisively called by the satellite community an “antenna farm.” Accordingly, this solution is normally not practical or desirable to implement because of the space required on the satellite's surface. The space required is not the only restriction, however. Each antenna must have its own unobstructed field of view. This greatly limits what else can be installed. Therefore, implementing even a small array usually requires that the satellite still be specifically designed to support it.
This is generally unacceptable since locating interfering emitters would be an auxiliary task, not the primary mission of most LEO satellites. So the array for locating an interfering transmitter must fit into an existing design, and not require a new one. The only way the array in FIG. 5A, for example, repeated in FIG. 7 by reference numeral 700, can fit onto an existing design is by eliminating antennas. If only three antennas are retained, such as shown by reference numeral 701 in FIG. 7B, the array has a much better chance of being acceptable. It will achieve the DOA accuracy required. But now, because of the phase measurement ambiguities 704, spurious DOAs 705 are produced, one possible DOA for each integer pair (n, m) 706. The ambiguous DOA vectors 702 each have an associated error cone 703.
This, of course, results in ambiguous emitter locations as shown in FIG. 8B, where for clarity an array 800 identical to array 701 shown in FIG. 7B is reproduced. In FIG. 8B, reference numeral 801 represents the range vector ({right arrow over (r)}) extended along the true DOA to an actual emitter location, while range vector 802 and the other range vectors indicate spurious locations. Note that even though the DOA associated with range line 802 is spurious, its error region 803 is formed by the associated error cone intersecting the earth's surface, just as for the true emitter.
Since the reduced array size requires relative motion to locate the emitter, it is natural to ask if the ambiguous sites may be eliminated by the same satellite movement. A technique for exploiting platform motion to resolve phase measurement ambiguities does exist for the two element array shown in FIG. 1. In U.S. Pat. No. 3,935,574, “Signal Source Position-Determining Process,” Pentheroudakis discloses a method utilizing either rotational motion or translational motion of a two element ambiguous horizontal interferometer to pick the correct sequence of AOA cones over a series of receiver dwells and hence eventually resolve the linear array.
At the first dwell Pentheroudakis establishes the set of possible ambiguity integers (ni) and uses each integer from this set to produce a candidate resolved phase. The phase rate is then measured and the phase roll over is tracked or changed in each integer ni as the array moves relative to the emitter. Under this phase unwrapping procedure, the correctly updated ambiguity integer sequence produces a stable location estimate that converges to the true emitter position. The other sequences eventually produce AOA that exhibit abrupt changes when the respective ambiguity integer gets incremented, causing the corresponding location estimates to diverge and hence eliminating those integer sequences as viable candidates.
Pentheroudakis' method requires almost continuous phase measurement updates to track the phase change and hence the integer roll over for each integer set or lobe. Although used to resolve a single two element interferometer, the method could be readily adapted to the three element planar array 800 shown in FIG. 8A. Now the roll over in two sets of ambiguity integers (ni,mi) must be tracked. This greatly extends and complicates the software processing required, but does not alter the basic method of using phase tracking to update the ambiguity integers (ni,mi), and then updating the candidate emitter locations.
A more significant drawback when trying to adapt the method to satellite applications is the extent of both the true and spurious error regions, e.g., regions 803 shown in FIG. 8B, especially for candidate emitter locations 804 relatively far from the suborbital point of range line 802. Also important is the fact the error regions for the ambiguous locations can overlap each other as shown by reference numeral 805.
The extent and overlap of the error regions 805 both have critical consequences. Reference will now be made to FIG. 8C. First assume that region 815 is a true site. As the satellite moves in its orbit from position 806 to 807, the spurious location 809 associated with DOA 808 may jump to new location 810 in a more erratic manner than estimates for the true site even before an incorrect integer roll over occurs. But this somewhat erratic movement is difficult or even impossible to detect with Pentheroudakis' method because of the extent of the error region 816. Further, the abrupt DOA jumps caused when phase tracking generates incorrect integer updates are a function of the measured phase change created by the true emitter DOA's movement relative to the interferometer baseline. This has a significant impact on ambiguity resolution performance.
To understand this impact, assume now that the true emitter happens to lie far from the suborbital point, for example at point 811 rather than point 815. Now a comparatively large satellite orbital translation and hence significant time is required to create enough true DOA change to trigger integer updates and thus cause eventual large abrupt jumps in the spurious DOA to occur at other distant sites such as site 809. When such jumps occur, because of the overlap of error regions these jumps may not eliminate wrong locations. For example, if suborbital point 811 is the true emitter location and it occurs in an overlap region 812, it cannot be easily statistically differentiated from spurious site 813. Even a phase roll-over may not clearly differentiate the two. It should be noted that there can be a significant number of these overlap regions, particularly at higher frequencies.
Another critical problem adapting Pentheroudakis' method to satellite based emitter location is the requirement for almost continuous sampling of the phase measurement. For the planar array 800 shown in FIG. 8A, the receivers for the two channels shown must switch via switch 814 between baselines to do the phase sampling, so there is a limit to the sample rate. But the most fundamental problem with continuous phase tracking is that the noncooperative emitter might not be transmitting or detected at each receiver dwell during the geolocation process. For example, a simple way to defeat the Pentheroudakis scheme is to blink the emitter with a duty cycle that still interferes with satellite communication, but does not allow unwrapping of the candidate phases. Also, as noted before, on a satellite all antennas in the array may not have the same unrestricted field of view. So even with the emitter continuously transmitting, satellite attitude may prevent phase measurements during a significant number of the receiver dwells.
The present invention overcomes the inherent problems associated with applying the Aubain, Attwood, Martinerie, and Pentheroudakis approaches to locating an emitter interfering with a satellite in low earth orbit (LEO). In particular, both cooperative and non-cooperative emitters are located with equal facility. The present invention does not require an emitter to transmit continuously, or require the transmitter to have special stability or polarization characteristics. It does not require downlinking data to a ground station. It does not require simultaneous detection of the emitter by multiple satellites, although it can be incorporated in such methods to increase their versatility.
The present invention is directed to an intrinsically low earth orbit technique that exploits the excellent DOA measurement capability of planar interferometer arrays. It can employ arrays designed using Malloy's optimal approach, but with the array not fully populated with antenna elements and hence producing ambiguous DOAs. If this is done special processing utilizing the antenna's relatively prime integer spacing in an array lattice can be incorporated, but this concept is not pursued in the present invention since it is not essential. Further, it is not an intrinsic requirement of the invention that the antenna element placement satisfy the Malloy, Dybdal and Rousseau or Cai restrictions. Their placement can be arbitrary, dictated by space available on the satellite. In fact the antenna spacing in the subject invention can vary from one measurement update to another and thus the interferometer array can be flexible or floating.
In performing geolocation, the present invention uses a minimal number of antennas required to generate ambiguous emitter DOAs. If no satellite attitude change is allowed during a receiver dwell the minimal number is three. But if some restricted attitude change is feasible, a modification to the method described in the present inventor's U.S. Pat. No. 5,457,466 “Emitter Azimuth and Elevation Direction Finding Using Only Linear Interferometer Arrays” permits the use of only two antennas. Also only two antennas may be required, if not coboresited, when incorporating the method described in the inventor's U.S. Pat. No. 5,608,411 “Apparatus for Measuring a Spatial Angle to an Emitter Using Squinted Antennas.”
The present invention does not generate a candidate ambiguity integer set at each receiver dwell by phase tracking. Thus maintaining a continuous common field of view for all the antennas is not a requirement. Gaps of many seconds can occur between phase updates. Instead of lobe tracking or phase unwrapping, the present invention uses the initial emitter locations obtained from the initial set of ambiguous DOA to predict ambiguity integers during the satellite's subsequent orbital motion. In other words, this invention does not use phase to predict location, but rather location to predict phase.