Emitter azimuth and elevation direction finding using only linear interferometer arrays

The invention provides a method for using single linear arrays for making AOA measurements only in sensor coordinates to perform emitter direction finding from an observing aircraft.

FIELD OF THE INVENTION 
This invention relates to a means and method for measuring angle of arrival 
(AOA) to perform emitter direction finding (DF). In particular this 
invention provides a technique for making such measurements using linear 
interferometer arrays only. 
BACKGROUND OF INVENTION AND RELATED ART 
Passive radar emitter direction-finding (DF) utilizing radio frequency (RF) 
interferometers mounted on aircraft requires finding the emitter's azimuth 
and elevation in the observer's local-level reference frame. In the 
description given hereinafter the term aircraft is meant to encompass any 
observational platform whose motion involves attitudinal changes, such as 
roll, pitch and yaw, as well as translational motion. In particular, an 
interferometer sensor array mounted on the leading edge of an airplane 
wing measures AOA in relation to the sensor's own system of three 
dimensional coordinates which are then transformed to the observational 
body's frame of coordinates and a level frame of coordinates to report 
azimuth and elevation. Finally target location is reported in a set of 
coordinates for the Earth. 
Finding emitter elevation and azimuth from aircraft has previously required 
the use of planar or conformal interferometer arrays. A linear 
interferometer could not be used, since a single linear array measures 
angle-of-arrival (AOA) and not direction-of-arrival (DOA). That is, a 
single linear interferometer produces an AOA cone, and the emitter can be 
anywhere on the intersection of that cone with the Earth. 
A linear interferometer designed to fit on the leading edge of an aircraft 
wing, is illustrated in FIGS. 1a and 1b. FIG. 1a illustrates a typical 
prior art linear interferometer array 10 having a plurality of antennas or 
sensors 12 arranged as shown to have a baseline d . In FIG. 1b array 10 
supplies through SPST switch 14 received radar signals to phase 
detector/receiver 16. The phase information from the receiver is supplied 
to a processor 18 which accomplishes phase ambiguity resolution; the 
phase-resolved signal 15 is then used for determination of AOA 
information, as shown at 19. The phase measurement of a plane wave with 
unit normal (DOA vector) u across one baseline d is 
##EQU1## 
Thus the quantity measured is the angle of arrival, or AOA between the 
interferometer baseline and wavefront. Any emitter lying on the AOA cone 
will produce the same measured phase .phi..sub.m. For a planar earth 
approximation, this means that any emitter lying on the hyperbola 
resulting from the intersection of the AOA cone with the earth can 
generate the same AOA, and hence emitter azimuth is available from this 
single measurement only in the special circumstance that the emitter lies 
in the plane containing the linear array baseline. When this is not true 
an ad hoc assumption about emitter elevation must be made, typically that 
the emitter lies on the radar horizon. For emitters not on the horizon the 
error in using AOA as the true azimuth measurement, typically called the 
"coning" error, is given by 
##EQU2## 
This equation is strictly only true for the sensor coordinates but this 
caveat is not important here. Equation 2 indicates the azimuth error 
becomes quite large when emitters are at steep elevations. It is 
negligible for emitters on the horizon if the aircraft is flying level, 
but may become important even for distant emitters when the aircraft has a 
significant roll or pitch attitude. 
Since emitter azimuth is an important parameter in many systems performing 
passive radar detection, e.g. for emitter classification and 
identification, this coning error is a severe drawback. Another deficiency 
AOA-only systems suffer is their lack of elevation measurement prevents 
"az/el" emitter location, i.e. finding emitter range r using phase 
measurements made in a single dwell along with the observer altitude h via 
a relationship such as 
##EQU3## 
However linear interferometer systems do perform location using 
bearings-only passive location techniques. Bearings-only ranging utilizing 
AOA essentially finds the intersection of the multiple AOA-hyperbola 
generated as the aircraft moves along its track. The accuracy of any such 
AOA-only location technique is characterized by a "geometric" 
signal-to-noise ratio or gSNR 
##EQU4## 
where .DELTA.B is the bearing spread at the emitter created by the 
observer's motion, and .sigma..sub.az is equivalent to .sigma..sub.AOA 
(for the purpose of characterizing bearings-only accuracy) when the 
aircraft flight is essentially straight and level. 
Thus a positive feature of bearings-only ranging is that the range accuracy 
can be improved by making the bearing spread larger. This is in marked 
contrast to az/el location. Az/el location estimates cannot be refined by 
sequential averaging because of the large bias errors typically present in 
the elevation measurement. These elevation errors can have a significant 
DOA dependent component, and since an important application of az/el 
ranging is to locate emitters near the observer flight path, the DOA may 
not change significantly. DOA dependent bias error is also present on the 
bearings-only measurement, but has a negligible effect for emitters at 
bearings essentially normal to the observer's flight path, which is often 
the case when AOA-only location is used. 
FIG. 2 (described below) summarizes the operation of an AOA-only system. 
This system, as in FIG. 1b, supplies phase information from receiver/phase 
detector 16 through switch 20 to processor 21 which provides ambiguity 
resolution for each of the arrays 10. The resolved baseline information is 
then used at 22 to compute AOA information in accordance with the sensor's 
set of coordinates. After a range estimate is supplied at 23, the AOA 
information is calculated in accordance with the platform or body's set of 
coordinates at 24, and then to level coordinates at 25. 
The benefits of using a single linear array doing bearings only ranging are 
the limited number of phase measurements required per dwell compared to 
multi-dimensional arrays, and compact installation. The drawbacks are the 
inability to go from AOA in the sensor frame to azimuth in the level frame 
without assuming an ad hoc emitter elevation, i.e. introducing an unknown 
and possibly large coning error, and the lack of any elevation measurement 
to use in rapidly estimating emitter range, particularly for emitters 
close to the aircraft. 
Overcoming these drawbacks and providing accurate azimuth has previously 
required utilizing an interferometer array extending in at least two 
dimensions, such as the conventional conformal array. In the latter array 
it is necessary to use a vertically disposed sensor array to form an 
elevation baseline while another sensor array generally disposed 
horizontally is used to resolve the elevation array ambiguities. 
The phase measurements in such a multi-baseline system cannot typically be 
made without receiver switching between the baselines, i.e. on a 
nonmonpulse basis. Besides increasing system complexity, such baseline 
switching complicates the detection of multipath errors on the phase 
measurements. 
There are other problems with switching. In the conformal array discussed 
above the horizontal array must have its phase measurements completed 
before making phase measurements on the elevation antennas. If the emitter 
is no longer detected after the "horizontal" phase measurements are made, 
because, for example, of emitter scanning or terrain blockage, elevation 
will not be obtained. 
Note that the possibility of not getting a full set of phase measurements 
is increased by the use of elevation arrays on low RCS (Radar Cross 
Section) aircraft, since stealth aircraft impose RCS restrictions on the 
antennas. Adding an elevation array increases the overall RCS, requiring 
antenna design trade-offs that reduce system sensitivity and hence may 
prevent detecting emitter side and backlobes. 
Obtaining the space to mount a planar array or three dimensional array is 
difficult on many smaller aircraft. Also, important delta-wing stealth 
aircraft designs do not provide extensive vertical area, and hence little 
space for a planar array no matter what the intrinsic aircraft size. 
Although by utilizing conformal design techniques elevation arrays can be 
mounted on the leading edge of delta-wing aircraft, the antenna elements 
do not have common boresights. This can introduce significant bias errors, 
especially when certain popular ESM system antenna elements, such as 
broadband multi-arm spirals are used. 
A positive aspect of multidimensional arrays is that, aside from the time 
required for baseline switching during a dwell, az/el location provides 
near monopulse emitter location. But this very desirable feature is 
mitigated by the following deficiency: 
The 1-.sigma. accuracy of az/el location is characterized by a "geometric" 
signal-to-noise ratio (gSNR) 
EQU cot(e).sigma..sub.e ( 5) 
Thus the estimate is intrinsically inaccurate at lower altitudes and at any 
altitude for emitters near the horizon, with no means of subsequent 
refinement, i.e. no bearing spread factor as for sequential AOA location. 
Because of multi-dimensional array installation limitations, baseline 
switching-induced system complexity, and intrinsic inaccuracy of az/el 
ranging, linear interferometer arrays measuring AOA-only have been used 
extensively in ESM systems. Flight tested linear interferometers working 
over emitter frequencies from 2 GHz to 18 GHz, such as those designed by 
the Amecom Division of Litton Systems, Inc. for the TEREC system and an 
advanced capability receiver for the EA6-B program are readily available. 
But, as noted above such arrays do not provide true emitter azimuth or 
monopulse location. 
It is therefore, an object of this invention to allow such linear arrays to 
be used to perform the functions associated with more complex 
multi-dimensional arrays, i.e generate azimuth, elevation, and emitter 
range in a manner that does not involve flying a base leg to produce 
bearing spread. 
It is the further object of this invention to allow emitter location by 
multiple platforms collocated, as in a formation, and to remove the 
defects associated with conventional az/el location by converting 
systematic bias errors to errors random in time, thus allowing improvement 
of the az/el range estimate by sequential averaging. 
SUMMARY OF THE INVENTION 
The foregoing objects, and others, are achieved in accordance with the 
invention which provides a method for using single linear arrays for 
making AOA measurements only in sensor coordinates to perform emitter 
direction finding from an observing aircraft. The linear arrays used may 
be mounted on a single or on multiple aircraft. Since emitter elevation 
information is generated, az/el ranging can be accomplished using only a 
linear interferometer, instead of two or three dimensional sensor arrays. 
This invention allows aircraft not fitted with elevation arrays to generate 
true azimuth and elevation, and to do az/el location with significantly 
greater accuracy at low altitudes than currently done. 
Thus it is the purpose of this invention to utilize linear interferometer 
arrays to: 
1.) Generate the DOA unit vector 
EQU u=cos(e)cos(a)i+cos(e)sin(a)j-sin(e)k (6) 
to provide azimuth with no coning error for sorting and other electronic 
security measures ESM uses and elevation for location. 
2.) Derive elevation from phase measurements in a way that allows 
sequential averaging to reduce az/el range estimate errors. 
3.) Provide elevation baselines that can be as long as those commonly used 
for azimuth measurement on aircraft with limited vertical aperture. 
When two or more platforms are used, monopulse phase measurements from each 
platform are utilized to DF and az/el locate the emitter. The measurements 
from the multiple platforms require no time-simultaneity. In fact, the 
time at which the measurement is made is not used at all, but instead only 
the platforms' locations and attitudes. The origin of the phase 
measurements, i.e. whether single platform or multiplatform, is immaterial 
to the new invention. 
A significant element of the new invention is the generation of a virtual 
spatial array from the linear arrays based on aircraft 
six-degree-of-freedom, or 6DOF, motion. 6DOF refers to the six parameters 
required to specify the position and orientation of a rigid body. The 
baselines at different times are assumed to generate AOA cones all having 
a common origin; the intersection of these cones gives the emitter DOA, 
from which az/el range can be derived. 
The generation and intersection of the AOA cones can be done in seconds, as 
opposed to the conventional multicone AOA approach, bearings-only passive 
ranging, discussed above. Bearings-only passive ranging requires that the 
origin of the cones be separated by some intrinsic flight path length in 
order to form a triangle, and subtend bearing spread at the emitter.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT 
In order to aid an understanding of the principles of the invention, FIGS. 
3a and 3b further contrast the two linear interferometer based approaches. 
The labeled blocks sufficiently identify the sequence of functions. As 
indicated in FIG. 3b, generating the virtual array involves storing the 
interferometer 6DOF position at the time the phase measurements are made. 
This process is iterative, as is the bearings-only approach of FIG. 3a. 
But the bearings-only iterations extend over minutes to obtain a solution, 
whereas the virtual array iterations intrinsically require only seconds. 
The baselines are formed by combining the two separate resolved linear 
array phase measurements, the arrays being located on the same platform. 
This creates a planar array. A virtual array can be created during a 
single aircraft observer snap roll. This creates a three dimensional 
array, as does the array created from multiple observers; in the latter 
case multiple aircraft in close formation can synthesize an array rather 
than relying on single aircraft attitude changes. 
During the course of DF'ing an emitter the virtual array embodied by D can 
be synthesized from any combination of these four methods. Thus intrinsic 
system bias errors can tend to random errors in time. For instance, DOA 
dependent errors randomize with time in the virtual array approach due to 
the relative change in emitter-to-array angle-of-arrival during a snap 
roll, compared to conventional az/el location. Thus sequential averaging 
can be used to reduce both angle-estimate errors, and location-estimate 
errors. 
The averages shown in FIG. 3b that reduce these errors represent both long 
term and short term averages. The location averaging is long term, 
extending over many dwells. As just noted, unlike conventional az/el 
location, the elevations e used to estimate range come from the 
interferometer array at many different attitudes. Hence the DOA dependent 
errors on e become random, and hence the range errors are random from 
update to update. By contrast, the azimuth and elevation estimate average 
occurs over measurements either close together in time, or observer 
location. Hence it is typically an average over a small set. 
FIG. 4 shows a preferred embodiment of the invention in a system 40 
employing two linear interferometers 41a and 41b. The arrays can be 
constructed like the interferometer pictured in FIG. 1, and located on the 
leading wing edge of a delta-wing aircraft. The operation is essentially 
same as that of the conventional system of FIG. 2 through the initial 
phase measurement ambiguity resolution process 44, but note the absence of 
the sector decision process. In conventional ESM systems the latter 
process determines which array will be used. In the new approach presented 
here all measurements available from all arrays will be used at each 
dwell. 
Utilizing the observer's NAV system 45, the interferometer baseline d.sub.i 
associated with phase measurement .phi..sub.i are stored in memory 46 
with their 6DOF position on the basis of baseline transformations 
occurring at 47. For example the baselines generated during a snap roll 
could be 
##EQU5## 
The rows of virbase contain the six parameters required to completely 6DOF 
characterize the individual baselines. The first three elements in this 
array are the projections of the baseline unit vector onto the level 
frame. This projection is done using platform roll, pitch and yaw angles 
from the navigation, or NAV, system. The second three elements represent 
the baseline distance from a common reference. The unit is nautical miles 
for this second set in the example. Thus, a baseline spatial position and 
attitude for the system is established. 
The first five rows of virbase are for the port array, while the second 
five rows are for the starboard array. The distance apart on the aircraft 
of the two arrays is too small to be discernible with the numerical 
precision used here. 
The virtual array is constructed sequentially at 48 by iteratively forming 
the array matrix D. In forming D only the angular orientation of the 
baselines are used, that is the d.sub.i are all assumed to have a common 
origin or (x,y,z) location. This common origin is taken as the centroid of 
all the actual translational positions of the baselines currently forming 
D. Thus the final array matrix in this example is 
##EQU6## 
However, the solution process begins before the complete array is formed. 
When two baselines are available an initial D can be formed and checked 
for "observability", i.e for the feasibility of solving for u in the 
equation 
##EQU7## 
where the set of phase measurements are collected into a vector .phi. 
whose elements have the same ordering as the baselines. If a solution is 
feasible the error variance 
EQU R=E(.epsilon..epsilon..sup.t) 
on the phase measurements for the virtual interferometer must be computed 
(50). The dominant error is that caused by the difference in phase at the 
assumed centroid origin compared to the actual position the phase 
measurement was made. This error (R) is a function of the emitter 
location, and hence is not known. The error can be bounded, though, by 
initially assuming minimum and maximum emitter ranges (49), and using the 
"dispersion" portion of virbase, which is 
##EQU8## 
The last column is zero because there was no altitude change in this 
example. The phase error actually caused by the different translational 
positions of the baselines is shown in FIG. 5. In later updates for the 
same emitter, estimated range is used to refine the bound on the 
dispersion phase error generated initially from the min/max range 
assumption. The other component of R is the intrinsic system error 
occurring in conventional interferometers, i.e. thermal noise and antenna, 
radome, and receiver bias. 
The constrained estimation problem for u, i.e 
##EQU9## 
is solved next at 52 in the local level frame using, for example, a 
sequential quadratic programming approach. Azimuth and elevation are 
computed at 54 from the components of 
##EQU10## 
according to the definition of the DOA unit vector in Equation 6, i. e by 
##EQU11## 
The error variance of this estimate is found next at 56. This is done by 
noting that the solution to Equation 8 can be written in the form 
EQU u.sub.est =D.sup.i .phi. 
and D.sup.i is the means by which the relative benefit of using additional 
or different sets of baselines can be assessed. This is seen by 
representing the desired azimuth a and elevation e measurements as a 
vector 
##EQU12## 
and finding the error on the estimate of a, which can be approximated by 
##EQU13## 
Hence the estimate error is strictly a function of D.sup.i and R. D.sup.i 
reflects the interaction of the relative orientations of the baselines 
with R, while R embodies predominantly the error introduced by the 
baseline relative distances apart. 
This error variance is used to provide a confidence measure (58) for the 
estimate, and also when performing a weighted average with future az/el 
range estimates, or averaging subsequent azimuth and elevation estimates 
as described below. 
This process is repeated with subsequent updates, iteratively forming 
D.sub.k at the kth update, and estimating u until the error variance 
computation indicates a decrease in accuracy because of increased 
dispersion from the virtual array centroid. Out of the set of estimates, 
the one with the smallest error is then saved for subsequent processing 
and reported as the emitter's DOA. Note that the estimate chosen from a 
given set may vary depending on the criteria used. For instance, azimuth 
accuracy may be more important than elevation accuracy, or vice versa. 
The estimate associated with a given virtual array centroidal position may 
be further refined in time if the aircraft is flying a pattern. An example 
is a racetrack pattern having its long axis oriented toward the emitter, 
as is commonly done in radar jamming applications. The flight path is a 
difficult one for bearings-only location, but particularly beneficial for 
az/el location as performed utilizing the virtual array. This is because 
as the aircraft repeats the pattern, virtual arrays with sets of phase 
measurements separated in time by many minutes, but whose centroidal 
origins are quite close, will be formed. The azimuth and elevation 
estimates from these independent but nearly collocated virtual arrays can 
be refined by a weighted average using the error variance estimates, and 
these smoothed estimates used to produce very accurate az/el location. 
If the aircraft is not flying a pattern, collocated virtual arrays will 
only occur randomly, if at all. The range estimate can still be averaged 
though, instead of the azimuth and elevation estimates. As the range 
estimate accuracy improves through averaging, estimated range can be used 
to refine the computation of the dispersion error in R, which leads to 
improved DOA estimates for a given set of phase and baseline measurements. 
Variations on the above approach are clear. For instance, if a terrain map 
is available the emitter range estimate can be improved by using virtual 
array azimuth and elevation coupled with the terrain map. If only azimuth 
is required from the system and not elevation, after emitter range is 
found with sufficient accuracy predicted elevation can be used to correct 
subsequent single baseline AOA to obtain true azimuth..sub.-- 
An intrinsic aspect of this invention is that for each particular class of 
airframe installations a special set of aircraft maneuvers will produce 
the best estimates of either azimuth, or elevation, or both together. 
These maneuvers encompass either a single platform in time, or multiple 
platforms simultaneously in space. Furthermore, it is clear, particularly 
for interferometers mounted on the wing's leading edge, that separate, 
fully resolved interferometer outputs on the same aircraft can be combined 
during a dwell to locate the emitter, without movement in space or change 
in attitude required, utilizing the same processing as for multiplatform 
or attitude-change cases. 
For a delta-wing installation, emitters close-in can be DF'd using both 
wing-mounted arrays in a single dwell with no further 6DOF motion 
required. For emitters at much smaller elevations, a roll generates very 
accurate azimuth and elevation. Several aircraft flying close together 
could produce a similar estimate. 
To illustrate these remarks, performance was simulated for an aircraft in 
level flight, an aircraft snap rolling, and an aircraft in a diving turn 
(Table I). 
TABLE I 
______________________________________ 
Aircraft Maneuvers Used To Generate Virtual 
Array Performance 
Aircraft Virtual Array 
480 kts 20000 ft No. Disper- 
Distance Attitude change 21" sive 
6DOF flown roll pitch 
heading base- 
error 
Motion 
(nm) deg deg deg Time lines 
(deg) 
______________________________________ 
Level 0 0 0 0 1 msec 
2 0 
Turn 2 45 -30 57 15 sec 
30 4.6 
Roll .67 360 5 5 5 sec 
5 .7 
______________________________________ 
The emitter characteristics for the three cases is shown in Table II. 
TABLE II 
______________________________________ 
Emitter Characteristics Used in Generating 
Performance 
Emitter 
10 GHz 
A/C 1 sec Revisit Rate 
6DOF Range SNR.sub.video 
Motion (nm) (dB) 
______________________________________ 
Level 7.38 20 
Turn 50 13 
Roll 50 13 
______________________________________ 
The performance is given in Table III. 
TABLE IIIa 
______________________________________ 
Level Flight Virtual Array Performance 
Contrasted with Conventional AOA System for Emitter at 
Significant Elevation 
Source az (deg) el (deg) Range (nm) 
______________________________________ 
True 9.90 -25.65 7.38 
Virtual Array 
9.92 -25.70 6.85 
Estimate 
Conventional 
12.31 none available 
none available 
Linear Array 
Virtual Array 
.15 .2 .13 
Predicted 1-.sigma. 
______________________________________ 
TABLE IIIb 
______________________________________ 
Turning Dive Virtual Array Performance 
Contrasted with Conventional AOA System for Emitter at 
Small Elevation 
Source az (deg) el (deg) Range (nm) 
______________________________________ 
True 9.90 -4.19 50.00 
Virtual Array 
9.96 -5.29 39.43 
Estimate 
Conventional 
10.18 none available 
none available 
Linear Array 
Virtual Array 
.74 .31 4.11 
Predicted 1-.sigma. 
______________________________________ 
TABLE IIIc 
______________________________________ 
Snap Roll Virtual Array Performance 
Contrasted with Conventional AOA System for Emitter at 
Small Elevation 
Source az (deg) el (deg) Range (nm) 
______________________________________ 
True 9.90 -4.19 50.00 
Virtual Array 
9.96 -4.189 50.29 
Estimate 
Conventional 
10.18 none available 
none available 
Linear Array 
Virtual Array 
.054 .023 .25 
Predicted 1-.sigma. 
______________________________________ 
In all cases the azimuth and elevation accuracy is certainly much greater 
than would be obtained using the conventional conformal array. The system 
implementation is also much less complex, while the DOA estimation time 
takes several, rather than one receiver dwell. 
The new phase errors, the dispersive error, intrinsic to this approach are 
shown in FIGS. 5 and 6 for the snap roll and diving turn. The level flight 
case had negligible dispersive error. FIG. 5 indicates that the snap roll 
introduces a dispersive error quite amenable to averaging over the set of 
baselines. FIG. 6 shows the diving turn introduces more a bias error. 
However, by varying subsequent maneuvers to change the sign on the error, 
sequential averaging can be used to reduce its effect on az/el range 
estimates. 
The dispersive error bias for the diving turn case caused the discrepancy 
between the predicted range accuracy and actual error shown in Table IIIb. 
The level flight example did not break up the DOA bias error much, which 
degraded the range estimate from the random-error only accuracy 
theoretically possible. But, as noted above, the proper set of maneuvers, 
or single maneuver, can reduce the dispersive and DOA bias and provide 
range accuracy estimates close to the random-error based theoretical 
value, as demonstrated by the snap roll in Table IIIc. But note this 
maneuver set may be different from the set generating the optimal angle 
estimates, since it will tend to emphasis elevation accuracy over azimuth 
accuracy. 
The principles of this invention are described hereinabove through the 
description of a preferred embodiment. It is to be understood that the 
described embodiment can be modified or changed without departing from the 
scope of the invention as defined by the appended claims.