High precision radar detection system and method

A radar detection system with four transducers accurately determines the azimuth angle of a radar emitting object. The three strongest signals from the four transducers are combined to generate two differential signal values. A table is provided which contains angle of arrival values associated with all possible combinations of the two differential signal values. To determine the angle or arrival of a particular object, an index value is derived from the corresponding pair of differential signal values, and that index value is used to select the record in the table with the angle of arrival of the object, relative to the transducer which received the strongest signal. The table also stores a signal measurement correction for each combination of the two difference signal values. The signal measurement correction is to adjust the measured signal strength when calculating the distance of the object from the radar detection system.

The present invention relates generally to radar detection systems and 
particularly to methods and systems used for accurately determining the 
direction of an object. 
BACKGROUND OF THE INVENTION 
Referring to FIG. 1, the present invention is an improved airborne radar 
detection system 100 which is intended to accurately determine the 
direction of a radar emitting object 110. The radar emitting object 110 is 
sometimes called an "emitter". Such systems typically have four 
transducers 120, 122, 124 and 126 mounted at reference angles of 45 
degrees, 135 degrees, 225 degrees and 315 degrees, respectively, relative 
to the forward direction of a plane 130. Such system configurations can be 
used in a variety of radar warning systems, typically in systems which 
warn the pilot of the direction (i.e., radar signal angle of arrival) and 
distance of nearby radars. 
The goal of the radar detection system 100 is to accurately determine the 
"angle of arrival" of a radar emitting object 110. The angle of arrival is 
typically defined to be the azimuth angle of a direct line to the radar 
110. Such systems are also used to determine the approximate distance of 
the radar 110 from the plane 130. Prior art systems generally compute the 
angle of arrival by first determining which two transducers 120-126 are 
receiving the strongest signals from the radar 110, and then using the 
relative strengths of these two signals to determine the azimuth angle to 
the radar. 
This prior art method of computing an azimuth angle is accurate when the 
radar emitting object is in the same plane as the four transducers 
120-126, and is reasonably accurate when the angle of elevation to the 
radar, with respect to the plane occupied by the transducers, is fairly 
small. However, the inventors have found that the azimuth angles generated 
by prior art systems are quite inaccurate when the angle of elevation is 
more than thirty degrees or so. 
One reason that such inaccuracies have been accepted in prior art systems 
is that it has been assumed that correcting the inaccuracy would require 
additional transducers, extra circuitry, exceed the allocated volume, and 
would slow down the response time of the system. In many such radar 
detection systems, fast determination of the azimuth angle of arrival is 
very important and speed cannot be sacrificed for better accuracy. 
The present invention is based on the discovery by the inventors that using 
the measurements from three transducers, one can very accurately determine 
the azimuth angle to an object as well as the angle of elevation. In 
addition, the inventors have found a way of performing the necessary 
computations using very high speed hard-wired logic, thereby providing 
more accurate angle of arrival measurements without any sacrifice in the 
speed at which the measurements are performed. 
It is therefore the primary object of the present invention to provide a 
radar detection system which accurately determines the angle of arrival of 
a radar, even when that angle includes a substantial elevation angle. 
Another object of the present invention is to provide a system which can 
determine the angle of arrival of a radar signal accurately and quickly. 
Yet another object of the present invention is to provide a system which 
can accurately determine the direction of an object using a standard set 
of four radar transducers. 
SUMMARY OF THE INVENTION 
In summary, the present invention is a radar detection system which 
accurately determines the angle of arrival of a radar signal. The system 
has four perpendicularly oriented transducers. When measuring the angle of 
arrival of a radar signal, the three strongest signals from the four 
transducers are combined to generate two differential signal values. A 
read only memory (ROM) is used to store the angle of arrival values 
associated with all possible values of these two differential signals. To 
determine the angle of arrival of a particular radar, the corresponding 
pair of differential values are used to access a corresponding angle value 
in the ROM, and then that value is summed with the reference angle 
associated with the transducer having the strongest signal.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
As discussed above with reference to FIG. 1, the antennas 120-126 on an 
aircraft 130 are generally set so that the boresight angles of the 
antennas 120-126 are oriented at reference angles of 45, 135, 225 and 315 
degrees relative to the forward direction of the aircraft 130. 
The antenna pattern of the transducers used in a typical radar warning 
receiver is Gaussian in both the azimuth and elevation directions. The 
attenuation of the antenna pattern as a function of off-boresight angle, 
theta, can be represented as: 
EQU loss=k*theta.sup.2 (1) 
Attenuation loss is generally expressed in terms of decibels (dB) down from 
the peak amplitude of the antenna pattern. The "k" in Equation 1 typically 
has a value on the order of 0.0015 to 0.0025 dB/degree.sup.2. The value of 
k varies with the frequency of the received signal. 
FIG. 2 schematically represents the overlapping antenna patterns of three 
of the four transducers 120-126. 
Referring to FIG. 3, AZR is the azimuth angle from the antenna to a radar 
emitting object 110, and EL is the elevation angle, measured from the 
plane of the four antennas 120-126 (i.e., the horizontal plane in FIG. 3) 
to the object 110. The off-boresight angle OBA for each antenna, (i.e., 
the angle between each antenna and the object, is a function of both the 
azimuth and elevation angles AZR and EL to the object 110. The 
relationship of the off-boresight angle, OBA, to the azimuth and elevation 
angles is: 
EQU cos(OBA)=cos(AZR)*cos(EL) (2) 
and thus: 
EQU OBA=arccos(cos(AZR)*cos(EL)) (3) 
For a given object location, the azimuth angle AZn of the object with 
respect to each of the transducers can be represented as: 
EQU AZn=n-AZR, where n={45,135,225,315} (4) 
Using this notation, the set of off-boresight angles OBAn for an object 
with respect to the four transducers can be represented as: 
EQU OBAn=arccos(cos(n-AZR)*cos(EL)) (5) 
and the signal attenuation LOSSn at each antenna is therefore 
EQU LOSSn=k*(arccos(cos(n-AZR)*cos(EL)).sup.2 (6) 
Referring to FIG. 2, the antenna producing the largest signal from the 
object will be the antenna such that AZn in equation 4 has a magnitude 
less than or equal to 45 degrees. The antenna producing the second largest 
signal will be adjacent to the one producing the largest signal. The 
antenna producing the third largest signal will be the one opposite the 
one producing the second largest signal. 
If the object 110 is positioned directly ahead or behind the aircraft 130, 
or perpendicular to the aircraft's heading, causing two antennae to have 
equal strength signals, either of the remaining two antennae can be 
selected as the third antenna for the purposes of the following analysis. 
FIG. 2 schematically represents the antenna patterns 150, 152 and 154 of 
the three antenna with the strongest signals. The relative signal 
strengths of the signals received by these antennae are represented as S1, 
S2 and S3. While FIG. 2 shows the antenna patterns in only one plane, each 
pattern is three dimensional. Thus, as will be clear to those who consider 
the matter, the relative strengths of the signals from the three antennae 
will change as the angle of elevation of the object is changed, because 
the object's emissions will be intersecting a different portion of each 
antenna pattern. For instance, two object locations with the exact same 
azimuth angle but different angles of elevation will produce different 
relative signals strengths. It is for this reason that the use of only two 
antennae signals is not adequate to make an accurate measurement of the 
azimuth angle of an object. 
However, the inventors have found that the elevation angle EL and the 
azimuth angle of an object AZ can be uniquely and accurately computed as a 
function of two differential signals: 
EQU D1=Largest Signal-Second Largest Signal 
EQU D2=Second Largest Signal-Third Largest Signal (7) 
where the values of D1 and D2 are represented in decibel units. In other 
words, the elevation and azimuth angles can be accurately computed as a 
function of the D1 and D2 values, as defined in Equation 7. 
The way this is done is as follows. Using Equation 6, one first builds a 
large look-up table of the D1 and D2 values for every possible combination 
of azimuth and elevation angles. For example, in the preferred embodiment, 
the D1 and D2 values were computed using Equation 6 for all possible 
azimuth angles between 0 and 45 degrees, in one degree increments, and all 
possible elevation angles between 0 and 90 degrees, in one degree 
increments. More specifically, for every such pair of azimuth and 
elevation angles, the loss values for all four antennae were computed 
using Equation 6, the three largest values selected, and then D1 and D2 
were computed. 
The result of these computations is a large set of records, where each 
record contains an azimuth angle, an elevation angle, and D1 and D2 
values. These records are then sorted by their D1 and D2 values. Finally, 
given any pair of D1 and D2 measurement values, all one needs to do to 
compute the corresponding azimuth and elevation angles is to find the 
closest set of D1 and D2 values in the table, and then read the 
corresponding azimuth and elevation values. 
FIG. 4 graphically represents the values of D1, D2, EL (elevation angle) 
and AZ (azimuth angle) computed using equation 6. D1 and D2 represent the 
two perpendicular axes of the graph. The downward sloping lines on the 
graphs represent isograms of elevation angle values and the upwardly 
sloping lines represent isograms of azimuth angle values. 
The inventors have found that FIG. 4, while mathematically accurate, does 
not account for the nonlinearities and individual differences of actual 
radar transducers. To generate an equivalent set of D1, D2, azimuth and 
elevation angle values based on measurements, the inventors flew an 
aircraft over a transmitter and recorded thousands of measurement records 
representing the actual angle of arrival (AOA) of the transmitter, and the 
actual transducer signal values generated by the four transducers on the 
aircraft during the flight. FIG. 5 represents the data recorded from one 
pass over (actually past) the transmitter. FIG. 5 also shows the AOA of 
the aircraft, calculated using the present invention, using the recorded 
transducer signal values. 
FIG. 6 graphically represents the values of D1, D2, EL (elevation angle) 
and AZ (azimuth angle) derived using actual measurement data obtained 
using the technique described with respect to FIG. 5. Comparing FIGS. 4 
and 6, it can be seen that while the isograms in FIG. 6 are generally 
similar in shape to the isograms in FIG. 4, the specific locations (and 
thus D1 and D2 values) of the isograms in FIG. 6 vary considerably in some 
places from those in FIG. 4. 
Referring to FIG. 7, there is shown a block diagram of a system for 
computing the azimuth and elevation angles of an object using the signals 
from the three antennae with the strongest signals. The four analog 
signals from antennae 120-126 are received by a converter and selection 
circuit 170. The converter 170 converts each of the analog antenna signals 
into a digital value, and sorts the four values by their magnitudes. D1 
and D2 are then computed as defined by Equation 7. In addition, the 
identities T1 and T2 of the antennae which received the first and second 
largest signals are denoted for later use. 
A large read only memory (ROM) 175 is used to store a table of azimuth and 
elevation angle values (and also a signal measurement correction, as will 
be explained below). To define the table entries, all the measurement 
records of D1, D2, EL and AZR values are sorted by their D1 and D2 values. 
Then a set of EL and AZR values is generated for every possible pair of D1 
and D2 values within a predefined range (such as 0 to 17 for D1 and 0 to 
23 for D2), in 0.1 dB increments. In other words, the ROM 175 will contain 
one record 178 for every possible pair of D1 and D2 values, measured in 
0.1 dB increments. 
For this purpose, the measured D1 and D2 values are rounded off to the 
closest 0.1 dB to determine which measurement records should go in which 
slots of the ROM 175. Unfilled slots in the ROM are filed using 
interpolation, as will be understood by those skilled in the art. 
To look up the azimuth and elevation angles for a given pair of D1 and D2 
values, one first computes an index that is essentially a pointer to the 
corresponding record in the ROM 175. In the preferred embodiment, the 
index is computed as: 
EQU Index=170*D2+10*D1 (8) 
More generally, the index will be a function of D1 and D2, the exact form 
of which will depend on the range of D1 and D2 values used and the spacing 
used between neighboring D1 and D2 values. 
Each record 178 in the ROM stores three values: a "relative" azimuth angle 
value AZR, an elevation angle value EL, and a signal measurement 
correction value RPC. The purpose of the RPC value is explained below. 
The azimuth value in the ROM is relative to direction of the transducer 
with the strongest signal. Depending on the location of the transducer 
with the second strongest signal, the relative azimuth value AZR will be 
added or subtracted from the azimuth angle of the first transducer. 
When the antennae which receive the first and second largest signals are 
denoted T1 and T2, the actual azimuth angle is: 
EQU AZ=azimuth(T1)+/-AZR (9) 
where the sign in equation 9 is defined by the following table: 
TABLE 1 
______________________________________ 
##STR1## 
______________________________________ 
Two of the values in each row and column of Table 1 are "not applicable" 
(NA) because the second strongest signal is always received by a 
transducer next to the transducer which receives the strongest signal. 
The arithmetic logic circuit 180 in FIG. 7 computes the value of the 
azimuth angle using the T1 and T2 values from circuit 170, and the AZR 
value from the ROM 175, in accordance with Equation 9. The arithmetic 
logic circuit 180 also may be used to compute the distance R.sub.s from 
the radar detection system to the radar emitting object 110, as will be 
explained in more detail below. 
FIG. 8 shows one preferred embodiment of the arithmetic logic circuit 180. 
This circuit uses two ROMs 190 and 192, and a standard adder 194. The 
first ROM 190 implements Table 1, shown above, so as determine whether 
adder 194 should add or subtract AZR from the azimuth of transducer T1. 
The second ROM 192 simply provides the azimuth of transducer T1 using the 
value of T1 as an index. As will be understood by those skilled in the 
art, ROM 190 could easily be replaced by a simple boolean logic circuit, 
and the ROM 192 is the equivalent of four digital registers with a 
selection circuit. 
FIG. 9 is a block diagram of a preferred embodiment of the converter and 
selection circuit 170. A analog to digital converter 200 receives the four 
analog transducer values SA, SB, SC and SD and digitizes them. Then a 
sorter 201 generates a sorted table of signal values S1-S4. The sorter 200 
also generates the identities T1 and T2 of the antennae which received the 
first and second largest signals. 
Two subtractors 202 and 204 subtract S2 from S1 to generate D1, and 
subtract S3 from S2 to generate D2. Finally, an index computation unit 206 
uses the D1 and D2 values from the subtractors 202 and 204 to generate an 
index value for reading the proper record in the ROM 175. Since the output 
of the index generator 206 is used to directly address the ROM 175, the 
index generator 206 can be said to perform table look ups. 
The preferred embodiment of the invention is designed for extremely fast 
computation. Using high speed bipolar circuitry, the entire computation 
process can be performed in approximately 100 nanoseconds. 
It should be noted that in other embodiments of the invention, the ROM 175 
could store additional values, such as the angle of arrival, computed from 
the azimuth and elevation angles using Equation 3. 
As noted above, a third value called the signal measurement correction 
value RPC is also stored in each record of the ROM 175. This value 
corresponds to the attenuation superimposed on the received radar signal 
by the antenna patterns. The attenuation is a function of the off-bore 
sight angle and is used to correct the measured signal strength of the 
radar. This, in turn, enables a more accurate calculation of distance to 
the radar emitting object, which is computed using the formula: 
##EQU1## 
where R.sub.s is the range (i.e., distance) in nautical miles from the 
radar to the radar detection system. RP is the actual signal strength 
present (i.e., measured) at the radar detection system in decibel "dBm" 
units. RPC is the measurement correction factor stored in the ROM 175 in 
the record corresponding to the D1 and D2 values. RPC typically varies 
between 0 and 6.0 dBm, which means that the signal measurement correction 
may change the computed range R.sub.s by as much as a factor of two. 
ERP in Equation 10 is the effective radiated power of the radar emitter, 
which is generally a predefined value that depends on the nature of the 
radar emitter. Finally, RF in Equation 10 is the radio frequency of the 
emitter measured in Megahertz units. 
Thus, to enable more accurate distance-to-object calculations, all that 
needs to be stored in the ROM 175 is a signal measurement correction value 
RPC, as defined above, for each pair of D1 and D2 values. To compute the 
value R.sub.s quickly, the arithmetic unit 180 in FIG. 7 will typically 
need to be a programmed floating point computation circuit, many of which 
are commercially available, although a general purpose computer could also 
be used. 
While the prior art systems use the measured signal strength to compute an 
estimate of the distance of the object, the present invention provides a 
signal measurement correction based on the actual angle of arrival, making 
it possible to generate a much more accurate distance to object value. 
In other embodiments of the invention, where speed is not critical, a 
somewhat larger table of values can be stored in a ROM or an equivalent 
computer file. The records in this expanded ROM or file will include the 
corresponding D1 and D2 values. The technique for generating elevation and 
azimuth angles is then to find the record with the pair of D1 and D2 
values closest to the actual D1 and D2 measurements. The elevation and 
azimuth values can then be taken directly from that record. Alternately, 
even more accurate angle values can be obtained by extrapolating from the 
values in two or three records in the table. 
While the present invention has been described with reference to a few 
specific embodiments, the description is illustrative of the invention and 
is not to be construed as limiting the invention. Various modifications 
may occur to those skilled in the art without departing from the true 
spirit and scope of the invention as defined by the appended claims. For 
instance, the techniques of the present invention can be used in 
stationary, land-based direction finders.