Direction finding apparatus

An efficient monopulse direction finding technique is based on the best algorithm in the least squares sense for a given antenna configuration. The algorithm simultaneously uses complex voltage data from all of the antenna ports, i.e., all of the available data received. No a priori emitter polarization information is assumed. Only a two dimensional search for the performance index minimum is needed to find the solution. The method is extended to N emitters with a search in only 2N space for the N emitter angles.

TECHNICAL FIELD OF THE INVENTION 
The present invention relates to direction finding and, in particular, to a 
direction finding apparatus that is based on an algorithm that 
simultaneously uses complex voltage data from a plurality of antenna 
ports, i.e., all of the available data received, and in which no a priori 
emitter polarization information is assumed. 
BACKGROUND OF THE INVENTION 
The present invention addresses the following direction finding problem: 
given voltage measurements at N antenna ports, find the angle of arrival 
of an emitter source without a priori knowledge of its polarization. That 
is a four dimensional identification problem. There are two angle 
parameters and two polarization parameters. Previously known direction 
finding algorithms have been devised for implementation by simple analog 
hardware. As a result the algorithms are simple but depend highly upon the 
design and tolerances of the antenna system and use limited calibration 
data and computations. Four lobe monopulse antennas, two plane 
interferometers, and multimode spiral antennas are examples of hardware 
that use simple direction finding algorithms. The accuracy of most current 
direction finding techniques depends upon the accuracy of the hardware in 
meeting the design requirements. For example, accurate direction finding 
using monopulse antennas and interferometers requires that the elements 
have identical responses, i.e., low cross-polarization response. Large 
costs are required to ensure that the hardware meets that requirement. 
Often performance is compromised, inasmuch as the hardware cannot meet the 
response requirements over all angles of space and polarizations. That is 
particularly true of the installed performance where the beams in space 
are influenced by the installation surroundings. 
The accuracy of direction finding using a four lobe monopulse antenna is 
limited by the amplitude and phase balance of the excitation of the four 
sub-apertures and by the cross-polarization in the sum beam region. In the 
side lobe region direction finding using a four lobe monopulse antenna can 
yield ambiguities. Thus a broad beam guard antenna is typically used to 
discriminate between the main beam region and the side lobe region. That 
approach yields additional challenges in designing a guard antenna without 
punch-through and polarization response equal to that of the sum beam. The 
accuracy of direction finding using interferometers is limited by 
element-to-element phase errors and the fact that all elements do not have 
the same polarization response. Interferometer installation effects cause 
these accuracy limitations in many cases. Direction finding accuracy from 
multimode spirals are limited by the element and mode former tolerances. 
It is assumed that each arm yields the same antenna response rotated by 
the proper angle (360 degrees divided by the number of arms). In each of 
these examples it is desired that each antenna port (mode) have the same 
polarization at any given angle of space. If indeed all ports are 
polarization matched, the direction finding problem is greatly simplified 
to a two-dimensional (two angles only) identification problem. The penalty 
is that the antenna system cannot receive cross-polarized signals and thus 
direction finding cannot be obtained for all emitting sources. Another 
general observation about previously known direction finding techniques is 
that they typically do not use all of the available information. With the 
availability of low cost computing, limited space for antennas, and the 
need for increased accuracy over wider bands for all polarizations, new 
direction finding techniques are needed. 
SUMMARY OF THE INVENTION 
The present invention is a direction finding apparatus that comprises an 
antenna having a plurality of wave-receiving elements or ports, each being 
adapted to generate complex voltage signals representative of the 
amplitude, phase, and polarization of a plane wave X from an emitter, and 
a processor that receives the voltage signals and is programmed to process 
the voltage signals in accordance with an algorithm in which the following 
computations are made: 
##EQU1## 
wherein 
V is the fixed received vector of complex voltages, 
MX is the port induced voltages (synthesized) by the plane wave X, 
Step 1 defines the plane wave and induced voltages that best match the 
received vector V at the specific direction and can be stated as a best 
plane wave, X.sub.b, in terms of the pseudo-inverse of M 
EQU X.sub.b (.theta., .phi.)=(M.sup.t M).sup.-1 M.sup.t V, 
and 
Step 2 determines the direction in space for which the synthesized voltages 
and measured voltages are best matched and is a direction finding 
estimate. The residual error R.sub.e is computed as a measure of whether 
the chosen direction is the correct direction by 
EQU R.sub.e (.theta., .phi.)=MX.sub.b -V=M(M.sup.t M).sup.-1 M.sup.t V-V. 
The norm of the residual error vector is defined as the performance index 
EQU .parallel...parallel.:C.sup.n .fwdarw.R, norm 
EQU .parallel.R.sub.e .parallel.=Performance Index 
and the performance index is minimized: 
##EQU2## 
The processor is, preferably, programmed to minimize the Performance Index 
by an iterative optimizer routine, such as the minimum of all points, the 
simplex method, conjugate gradients, and Fletcher-Powell. The antenna of 
the apparatus may be an r-lobe monopulse, a phase interferometer, an 
amplitude-phase interferometer, or a multi-arm spiral. 
In an exemplary implementation of the algorithm, a low noise amplifier 
receives the voltage signals from each antenna element and supplies 
amplified signals to a mixer, which down converts the low noise amplified 
voltage signals to an intermediate frequency. A channelized receiver 
receives all of the intermediate frequency signals and subdivides them 
into frequency bands with manageable small bandwidths for analog to 
digital conversion. An analog to digital converter receives each output 
signal from the channelized receiver and supplies digitized voltage 
signals to processors that implement the algorithim. 
For a better understanding of the present invention, reference may be made 
to the following detailed description of the invention. An exemplary 
embodiment is also described with reference to the accompanying drawing.

DETAILED DESCRIPTION OF THE INVENTION 
The drawing shows a channelized direction finding system. The system 
includes a multi-aperature/element antenna 10 with polarization 
diversities. The complex antenna patterns are known for two polarizations 
which allows characterization for all polarizations. Output from the 
antenna(s) pass through a low noise amplifier 12 and a mixer 14 to down 
convert the signal for an intermediate frequency (IF). The IF signals are 
conducted to a channelized receiver 16, which subdivides the frequency 
bands so that the output is manageable with sufficiently small bandwidth 
that analog to digital converters 18 can handle the throughput. The 
processed digital outputs from each antenna element (at a given frequency) 
are sent to a computational unit for processing using the previously 
described least mean square algorithm to find the estimate for the 
direction of arrival of the emitter source. Hardware and software can be 
designed to provide real-time direction finding, which can be used for 
direction control. 
The present invention involves a new direction finding technique that uses 
complex information from each of a plurality of antenna elements/ports and 
does not depend upon the absolute accuracy of the hardware. There may be 
differences in the antenna patterns or changes in the installed 
performance. The invention depends instead upon a characterization of the 
beams in space and requires complex measurements of the beams in space for 
two independent polarizations. 
The invention is based upon the fact that the antenna system is linear. 
This is not a very restrictive condition. As a background, a few issues in 
the direction finding problem are considered here. Typically, the general 
direction finding problem is considered as a four dimensional problem, two 
angles and two for polarizations. Formulated in this manner, the direction 
finding problem is nonlinear in the two angle variables and two 
polarization variables. Thus, it is time consuming to search the 
four-dimension space for the solution to the nonlinear problem. The 
present invention casts the problem in a six-dimensional space in order to 
formulate the problem in a linear format. A key aspect to that formulation 
is the following fact about plane waves. All plane waves propagating in a 
given direction can be represented by two complex numbers. For example, a 
wave propagating in the z direction can be represented as 
EQU E=(u.sub.1 .multidot.e.sub.1 +u.sub.2 .multidot.e.sub.2) e.sup.-jkz ; 
u.sub.1, u.sub.2 .epsilon. C; e.sub.1 .multidot.z=e.sub.2 .multidot.Z=0(1) 
The complex variables u.sub.1 and u.sub.2 contain the amplitude, phase and 
the polarization of the plane wave with respect to the complex linearly 
independent basis vectors, e.sub.1 and e.sub.2 of unit norm. Two examples 
are linear and circular polarization basis vectors. For the linear case, 
e.sub.1 =x, and e.sub.2 =y. And for the circular polarization case e.sub.1 
=(x-jy).sqroot.2, and e.sub.2 =(x+jy)/.sqroot.2. With respect to fixed 
basis vectors, X=[u.sub.1, u.sub.2 ].sup.t .epsilon. C.sup.2 (plane wave 
space at a specific angle) represents all plane waves propagating in the z 
direction. Given an antenna with N ports, the plane wave induces a complex 
voltage at each of its ports, v=[v.sub.1, v.sub.2, . . . v.sub.N ].sup.t. 
This process can be represented by an N by 2 matrix, M, that maps plane 
waves into port voltages. The first and second columns of M are 
respectively the pattern port voltages with respect to the two 
polarization basis vectors, e.sub.1 and e.sub.2. 
EQU M: C.sup.2 .fwdarw.C.sup.N, MX=V (2) 
A row of M gives the pattern values of the two polarizations for the 
antenna port. Since M is a linear transformation of the C vector space, 
the image in C is a linear subspace of dimension less than or equal to 
two; i.e., every antenna response lies in this subspace. Thus an arbitrary 
choice of port voltages is not possible; only those that lie in the image 
subspace. However, if errors occur in the received antenna channels, then 
the received signal vector may not lie in the image space of M. The 
direction finding optimization problem is readily defined as a two step 
process in terms of this formulation. 
##EQU3## 
V is the fixed received vector of complex voltages. At a specific 
direction in space, MX is the port induced voltages (synthesized) by the 
plane wave X. Step 1 defines the plane wave and induced voltages that best 
match the received vector V at the specific direction. Step 2 finds the 
direction in space for which the synthesized voltages and the measured 
voltages are best matched. This best direction is the direction finding 
estimate to the problem. 
Step 1 can be easily solved since it is based upon a linear problem 
formulation. The best plane wave, X.sub.b, at the specific direction is 
defined in terms of the pseudo-inverse of M. 
EQU X.sub.b (.theta., .phi.)=(M.sup.t M).sup.-1 M.sup.t V (4) 
Recall that M is a function of theta and phi whereas V is not. The residual 
error in solving the linear problem is a measure whether the chosen 
direction is the correct direction. 
EQU R.sub.e (.theta., .phi.)=MX.sub.b -V=M(M.sup.t M).sup.-1 M.sup.t V-V(5) 
The norm of the residual error vector can be defined as the performance 
index. 
EQU .parallel...parallel.: C.sup.n .fwdarw.R, norm 
EQU .parallel.R.sub.e .parallel.=Performance Index (6) 
The performance index is a non-negative real valued function of the 
direction in space. Minimization of the performance index is Step 2. 
##EQU4## 
If there are no errors in the received voltages from the emitter, then 
there is at least one direction in which the residual error and hence the 
performance index is zero. There may be more than one solution, which 
causes ambiguities in the direction finding. 
In the case of no errors in the received voltages and more than one 
solution, that is not the fault of the direction finding algorithm since 
it provides the best direction finding estimate of all possible 
algorithms. Recall that the algorithm uses all of the available pattern 
and received signal information--amplitude, phase, and polarization--for 
all antennas. Also recall that the direction finding algorithm uses the 
available information in a unified and unbiased manner. Instead, the 
ambiguity situation is caused by the antenna configuration being used. 
That is, when there is a direction finding ambiguity, there are two 
direction and two plane waves that induce the same voltages at the ports. 
Thus, the receiver has no way to resolve the direction finding ambiguity 
since all of the available information has been used. To resolve the 
ambiguity, the antenna configuration must be changed. An additional 
antenna may be added as in a guard antenna, or the configuration changed 
so that the set of antenna patterns do not result in the ambiguous 
situation. 
Throughout the following description of the implementation of the 
algorithm, it is assumed that the frequency has been determined. In a 
practical application, the direction finding algorithm must be implemented 
to simplify the hardware (CPU and memory) requirements and to achieve 
acceptable processing speed. Accuracy requirements, field of regard, and 
vehicle dynamics drive the implementation choices. Each antenna pattern 
and polarization must be sampled over the field of regard. One possibility 
is to sample the field of regard with the resolution of the desired 
direction finding accuracy and then select the point with the minimum 
performance index. That requires storing a lot of pattern data and 
calculating the field of regard at each of the data points. Alternatively, 
the data may be sampled to be the Nyquist rate and interpolated between 
data points. Linear, quadratic, or spline interpolation may be used, 
trading the number of data points for increased operational count. With 
pattern interpolation, the field of regard can be calculated at an 
arbitrary point in the field of regard. The minimum field of regard can be 
found using an iterative optimizer routine, such as the minimum of all 
points, the simplex method, conjugate gradients, and Fletcher-Powell. In 
this approach, the solution can be found by only computing the field of 
regard at those points used in the downhill search for the minimum, thus 
saving operations count. 
The direction finding algorithm of the present invention can be used in a 
number of applications. In principle, the algorithm can be used as an 
alternative to the conventional approaches, such as r-lobe monopulse, 
phase interferometer, amplitude-phase interferometer, or multi-arm spiral. 
In an ideal situation, those approaches utilize simple algolrithms. 
However, the accuracy is limited by the fabrication and the installation 
environment influences, such as surface curvature or scattering obstacles. 
In the case of the 4-lobe monopulse, as typically used in airborne radar 
or phased arrays, four options are possible 
3 ports--.epsilon., .DELTA..sub.a, .DELTA..sub.e 
4 ports--.epsilon., .DELTA..sub.a, .DELTA..sub.e, .DELTA..sub..DELTA. 
4 ports--.epsilon., .DELTA..sub.a, .DELTA..sub.e, guard 
5 ports--.epsilon., .DELTA..sub.a, .DELTA..sub.e, .DELTA..sub..DELTA., 
guard. 
In the ideal phase interferometer, the amplitude patterns are identical. 
That assumption is not valid in a number of practical applications. 
Placement of an interferometer system on the leading edge of an airplane 
gives an acceptable field of regard but modifies the complex patterns. The 
body of a missile significantly alters the complex patterns of antennas 
placed around the circumference of the missile. Diffraction from the body 
changes the polarization and may cause shadowing. This can be used to an 
advantage. When linearly polarized antennas are placed around the body, 
the diversity of the amplitude, phase, and polarization of the patterns 
allows direction finding for all polarizations in a wide field of regard. 
A multi-arm spiral normally uses a mode former like a Butler matrix to 
achieve multiple antenna patterns for direction finding. Often a four-arm 
spiral uses a sum (mode 1) and difference (mode 0) pattern for direction 
finding. The ratio of amplitudes gives theta direction finding while the 
difference in phases gives phi direction finding. Using only two of the 
four possible modes can give rise to direction finding ambiguities, 
especially at wider theta angles. The least mean squares direction finding 
algorithm can be used with the modes (ports) out of the beam former or 
straight out of each spiral arm. By using all of the modes or ports, there 
is less likelihood that there will be direction finding ambiguities. It 
should be noted that if the mode former is used, the antenna patterns are 
circularly polarized. Thus, the opposite sense circular polarization will 
have a signal loss and direction finding cannot be achieved. If the 
multi-arm antenna is a sinuous or interlog antenna with dual polarization, 
then the algorithm will be effective against emitting sources of any 
polarization. 
Although one embodiment has been illustrated and described in detail, it 
will be understood tha various substitutions and alterations are possible 
without departing from the spirit and scope of the invention, as defined 
by the following claims.