Self-calibrating, eigenstructure based method and means of direction finding

A method of estimating the directions of radiating sources (56, 58, 60) with respect to an array (46) of a number of antenna elements (48), each of which elements has a separate gain/phase control (50). With nominal gain and phase selected a first estimte of the radiating sources directions (.theta.) is accompished by application of the MUSIC algorithm (2). The algorithm is iteratively applied to a microprocessor (54) using updated gain and phase values. Iteration is terminated at that iteration which produces the maximum difference values of the smallest eigenvalue pair of Q.sub.(i).

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates generally to a method and means of radar 
signal processing for direction finding purposes, and, more particularly, 
to such a method and means especially advantageous for use with a radar 
target seeker. 
2. Discussion of Related Art 
A radar seeker operates generally by emitting radar beam pulses toward a 
target, measuring the time traveled by pulses reflected from the target 
and adjusting the radar beam for maximum response, which enables both the 
direction and distance of the target to be determined. 
In the usual situation, there may be other objects adjacent the sought 
after target which will produce radar reflections and, in that way, induce 
confusion and error into the tracking system. Also, in a military context 
defensive measures are taken to intentionally interfere with the operation 
and accuracy of a radar seeker aboard, say, an aircraft. For example, 
large quantities of radar reflecting foil strips ("window") dropped in the 
vicinity of a flying target aircraft can effectively block out radar 
detection of the craft. Another frequently employed radar camouflaging 
technique for an aircraft consists of having one or more escort craft 
flying near the target aircraft which direct "jamming" radar beams of 
appropriate frequency toward the search radar source to confuse and induce 
spurious direction information into the search tracking system. 
Direction-finding techniques based upon eigenstructure methods have been 
proposed and experimentally verified and have shown themselves to be 
superior to conventional direction-finding equipment for overcoming 
standard defensive measures. Application of eigenstructure techniques 
requires a radar system having an active antenna array, that is, a 
plurality of antennae arranged in a matrix for sending and receiving radar 
pulses over a relatively large area including a sought after target and 
which antennae are controllable as to phase and gain. 
A more detailed discussion of a prior eigenstructure method can be found in 
the article, "Eigenstructure Methods for Direction Finding with Sensor 
Gain and Phase Uncertainties" by Anthony J Weiss and Benjamin Friedlander, 
Proceedings IEEE, ICASSP 198, New York, N.Y. This technique requires at 
least two sources (i.e., two reflected radar signals) for proper operation 
which excludes applicability to a very frequently encountered situation, 
namely, a single-source encounter. Moreover, in this and in all known 
prior eigenstructure techniques precise knowledge of signals received by 
the sensor array is required which, in turn, requires initial calibration 
of the entire seeker data collection system, a time consuming and 
difficult task. Still further, there is the necessity for maintaining 
array calibration in these known systems which is additionally difficult 
and time consuming. 
SUMMARY OF THE DISCLOSURE 
It is a primary aim and object of the present invention to provide a radar 
direction finding means and method capable of satisfactory operation with 
radar return signals being imprecisely sensed as to both gain and phase. 
Another object is the provision of means and method in accordance with the 
previous object by which a given target can be readily resolved from among 
relatively closely spaced multiple targets. 
Yet another object is the provision in the above-identified objects of a 
method and means utilizing an active array radar seeker which does not 
require initial sensor array calibration or maintaining precise sensor 
calibration. 
The described method includes receiving radiation from one or more 
radiating sources in a monitored region by the antenna array. With 
selected nominal gain and phase values for each antenna element of the 
array, a first estimate of directions of the radiating sources with 
respect to the array is calculated in a microprocessor by the use of an 
algorithm referred to as MUSIC. Updating of the gain and phase for each 
antenna element is accomplished by signals received by the array. 
Iterations of direction estimates are made based upon this and further 
updated gain and phase values until that iteration is reached which 
produces the maximum difference value of the smallest eigenvalue pair of

DESCRIPTION OF A PREFERRED EMBODIMENT 
With reference now to FIG. 1 of the drawing, a typical radar seeker system 
10 is shown including generally a source 12 of high frequency pulses 13 
which are fed through a so-called duplexer 14 to an antenna 16 where they 
are radiated toward a target 18. These pulses 13 are reflected off the 
target and return to the antenna 16. The duplexer 14 is essentially a 
switch that enables common use of one antenna for both transmitting and 
receiving reflected pulses which are then sent on to the receiver 20 for 
processing and display. By noting antenna orientation for maximum strength 
pulse reception and the time for pulse transmission, both the direction 
and distance to a target 18 can be determined. 
FIG. 2A depicts the camouflaging effect that is produced when a large 
number of foil pieces 22 ("window") are released in the vicinity of a 
target aircraft 24. As shown, a plurality of pulse echoes are received 
from the target 24 as well as foil pieces 28, 28' which serves to hide or 
make it difficult to locate the target within the many false echoes 
produced by the individual pieces of foil as seen on a display 30, for 
example. 
FIG. 2B depicts another defensive technique used against a seeker in which 
several target escort craft 32 and 34 each emit separate radar waves 36 
and 38, respectively, directed toward the seeker antenna 16. These radar 
waves are of proper frequency and produce readily detectable signals 40 
and 42 in the seeker receiver which can be easily confused with the echo 
signal 44 from the true target 24. 
A seeker having a single element antenna or fixed array antenna, such as 
the antenna 16 in FIG. 1, merely receives all signals and echoes directed 
toward it and forwards the signals for processing and display. As has just 
been illustrated this can result in a composite set of signal displays 
resulting from both the actual target and other spurious targets located 
at a considerable spacing from the actual target and homing in on the 
wrong target. A seeker of this kind is not able to distinguish a very 
broad range of radar returns and separate defensive radar beams from true 
target returns. 
With reference now to FIG. 3, there is shown partially in schematic form an 
active antenna array enumerated generally as 46 which is especially useful 
with a seeker operating on an eigenstructure basis as the present 
invention does. More particularly, the active array is seen to include a 
plurality of individual antenna elements 48 with corresponding individual 
transmission and receive (T/R) controls 50 which can be controlled by 
lines 52 to detect or selectively modify the gain and phase of each of the 
antenna elements. A microprocessor 54 is appropriately programmed to cause 
the active array 46 to be selectively modified in a manner to be described 
to determine the actual target from among the various signal radiation 
sources 56, 58, 60--that the system may be receiving, including 
defensively produced radar beams, for example. Such an active antenna 
array is to be found more particularly described in copending patent 
application AN ACTIVE ANTENNA ARRAY, Ser. No. 08/047,937 by J. Conrad et 
al. assigned to the same assignee as the present application. 
In the referenced Weiss et al. article an eigenstructure method is provided 
for direction finding in the presence of sensor gain and phase 
uncertainties. This method requires a minimum of two radiation sources for 
use (e.g., a target and one false echo) and, therefore, excludes 
applicability to single-source encounters which are a most frequent 
occurrence. Also, this method requires a subjectively preselected 
threshold to terminate iteration. This latter feature makes it difficult 
to optimize performance since in certain cases the process does not 
converge to the correct result. For example, in the situation where there 
are several closely spaced radiation sources and a low preselected 
threshold, the algorithm may not be resolvable. 
Before proceeding with the description of the present invention, 
development of estimates by the so-called MUSIC algorithm for K observable 
radiating sources by an array of M antenna elements will be set forth and 
it is submitted will be of assistance in understanding the advantages of 
the invention. A detailed description of this technique can be found in 
PRIMARY SIGNAL PROCESSING, S.U. Pillai, Springer Verlag (1989). Initially, 
the M.times.1 output data vector of the array can be described by 
x(t)=GAs(t)+n(t) where 
G=diag[g.sub.1, g.sub.2, . . . , g.sub.m ]: M.times.M diagonal matrix 
g.sub.1 (.epsilon. complex): the unknown gain and phase of the i-th sensor 
A=[a (.theta..sub.1), a(.theta..sub.2), . . . , a(.theta..sub.K)]: 
M.times.K matrix with unknown .theta..sub.1, .theta..sub.2, . . . , 
.theta..sub.k 
a(.theta..sub.k): M.times.1 direction vector of the k-th source 
s(t): K.times.1 complex Gaussian signal vector with E[s(t)]=O; 
E[s(t)s.sup.+ (t)]=R.sub.s 
n(t): M.times.1 complex Gaussian noise vector, independent of s(t), with 
E[n(t) ]=O; E[n(t)n.sup.+ (t) ]=.sigma..sup.2 I . 
(The superscripts T and + represent the transpose and complex conjugate 
transpose, respectively and E[.] is the expectation operator.) 
The covariance matrix of x(t) is given by 
##EQU2## 
where .lambda..sub.i, e.sub.i ; i=1, 2, . . . , M are the eigenvalues and 
eigenvectors of R.sub.x. With rank (R.sub.s)=K (i.e., K sources are not 
fully correlated), we have 
##EQU3## 
where 
E.sub.N =[e.sub.K+1, . . . , e.sub.M ]: M.times.(M-K)noise-subspace 
eigenmatrix 
A(.theta..sub.k)=diag(a(.theta..sub.k)) : M.times.M diagonal matrix with 
elements of a(.theta..sub.k) 
g=[g.sub.1, . . . , g.sub.m ].sup.T : M.times.1 vector. 
The MUSIC spatial spectrum estimator, given by 
##EQU4## 
produces the K-highest spectral peaks at the different angles of arrival 
.theta..sub.1, .theta..sub.2, . . . , .theta..sub.k if the sensor gains 
and phases are known. In practice, however, we only know the sensor gains 
and phases approximately within some specified manufacturing-tolerance 
limits. As a consequence, the resolution performance of the MUSIC 
algorithm can be severely degraded and may not provide spectral peaks for 
all angles of arrival. 
In order to substantially reduce the effects of sensor-channel gain and 
phase uncertainties, the method of this invention was developed arising 
out of the following theorem. 
Given an error-free estimate of E.sub.n (i.e., E.sub.n =E.sub.N) and 
##EQU5## 
define 
##EQU6## 
Then, there exists a unique g, where 
ti g=k v.sub.m, k .epsilon.complex (4) 
and v.sub.M is the eigenvector corresponding to the smallest eigenvalue of 
Q, if 
EQU rank (Q)=M-1. 
(.LAMBDA. represents the estimate from the finite-sample data vectors). 
At this time it is believed presentation of a proof of the above theorem 
would be of assistance in understanding the invention. By the hermitian 
structure of Q and the orthogonality property stated in (1), we have 
EQU J=g.sup.+ Qg=0 
which implies 
EQU rank (Q)&lt;M-1. 
Assuming that rank (Q)=M'(&lt;M-2) and 
##EQU7## 
by eigendecomposition, then 
EQU .sigma..sub.1 &lt;.sigma..sub.2 &gt;. . . &gt;.sigma..sub.M' &gt;.sigma..sub.M'+1 =. . 
. =.sigma..sub.M =0 
and g can be expressed as a linear combination of v.sub.M'+1, 
.sup.v.sub.M'+2, . . . , .sup.v.sub.M, i.e., 
##EQU8## 
Thus, to have a unique solution for g, M'=M-1. The disclosed technique 
starts with nominal gain and phase values and estimate {.theta..sub.k 
}.sub.k=1.sup.K by MUSIC as discussed above. Then, with {.theta..sub.k 
}.sub.k=1.sup.K, a new estimate of g is obtained by (3) and (4). 
As initial condition for practice of the invention, set i=0 and g.sup.(i) 
=g.sub.o, where g.sub.o can be based on the nominal gains and phase 
values, or on any recent calibration data. In the usual situation, a 
nominal g is selected to be recent calibrated gain and phase values among 
"off-board" and "on-board" data. Then, by application of MUSIC, values for 
.theta..sup.(i), .theta..sub.2.sup.(i), . . . .theta..sub.k.sup.(i), 
EQU P(.theta..vertline.g.sup.(i))=.parallel.E.sub.N.sup.+ A(.theta.)g.sup.(i) 
.parallel..sup.-2 
Construct 
##EQU9## 
and compute d.sub.(i) =.sigma..sub.M-1.sup.(i) -.sigma..sub.M.sup.(i), 
whereby eigendecomposition 
##EQU10## 
If d(i-1)-d.sub.(i) &lt;0, then i=i+1 and you proceed by updating g.sup.(i) 
with the eigenvector corresponding to the smallest eigenvalue of 
Q.sub.(i), namely, g.sup.(i) =v.sub.M.sup.(i). Now, proceed to the step 
after initializing (i.e., providing .theta..sub.1.sup.(i). . . by MUSIC) 
and continue as just described. After a sufficient number of iterations 
are accomplished so that d.sub.(i-1 -d.sub.(i) &gt;0, then the iteration 
cycle is terminated. In further explanation, it can be shown that for a 
unique g, rank (Q) must be (M-1). The difference in d values tells whether 
rank (Q) is (M-1) or not. If rank (Q)&lt;M-1, the difference in d values is 
zero whereas the maximum value of the difference value insure that rank 
(Q) is at least M-1. Accordingly, iteration continues until the indicated 
difference in d values reaches its maximum. 
As to practical accomplishment of the method, with initial g selected from 
the most recent calibration gain and phase values and a set of 
measurements from an active array, the described algorithm proceeds in a 
microprocessor. At each iteration, the angle/gain/phase estimates are 
updated and utilized for the next iteration until the process is 
terminated. After termination, the calculated final angle estimates from 
MUSIC are utilized for the tracking system, and the final gain/phase 
estimates are applied to a new set of array measurements as the new 
on-board, calibrated data. 
FIG. 3 depicts a flow block diagram of the described method of this 
invention. FIG. 4A shows the results obtained when the method of this 
invention is applied to a three-source scene. Similarly, FIG. 4B shows 
results obtained for a two-source scene, and FIG. 4C is a single-source 
scene. 
As already alluded to, the present method can be applied to a single-source 
scene whereas the Weiss and Friedlander technique referenced earlier 
cannot, since that would require calculation of Q.sup.-1. The advantage of 
a seeker being able to handle the single radiation source situation has 
already been discussed. 
Although the invention has been described in connection with a preferred 
embodiment, it is to be understood that those skilled in the appertaining 
arts may make changes which come within the spirit of the disclosure and 
ambit of the appended claims.