U.S. patent application number 12/879288 was filed with the patent office on 2012-03-15 for method for detecting targets using space-time adaptive processing and shared knowledge of the environment.
Invention is credited to Man-On Pun, Zafer Sahinoglu, Pu Wang.
Application Number | 20120062409 12/879288 |
Document ID | / |
Family ID | 45806150 |
Filed Date | 2012-03-15 |
United States Patent
Application |
20120062409 |
Kind Code |
A1 |
Pun; Man-On ; et
al. |
March 15, 2012 |
METHOD FOR DETECTING TARGETS USING SPACE-TIME ADAPTIVE PROCESSING
AND SHARED KNOWLEDGE OF THE ENVIRONMENT
Abstract
A method detects a target in a radar signal using space-time
adaptive processing. A test statistic is T = max .alpha. max
.lamda. .intg. R f 1 ( x 0 , x 1 , , x K .alpha. , .lamda. , R ) p
( R ) R max .lamda. .intg. R f 0 ( x 0 , x 1 , , x K .lamda. , R )
p ( R ) R , ##EQU00001## where x.sub.0 is a test signal, x.sub.k
are K training signals, .alpha. is an unknown amplitude of a target
signal within the test signal, .lamda. is a scaling factor, R is a
covariance matrix of the training signals, and a function max
returns a maximum values. The test statistic is compared to a
threshold to determine whether the target is present, or not.
Inventors: |
Pun; Man-On; (Jersey City,
NJ) ; Sahinoglu; Zafer; (Boston, MA) ; Wang;
Pu; (Ridgefield, NJ) |
Family ID: |
45806150 |
Appl. No.: |
12/879288 |
Filed: |
September 10, 2010 |
Current U.S.
Class: |
342/27 ;
342/159 |
Current CPC
Class: |
G01S 7/292 20130101;
G01S 13/04 20130101 |
Class at
Publication: |
342/27 ;
342/159 |
International
Class: |
G01S 13/04 20060101
G01S013/04; G01S 13/00 20060101 G01S013/00 |
Claims
1. A method for detecting a target in a radar signal using
space-time adaptive processing, comprising the steps: determining a
test statistic T = max .alpha. max .lamda. .intg. R f 1 ( x 0 , x 1
, , x K .alpha. , .lamda. , R ) p ( R ) R max .lamda. .intg. R f 0
( x 0 , x 1 , , x K .lamda. , R ) p ( R ) R , ##EQU00012## where
x.sub.0 is a test signal, x.sub.k are K training signals, .alpha.
is an unknown amplitude of a target signal within the test signal,
.lamda. is a scaling factor, R is a covariance matrix of the
training signals, and a function max returns a maximum values; and
comparing the test statistic to a threshold to determine whether
the target is present, or not.
2. The method of claim 1, wherein a hypothesis testing problem is
used as follows H.sub.0x.sub.0=d.sub.0, x.sub.k=d.sub.k, k=1, . . .
,K, H.sub.1:x.sub.0=.alpha.s+d.sub.0, x.sub.k=d.sub.k, k=1, . . .
,K, where a hypothesis H.sub.0 is that the target is not present in
the test signal, a hypothesis H.sub.1 is that the target is present
in the test signal, and d.sub.0 and d.sub.k are noise terms for
covariance matrices of the test signal and training signals,
respectively.
3. The method of claim 1, wherein the covariance matrix R is random
and has a probability density function p(R), which is a function of
a covariance matrix prior probability matrix R.
4. The method of claim 1, further comprising: replacing the unknown
amplitude .alpha. by a maximum likelihood estimate of the amplitude
.alpha..
Description
FIELD OF THE INVENTION
[0001] This invention relates generally to signal processing, and
in particular to space-time adaptive processing (STAP) for target
detection using radar signals.
BACKGROUND OF THE INVENTION
[0002] Space-time adaptive processing (STAP) is frequently used in
radar systems to detect a target. STAP has been known since the
early 1970's. In airborne radar systems, STAP improves target
detection when interference in an environment, e.g., ground clutter
and jamming, is a problem. STAP can achieve order-of-magnitude
sensitivity improvements in target detection.
[0003] Typically, STAP involves a two-dimensional filtering
technique applied to signals acquired by a phased-array antenna
with multiple spatial channels. Coupling the multiple spatial
channels with time dependent pulse-Doppler waveforms leads to STAP.
By applying statistics of interference of the environment, a
space-time adaptive weight vector is formed. Then, the weight
vector is applied to the coherent signals received by the radar to
detect the target.
[0004] FIG. 1 shows the signal model of the conventional STAP. When
no target is detected, acquired signals 101 include a test signal
x.sub.0 110 consisting of the disturbance d.sub.0111 only, and a
set of training signals x.sub.k, k=1, 2, . . . , K, 120, which are
independent and identically distributed (i.i.d.) with the
disturbance d.sub.0 111. When a target is detected, acquired
signals 102 include the test signal 110 consisting of a target
signal and the disturbance d.sub.0111, and a set of i.i.d. training
signals x.sub.k 120 with respect to d.sub.0 111. The target signal
can be expressed as a product of a known steering vector s 130 and
an unknown amplitude .alpha..
[0005] As shown in FIG. 2 for conventional target detection with
STAP, two types of the estimation sources of the disturbance
covariance matrix are usually used for a homogeneous environment
where the covariance matrix of the test signal 110 is the same as
that of the training signal 120. These two methods are the
estimation of disturbance covariance matrix 220 from training
signals 120 via a covariance matrix estimator 210, and the
generation of the disturbance covariance matrix 250 from prior
knowledge 230 via a covariance matrix generator 240. The knowledge
database can include maps of the environment, past measurements,
etc.
[0006] As shown in FIG. 3, a conventional method, known as Kelly's
generalized likelihood ratio test (GLRT), takes the acquired
signals including the test signal 110 and training signals 120 as
input, and then determines the ratio 330 of
max .alpha. max R f 1 ( x 0 , x 1 , , x K .alpha. , R ) 310
##EQU00002## and ##EQU00002.2## max R f 0 ( x 0 , x 1 , , x K R ) ,
320 ##EQU00002.3##
[0007] where .alpha. is the amplitude of the target signal, x.sub.k
are target free training signals, x.sub.0 is the test signal, R is
the covariance matrix of the training signals, and f.sub.1( ) and
f.sub.0( ) are likelihood functions under two hypothesis H.sub.1,
i.e., the target is present in the test signal, and H.sub.0, i.e.,
the target is not present in the test signal, respectively. The
resulting test statistic 340 is compared to a threshold 350 to
detect 360 the target.
[0008] FIG. 5 shows a conventional Bayesian treatment for the
detection problem in a homogeneous environment, which assumes the
disturbance covariance matrix is randomly distributed with some
prior probability distribution.
[0009] Inputs are the test signal 110, the training signals 120 and
a knowledge database 230. The resulting detectors are often
referred to as the knowledge aided (KA) detectors for the
homogeneous environment. The detector determines the ratio 530
of
max .alpha. .intg. R f 1 ( x 0 , x 1 , , x K .alpha. , R ) p ( R )
R 510 ##EQU00003## and ##EQU00003.2## .intg. R f 0 ( x 0 , x 1 , ,
x K R ) p ( R ) R 520. ##EQU00003.3##
[0010] The resulting test statistic T 540 is compared to a
threshold 550 to detect 560 whether a target is present, or
not.
[0011] For non-homogeneous environments, several models are known.
One model is the well-known compound-Gaussian model, in which the
training signal is a product of a scalar texture, and a Gaussian
vector. The texture is used to simulate power oscillations among
the signals.
[0012] Another model is the partially homogeneous environment, by
which the training signals 120 share the covariance matrix with the
test signal 110 up to an unknown scaling factor X.
[0013] FIG. 4 shows a conventional GLRT treatment on the detection
problem, which results in the well-known adaptive coherence
estimator (ACE) for the partially homogeneous environment. In that
method, the input includes the acquired signals 101 comprising the
test 110 and training signals 120. Then, the ratio 430 of
max .alpha. max .lamda. max R f 1 ( x 0 , x 1 , , x K .alpha. ,
.lamda. , R ) . , 410 ##EQU00004## and ##EQU00004.2## max .lamda.
max R f 0 ( x 0 , x 1 , , x K .lamda. , R ) 420 ##EQU00004.3##
is determined, where .alpha. is amplitude of the test signal,
x.sub.k are target free training signals, x.sub.0 is the test
signal, R is the covariance matrix, f.sub.1( ) and f.sub.0( ) are
the likelihood functions under two hypothesis H.sub.1, i.e., the
target is present in the test signal, and H.sub.0, i.e., the target
is not present in the test signal. The resulting test statistic 440
is compared to a threshold 450 to detect 460 the presence of a
target.
SUMMARY OF THE INVENTION
[0014] The embodiments of the invention provide a method for
detecting targets in radar signals using space-time adaptive
processing (STAP). Different from the conventional partially
homogeneous model, a stochastic partially homogeneous model is used
by the embodiments of the invention, which incorporate some a
priori knowledge to the partially homogeneous model. The stochastic
partially homogeneous retains the power heterogeneity between the
test signal and the training signals with an additional power
scaling factor.
[0015] In this invention, according to the stochastic partially
homogeneous model, the scale invariant generalized likelihood ratio
test is developed from using Bayesian framework.
[0016] Accordingly, a likelihood function is integrated over a
prior probability distribution of the covariance matrix to obtain
an integrated likelihood function. Then, the integrated likelihood
function is maximized with respect to deterministic but unknown
parameters, a scaling factor .lamda. and a signal amplitude
.alpha..
[0017] Finally, an integrated generalized likelihood ratio test
(GLRT) is derived in a closed-form. The resulting scale-invariant
GLRT is a knowledge-aided (KA) version of an adaptive coherence
estimator (ACE).
[0018] Specifically, our KA-ACE uses a linear combination of the
sample covariance matrix and the a priori matrix R as its weighting
matrix. The loading factor of R is linear with respect to the
parameter .mu., which reflects the accuracy of the priori matrix
R.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] FIG. 1 is a block diagram of prior art signals when a target
is present or not;
[0020] FIG. 2 is a block diagram of prior art covariances matrix
estimates of background clutter from training signals and from a
knowledge database via the estimates;
[0021] FIG. 3 is a block diagram of prior art generalized
likelihood ratio test (GLRT) for homogeneous environments in the
prior art;
[0022] FIG. 4 is a block diagram of prior art GLRT for partially
homogeneous environments, referred to as adaptive coherence
estimator (ACE);
[0023] FIG. 5 is a block diagram of prior art knowledge aided GLRT
for stochastic homogeneous environments; and
[0024] FIG. 6 is a block diagram of knowledge aided ACE for
stochastic partially homogeneous environments according to
embodiments of the invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0025] As shown in FIG. 6, the embodiments of the invention provide
a method for detecting targets using space-time adaptive processing
(STAP) of test signals, and a generalized likelihood ratio test
(GLRT). Our scale-invariant GLRT is a knowledge-aided (KA) version
of an adaptive coherence estimator (ACE). The steps of the method
can be performed in a processor 600 connected to a memory and
input/output interfaces as known in the art.
[0026] Specifically, we use the following hypothesis testing
problem:
H.sub.0x.sub.0=d.sub.0,
x.sub.k=d.sub.k, k=1, . . . ,K,
H.sub.1:x.sub.0=.alpha.s+d.sub.0,
x.sub.k=d.sub.k, k=1, . . . ,K, (1)
where the hypothesis H.sub.0 is that the target is not present in
the test signal, H.sub.1, the target is present in the test signal,
x.sub.k are target free training signals 120, x.sub.0 is the test
signal 110, s is an array of a presumed known response, a is an
unknown complex-valued amplitude of the test signal, and d.sub.0
and d.sub.k are the disturbance covariance matrices R.sub.0 and R
of the test and training signals, respectively.
[0027] The covariance matrix R of the training signals is random
and has a probability density function p(R), which is a function of
the covariance matrix prior probability matrix R.
[0028] A test statistic T 630 is determined from a Bayesian
framework according to Equation (2), a ratio 330 of 610 to 620, and
a scaling factor .lamda.
T = max .alpha. max .lamda. .intg. R f 1 ( x 0 , x 1 , , x K
.alpha. , .lamda. , R ) p ( R ) R max .lamda. .intg. R f 0 ( x 0 ,
x 1 , , x K .lamda. , R ) p ( R ) R , ( 2 ) ##EQU00005##
wherein a function max returns a maximum value, and .lamda. can be
in a range of about [1-16].
[0029] The GRLT in Equation (2) can be reduced to
T = max .alpha. max .lamda. .lamda. - N 1 _ - L max .lamda. .lamda.
- N 0 _ - L , ( 3 ) ##EQU00006##
where L=K+.mu.+1, and
.SIGMA..sub.i=.SIGMA..sub.i+(.mu.-N)
R=.lamda..sup.-1Y.sub.iy.sub.i.sup.H+S+(.mu.-N) R,
[0030] with y.sub.i=x.sub.0-.beta..sub.i.alpha.s, .beta..sub.1=1,
.beta..sub.0=0, and
S = k = 1 K x k x k H . ##EQU00007##
[0031] After deriving and substituting the maximum likelihood
estimate of the scalar .lamda. into Equation (3), the our test
statistics T becomes
T = max .alpha. .lamda. ^ ML , 0 N 0 _ ( .lamda. ^ ML , 0 ) L
.lamda. ^ ML , 1 N 1 _ ( .lamda. ^ ML , 1 ) L = [ x 0 H .GAMMA. - 1
x 0 min .alpha. ( x 0 - .alpha. s ) H .GAMMA. - 1 ( x 0 - .alpha. s
) ] N . ( 4 ) ##EQU00008##
[0032] Next, the amplitude .alpha. in Equation (4) is replaced by a
maximum likelihood estimate of the amplitude .alpha. according
to
.alpha. ^ ML = s H .GAMMA. - 1 x 0 s H .GAMMA. - 1 s ( 5 )
##EQU00009##
[0033] Taking the N.sup.th square root of Equation (4) and using
monotonic properties of the function f(x)=1/(1-x), the new test
statistic 630 is
T KA - ACE = s H .GAMMA. - 1 x 0 2 ( s H .GAMMA. - 1 s ) ( x 0 H
.GAMMA. - 1 x 0 ) .gamma. KA - ACE ( 6 ) ##EQU00010##
where .gamma.KA-ACE denotes a threshold subject to a probability of
a false alarm.
[0034] The KA-ACE for the stochastic partially homogeneous
environment takes the form of the standard ACE, except that the
whitening matrix is
.GAMMA. = S + ( .mu. - N ) R _ = k = 1 K x k x k H + ( .mu. - N ) R
_ , ( 7 ) ##EQU00011##
which uses a linear combination between the sample covariance
matrix S and the prior knowledge covariance matrix R. The weighting
factor of the prior knowledge is controlled by .mu.. It makes sense
that the KA-ACE puts more weights on the prior matrix R, when the
prior matrix is more accurate, i.e., .mu. is relatively large.
[0035] In comparison, the conventional ACE also takes the same
form, but with the whitening matrix given by the sample covariance
matrix=.GAMMA.=statistic is finally compared to a threshold 350 to
detect 360 whether a target signal 130 is present in the test
signal 110.
Effect of the Invention
[0036] The embodiments of the invention provide a method for
detecting targets. A knowledge-aided adaptive coherence estimator
ACE is provided for a stochastic partially homogeneous environment,
which models the power oscillation between the test and the
training signals and treats the disturbance covariance matrix as a
random matrix.
[0037] The KA-ACE has a color-loading form between the sample
covariance matrix and the prior knowledge used for the whitening
matrix. We note that the KA-ACE is scale invariant and performs
better than the conventional ACE in various applications.
[0038] Although the invention has been described by way of exes of
preferred embodiments, it is to be understood that various other
adaptations and modifications may be made within the spirit and
scope of the invention. Therefore, it is the object of the appended
claims to cover all such variations and modifications as come
within the true spirit and scope of the invention.
* * * * *