A range profile is the spatial distribution, including down ranges and scattering strengths, of scatterers on the target2 at some particular aspect angle. It can be ...
Radar Target Recognition Using Superresolution Range Profiles as Features Xuejun Liao Zheng Bao Key Laboratory of Radar Signal Processing Xidian University, Xi'an 710071 , P.R.China
E-mail: xj1iaorsp.xidian.edu.cn ABSTRACT In this paper, we propose a scheme of using superresolution range profiles (SRRP) as features to recognize radar targets and present an algorithm for SRRP's matching. The superresolution property ofSRRP's relax their dependence on aspect and achieve a larger allowable aspect increment for the SRRP templates to fully characterize the target. The template library is reduced to a small size and the matching process is accelerated. Performance of our scheme is evaluated using a dataset of three scaled aircraft models. The experimental results show that the reduced template library can still achieve high recognition rates.
Key Words: Radar target recognition, Superresolution Range Profile (SRRP), Data Reduction, Matching Range Profiles as Graphs (MRPGRH)
1. INTRODUCTION Radar target recognition schemes using range profiles as features have been studied extensively -2 However, many critical issues arise when range profiles are used, one of which is their sensitivity to aspect changes. Since small aspect variations can impose drastic changes on range profiles'2 a large library ofrange profiles measured at densely spaced aspect angles must be stored as templates to fully characterize the target. This entails heavy storage and computation burdens on the recognition system. Additionally, a range profile is usually high dimensional and the recognition efficiency again suffers. How to reduce range profiles' dimension and yet not to decrease their discrimination power remains to be much explored.
In this paper, we propose a scheme of using superresolution range profiles (SRRP) as features to recognize radar targets. The superresolution property of SRRP's relax their dependence on aspect and achieve a larger allowable aspect increment for the SRRP templates to fully characterize the target. The data storage is therefore reduced to accelerate the SRRP matching process. A SRRP can be regarded as a discrete spectrum whose spectral lines are usually not equally spaced on the frequency 12 .We here devise a axis, hence it is of no meaning to match two SRRP's by their correlation, as did for range computationally simple measure called Matching Range Profiles as Graphs (MRPGRH) to evaluate the similarity between two SRRP's.
2. RANGE PROFILES AND THEIR ASPECT-DEPENDENCE A range profile is the spatial distribution, including down ranges and scattering strengths, of scatterers on the target2 at some particular aspect angle. It can be obtained by inversely Fourier transforming the frequency response of the target, which can be written as K 2 (1) kexp(-j2—f) Xa(f)= C
k=l
where f denotes the frequency, c denotes the speed of light, K denotes the number of scatterers on the target, a k and rk
denote the scattering strength and down range of the k th scatterer, respectively. Eq.( I ) can be interpreted as the superimposition of K complex sinusoids, whose parameters ak and
, k =1 , 2,
K , correspond to the scattering
strengths and down ranges of scatterers on the target, respectively. When parameters of the complex sinusoids in Eq.(1 ) are estimated by IDFT, only limited resolution can be achieved. Specifically it follows from Eq.(l) and the properties of IDFT that the bandwidth B of the frequency response and the dimension zlr of the range cell are related by
z1r= SPIE Vol. 3545 • 0277-786X198/$1O.OO
(2)
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where c is the speed of light. The aspect-dependence ofrange profiles is seen from Eq.(1) and (2). According to the resolution limit ofIDFT in Eq.(2), scatterers separated by less than Ar in range can not be resolved (lie in the same range cell) and are represented by one same value in a range profile. This value corresponds to the phasor sum of radar returns from all scatterers within that range cell. When aspect changes, or equivalently, the target rotates, each scatterer with range rk in the cell has its own change in range
öTk and produces its own phase factor exp(—j2it ?11Lf) in the right side of Eq.(1). This implies that aspect changes bring two consequences: ( 1) scatterers in one range cell shift relative to each other and (2) some scatterers may shift from one cell into another. The above two phenomena are usually referred to as interference effect and range migration 2 Interference effects cause fluctuation of the range profile as constructive interference of scatterers is switched to destructive interference or vice versa. Range migration is serious at large cross ranges and alter range profiles drastically. When aspect changes greatly, the scatterers' model, i.e., the scattering distribution ofthe target changes, hence o rk and K in Eq.(1) change, and range profiles change independently ofthe IDFT resolution limit.
3. THE RECOGNITION SCHEME BASED ON SUPERRESOLUTION RANGE PROFILES In this section, we try to relax range profiles' aspect-dependence caused by interference effects and range migration. This is achieved by extracting superresolution range profiles from the target' s frequency response Xa(f) . As shown in Eq.(l),
Xa(f) S the superimposition of K complex sinusoids. Hence the range profile, i.e., IFT of Xa(f) ' is in fact a finite and discrete spectrum, each spectral line corresponding to a scatterer on the target. This observation leads us naturally to using to overcome the resolution limit of IDFT. In the Prony model , parameters parametric spectrum estimation techniques
called amplitudes and zeros are estimated. The amplitudes in the Prony model, though corresponding to scattering mechanisms, does not provide scattering strengths of the scatterers directly. Whereas the Modified CLEAN and its improved version RELAX , give direct estimates ofboth down ranges and scattering strengths ofthe scatterers on the target. For this reason, we shall use RELAX to extract superresolution range profiles from the measured frequency response of the target.
3.1 Review of the RELAX algorithm Suppose X(n) is the discrete, sampled representation of X(f) in Eq.(1), that is, X(n) =X(nzlf), where 4f is the sampling interval that satisfies the Nyquist criterion. Using matrix notations, the discrete representation of Eq.(1) can be written as
x=Wa
(3)
where
x=[X(O) X(2) with
...
X(N—1)]T
(5)
N=—
and
0) = [1
with
(4)
a=[c1 2
KI
(6)
W=[o w2
Kl
(7)
exp(—j2z ?LJf). . . exp(—j2ic --(N — 1)4f)]T
(8)
for k = 1,2, . . . , K . Note that B in Eq.(5) is the same as in Eq.(2). The parameter estimation problem of Eq.(3) now is to
estimate r 's and k
that
is, W and a from x . This can be achieved by minimizing the square error Ix — Wall2 .
The
optimization proceeds in two steps. First suppose r 's (hence W ) are known, then the square error is minimized by orthogonally projecting x onto the column space of W , that is, setting a = Wx , where W (WHW)_l W" is the pseudo inverse of W. Next, we optimize W to minimize e2 x — WW+xfl2, which is equivalent to maximizing
398
lIWWxM2 because WW is the orthogonal projector on the column space of W .
w = [1 exp(-j27r-Af). • • exp(—j27r-(N C
C
—
When
K = I,
, which can be approximated by 1)Af)]' and IWWxJI2 1JIWHxfl2 K
squared moduli ofIFFT of x. RELAX is an algorithm that iteratively finds the strongest complex sinusoid present in x using the above methods and then cleans the found complex sinusoid form x . At each iteration when the k th strongest complex sinusoid is found, the I St _ k th complex sinusoids are reestimated, again iteratively, until relative change of the residue energy in x is smaller than
satisfied. This finely tunes the parameters to their real values. In the case that the number of complex sinusoids K is unknown, the RELAX algorithm can be stopped at the step where the residue energy in x is small than desired.
3.2 The Matching Range Profiles as Graphs (MRPGRH) measure
}
The superresolution range profiles (SRRP) derived from the measured frequency response by RELAX are described by a
r 's are not necessarily equally spaced on the range axis, there is no way to interpret SRRP's as discrete signals or vectors and the Euclidean distance or correlation can no longer be used to measure their similarity.
set ofrange-strength pairs {r, ck
. Because the
in this section we propose a computationally simple measure called Matching Range Profiles as Graphs (MRPGRH) to evaluate the similarity between SRRP's. Given a SRRP, SRRP = {r cik }= interpret it as a graph, with its nodes defined as
node : {k
(r ,a k )( k = 1 - K}
on the Cartesian coordinate plane, and its edges connecting only nodes whose r 's are
adjacent. We define the n th order center ofthe graph as
C"(SRRP)((— rkn),
(9)
Then the N th order MRPGRH measure is defined as Def
N
(10)
for any two given SRRP's. in Eq.(10) d is the Euclidean distance. We omit the superscript N except when we want to specify the order of the measure. We can easily prove the following three properties of MRPGRH measure from Eq.(9) and (10):
(I) MRPGRH(SRRP,SRRP)= 0. (2) MRPGRH(SRRP , SRRP ) MRPGRH(SRRP, SRRP). (3) MRPGRH(SRRP , SRRP ) MRPGRH(SRRP , SRRP ) + MRPGRH(SRRP , SRRF). Since the MRPGRH measure satisfies the above three conditions of general distance measures in a metric space, it can be used in place of the Euclidean distance measure in radial basis function networks (RBFN) for classification of SRRP's. The computational simplicity of the MRPGRH measure ensures fast training and efficient recalling of the RBFN as if Euclidean distance measure were being used..
4. EXPERIMENTAL RESULTS In this section we evaluate the performance of our SRRP's based radar target recognition scheme on a dataset of three scaled aircraft models B-52, Q-6 and Q-7, with scaling ratio of 1 :92, 1 :20 and I :15, respectively. The three models have
similar sizes, with length/width/height of 69OmmI8l5mmIl7Omm for B-52, 700minI435mm/l9Omm for Q-6 and 1048mm/477mm/22Omni for Q-7. The raw data are collected by placing the scaled models on a rotating platform in a microwave anechoic chamber and measuring the radar returns at stepped frequencies ranging roughly from 12 0Hz to I 8 GHz. The data are collected at aspect angles changing from 0 to 155* ( Ø degrees is defined as the head direction) with an average increment of 0.43, while the elevation angles remain constant (5). The dataset consists of 322, 310, 45! radar returns for B-52, Q-6 and Q-7, respectively. The radar returns are measured in frequency domain.
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The superresolution range profiles are derived from the frequency measurements using the RELAX algorithm. The training templates consist of SRRP's at some chosen aspect angles to the end that they can represent SRRP's at other aspect angles very well. There are 22, 22, 23 templates for B-52, Q-6 and Q-7, respectively. We use these templates to train the RBFN using MRPGRH measure.
After the RBFN has been trained, it is used to classify the remaining SRRP's. The classification results are shown in Table It is seen that although the template library is reduced to a pretty small size (corresponding to an aspect increment of approximately 7 ), the three targets can still be correctly classified with an average correct rate of 95%. This demonstrates the relaxed dependence of SRRP's on aspect due to the superresolution of scatterers within one IDFT defined range cell. The interference effects and range migration are reduced, and therefore the fluctuation of SRRP's are much alleviated. I.
Table I . Classification results of SRRP'; actual class classification results correct rate B-52 Q-6 Q-7 B-52 0 298 2 99% 0 270 94% 18 Q-6 8 27 393 92% Q-7
5. CONCLUSIONS In this paper, a scheme is proposed to use superresolution range profiles as features to recognize radar targets and an algorithm is presented to match SRRP's as graphs. The SRRP's are much less dependent on aspect than common range profiles because the scatterers that lie in within one IDFT defined range cell are now well resolved and the interference effects and range migration are therefore reduced. This achieves a larger allowable aspect increment for the SRRP templates to filly characterize the target. The matching process is accelerated by the reduced template library. Experiments are made using a dataset ofthree scaled aircraft models and the results show that the reduced template library can still achieve high recognition rates.
6. ACKNOWLEDGMENTS This research is supported by the National Defense Preliminary Research Foundation of China.
7. REFERENCES I . H.J. Li,
S.H. Yang: "Using Range Profiles as Feature Vectors to Identify Aerospace Objects", IEEE Trans. Antennas and Propagation, Vol.41, No.3, pp.261-268, 1993 2. S. Hudson and D. Psaltis: "Correlation Filters for Aircraft Identification From Radar Range Profiles", iEEE Trans. Aerospace and Electronics System, Vol. 29, No.3, pp.741-748, 1993 3. R. Carriere and R.L. Moses, "High Resolution Radar Target Modeling Using a Modified Prony Estimator", iEEE Tranns. Antennas and Propagation, Vol.40, No.!, pp.13-18, 1992 4. P.T. Gough, "A Fast Spectral Estimation Algorithm Based on the FFT", IEEE Trans. Signal Processing, Vol.42, No.6, pp.1317-1322, 1994 5. J. Li, P. Stoica, "Efficient Mixed-Spectrum Estimation with Application to Target Feature Extraction", IEEE Trans. Signal Processing, Vol.44, No.2, pp.28 1 -295, 1996
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