RADAR TARGET RECOGNITION BASED ON PARAMETERIZED HIGH RESOLUTION RANGE PROFILES

Transcription

1 RADAR TARGET RECOGNITION BASED ON PARAMETERIZED HIGH RESOLUTION RANGE PROFILES XUEJUN LIAO and ZHENG BAO Key Lab. For Radar Signal Proessing Xidian University, Xi an , P. R. China xjliao@rsp.xidian.edu.n A new sheme of radar target reognition based on parameterized high resolution range profiles (PHRRP) is presented in this paper. A novel riterion alled generalizedweighted-normalized orrelation (GWNC) is proposed for measuring the similarity between PHRRP s. By properly hoosing the parameter of the mainlobe width in GWNC, aspet sensitivity of PHRRP s an be redued without sarifiing their disriminative power. Performane of the sheme is evaluated using a dataset of three saled airraft models. The experimental results show that by using GWNC, only a small number of most dominant satterers an ahieve the same reognition rates as HRRP s, thus leading to a signifiant data redution for the reognition system. Keywords: Radar target reognition; high resolution range profiles (HRRP); dominant satterers; parameterized HRRP (PHRRP); generalized-weighted-normalized orrelation (GWNC). 1. INTRODUCTION Radar target reognition based on high resolution range profiles (HRRP) has reeived muh attention in reent years. 2,5 A HRRP is basially the distribution of the target s satterers along the radar line of sight and is usually obtained via Fourier transform of the radar return reorded in the frequeny domain. Sine satterers our only at the peaks of a HRRP and the frequeny domain data are usually zero padded in order to loate all signifiant satterers orretly, information redundany is quite severe in HRRP s. Based on the satterers model, parameterizations of HRRP s have been proposed to ahieve data redution using the modified Prony algorithm 1 and the least squares fitting method. 3 Sine the distribution of satterers is target-dependent and usually nonuniform, the parameterized HRRP s (PHRRP) annot be regarded as disrete signals and the normalized orrelation (NC) based reognition sheme an no longer be used to lassify them. In this paper, we present a new sheme of radar target reognition based on PHRRP s. We first use the RELAX algorithm 4 to extrat PHRRP s from the frequeny domain measurements. Then we propose a novel riterion alled generalized-weighted-normalized orrelation (GWNC) for measuring the similarity of PHRRP s, and use it to lassify the extrated PHRRP s. This work is supported by the National Siene Foundation of China and the National Defense Pre-researh Foundation of China. International Journal of Pattern Reognition and Artifiial Intelligene, Vol. 14, No. 7 (2000) World Sientifi Publishing Company 979

2 980 X. LIAO & Z. BAO The rest of the paper is organized as follows. Setion 2 gives a brief introdution of the data model and the RELAX algorithm. Setion 3 establishes the GWNC riterion. Setion 4 presents experimental results. Finally Se. 5 onludes the paper. 2. DATA MODEL AND EXTRACTION OF PHRRP S 2.1. Data Model The frequeny domain radar return an be modeled as K ( X(f) = σ k exp j2π 2r ) k (f + f 0) where r k and σ k, respetively, are the down range and sattering strength of the kth satterer, K is the number of satterers on the target, f 0 is the enter frequeny, and is the speed of light. Equation (1) an be interpreted as the superimposition of K omplex sinusoids with omplex amplitudes σ k exp(j2π 2r k f 0 ) and frequenies 2r k, k =1,2,...K. Hene the HRRP, i.e. Fourier transform of X(f), is in fat a band limited and disrete spetrum, eah spetral line orresponding to a satterer on the target. This observation leads us naturally to using parametri spetrum estimation tehniques 1,3,5 to extrat the parameters, i.e. {σ k exp(j2π 2r k f 0 ),r k } K, in Eq. (1). Usually we are not onerned with the phase of the omplex amplitudes. Therefore the parameters that serve for later reognition purpose are represented by { σ k 2,r k } K, whih are referred to as the parameterized HRRP (PHRRP). Various methods are available for extration of PHRRP s, inluding the modified Prony algorithm 1 and the least squares fitting method. 3 The more reently proposed RELAX algorithm 4 gives the estimates of spetrum parameters diretly and has been demonstrated to be robust to noise. For this reason, it shall be used in this paper to extrat the PHRRP s from the frequeny domain measurements. (1) 2.2. Extration of PHRRP s Using matrix notations, the disrete version of Eq. (1) an be written as x = Ωa (2) where a is olumn vetor representing σ k exp(j2π 2r k f 0 )fork =1, 2,...K,and Ω and x are matrix and olumn representations of exp(j2π 2r k f)andx(f), respetively, at disrete samples of f. The parameter estimation of Eq. (2) is to estimate Ω and a from x, whih is the frequeny domain measurements reorded by the radar. This an be ahieved by minimizing the square error e 2 = x Ωa 2. The optimization an proeed in two steps. First suppose Ω is known, then the square error is minimized by orthogonally projeting x onto the olumn spae of Ω, i.e. setting a = Ω + x,whereω + =(Ω H Ω) 1 Ω H is the pseudo inverse of Ω. Next, we optimize Ω to minimize e 2 = x ΩΩ + x 2, whih is equivalent to maximizing ΩΩ + x 2 beause ΩΩ + is the orthogonal projetor on the olumn spae of Ω. WhenK =1,Ω = [1 exp(j2π 2r1 f) exp(j2π 2r1 f(n 1))]T, with f

3 RADAR TARGET RECOGNITION BASED ON PHRRP 981 being the sampling interval of X(f) andn the number of sampling points, and ΩΩ + x 2 = 1 N ΩH x 2, whih an be implemented by FFT. The RELAX algorithm 4 is an algorithm that iteratively finds the strongest omplex sinusoid present in x using the above methods and then leans the omplex sinusoid formx. At eah iteration when the kth strongest omplex sinusoid is found, the 1st kth strongest omplex sinusoids are reestimated, again iteratively, until the relative hange of the residue energy of x is smaller than satisfied. This finely tunes the parameters to their real values. For the ase, when the number of omplex sinusoids K is unknown, the RELAX algorithm stops when the residue energy of x is smaller than desired. 3. GENERALIZED-WEIGHTED-NORMALIZED CORRELATION (GWNC) The model of frequeny domain radar return of Eq. (1) is rewritten as ) X(f) = σk (j2π x exp 2rx k (f + f 0) (3) where the supersript x is used to denote the assoiated data reord. Taking Fourier transform of eah side of Eq. (3) yields the range domain signal x(r) = A x kw(r rk) x (4) where x(r) = x 1 (2r/) with x 1 (r) being Fourier transform of X(f), A x k = σ x k exp(j4πf 0r x k /), and w(r) =w 1(2r/) with w 1 (r) being Fourier transform of the frequeny domain window funtion. Multiplying x(r) by its onjugate and dropping the ross-term yields x(r) Def = x(r) 2 A x k Ax l w(r rk x )w (r rl x ) = l=1 l k σ k x w(r rx k ) 2 (5) where x(r) is the ross-term free HRRP, * denotes the omplex onjugate, and σ x k = Ax k 2 = σ x k 2. For two ross-term free HRRP s x(r) andỹ(r), we define C(x, y) Def = p=1 x(r x p )ỹ(rx p ) / w(0) 2 K y p=1 l=1 l p σ k l σ y k w(rx p r x l ) 2 w(r x p r y k ) 2 / w(0) 2 = K y σ l x σ y k w(rx l r y k ) 2. (6) l=1

4 982 X. LIAO & Z. BAO Note that the ross-terms are again dropped in Eq. (6). Obviously, C(y, x) = C(x, y). Define ρ(x, y) Def = C(x, y) C(x, x)c(y, y) (7) ρ(x, y) is referred to as generalized-weighted-normalized orrelation (GWNC), with the weights w(r x,l r y,k ) 2 being a funtion of relative distane between satterers. Just as normalized orrelation (NC) is used to measure the similarity of HRRP s, GWNC an be used to measure the similarity of PHRRP s, eah of whih is designated as { σ k x,rx k }Kx, with σx k, rx k and Kx defined to be the same as in Eqs. (3) and (5). It should be noted that the hoie of a proper mainlobe width for w(r) is important in the appliation of GWNC. With a wide mainlobe, GWNC is robust to the azimuth variation. However, GWNC will lose its disriminating power if the mainlobe is too wide. From our experienes, the mainlobe width an be hosen to be 2 5 times the width of a range ell ahieved by DFT. It is easily seen from Eqs. (6) and (7) that GWNC is effiient in omputation when the number of satterers is not too large. For PHRRP templates { σ k x,rx k }Kx, C(x, x) an be omputed offline and stored in memory. For an unknown PHRRP { σ y k,ry k }Ky, C(y, y) needs to be omputed only one before it is mathed against all templates. Thus the omputation of GWNC an be further redued. The storage effiieny of GWNC is obvious, as there are only 2K data points for K satterers, and this is muh smaller than the data points of a HRRP. To ompensate for the translational range shift, the numerator of Eq. (7) should be modified as C(x, y) = max r K y σ l x σy k w( r + rx l ry k ) 2. (8) l=1 In pratie, the searh for r an be done in the neighborhood of r, where K y r = σ y k ry k / K y x K σ y k l=1 σ x l r x l / K x σ l x. (9) l=1 4. EXPERIMENTAL RESULTS We evaluate the performane of GWNC using the dataset of three saled airraft models: B52 (sale 1:91), Q6 (sale 1:20) and Q7 (sale 1:15). The raw data are olleted by plaing the saled models on a turntable in a mirowave anehoi hamber and measuring the radar returns at stepped frequenies ranging from 12 GHz to 18 GHz with a 0.06 GHz inrement. Azimuthal angles of the measurements are from 0 to 155 (0 is the nose-on azimuth) with an average inrement of 0.43.The elevation angles remain onstant at 5. The PHRRP s are obtained by extrating the parameters of K most dominant satterers from the stepped-frequeny measurements using the RELAX algorithm. 5 The orresponding HRRP s are obtained via FFT of the stepped-frequeny measurements.

5 RADAR TARGET RECOGNITION BASED ON PHRRP 983 (a) (b) Fig. 1. Examples of HRRP s of the airraft models. (a) B52, at the azimuth of 48.5 ;(b)q6,at the azimuth of (a) (b) Fig. 2. Examples of PHRRP s of the airraft models. (a) B52, at the azimuth of 48.5 ;(b)q6, at the azimuth of Figure 1 gives some examples of HRRP s of the three airraft models and Fig. 2 gives the orresponding PHRRP s. The absissas range in meters. It is seen that the PHRRP is a good representation of the dominant satterers as indiated by the peaks in the orresponding HRRP. Figure 3 gives the NC of HRRP s and GWNC of PHRRP s, respetively, of B52 for all three targets. The absissas are azimuth variation in degrees. Figure 4 gives similar plots of the Q6 airraft. In Figs. 3(b) and 4(b), the number of most

6 984 X. LIAO & Z. BAO (a) (b) Fig. 3. (a) NC between the HRRP s of B52 and those of all three targets. (b) GWNC between the PHRRP s of B52 and those of all three targets Solid with o : B52, Dashed with : Q6, Dotted with : Q7. Referene azimuth: (a) (b) Fig. 4. (a) NC between the HRRP s of Q6 and those of all three targets. (b) GWNC between the PHRRP s of Q6 and those of all three targets Solid with o : B52, Dashed with : Q6, Dotted with : Q7. Referene azimuth: dominant satterers are all 12. Sine translational range shifts do not our for turntable targets, the GWNC is omputed using Eqs. (6) and (7), with w(r) is hosen as Fourier transform of the Hamming window funtion to redue the effet of sidelobes. The mainlobe width of w(r) is hosen to be three times the width of a

7 RADAR TARGET RECOGNITION BASED ON PHRRP 985 range ell ahieved by DFT. It is seen from Figs. 3 and 4 that the azimuth sensitivity of PHRRP s an be redued without sarifiing their disriminative power if the mainlobe width of w(r) is hosen properly. Now we evaluate the performane of GWNC via omparison of lassifiation rates. We onstrut the template set for PHRRP (or HRRP) by fething PHRRP s (or HRRP s) from every 4.7 azimuths starting from the 2 azimuth, thus obtaining a total of 99 templates for PHRRP (or HRRP) over the azimuth range for the three airraft models. An unknown PHRRP (or HRRP) is lassified by first omputing its GWNC (or NC) with all PHRRP (or HRRP) templates and then assigning it to the lass of whih a template has the maximum GWNC (or NC) with the unknown PHRRP (or HRRP). In omputation of GWNC, w(r) is again hosen as Fourier transform of the Hamming window funtion with its mainlobe width hosen to be three times the width of a range ell ahieved by DFT. The lassifiation results are summarized in Table 1. It is seen from Table 1 that the lassifiation rates ahieved by PHRRP s inrease rapidly as an inreased number of dominant satterers are used and the lassifiation rates ahieved by only 12 dominant satterers are already omparable to those ahieved by HRRP s, thus demonstrating the effetiveness of GWNC. The number of data points for a HRRP is 101 and it an be redued to 64 by disarding the range ells at eah end, whih arry little target features. On the other hand, there are only 2K data points for K most dominant satterers. This results in a 62% data redution for 12 dominant satterers. Table 1. Corret lassifiation rates in perentage. Corret lassifiation rates (%) B52 Q6 Q7 Average NC applied to HRRP s GWNC K = applied to K = PHRRP s K = CONCLUSIONS In this paper we have presented a new sheme for radar target reognition based on parameterized high resolution range profiles (PHRRP). We have proposed a novel riterion alled generalized-weighted-normalized orrelation (GWNC), whih an be used to measure the similarity between PHRRP s. With a properly hosen mainlobe width of GWNC, the PHRRP s azimuth sensitivity an be redued and yet their disriminative power does not suffer. The experimental results with the dataset

8 986 X. LIAO & Z. BAO of three saled airraft models show that by using GWNC only a small number of most dominant satterers an ahieve the reognition rates as good as those of HRRP s, thus leading to a signifiant data redution for the reognition system. REFERENCES 1. R. Carriere and R. L. Moses, High resolution radar target modeling using modified prony estimator, IEEE Trans. Antennas and Propagation 40, 1 (1992) S. Hudson and D. Psaltis, Correlation filters for airraft identifiation from radar range profiles, IEEE Trans. Aerosp. Eletron. Syst. 29, 3 (1993) Q. Li, E. J. Rothwell, K. M. Chen and D. P. Nyquist, Radar target disrimination shemes using time-domain and frequeny-domain methods for redued data storage, IEEE Trans. Antennas and Propagation 45, 6 (1997) J. Li and P. Stoia, Effiient mixed-spetrum estimation with appliation to target feature extration, IEEE Trans. Sign. Proess. 44, 2 (1996) H. J. Li and S. H. Yang, Using range profiles as feature vetors to identify aerospae objets, IEEE Trans. Antennas and Propagation 41, 3 (1993) Xuejun Liao reeived the B.S. and M.S. degrees in eletrial engineering, from Hunan University, China, in 1990 and 1993, respetively, and Ph.D. in eletrial engineering from Xidian University, China, in He is urrently with the National Key Lab for Radar Signal Proessing, Xidian University. His urrent researh interests are in the area of radar imaging and target reognition, array signal proessing and statistial signal proessing. Zheng Bao graduated from the Communiation Engineering Institute of China in Currently he is a professor at Xidian University and a member of the Chinese Aademy of Siene. His researh fields are radar systems, signal proessing and iruit theory.