ISAR IMAGING OF MULTIPLE TARGETS BASED ON PARTICLE SWARM OPTIMIZATION AND HOUGH TRANSFORM

Transcription

1 J. of Electromagn. Waves and Appl., Vol. 23, , 2009 ISAR IMAGING OF MULTIPLE TARGETS BASED ON PARTICLE SWARM OPTIMIZATION AND HOUGH TRANSFORM G.G.Choi,S.H.Park,andH.T.Kim Department of Electronic & Electrical Engineering Pohang University of Science and Technology (POSTECH) San 31, Hyoja-Dong, Nam-Ku, Pohang, Kyoung-buk , Korea K. T. Kim School of Electrical and Computer Science Yeungnam University 214-1, Dae-Dong, Gyeongsan-si, Kyoung-buk , Korea Abstract This paper proposes an accurate method to obtain Inverse Synthetic Aperture Radar (ISAR) images of multiple targets. The existing method using the Hough transform and edge detection has a demerit that its fitting ability of flight trajectory is not sufficient if a range profile has high order terms. For better quality of ISAR imaging, we use particle swarm optimization (PSO) to find residual high order coefficients. Simulation results show that two moving targets are successfully separated from each other. 1. INTRODUCTION Inverse Synthetic Aperture Radar (ISAR) image shows the twodimensional reflectivity of a target by synthesizing the signal reflected from a target [1 3]. Its down-range resolution is decided by the bandwidth. The cross-range is obtained by the Doppler frequency caused by the relative rotational motion between the target and the radar. The range-doppler algorithm has been proposed to obtain ISAR images [4]. However, existing methods deal with only the single target case. Because echoes of different targets are mixed with each other, it is difficult to find each range profile history, which is needed to obtain each ISAR image. Some algorithms were proposed Corresponding author: K. T. Kim (juniorf@yumail.ac.kr).

2 1826 Choi et al. to separate images of multiple targets. The time-doppler frequency analysis technique is a method which is limited in practice because it requires equal range migrations of all targets [5]. Another method based on maximum likelihood estimation assumes that the number of target is known, which is not true in real cases [6]. The method using a frequency image to detect lines is not applicable to complex targets [7]. Recently proposed methods utilized Hough transform and edge detection to separate range profiles [8 10]. However, these methods modeled the flight trajectories with linear lines. High order terms should be estimated to improve the quality of ISAR images. We use particle swarm optimization (PSO) and Hough transform (HT) to obtain more accurate separation of the range profile history of each target. The ISAR images of each target are found by a conventional motion-compensation method using these extracted flight trajectories. 2. RADAR SIGNAL MODEL AND RANGE-DOPPLER ALGORITHM For the radar signal model, the transmitted chirp signal used for high resolution can be expressed as: [ )] ( ) x(t) =A 0 exp j2π (f 0 t + Bt2 t rect, (1) 2τ τ where x(t) is a transmitted signal at time t; A 0 is the amplitude of the signal; f 0 is the carrier frequency; B is the bandwidth of the signal; τ is the pulse duration; rect is a rectangular function whose value is 1 for τ/2 t<τ/2 and 0 otherwise. The echoed signal from scattering centers of multiple targets is M N m [ r(t) = A m,n exp j2π (f 0 (t t m,n )+ B(t t m,n) 2 )] m=1 n=1 ( t tm,n rect τ 2τ ), (2) where A m,n is the amplitude of the nth scattering center of the mth target; M is the number of targets; ( N m ) is the number of scattering t tm,n centers of the mth target; rect τ = 1 if 0 t tm,n τ < 1 ( ) t tm,n and rect τ = 0 otherwise; t m,n is the time delay between the radar and the nth scattering center of the mth target; t m,n =

3 ISAR imaging based on PSO and hough transform 1827 (x 2 m,n) 2 +(y m,n) 2 c ;(x m,n,y m,n ) is the two dimensional position of the nth scatterer of mth targets. We obtain range profiles from this reflected signal at a certain aspect angle through a matched-filtering process. Then, we get data through translational motion compensation, such as range alignment and phase adjustment, and obtain ISAR images by applying the Fast Fourier transform (FFT) to each range bin. 3. ISAR IMAGING USING PROPOSED MOTION COMPENSATION METHOD The system block diagram of the proposed method is shown in Fig. 1. Before extracting each range profile of target in mixed range profiles of multi-targets, we make a new image whose component is 1 if the corresponding component is higher than ten percent of maximum component and 0 otherwise to reduce the effect of noise. We model the target trajectory as a polynomial. If there are M range profiles having N range bins, the trajectory fitting function is S(x) = L a i x i 1+ i=0 3 a i x i (3) where S(x) is the trajectory function, x = 0 M 1 with the increment of 1, and a i are parameters for the polynomial. Because very high order terms are difficult to fit to the target trajectory in short observation time condition, we limit the order of the polynomial to 3. Then, the parameters can be optimized by performing HT and PSO. We use HT, which easily intercepts slopes of stretched lines, to i=1 Figure 1. Motion compensation process.

4 1828 Choi et al. find the first order coefficient a 1. Then, the second and third order coefficients are estimated by PSO. The Hough transform (HT) is designed to detect lines. The parametric representation of lines through HT is ρ = x cos θ + y sin θ, (4) where ρ is the distance from the origin to the line along a vector perpendicular to the line, and θ is the angle between this vector and the x-axis. PSO is a population-based global optimization search algorithm, modeled on the social behavior birds within a flock [11 13]. It is easier to implement than other global optimization algorithms. Let x i denote the position of particle P i in hyperspace, at time step t. Theposition of P i is then changed by adding a velocity v i (t) to the current position. The velocity vector drives the optimization process and reflects social exchanged information. The general particle dynamics process which updates each particle is as follows: v i (t) =φ v i (t 1) + ρ 1 ( x pbest x i (t)+ρ 2 ( x gbest x i (t)), where ρ 1 = c 1 r 1,ρ 2 = c 2 r 2, c 1,c 2 > 0, r 1,r 2 r and, c 1 + c 2 < 4 (5) t is the number of generations, and rand is a uniform random number having a uniform distribution between 0 and 1. The cost function of the PSO is the sum of the values of pixels which exist at the polynomial location on the new image. Shifting S(x) continually from the first to the last range bins and summing the pixel values on the polynomial for each shift, we use as the cost function the sum of the 20 highest sums that best represent the range profile history. The larger the sum is, the better the polynomial represents the trajectory. The purpose of the PSO is to find polynomial coefficients that maximize the cost function. After the PSO, we extract the range profile of each target. Range bin alignment is performed on each range profile using a global method and a 1D entropy minimization method for fast and accurate imaging [14 15]. After range alignment, phase adjustment is performed on all data using 2D entropy minimization methods [16]. 4. SIMULATION RESULT The plan of flight trajectory of two targets is shown in Fig. 2. The scattering center models of the targets are shown in Fig. 3. Simulation parameters are as follows. The center frequency is 9.15 GHz; bandwidth is 200 MHz; pulse repetition frequency is 2000 Hz; 1024 pulses are generated. Let the position of the radar be the origin.

5 ISAR imaging based on PSO and hough transform 1829 Figure 2. The flight plan of two targets. (a) Target1 (b) Target2 Figure 3. The scattering center model of two targets. The distance (R(t) =R 0 + vt +0.5at 2 ) between radar and the mass centers of targets 1 and 2 are (0.1, 10.1) km and (0.1, 10.12) km respectively. The initial velocity of target 1 is 250 m/s with a 210 direction angle with respect to the x-axis and an acceleration of 2 m/s 2. The initial velocity of target 2 is 300 m/s with a 225 direction angle with respect to the x-axis and an acceleration of 3 m/s 2. The total mixed range profile history of the two targets is shown in Fig. 4(a). We find the first order coefficients a 1, 1/slope, of each trajectory using the HT. Because peak values are 12.0 and 19.8,1/ tan(( ) ), and 1/ tan(( ) ) are the first order coefficients of the polynomial model for each range profile (Fig. 4(b)). Then, we extract the second and third order coefficients of trajectories of the two targets using PSO. The parameters used in PSO were φ = 0.6, c 1 = c 2 = 1.49, population size = 50, and number of generations = 10. The estimated parameters for Target1 are a 2 = and a 3 = , and those for Target2

6 1830 Choi et al. (a) (b) Figure 4. (a) The mixed range profile history. (b) Finding the first order coefficient of the polynomial using the HT. (a) Target1 (b) Target2 Figure 5. The extracted range profile of each target. are a 2 = , a 3 = The extracted range profile of each target using these parameters is shown in Fig. 5. Range alignment was performed on these separated range profiles. Alignment results of the two targets are shown in Fig. 6. Finally, ISAR images of the two targets are obtained after phase adjustment. The separated ISAR images of the two targets are shown in Fig. 7. We calculated the energy of sum envelopes and entropy of images to measure the accuracy and quality of images. The entropy of the image calculated as follows [17]: Entropy = M i=1 j=1 N I n (i, j) 2 ln I n (i, j) 2, (6)

7 ISAR imaging based on PSO and hough transform 1831 (a) Target1 (b) Target2 Figure 6. Range alignment of each target using proposed method. (a) Target1 (b) Target2 Figure 7. The separated ISAR images of each target. Table 1. Comparison of image quality of method using the Hough transform and the proposed method (Target1). Method Energy of sum envelope Entropy of images hough e6 4.45e-2 proposed e6 2.83e-2 where M,N are matrix size of the image, and I n (i, j) isthe(i, j)th pixel value of the image normalized by the total power. The ISAR images of the proposed method (HT and PSO) and the method using HT only are compared in Fig. 8, Table 1, and Table 2. The image accuracy and quality of the proposed method are better than those of the other method.

8 1832 Choi et al. (a) proposed (HT+PSO) (b) HT only Figure 8. The ISAR images of Target2 using the two dierent methods. Table 2. Comparison of image quality of method using the Hough transform and the proposed method (Target2). Method Energy of sum envelop Entropy of images hough e6 4.28e-2 proposed e6 2.66e-2 5. CONCLUSION The proposed method successfully separates each range profile for ISAR imaging of multiple targets and provides well-focused images. The flight trajectory of each target is modeled using a polynomial. HT is used to find the linear component of the polynomial, and higher order terms are searched for using PSO and the proposed cost function. Then, each separated range profile is aligned and phase-adjusted, yielding further enhanced images. Computer simulation proves that the proposed method gives better quality images than the method using HT only. REFERENCES 1. Chen, C. C. and H. C. Andrews, Target-motion-induced radar imaging, IEEE Trans. Aerospace and Electronic Systems, Vol. 16, No. 1, 2 14, Jan Park,S.H.,K.K.Park,J.H.Jung,H.T.Kim,andK.T.Kim, Construction of training database based on high frequency RCS

9 ISAR imaging based on PSO and hough transform 1833 prediction method for ATR, Journal of Electromagnetic Waves and Applications, Vol. 22, No. 5 6, , Ma,C.-Z.,T.S.Yeo,H.S.Tan,andG.Lu, InterferometricIsar imaging on squint model, Progress In Electromagnetics Research Letters, Vol. 2, , Ausherman, D. A., A. Kozma, J. L. Walker, H. M. Jones, and E. C. Poggio, Development in radar imaging, IEEE Trans. Aerospace and Electronic Systems, Vol. 20, No. 4, , Jul Wang, A., Y. Mao, and C. Chen, Imaging of multi-targets with ISAR based on the time-frequency distribution, Proc. IEEE Int. Conf. Acoust Speech Signal Processing, Vol. 5, , Wu, X. and Z, Zhu, Simultaneous imaging of multiple targets in and inverse synthetic aperture radar, Proc. IEEE 1990 Natioanl Aerospace and Electronics Conference, Vol. 1, , May Fu, X. and M. Gao, ISAR imaging for multiple targets based on randomized hough transfrom, IEEE 2008 Congress on Image and Signal Processing, , Zhang, Y., D. Zhang, W. Chen, and D. Wang, ISAR imaging of multiple moving targets based on RSPWVD-Hough transform, IEEE Trans. Aerospace and Electronic Systems, Vol. 43, No. 3, , Jul Park,S.H.,K.K.Park,J.H.Jung,H.T.Kim,andK.T.Kim, ISAR imaging of multiple targets using edge detection and hough tranform, Journal of Electromagnetic Waves and Applications, Vol. 22, No. 2 3, , Sauer, T. and A. Schroth, Robust range alignment algorithm via Hough transform in an ISAR imaging system, AES, IEEE, Vol. 31, No. 3, , Jul Liu, X. F., Y. C. Jiao, and F. S. Zhang, Conformal array antenna design using modified particle swarm optimization, Journal of Electromagnetic Waves and Applications, Vol. 22, No. 2 3, , Lu, Z. B., A. Zhang, and X. Y. Hou, Pattern synthesis of cylindrical conformal array by the modified particle swarm optimization algorithm, Progress In Electromagnetics Research, PIER 79, , Park, S.-H., H.-T. Kim, and K.-T. Kim, Stepped-frequency Isar motion compensation using particle swarm optimization with an island model, Progress In Electromagnetics Research, PIER 85, 25 37, 2008.

10 1834 Choi et al. 14. Wang, J. and X. Liu, Improved global range alignment for ISAR, IEEE Trans. Aerospace and Electronic Systems, Vol. 43, No. 3, , Jul Li, X., G. Liu, and J. Ni, Autofocusing of ISAR images based on entropy minimization, IEEE Trans. Aerospace and Electronic Systems, Vol. 35, No. 4, , Oct Wang, J., X. Liu, and Z. Zhou, Minimum-entropy phase adjustment for ISAR, IEE Proceedings of Radar, Sonar and Navigation, Vol. 151, No. 4, , Aug Lazarov, A. D. and C. Minchev, ISAR signal modeling and image reconstruction with entropy minimization autofocussing, 25th Digital Avionics Systems Conference (25th DASC), Portland, OR, USA, Oct. 15, 2006.