436 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 10, NO. 3, MARCH 2001 Three-Dimensional ISAR Imaging of Maneuvering Targets Using Three Receivers Genyuan Wang, Xiang-Gen Xia, Senior Member, IEEE, and Victor C. Chen, Senior Member, IEEE Abstract—The conventional ISAR image is a two-dimensional (2-D) projection of a three-dimensional (3-D) object surface. The image (projection) plane is related to the motion of a target with respect to the line of radar sight (LOS). In general, the image plane and the image scale in the cross range direction can not be de- termined by the traditional ISAR system with one receiver unless the target motion knowledge is known. In this paper, we propose a new ISAR system with three receivers. Using the three-receiver ISAR system, 3-D images of maneuvering targets can be generated, where the knowledge of the target motion is not required. Index Terms—ISAR imaging, maneuvering targets. I. INTRODUCTION M OST OF the current inverse synthetic aperture radar (ISAR) imaging techniques form two-dimensional (2-D) images of moving targets, which are 2-D projections of three-dimensional (3-D) moving targets. The fine resolution in the range direction is obtained by transmitting a wide band signal and the high cross range resolution is achieved by exploiting the relative motion between the radar and targets. The absolute scale in the cross range, however, depends on the angular rotation of the target. When the rotation is uniform, the scale depends on the rotation velocity that is usually not known. When the rotation is nonuniform, the scale is even more complicated to determine. In both cases, the scale in the cross range of an ISAR image is not known in the conventional ISAR. Since the absolute scale in ISAR imaging is not known, the true locations of scatterer can not be determined even in the image projection plane. Furthermore, in the conventional ISAR, it is only possible to form one image plane. Therefore, even the scale in this image plane is known, it is still not possible to form other image planes with different orientations, and therefore it is not possible to form a 3-D image of a maneuvering target through the conventional ISAR. Recently, there are a few algorithms on the 3-D ISAR imaging [5], [6], [16]–[21]. The algorithms in [5], [6] are proposed for the near field turning table targets with the knowledge of the target motions through the measurements. The algorithms in [16]–[20] require the knowledge of the relative positions of the radar and target, and Manuscript received March 16, 2000; revised November 16, 2000. This work was supported in part by the 1998 Office of Naval Research (ONR) Young Investigator Program (YIP) under Grants N00014-98-1-0644 and N00014-0- 110059 and the Air Force Office of Scientific Research (AFOSR) under Grant F49620-00-1-0086. G. Wang and X.-G. Xia are with the Department of Electrical and Com- puter Engineering, University of Delaware, Newark, DE 19716 USA (e-mail: gwang@ee.udel.edu; xxia@ee.udel.edu). V. C. Chen is with the Radar Division, Naval Research Laboratory, Wash- ington, DC 20375 USA (e-mail: vchen@radar.nrl.navy.mil). Publisher Item Identifier S 1057-7149(01)01666-9. several different view angles and different heights of the air- craft. In [21, sec. 8.5, p. 596], multiple antenna ISAR imaging is proposed, where it is proposed that the motion parameters of a target are first estimated before the ISAR imaging. In this paper, we propose a new ISAR imaging system with three receiving antennas, where we propose a method to solve for the 3-D scatterer position information and therefore we are able to form 3-D ISAR images. The principle is as follows. Two receivers and one transmitter that is also a receiver, are located in the same plane orthogonal to the LOS as shown in Fig. 1. Using the three receivers, three conventional 2-D complex ISAR im- ages are obtained. All of them have the same range and the cross range resolutions but with different phases that contain the po- sition information of the scatterer. Using the phase information, the 3-D geometric positions of scatterer can be solved. If all the 3-D geometric positions of the scatterer are correctly solved, the 3-D ISAR image can be, of course, formed. However, in our system, there may be a few scatterer positions not correctly solved as we will see the reason later, which may affect the 3-D ISAR image quality. The method to resolve this issue is that, from the majority of the correctly detected scatterer locations, the scale of a 2-D ISAR image in the cross range direction in any image plane can be obtained, which allows us to form im- ages with different image planes (projections) of the three di- mensional target. From the image collection at different image plane orientations the actual 3-D information can be obtained. This paper is organized as follows. In Section II, received signals of the three receivers are described. In Section III, the 2-D and 3-D ISAR imaging algorithm of maneuvering targets is described. In Section IV, some simulation results are presented. II. RECEIVED SIGNALS FROM A THREE RECEIVER ISAR SYSTEM A three-receiver ISAR system is shown in Fig. 1. The coor- dinate system is defined as in Fig. 1, i.e., the location of the transmitter as well as the first receiver is chosen at the origin, the LOS is the axis , the second and the third receivers are lo- cated on the axis and axis with the coordinates and , respectively. Suppose that the radar transmits a linear frequency modulated (LFM) signal (2.1) where amplitude; carrier frequency; 1057–7149/01$10.00 © 2001 IEEE