Interferometric Three-Dimensional Imaging for
Spinning Targets Based on Narrow-Band Radar
Chao Sun
School of Electronics and Information
Northwestern Polytechnical University
Xi'an, China
E-mail: sunchao13@126.com
Baoping Wang
Science and Technology on UAV Laboratory
Northwestern Polytechnical University
Xi'an, China
E-mail: wbpluo@sina.com
Yang Fang
School of Electronics and Information
Northwestern Polytechnical University
Xi'an, China
E-mail: fang_yang122@sina.cn
Abstract—In this paper, a novel interferometric 3-D imaging
algorithm for spinning targets is proposed based on narrow-band
radar. The height information of the scatterer is estimated by the
phase difference between the same scatterer in two 2-D images
generated by two antennas at closely-separated elevation angles
via narrow-band radar imaging algorithms. For imaging of
rapidly spinning targets, however, spurious peaks appear due to
azimuth sample deficiency. Furthermore, the compressed sensing
theory is applied into interferometric 3-D imaging based on joint
sparsity of two images. The simulation results have proved the
validity of the proposed algorithm.
Keywords—Narrow-band radar; spinning targets; three-
dimensional (3-D) imaging; compressed sensing
I. INTRODUCTION
For radar imaging of spinning targets, such as space debris,
flying missiles, airscrews of airplane, conventional imaging
approaches are invalid due to the violation of the rigid body
assumption. However, spinning targets detection and imaging
are essential to some special applications, such as missile
defense, spacecraft safety, targets classification and recognition,
etc. Recently, many investigators have devoted their work to
high-resolution radar imaging of spinning targets. In [1]-[3],
SRDI, SRMF-CLEAN, and SRIF imaging algorithms are
proposed for 2-D imaging of spinning targets via narrow-band
radar. Sample deficiency is usually inevitable in practice due
to low pulse repetition frequency (PRF) radar and the
existence of the shadowing effect, which will lead to generate
aliased images. Thus, the newly compressed sensing (CS)
theory [4]-[5] is applied into narrow-band radar imaging,
improving the imaging performance greatly [6]-[7].
3-D images are capable of providing a more reliable
description of target features and the identification of any given
specific scatterers on the targets. Therefore, in [8]-[10], 3-D
imaging algorithms are proposed for wide-band radars. In [8],
the GRT-CLEAN algorithm makes use of the sinusoidal
envelopes of the spinning scatterers in the range-slow time
domain and obtains an image via noncoherent accumlation.
Furthermore, the CLEAN technique is adopted in this
algorithm for sidelobe reduction. A matched-filter-bank-based
3-D imaging algorithm is proposed in [9], based on target
motion features. For a given matching parameter, a 2-D image
slice is generated. Then, a series of 2-D image slices are
obtained by changing the matching parameters of the matched
filter bank, and finally, the 3-D target image is obtained. At the
same time, a high-resolution 3-D imaging algorithm via the
back-projection transform is proposed in [10], which makes
use of both the sinusoidal envelope and phase information in
the range-slow-time domain. Since the image is obtained via
coherent accumulation, this algorithm is high in resolution and
robust to additive noise. Although these algorithms are capable
of providing high-resolution 3-D images and a more reliable
description of target features, these algorithms based on wide-
band radar are of high complexity and are difficult for real
implementation of 3-D imaging. Besides, sample deficiency
will lead to generate aliased images, influencing the target
identification.
In this paper, a novel interferometric 3-D imaging
algorithm for spinning targets is proposed based on narrow-
band radar. This algorithm requires a radar system equipped
with two receiving antennas. The echoes from the target are
simultaneously received by the two receivers and are processed
to obtain a pair of 2-D images, respectively, via narrow-band
radar imaging algorithms. The height information of the
scatterer is estimated by the phase difference between the same
scatterer in two 2-D images. Furthermore, by defining a joint
sparsity of image pairs, a CS algorithm is proposed to jointly
form CS images, which can generate 3-D imaging result using
limited measurements. At last, simulation results verify the
effectiveness of the proposed algorithm.
II. I
NTERFERMETRIC 3-D IMAGING FOR SPINNING TARGETS
BASED ON NARROW
-BAND RADAR
A. Signal model
The discussion in this paper are based on the following
assumptions. First, the translational motion of the spinning
target is compensated completely. Second, the spinning speed
is constant in the imaging interval. The geometry for
interferometric 3-D imaging system is shown in Fig. 1. The
two antennas
O and
are located separately along the
elevation direction, and the radar line of sight (LOS) is along
the
Y/ Y
′
axis. The target angular velocity is Ω , with R as its
spinning axis.
α
denotes the angle between R and the Y/ Y
′
axis. 2-D image is a projection of a 3-D target onto 2-D
imaging plane
XOY
′′′
. The angular velocity Ω is supposed to
This work was sponsored by the National Nature Science Foundation of
China (NSFC) under Grants 61472324 and 61073106.
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