5242
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 55, NO. 9, SEPTEMBER 2017
Ground Moving Target Imaging and Motion Parameter Estimation With Airborne Dual-Channel CSSAR Yongkang Li, Tong Wang, Baochang Liu, Lei Yang, Member, IEEE, and Guoan Bi, Senior Member, IEEE
Abstract— This paper deals with the issue of ground moving target imaging and motion parameter estimation with an airborne dual-channel circular stripmap synthetic aperture radar (CSSAR) system. Although several methods of ground moving target motion parameter estimation have been proposed for the conventional airborne linear stripmap SAR, they cannot be applied to airborne CSSAR because the range history of a ground moving target for airborne CSSAR is different than that for airborne linear stripmap SAR. In this paper, the moving target’s range history for airborne dual-channel CSSAR and the target signal model after the displaced phase center antenna processing are derived, and a new ground moving target imaging and motion parameter estimation algorithm is developed. In this algorithm, the estimation of baseband Doppler centroid and its compensation are first performed. Then focusing is implemented in the 2-D frequency domain via phase multiplication, and the target is focused in the SAR image without azimuth displacement due to the compensation of the Doppler shift caused by its motion. Finally, the target’s motion parameters are estimated with its Doppler parameters and its position in the SAR image. Numerical simulations are conducted to validate the derived range history and the performance of the proposed algorithm. Index Terms— Airborne circular stripmap synthetic aperture radar (CSSAR), ground moving target imaging, ground moving target indication (GMTI), motion parameter estimation.
I. I NTRODUCTION A. Background of Airborne Circular SAR
A
S A modern sensor being capable of providing highresolution observation under various environment conditions, synthetic aperture radar (SAR) has proven to be of great value in many civilian and military applications [1], [2].
Manuscript received May 17, 2016; revised February 14, 2017; accepted April 5, 2017. Date of publication June 8, 2017; date of current version August 25, 2017. This work was supported in part by the Fundamental Research Funds for the Central Universities under Grant 3102017OQD061, in part by the National Natural Science Foundation of China under Grant 61372133, Grant 41606201, and Grant 61601470, and in part by the Natural Science Foundation of Tianjin under Grant 20162898. (Corresponding author: Yongkang Li.) Y. Li is with the School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, China (e-mail:
[email protected]). T. Wang is with the National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China (e-mail:
[email protected]). B. Liu is with the School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China. L. Yang is with the Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300, China. G. Bi is with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2017.2704086
One of the typical SAR applications is air-to-ground surveillance and reconnaissance, which includes land and maritime traffic monitoring and military surveillance [3]–[10]. Conventional airborne SAR systems, which normally travel along a straight line, have been widely investigated for many years. In recent years, considerable attention has been paid to airborne circular path SAR [11]–[22] whose platform flies along a circular path. Generally, there are two acquisition modes of circular path SAR: the spotlight mode and the stripmap mode [17]. For the spotlight mode circular SAR [11]–[17], the antenna is side-looking and points inward from its circular path. The spotlight mode circular SAR is capable of collecting data of a spotlighted target region over 360° thanks to its circular trajectory and electronic beam steering. Due to the 360° aperture, the spotlight mode circular SAR can achieve multiangular observation of a target, super-resolution imaging, and 3-D imaging. Moreover, it can also be used for ground moving target tracking and trajectory reconstruction thanks to its long synthetic aperture time [14]–[16]. However, the illuminated area of the spotlight mode circular SAR is small. Usually, the radius of the illuminated area is about several hundreds of meters [19]. Thus, the spotlight mode circular SAR may not be suitable for wide-area surveillance and reconnaissance. For the stripmap mode circular SAR [17]–[22], the antenna is also side-looking but points outward from its circular path, and the antenna pointing direction is held constant as the radar platform moves. The illuminated area of the stripmap mode circular SAR is annular, as shown in Fig. 1. To our knowledge, the stripmap mode airborne circular SAR was first introduced in [18], where it was mounted on an unmanned aerial vehicle for imaging a wide area within a short time period. The stripmap mode airborne circular SAR, which is called circular stripmap SAR (CSSAR) in this paper, has the advantages of short revisit time and large coverage. The revisit time can be as short as several minutes. Since the antenna points outward from the circular path, the illustrated area of airborne CSSAR can be much larger than that of the spotlight mode airborne circular SAR.1 These advantages make airborne CSSAR suitable for wide-area surveillance and reconnaissance.
1 Note that the cost brought by the outward antenna pointing is that airborne CSSAR cannot observe targets located inside its path.
0196-2892 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
LI et al.: GROUND MOVING TARGET IMAGING AND MOTION PARAMETER ESTIMATION
Fig. 1.
Airborne CSSAR acquisition geometry.
B. Motivations and Objectives of This Paper Air-to-ground surveillance and reconnaissance with SAR systems usually involves ground moving target indication (GMTI) for both civilian and military applications. From a civilian viewpoint, SAR–GMTI systems offer great potential for traffic monitoring, which is of great importance in designing transportation infrastructures and increasing transportation safety and efficiency [23], [24]. From a military viewpoint, SAR–GMTI systems can be used to monitor military activities and improve existing operational capabilities [25]. As is known, short revisit time and large coverage are desirable for SAR–GMTI systems. However, traditional airborne linear stripmap SAR suffers from long revisit time, while the spotlight mode circular SAR suffers from limited observation area. In contrast, the airborne CSSAR is able to avoid these problems and becomes very attractive for GMTI applications. Therefore, it is necessary to investigate various issues of GMTI based on airborne CSSAR. Several stationary scene imaging algorithms have been reported for airborne single-channel CSSAR [17]–[20]. Li and Wang [20], [21] investigated ground moving targets’ range histories and ground moving target imaging for airborne single-channel CSSAR. In [22], an autofocus-based movingtarget detection algorithm was proposed for airborne CSSAR. However, none of the published literature studies the issue of ground moving target motion parameter estimation with airborne CSSAR. Although several ground moving target motion parameter estimation methods have been proposed for airborne linear stripmap SAR systems [3]–[5], they cannot be applied to airborne CSSAR because the range history of a ground moving target for airborne CSSAR is different than that for airborne linear stripmap SAR. The main objective of this paper is to propose a ground moving target imaging and motion parameter estimation
Ri (ta ) =
5243
algorithm for airborne dual-channel CSSAR. Based on the ground moving target’s range history for airborne singlechannel CSSAR [20], we also further derive the target’s range history for airborne dual-channel CSSAR and its signal model after the displaced phase center antenna (DPCA) operation. Moreover, numerical simulations are conducted to validate the derived range history and the proposed algorithm. This paper is organized as follows. In Section II, the moving target’s range history for airborne dual-channel CSSAR is derived. In Section III, the target signal model after the DPCA processing is presented. In Section IV, the proposed algorithm is described in detail. The performance of the proposed algorithm is validated in Section V by numerical results. Finally, the conclusion is made in Section VI. Note that in this paper, the targets are assumed to be isotropic point-like targets and to move with constant velocities (in Appendix D, the influences of accelerations on the proposed algorithm are briefly discussed). Moreover, the motion errors of the radar platform are assumed to have been compensated. II. S IGNAL M ODEL The geometry of an airborne dual-channel CSSAR with a point-like ground moving target is shown in Fig. 1. The aircraft flies along a circular path of radius ra with constant angle velocity ω. The radar at a fixed altitude h is side-looking with a pointing angle orthogonal to the flight velocity vector. The target is assumed to move with constant velocities v x and v y along the x- and y-axes, respectively. At ta = 0, where ta is the slow time, the target is assumed to be located at position (r0 cos θ0 , r0 sin θ0 , 0), where r0 is the initial distance of the target with respect to the coordinate origin, and θ0 is the target’s azimuth angle. The coordinates of the effective phase centers of channel 1 (the reference channel) and channel 2 at ta = 0 are (ra , 0, h) and (ra , −d, h), respectively, where d is the separation between adjacent effective phase centers. The instantaneous range of the target with respect to the effective phase center of the i th (i = 1, 2) channel can be expressed as (1), as shown at the bottom of the page. Applying a second-order Taylor series expansion to (1) around the time tb when the effective phase center of the reference channel is broadside to the target, we obtain Ri (ta ) ≈ (ra − rb )2 + h 2 (i − 1)d + v tr + (v ta − rb ω) (ta − tb ) (ra − rb )2 + h 2 +
v t2 − 2v ta ra ω + ra rb ω2 − v tr2 (ta − tb )2 2 (ra − rb )2 + h 2
where vt =
v x2 + v 2y
(2)
(3)
(r0 cos θ0 + v x ta − ra cos(ωta ) − (i − 1)d sin(ωta ))2 + (r0 sin θ0 + v y ta − ra sin(ωta ) + (i − 1)d cos(ωta ))2 + h 2 (1)
5244
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 55, NO. 9, SEPTEMBER 2017
is the speed of the target, rb is the range from the coordinate origin to the target at ta = tb , v tr is the projection of the target velocity onto the radial direction at ta = tb , and v ta is the projection of the target velocity onto the direction of the radar platform velocity at ta = tb . The derivation and validation of (2) are given in Appendix A, and the expressions for rb , v tr , and v ta are given in (A7a)–(A7c). As can be seen from (1)–(3) and (A7a)–(A7c), due to the circular path of the radar platform, the target’s range history for airborne CSSAR is different than that for airborne linear stripmap SAR (see [4, eq. (4)]), which makes the issue of ground moving target imaging and motion parameter estimation for airborne CSSAR more challenging. After demodulation to the baseband and range compression, the received target signal of the i th channel can be modeled as [26], [27] 2Ri (ta ) Ri (ta ) si (tr , ta ) = pr tr − wa,i (ta ) exp − j 4π c λ (4) where pr (·) is the range impulse response envelope, tr is the fast time, c is the speed of light, wa,i (·) is the two-way antenna pattern of the i th channel, and λ is the wavelength. The constant amplitude term in the signal has been omitted for simplicity of presentation. III. M OVING TARGET S IGNAL A FTER DPCA In this paper, it is assumed that the moving target signal is extracted after applying the DPCA technique [5] to implement clutter cancellation and target detection. The objective of this section is to derive the target signal model after the DPCA processing in the raw data domain. After calibration and co-registration [28] with respect to channel 1, i.e., the reference channel, the signal of channel 2 can be expressed as 2R2,reg (ta ) wa,1 (ta ) s2,reg (tr , ta ) = pr tr − c R2,reg (ta ) × exp − j 4π (5) λ where
d R2,reg (ta ) = R2 ta + ra ω d (6) ≈ R1 (ta ) + v tr ra ω is the co-registered range equation of channel 2. The derivation and validation of (6) are given in Appendix B. Given that the difference between R2,reg (ta ) and R1 (ta ), i.e., v tr d/(ra ω), is much smaller than one half of the range resolution, the DPCA signal can be expressed as sDPCA (tr , ta ) = s1 (tr , ta ) − s2,reg (tr , ta ) 2R1 (ta ) 4π R1 (ta ) ≈ pr tr − wa,1 (ta ) exp − j c λ 4π d · v tr × 1 − exp − j . (7) λ ra ω
Transforming (7) into the range frequency domain, we obtain R1 (ta ) sDPCA ( fr , ta ) ≈ Wr ( fr )wa,1 (ta ) exp − j 4π( f c + f r ) c (8) where fr is the range frequency, f c is the carrier frequency, and Wr (·) is the range frequency window function. Note that the amplitude of the DPCA signal is assumed to be nonzero and the constant terms are not shown in (8) for simplicity of presentation. IV. A LGORITHM D ESCRIPTION Several ground moving target motion parameter estimation algorithms (e.g., the algorithms presented in [3]–[5]) have been proposed for airborne linear stripmap SAR, and they are based on the target’s range history. Because the range history of the target for airborne CSSAR is different from that for airborne linear stripmap SAR, these algorithms cannot be applied to airborne CSSAR. In this section, we will propose a novel algorithm of ground moving target imaging and motion parameter estimation for airborne dual-channel CSSAR based on the target’s range history and signal model derived in Sections II and III. A. Baseband Doppler Centroid Estimation and Compensation It is known that the target’s motion may induce a Doppler centroid shift which results in azimuth displacement of the target in the SAR image, when it is not compensated by the matched filter. This displacement is a key issue that should be addressed by SAR–GMTI processors [29]. To avoid azimuth displacement and to estimate the target’s motion parameters, we first estimate and compensate the baseband Doppler centroid of the target before azimuth focusing. Many methods have been proposed for estimating the baseband Doppler centroid. A widely used method is the one reported in [30], which is based on measuring the phase of the average cross-correlation coefficient (ACCC) between adjacent azimuth samples in the range time domain. However, this method cannot be directly applied to the moving target because the target’s range cell migration has not been corrected. In this paper, we make a minor modification to this method: we measuring the ACCC in the range frequency domain to avoid the influence of the range cell migration. To derive the signal model after the baseband Doppler centroid compensation, we rewrite R1 (ta ) as R1 (ta ) = Rb − with
λ f ac λK a (ta − tb ) + (ta − tb )2 2 4
(9)
(ra − rb )2 + h 2 (10a) 2 f ac = − v tr (10b) λ 2 2 2 4 v − 2v ta ra ω + ra rb ω − v tr Ka = · t (10c) λ 2Rb where K a and fac are the target’s Doppler frequency chirp rate and absolute Doppler centroid, respectively. Moreover, f ac can Rb =
LI et al.: GROUND MOVING TARGET IMAGING AND MOTION PARAMETER ESTIMATION
be further expressed as f ac = f ac,b + M · PRF, where f ac,b is the baseband Doppler centroid, M is the Doppler ambiguity number, and PRF is the pulse repetition frequency. Note that, since the antenna is assumed to point orthogonally to the flight velocity vector of the radar platform, the Doppler centroid caused by the acquisition geometry is zero. Thus the target’s Doppler centroid depends only on its motion. Assuming that the estimated baseband Doppler centroid is fˆac,b , the following compensation function can be deduced from (8) and (9):
fˆac,b ( fc + fr ) ta . (11) H1( fr ) = exp − j 2π fc According to (8), (9), and (11), the signal after the baseband Doppler centroid compensation can be expressed as S( fr , ta ) = Wr ( fr )wa,1 (ta )
f c + fr λ fac λM · PRF tb − ta × exp − j 4π Rb + c 2 2 f c + fr × exp − j π K a (ta − tb )2 . (12) fc B. Imaging and Doppler Parameters Estimation By using the principle of stationary phase [26], the signal modeled by (12) can be transformed into the 2-D frequency domain S( fr , fa )
2 f ac,b Rb + tb ≈ Wr ( fr )Wa ( f a ) exp − j 2π( f c + fr ) c fc × exp{− j 2πtb ( f a + M · PRF)} f c + fr M 2 PRF2 × exp j π fc Ka M · PRF × exp − j 2π ( f a + M · PRF) Ka f c ( f a + M · PRF)2 × exp j π (13) K a ( f c + fr )
where f a is the azimuth frequency and Wa (·) is the azimuth frequency window function. From (13), it can be seen that the target can be focused by removing the last three exponential terms with the following reference function: H2( fr , fa ; K a , M) f c + fr M 2 PRF2 = exp − j π fc Ka M · PRF × exp j 2π ( f a + M · PRF) Ka f c ( f a + M · PRF)2 × exp − j π . K a ( f c + fr )
(14)
Multiplying (14) with (13) and then performing the 2-D inverse Fourier transform, one can obtain the target signal in
5245
the SAR image domain 2 f ac,b Rb + tb pa (ta − tb ) s(tr , ta ) = pr tr − c f c 2Rb × exp − j 2π (15) + f ac,b tb λ where pa (ta ) is the azimuth impulse response function. From (15), it can be seen that the focused target is located at coordinates (2Rb / f c , tb ) in the SAR image, i.e., there is no azimuth displacement. However, there is still a range displacement related to f ac,b and tb . This range displacement is caused by the baseband Doppler centroid compensation (there is a linear term of fr in the compensation function). It should be noted that the reference function of (14) is dependent on the target’s Doppler ambiguity number and Doppler chirp rate, which are usually unknown in practice and should be estimated. Here, we estimate M and K a by maximizing the image contrast ( Kˆ a , Mˆ ) = arg max{Contrast[s(tr , ta ; ka , m)]} ka ,m
(16)
where Contrast[s(tr , ta ; ka , m)] E{[|s(tr , ta ; ka , m)|2 − E(|s(tr , ta ; ka , m)|2 )]2 } = E{|s(tr , ta ; ka , m)|2 } (17a) s(tr , ta ; ka , m) = IDFT2 {S( fr , fa ) · H2 ( fr , fa ; ka , m)}
(17b)
with IDFT2 denoting the 2-D inverse Fourier transform, E(·) denoting the spatial average operator, and contrast (·) denoting the image contrast [31].
C. Motion Parameter Estimation In [3]–[5], ground moving target motion parameter estimation methods were proposed for airborne linear stripmap SAR. These methods allow for the estimation of a target’s across-track velocity and along-track velocity from the target’s Doppler centroid and Doppler chirp rate, respectively. However, from (10a)–(10c) and (A7a)–(A7c), it can be seen that the target’s two motion parameters (i.e., v x and v y ) and two position parameters (i.e., rb and θb ) are all coupled in both the target’s Doppler centroid and Doppler chirp rate. Therefore, methods proposed in [3]–[5] cannot be applied to airborne CSSAR. In what follows, we will propose a new motion parameter estimation method for airborne dualchannel CSSAR, which utilizes not only the target’s Doppler parameters but also the target’s position information in the SAR image. Since the target is focused without azimuth displacement by the proposed algorithm, its position parameters at ta = tb can be easily estimated. Assuming that, in the focused image, the target’s location in azimuth and range are ta,img and tr,img , respectively. Then, according to (15), θb and Rb can
5246
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 55, NO. 9, SEPTEMBER 2017
TABLE I A IRBORNE CSSAR S YSTEM PARAMETERS FOR S IMULATION
TABLE II PARAMETERS OF THE S IMULATED M OVING TARGETS
Fig. 2.
Flowchart of the proposed algorithm.
be estimated by θˆb = ω · ta,img ˆac,b c f Rˆ b = ta,img . tr,img − 2 fc
(18a) (18b)
With the estimated Doppler parameters and the estimated position parameters (i.e., θˆb and Rˆ b ), according to (10a)–(10c) and (A7a)–(A7c), the target’s motion parameters, i.e., v x and v y , can be estimated following (19a) and (19b), as shown at the bottom of the page, with fˆac = Mˆ · PRF + fˆac,b rˆb = Rˆ b2 − h 2 + ra
(20a) (20b)
where fˆac and rˆb are the estimates of f ac and rb , respectively. The derivations for (19a) and (19b) are given in Appendix C. The main steps of the proposed algorithm are summarized in Fig. 2. The algorithm begins with the extracted target data in the raw data domain. For targets with large signalto-noise ratios (SNRs), we can utilize the algorithm proposed in [32] to implement target detection and extraction in the raw data domain after the DPCA clutter cancellation. For targets with low SNRs, however, target detection and extraction may need to be implemented in the SAR image domain, and a reverse focusing operation should be implemented to transform the extracted target data back into the raw data domain. In this case, we can apply the imaging algorithm proposed in [20] to the DPCA processed data to obtain the SAR image. Then the magnitude-based CFAR detector proposed in [33] can be used to detect moving targets, and the detected targets can be extracted via utilizing a window. Note that,
Fig. 3.
SAR image after clutter cancellation using DPCA.
the smearing of fast moving targets will affect the efficacy of magnitude-based detectors. Fortunately, the autofocus-based detectors [22] could be used to detect these targets. V. N UMERICAL R ESULTS In this section, numerical simulations are conducted to validate the proposed algorithm and to investigate the motion parameter estimation accuracy. In these simulations, the signals received by the airborne dual-channel CSSAR have been simulated. The stationary background clutter is assumed to be heterogeneous and the clutter model used in this paper are the same as that used in [22] (see [22, eq. (28)], and the texture parameter v is set to be 3.8). The coherence between the clutter
λ fˆac Rˆ b cos(θˆb ) − ra ω − ra2 ω2 − ra rˆb ω2 − λ2 fˆac2 h 2 /4(ˆrb − ra )2 + λ Kˆ a Rˆ b /2 sin(θˆb ) 2(ˆrb − ra ) ˆ λ fac Rˆ b sin(θˆb ) 2 h 2 /4(ˆ + ra ω − ra2 ω2 − ra rˆb ω2 − λ2 fˆac vˆ y = − rb − ra )2 + λ Kˆ a Rˆ b /2 cos(θˆb ) 2(ˆrb − ra )
vˆ x = −
(19a) (19b)
LI et al.: GROUND MOVING TARGET IMAGING AND MOTION PARAMETER ESTIMATION
Fig. 4.
Imaging results of Target 1. (a) Focused image. (b) Azimuth profile. (c) Range profile.
Fig. 5.
Imaging results of Target 2. (a) Focused image. (b) Azimuth profile. (c) Range profile.
Fig. 6.
Imaging results of Target 3. (a) Focused image. (b) Azimuth profile. (c) Range profile.
signals received by the two channels is set to be 0.97, and we use the way presented in [34] to generate the correlated dualchannel signals. The clutter-to-noise ratio is set to be 20 dB. The airborne dual-channel CSSAR system parameters for these simulations are given in Table I. In estimating the target’s Doppler ambiguity number and Doppler chirp rate, i.e., M and K a , by maximizing the image contrast, the search ranges of M and K a are set to be [−1, 1] and [563, 634], respectively. With these ranges of values for M and K a , the proposed algorithm can deal with targets with the values of both v x and v y ranging from −35 to 35 m/s. The search step size for K a is set to be 1 Hz/s, which can keep the impulse response width (IRW) broadening [26] within 2%.2 A. Parameter Estimation and Imaging In this section, simulations are conducted to validate the proposed algorithm. Six moving targets are simulated, and 2 According to [26], the IRW broadening will be less than 2% when the error of K a , which is defined as K a , meets the following inequality: |K a | ≤ 1/Ta2 , where Ta is the synthetic aperture time.
5247
their parameters are given in Table II. The SNR is set to be 30 dB. Fig. 3 shows the SAR image after the DPCA processing. It is seen that these targets are clearly visible over the residual background. We manually detect these targets in the SAR image domain and the size of the window used to extract these targets is set to be 55 pixels (azimuth) × 15 pixels (range). The baseband Doppler centroid estimation results are shown in Table III, from which we can see that the targets’ baseband Doppler centroids are well estimated with absolute errors less than 3.3 Hz. In Table IV, the motion parameter estimation results are presented. It is seen that the target’s motion parameters are well estimated by the proposed algorithm, with absolute errors smaller than 0.4 m/s. Figs. 4–6 show the imaging results of three of the six targets (Target 1, Target 2, and Target 3). The measured image quality parameters [26] of the six targets are summarized in Table V, including the IRW broadening, the integrated sidelobe ratio (ISLR), the left peak SLR (PSLR L ), and the right PLSR (PSLR R ). The PSLR L is defined as the ratio between the height of the largest sidelobe on the left side and
5248
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 55, NO. 9, SEPTEMBER 2017
TABLE III
TABLE VI
BASEBAND D OPPLER C ENTROID E STIMATION R ESULTS
M EASURED RMS E RRORS
TABLE IV M OTION PARAMETER E STIMATION R ESULTS
TABLE V M EASURED I MAGE Q UALITY PARAMETERS
that of the main lobe, and the PSLR R is defined as the ratio between the height of the largest sidelobe on the right side and that of the main lobe [35]. From Figs. 4–6 and Table V, we can see that the targets are well focused by the proposed algorithm. Moreover, it can also be seen that all the IRW broadenings in azimuth are less than 2%, and the IRW broadenings in range are all equal to zero. B. Motion Parameter Estimation Accuracy Analysis In this section, the motion parameter estimation accuracy is further investigated via 1000 Monte Carlo trials that are performed under different SNR conditions. The root-meansquare (rms) errors [36] of vˆ x and vˆ y , denoted σv x and σv y , respectively, are measured to indicate the estimation accuracy. The measured rms errors are given in Table VI, from which we can see that the motion parameter estimation accuracy
increases with SNR. It can also be seen that all the rms errors of vˆ x and vˆ y are less than 0.4 and 0.9 m/s, respectively. From Table VI, it is seen that the rms errors are of almost the same for SNRs larger than 25 dB. This could be explained as follows. The estimation accuracy of f ac and K a are mainly determined by the SNR and the search step sizes of K a , respectively. Since the azimuth angles of the six targets are very close to zero and the coefficient of the quadratic term of fˆac under the square root in (19b) is also very close to zero, the rms error of vˆ y is mainly determined by the estimation error of K a . Therefore, σv y are almost the same for SNRs larger than 25 dB because the search step sizes of K a used in different SNR conditions are identical. VI. C ONCLUSION In this paper, the target’s range history for airborne dualchannel CSSAR and the target signal model after the DPCA processing is first derived, and then a ground moving target imaging and motion parameter estimation algorithm is proposed. The proposed algorithm is based on the derived range history and signal model. The moving target imaging is efficiently implemented in the 2-D frequency domain and the target is focused without azimuth displacement thanks to the compensation of the Doppler shift caused by its motion. In estimating the target’s motion parameters, besides the target’s Doppler parameters, the target’s position in the SAR image are also used. The imaging and motion parameter estimation capabilities of the proposed algorithm have been tested and demonstrated by numerical results.
LI et al.: GROUND MOVING TARGET IMAGING AND MOTION PARAMETER ESTIMATION
5249
(v x − (i − 1)d · ω)2 + (v y − ra ω)2 − ra2 + (i − 1)2 d 2 ω2 + ra r0 ω2 2Ri (0) 2 (i−1)d 0 (v x − (i − 1)d · ω) rRai−r − (v − r ω) y a (0) Ri (0) − 2Ri (0) 2 ra −r0 √ vx (r0 −ra )2 +h 2 v 2 + (v y − ra ω)2 − ra2 ω2 + ra r0 ω2 ≈ x − 2 (r0 − ra )2 + h 2 2 (r0 − ra )2 + h 2 2 2 2 v − 2v y ra ω + ra r0 ω − v tr = t 2 (r0 − ra )2 + h 2
R¨ i (0) =
(A4)
The proposed algorithm is based on the assumption that targets move with constant velocities. Appendix D briefly investigates the influences of targets’ accelerations on the proposed algorithm using a combination of theory and simulations. It is shown that the proposed imaging method may still work when targets exhibit moderate accelerations. However, the accelerations may significantly bias the estimates of v x and v y . Note that, since the synthetic aperture time of airborne CSSAR is relatively short (0.9 s in this paper), it is possible that targets travel at a constant velocity during the illumination time.
The expression of R¨ i (0) can be expressed (A4), as shown at the top of the page. The approximation in (A4) is due to the fact that the terms containing d are ignored. Therefore, (A1) can be rewritten as Ri (ta ) ≈ (r0 − ra )2 + h 2 (i − 1)d + v tr + (v y − r0 ω) ta t (r0 − ra )2 + h 2
A PPENDIX
(A5) is derived using the assumption that θ0 is equal to zero. Define v ta as the projection of the target velocity onto the direction of the radar platform velocity at ta = tb , and rb the range from the coordinate origin to the target at ta = tb , then (A5) can be easily generalized to the cases with arbitrary θ0 by replacing v y and r0 with v ta and rb , respectively Ri (ta ) ≈ (rb − ra )2 + h 2 (i − 1)d + v tr + (v ta − rb ω) (ta − tb ) (rb − ra )2 + h 2
A. Derivation of (2) In this Appendix, the derivation and validation of (2) are presented. To avoid tedious mathematics, we first assume θ0 to be zero in the following derivation. In this case, tb = 0 by definition, and the second-order Taylor series expansion of (1) around tb can be expressed as Ri (ta ) ≈ Ri (tb ) + R˙ i (tb )(ta − tb ) + R¨ i (tb )(ta − tb )2 = Ri (0) + R˙ i (0)ta + R¨ i (0)ta2 (A1) where R˙ i (ta ) and R¨ i (ta ) are the first-order and second-order derivatives of Ri (ta ), respectively. The expression of Ri (0) can be easily obtained by definition Ri (0) = (r0 − ra )2 + (i − 1)2 d 2 + h 2 ≈ (r0 − ra )2 + h 2 (A2) where (i − 1)2 d 2 has been dropped given that d 2 (r0 − ra )2 + h 2 . The expression of R˙ i (0) is derived as follows: (v x − (i − 1)d · ω)(r0 − ra ) + (i − 1)d(v y − ra ω) R˙ i (0) = Ri (0) (i − 1)d r0 −ra vx + (v y −r0 ω) ≈ 2 2 (r0 − ra ) + h (r0 − ra )2 + h 2 (i − 1)d = v tr + (v y − r0 ω) (A3) (r0 − ra )2 + h 2 where v tr = v x (r0 − ra )/((r0 − ra )2 + h 2 )1/2 is the projection of the target velocity onto the radial direction at ta = tb (note that, in this case, tb = 0).
+
+
v t2 − 2v y ra ω + ra r0 ω2 − v tr2 2 ta . 2 (r0 − ra )2 + h 2
v t2 − 2v ta ra ω + ra rb ω2 − v tr2 (ta − tb )2 . 2 2 2 (rb − ra ) + h
(A5)
(A6)
Note that, the parameters rb , v tr , and v ta are defined at the slow time ta = tb . In the cases of arbitrary θ0 , their expressions are as follows: (A7a) rb = (r0 cos θ0 + v x tb )2 + (r0 sin θ0 + v y tb )2 rb − ra v tr = (v x cos(θb ) + v y sin(θb )) (A7b) (rb − ra )2 + h 2 v ta = v y cos(θb ) − v x sin(θb ) (A7c) where θb = ω · tb is the target’s azimuth angle at ta = tb . Note that, the value of tb can be obtained by numerically solving the following equation: r0 sin θ0 + v y tb ω · tb = atan . (A8) r0 cos θ0 + v x tb Since several approximations are made in the derivation of (A6), simulations are performed to validate (A6). The CSSAR system parameters for the simulation are given in Table I. The position of the target at ta = 0 is assumed to be r0 = 19.821 km and θ0 = 0.03 rad.
5250
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 55, NO. 9, SEPTEMBER 2017
Fig. 7. Relationships between the errors of (A6) and the target’s motion parameters. (a) First channel. (b) Second channel. Color coding is used to indicate the value of the error (the unit is meter).
Fig. 8. Relationships between the error of (B3) and the target’s motion parameters. Color coding is used to indicate the value of the error (the unit is meter).
In Fig. 7, the relationships between the errors of (A6) and the motion parameters (i.e., v x and v y ) are shown.3 From Fig. 7 we can see that the errors are much smaller than λ/16 (0.0019 m) and thus can be neglected [37].
During the target synthetic aperture time, (ta ) is smaller than λ/16 and thus can be neglected [33]. Therefore, R2 (ta + d/(ra ω)) can be expressed as d d . (B3) R2 ta + ≈ R1 (ta ) + v tr · ra ω ra ω
B. Derivation of (6)
Similar to what we have done in Appendix A, simulations are conducted here to validate (B3), and the result is shown in Fig. 8. It is seen that the error of (B3) is much less than λ/16 and thus can be neglected [33]. Note that, the parameters that are used to obtain Fig. 8 are the same as those used in Appendix A.
In this Appendix, the derivation and validation of (6) are presented. According to (2) and (A6), the expression of R2 (ta + d/(ra ω)) can be written as d R2 ta + ra ω = (rb − ra )2 + h 2 d d − tb + v tr + (v ta − rb ω) ta + ra ω (rb − ra )2 + h 2 2 d v t2 − 2v ta ra ω + ra rb ω2 − v tr2 − tb + ta + ra ω 2 (rb − ra )2 + h 2 = (rb − ra )2 + h 2 + v tr (ta − tb ) v 2 − 2v ta ra ω + ra rb ω2 − v tr2 d + t (ta − tb )2 + v tr · 2 2 ra ω 2 (rb − ra ) + h d(v ta − rb ω) d − tb + ta + ra ω (rb − ra )2 + h 2 2 v t2 − 2v ta ra ω + ra rb ω2 − v tr2 d d + 2(ta −tb ) + ra ω ra ω 2 (rb − ra )2 + h 2 = R1 (ta ) + v tr · with
d + (ta ) ra ω
d(v ta − rb ω) d (ta ) = − tb ta + ra ω (rb − ra )2 + h 2 2 2 v − 2v ta ra ω + ra rb ω − v tr2 + t 2 (rb − ra )2 + h 2 d 2 d + × 2(ta − tb ) . ra ω ra ω
(B1)
C. Derivation of (19a) and (19b) Let us first derive the expressions of v ta and v tr , respectively. The expression of v tr can be directly obtained from (10b) λ f ac . (C1) 2 To obtain the expression of v ta , we rewrite (10c) into v tr = −
4 ra rb ω2 − 2v ta ra ω + v t2 − v tr2 · λ 2Rb ⎛ ⎞ 2 2 2 + Rb v tr v ta 4 ⎝ ra rb ω2 − 2ra ω · v ta v tr2 ⎠ (rb −ra )2 = · + − λ 2Rb 2Rb 2Rb 4 ra rb ω2 − 2ra ω · v ta v2 h2 2 = · + ta + v λ 2Rb 2Rb 2Rb (rb − ra )2 tr (C2)
Ka =
2 + R 2 v 2 /(r − r )2 is used. where v t2 = v ta b a b tr Solving (C2) for v ta , one can obtain v ta = ra ω ± ra2 ω2 −ra rb ω2 −v tr2 h 2 /(rb −ra )2 +λ · K a Rb /2.
(C3) Given that, for a common ground moving target, its speed is usually smaller than the speed of the aircraft (i.e., ra ω), the expression of v ta should be (B2)
3 The error is indicated by the maximum of the difference between the original range equation [i.e., (1)] and the Taylor-expanded range equation [i.e., (A6)].
v ta
= ra ω − ra2 ω2 − ra rb ω2 − v tr2 h 2 /(rb − ra )2 + λ · K a Rb /2 = ra ω− ra2 ω2 −ra rb ω2 −λ2 fac2 h 2 /4(rb −ra )2 +λ· K a Rb /2. (C4)
LI et al.: GROUND MOVING TARGET IMAGING AND MOTION PARAMETER ESTIMATION
5251
(r0 cos θ0 + v x ta + 0.5ax ta2 − ra cos(ωta ) − (i − 1)d sin(ωta ))2 Ri,ac (ta ) = +(r0 sin θ0 + v y ta + 0.5a y ta2 − ra sin(ωta ) + (i − 1)d cos(ωta ))2 + h 2
Now, we derive the expressions for v x and v y . Combining (A7b) and (A7c), one can obtain Rb v tr cos(θb ) − v ta sin(θb ) rb − ra Rb vy = v tr sin(θb ) + v ta cos(θb ). rb − ra
vx =
(C5a) (C5b)
Substitute (C1) and (C4) into (C5a) and (C5b), one can obtain the expressions for v x and v y as follows:
(D1)
Similar to the derivation of (2), the second-order Taylor series expansion of (D1) can be expressed as Ri,ac (ta ) ≈ (ra − rb )2 + h 2 (i − 1)d + v tr + (v ta − rb ω) (ta − tb ) (ra − rb )2 + h 2 v t2 − 2v ta ra ω + ra rb ω2 + ar (rb − ra ) − v tr2 2 (ra − rb )2 + h 2 × (ta − tb )2 (D2) +
Rb λ vx = − cos(θb ) · f ac − sin(θb ) where ar = ax cos(θb ) + a y sin(θb ) is the acceleration comr − ra 2 ⎛b ⎞ ponent perpendicular to the velocity vector of the radar at λ2 f ac2 h 2 λ · K a Rb ⎠ ta = tb . · ⎝ra ω − ra2 ω2 − ra rb ω2 − + 2 Now, we investigate the accuracy of (D2) via simulation. 4(rb − ra ) 2 In conducting the simulation, both ax and a y are assumed to (C6a) range from −3.8 to 3.8 m/s2 , and both v and v are assumed x y Rb λ to range from −40 to 40 m/s, and other parameters are the sin(θb ) · f ac + cos(θb ) vy = − r − ra 2 ⎞ same as those used in Appendix A. The relationships between ⎛b the errors of (D2) and the accelerations are shown in Fig. 9. 2 f 2 h2 R λ λ · K a b ⎠ ac . From Fig. 9, we can see that the errors are smaller than λ/16 · ⎝ra ω − ra2 ω2 −ra rb ω2 − + 2 4(rb − ra ) 2 (0.0019 m) and thus can be neglected [37]. In other words, for (C6b) a target whose |ax | and |a y | are all less than 3.8 m/s2 , its range history still can be approximated by a second-order Taylor According to (C6a) and (C6b), one can obtain (19a) and series. Therefore, even in the case where targets have moderate (19b). accelerations, the proposed imaging method may still work. The influence of accelerations on the motion parameter estimation is briefly analyzed as follows. Similar to the derivation D. Influences of Accelerations on the Proposed Algorithm of (19a) and (19b), in the case where a target has accelerations, In this Appendix, the influences of the target’s accelerations the expressions for v x and v y are given in (D3a) and (D3b), as shown at the bottom of the page. on the proposed algorithm are briefly analyzed. From (D3a) and (D3b) it is seen that, in order to estimate v x Assuming that the target’s accelerations along the x- and and v y , ar (the acceleration component perpendicular to the y-axes are ax and a y , respectively. Then, the range history can velocity vector of the radar at ta = tb ) should be known. If we be expressed (D1), as shown at the top of the page.
vx = −
Rb λ cos(θb ) · f ac − sin(θb ) · ra ω − rb − ra 2
Rb λ sin(θb ) · f ac + cos(θb ) · ra ω − vy = − rb − ra 2
ra2 ω2 − ra rb ω2 − ar (rb − ra ) − λ2 f ac2 h 2 /4(rb − ra )2 + λ · K a Rb /2 (D3a) ra2 ω2 − ra rb ω2 − ar (rb − ra ) − λ2 f ac2 h 2 /4(rb − ra )2 + λ · K a Rb /2 (D3b)
v x = sin(θb ) · ra2 ω2 −ra rb ω2 −ar (rb −ra )−λ2 f ac2 h 2 /4(rb −ra )2 +λ · K a Rb /2− ra2 ω2 −ra rb ω2 −λ2 f ac2 h 2 /4(rb −ra )2 +λ· K a Rb /2 (D4a) v y = cos(θb ) 2 h 2 /4(r −r )2 +λ · K R /2− r 2 ω2 −r r ω2 − a (r −r )−λ2 f 2 h 2 /4(r −r )2 +λ· K R /2 · ra2 ω2 −ra rb ω2 −λ2 f ac b a a b a b r b a b a a b a ac (D4b)
5252
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 55, NO. 9, SEPTEMBER 2017
Fig. 9. Relationships between the errors of (D2) and the target’s accelerations. (a) First channel. (b) Second channel. Color coding is used to indicate the value of the error (the unit is meter).
Fig. 10. Relationships between the estimation biases and the accelerations. (a) Bias in the estimate of v x . (b) Bias in the estimate of v y . Color coding is used to indicate the value of the bias (the unit is m/s).
assume that the accelerating target travel at a constant velocity and use the method proposed in Section IV-C to estimate its v x and v y , then the estimation biases caused by the accelerations are given in (D4a) and (D4b), as shown at the bottom of the previous page, where v x and v y are the estimation biases of v x and v y , respectively. Now, by using numerical simulations, we investigate the estimation biases caused by the accelerations. In the simulations, it is assumed that v x = 15 m/s, v y = 13 m/s, ax ∈ [−0.5 m/s2 , 0.5 m/s2 ], a y ∈ [−0.5 m/s2 , 0.5 m/s2 ], θ0 = 0.1 rad, and other parameters are the same as those used in Appendix A. Fig. 10 shows the relationships between the estimation biases and the accelerations. From Fig. 10, it can be seen that the accelerations introduce significant biases in the estimates of v x and v y . ACKNOWLEDGMENT The authors would like to thank the Associate Editor and the reviewers for their valuable comments that were crucial in improving the quality of this paper. R EFERENCES [1] M. V. Dragosevic, W. Burwash, and S. Chiu, “Detection and estimation with RADARSAT-2 moving-object detection experiment modes,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 9, pp. 3527–3543, Sep. 2012. [2] L. Yang, G. Bi, M. Xing, and L. Zhang, “Airborne SAR moving target signatures and imagery based on LVD,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 11, pp. 5958–5971, Nov. 2015. [3] S. Chiu, “Application of fractional Fourier transform to moving target indication via along-track interferometry,” EURASIP J. Adv. Signal Process., vol. 2005, no. 20, pp. 3293–3303, 2005. [4] C. H. Gierull, “Ground moving target parameter estimation for twochannel SAR,” IEE Proc.-Radar Sonar Navigat., vol. 153, no. 3, pp. 224–233, Jun. 2006.
[5] J. J. Sharma, C. H. Gierull, and M. J. Collins, “The influence of target acceleration on velocity estimation in dual-channel SAR-GMTI,” IEEE Trans. Geosci. Remote Sens., vol. 44, no. 1, pp. 134–147, Jan. 2006. [6] M. D. Henschel, M. V. Dragosevic, and C. E. Livingstone, “Characterization of vessel heave and horizontal velocities with airborne SAR,” in Proc. IEEE Radar Conf., Boston, MA, USA, Apr. 2007, pp. 794–799. [7] M. V. Dragosevic, M. D. Henschel, and C. E. Livingstone, “An adaptive technique for estimating ship motion in SAR data,” in Proc. EuRAD, Munich, Germany, Oct. 2007, pp. 95–98. [8] D. Zhu, Y. Li, and Z. Zhu, “A keystone transform without interpolation for SAR ground moving-target imaging,” IEEE Geosci. Remote Sens. Lett., vol. 4, no. 1, pp. 18–22, Jan. 2007. [9] L. Yang, L. Zhao, G. Bi, and L. Zhang, “SAR ground moving target imaging algorithm based on parametric and dynamic sparse Bayesian learning,” IEEE Trans. Geosci. Remote Sens., vol. 54, no. 4, pp. 2254–2267, Apr. 2016. [10] X. Zhang, G. Liao, S. Zhu, C. Zeng, and Y. Shu, “Geometry-informationaided efficient radial velocity estimation for moving target imaging and location based on radon transform,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 2, pp. 1105–1117, Feb. 2015. [11] M. Soumekh, “Reconnaissance with slant plane circular SAR imaging,” IEEE Trans. Image Process., vol. 5, no. 8, pp. 1252–1265, Aug. 1996. [12] Y. Lin, W. Hong, W. Tan, and Y. Wu, “Extension of range migration algorithm to squint circular SAR imaging,” IEEE Geosci. Remote Sens. Lett., vol. 8, no. 4, pp. 651–655, Jul. 2011. [13] Z. Zhang, H. Lei, and Z. Lv, “Vehicle layover removal in circular SAR images via ROSL,” IEEE Geosci. Remote Sens. Lett., vol. 12, no. 12, pp. 2413–2417, Dec. 2015. [14] D. Henke, E. M. Dominguez, D. Small, M. E. Schaepman, and E. Meier, “Moving target tracking in single- and multichannel SAR,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 6, pp. 3146–3159, Jun. 2015. [15] D. Henke and E. Meier, “Tracking and refocusing of moving targets in multichannel SAR data,” in Proc. IGARSS, Milan, Italy, Jul. 2015, pp. 3735–3738. [16] J. B. Poisson, H. M. Oriot, and F. Tupin, “Ground moving target trajectory reconstruction in single-channel circular SAR,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 4, pp. 1976–1984, Oct. 2015. [17] Y. Liu, “Study of high-resolution SAR and new type SAR imaging,” Ph.D. dissertation, Dept. Elect. Eng., Xidian Univ., Xi’an, China, 2012. [18] B. Sun, Y. Zhou, J. Chen, and C. Li, “Operation mode of circular trace scanning SAR for wide observation,” J. Electron. Inf. Technol., vol. 30, no. 12, pp. 2805–2808, Dec. 2008. [19] Y. Liao, M. Xing, L. Zhang, and Z. Bao, “A novel modified OmegaK algorithm for circular trajectory scanning SAR imaging using series reversion,” EURASIP J. Adv. Signal Process., vol. 64, pp. 1–12, Dec. 2013. [20] Y. Li and T. Wang, “Efficient imaging algorithm for airborne CSSAR/GMTI systems,” Electron. Lett., vol. 50, no. 19, pp. 1390–1391, Sep. 2014. [21] Y. Li and T. Wang, “Ground moving target imaging algorithm for single channel airborne CSSAR,” Electron. Lett., vol. 50, no. 24, pp. 1872–1873, Nov. 2014. [22] Y. Li and T. Wang, “Detection of moving targets by refocusing for airborne CSSAR,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., vol. 9, no. 7, pp. 3026–3036, Jul. 2016. [23] D. Cerutti-Maori, I. Sikaneta, and C. H. Gierull, “Optimum SAR/GMTI processing and its application to the radar satellite RADARSAT-2 for traffic monitoring,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 10, pp. 3868–3881, Oct. 2012. [24] S. V. Baumgartner and G. Krieger, “Fast GMTI algorithm for traffic monitoring based on a priori knowledge,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 11, pp. 4626–4641, Nov. 2012. [25] B. Liu, K. Yin, Y. Li, F. Shen, and Z. Bao, “An improvement in multichannel SAR-GMTI detection in heterogeneous environments,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 2, pp. 810–827, Feb. 2015. [26] I. G. Cumming and F. H. Wong, Digital Processing of Synthetic Aperture Radar Data: Algorithm and Implementation. Norwood, MA, USA: Artech House, 2005. [27] J. Xu, Y. Zuo, B. Xia, X.-G. Xia, Y.-N. Peng, and Y.-L. Wang, “Ground moving target signal analysis in complex image domain for multichannel SAR,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 2, pp. 538–552, Feb. 2012. [28] J. H. G. Ender, “The airborne experimental multi-channel SAR system AER-II,” in Proc. EUSAR Conf., Konigswinter, Germany, 1996, pp. 49–52.
LI et al.: GROUND MOVING TARGET IMAGING AND MOTION PARAMETER ESTIMATION
[29] S. Zhang et al., “Robust clutter suppression and moving target imaging approach for multichannel in azimuth high-resolution and wide-swath synthetic aperture radar,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 2, pp. 687–709, Feb. 2015. [30] S. N. Madsen, “Estimating the Doppler centroid of SAR data,” IEEE Trans. Aerosp. Electron. Syst., vol. 25, no. 2, pp. 134–140, Mar. 1989. [31] F. Berizzi and G. Corsini, “Autofocusing of inverse synthetic aperture radar images using contrast optimization,” IEEE Trans. Aerosp. Electron. Syst., vol. 32, no. 3, pp. 1185–1191, Jul. 1996. [32] C. H. Gierull and I. C. Sikaneta, “Raw data based two-aperture SAR ground moving target indication,” in Proc. IGARSS, vol. 2. Toulouse, France, Jul. 2003, pp. 1032–1034. [33] C. H. Gierull, I. Sikaneta, and D. Cerutti-Maori, “Two-step detector for RADARSAT-2’s experimental GMTI mode,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 1, pp. 436–454, Jan. 2013. [34] B. Liu, Y. Li, T. Wang, F. Shen, and Z. Bao, “An analytical formula approximating the multilook interferometric-phase variance for InSAR,” IEEE Geosci. Remote Sens. Lett., vol. 11, no. 4, pp. 878–882, Apr. 2014. [35] Y. Li, T. Wang, B. Liu, and R. Hui, “High-resolution SAR imaging of ground moving targets based on the equivalent range equation,” IEEE Geosci. Remote Sens. Lett., vol. 12, no. 2, pp. 324–328, Feb. 2015. [36] B. Liu, T. Wang, Y. Li, F. Shen, and Z. Bao, “Effects of Doppler aliasing on baseline estimation in multichannel SAR-GMTI and solutions to address these effects,” IEEE Trans. Geosci. Remote Sens., vol. 52, no. 10, pp. 6471–6487, Oct. 2014. [37] W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Synthetic Aperture Radar: Signal Processing Algorithms. New York, NY, USA: Artech House, 1995. Yongkang Li was born in Hunan, China, in 1988. He received the B.Eng. degree in electronic information engineering and the Ph.D. degree in signal and information processing from Xidian University, Xi’an, China, in 2011 and 2016, respectively. From 2015 to 2016, he was a Visiting Ph.D. Student with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. Since 2015, he has been an Assistant Professor with the School of Electronics and Information, Northwestern Polytechnical University, Xi’an. His research interests include synthetic aperture radar/ground moving target indication. Tong Wang was born in Xi’an, China, in 1974. He received the B.Eng. and Ph.D. degrees in signal processing from Xidian University, Xi’an, in 1996 and 2002, respectively. He is currently a Professor with the National Laboratory of Radar Signal Processing, Xidian University. His research interests include space-time adaptive processing and ground moving target indication.
5253
Baochang Liu was born in Shandong, China. He received the B.S. degree in electrical engineering from Liaocheng University, Liaocheng, China, in 2004, and the Ph.D. degree in signal processing from the National Laboratory of Radar Signal Processing, Xidian University, Xi’an, China, in 2010. He is currently a Lecturer with the School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing, China. His research interests include SAR signal processing and ocean microwave remote sensing.
Lei Yang (M’15) was born in Tianjin, China, in 1984. He received the B.S. degree in electronic engineering and the Ph.D. degree in signal and information processing from Xidian University, Xi’an, China, in 2007 and 2012, respectively. Since 2016, he has been with the Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin. His research interests include synthetic aperture radar moving target imaging and various signal processing methods for radar imaging.
Guoan Bi (SM’89) received the B.Sc. degree in radio communications from the Dalian University of Technology, Dalian, China, in 1982, and the M.Sc. degree in telecommunication systems and the Ph.D. degree in electronics systems from the University of Essex, Colchester, U.K., in 1985 and 1988, respectively. Since 1991, he has been with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. His research interests include digital signal processing algorithms and signal processing for various applications including sonar, radar, and communications.
