Ground Moving Target Indication via Coprime Array MIMO 2-D-VSAR Joint EGO-DPCA Filter

Fig. 1.

Geometry of coprime array SAR.
(a) Configuration of coprime array SAR.
(b) Equivalent virtual arrays.
(c) Geometry of the coprime array VSAR.

GMTI via Coprime Array MIMO 2-D-VSAR Joint EGO-DPCA Filter

Summary

One of the limitations of the Lynx SAR/GMTI radar used on the General Atomics Aeronautical Systems (GA-ASI)  MQ-9 Reaper UAV is that SAR and GMTI were separate modes. This processing developed by researchers at Iran's K. N. Toosi University of Technology seems to get around this. Here is a summary of the key points from the abstract and introduction of this article on improved VSAR techniques for moving target detection in SAR:

Key points:

1. The paper proposes improvements to the velocity synthetic aperture radar (VSAR) algorithm for slow ground-moving target indication (GMTI) and parameter estimation.

2. It uses a coprime array configuration with smaller element spacing to improve unambiguous velocity estimation range, allowing detection of faster moving targets.

3. An improved coprime VSAR algorithm is proposed that uses azimuth time shift instead of two-step phase compensation to reduce computational burden.

4. An extended greatest of displacement phase center antenna (EGO-DPCA) filter is introduced to detect weak and slow-moving targets that are missed by basic coprime VSAR.

5. The algorithm is extended to 2D VSAR to estimate azimuth direction velocity of moving targets, which was neglected in conventional VSAR. This improves azimuth resolution of moving target imaging.

6. Processing is focused only on detected moving target pixels, significantly reducing complexity and computational burden compared to conventional methods.

7. The technique aims to address limitations of existing methods like STAP in terms of computational cost while improving detection and parameter estimation performance.

In essence, this paper proposes a more computationally efficient VSAR technique using coprime arrays and specialized filtering to detect and characterize a wider range of moving targets in SAR imagery, including weak/slow targets in strong clutter environments. The 2D velocity estimation also improves imaging quality for moving targets. 

N. Najian, M. A. Sebt and A. Hosein Oveis, "Ground Moving Target Indication via Coprime Array MIMO 2-D-VSAR Joint EGO-DPCA Filter," in IEEE Transactions on Geoscience and Remote Sensing, vol. 62, pp. 1-15, 2024, Art no. 5219915, doi: 10.1109/TGRS.2024.3446046.

Abstract: The velocity synthetic aperture radar (VSAR) algorithm is a method used for slow ground-moving target indication (GMTI) and parameter estimation based on array processing. However, this method is limited by an expensive computational burden and is disabled for detecting fast-moving targets.

This article uses a coprime array configuration with smaller element spacing to improve the unambiguous range velocity estimation. This improvement results in the detection of fast-moving targets. Additionally, we propose an improved coprime VSAR algorithm that uses azimuth time shift instead of two-step phase compensation in every pixel of channel images to decrease the computational burden. However, the weak and slow-moving targets are not detected using the coprime VSAR method. 

Thus, we introduce a filter called the extended greatest of displacement phase center antenna (EGO-DPCA) to detect weak and slow-moving targets. Furthermore, the proposed algorithm is extended to the coprime 2-D VSAR to estimate the azimuth direction velocity of moving targets neglected in the conventional VSAR algorithm. Therefore, the azimuth resolution of moving target imaging significantly increases by estimating the azimuth direction velocity. Since all processes are performed in the detected pixel of moving targets, the complexity and computational burden are significantly reduced. 

keywords: {Clutter;Azimuth;Estimation;Filtering algorithms;Accuracy;Object detection;Information filters;Coprime;extended greatest of displacement phase center antenna (EGO-DPCA);ground-moving target indication (GMTI);synthetic aperture radar (SAR);velocity SAR (VSAR)}, 

URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10639456&isnumber=10354519

Authors

Here is a summary of the key details of the authors:

1. Negar Najian:
- PhD student at K. N. Toosi University of Technology in Tehran, Iran
- Research interests: SAR signal processing, array processing, detection and estimation theory

2. Mohammad Ali Sebt:
- Faculty member at K. N. Toosi University of Technology since 2011
- PhD from Sharif University of Technology in 2011
- Research interests: radar signal processing, detection and estimation theory, array signal processing

3. Amir Hosein Oveis:
- PhD from K. N. Toosi University of Technology in 2018
- Currently a Researcher at National Laboratory of RaSS—CNIT in Italy
- Previously Associate Post-Doctoral Researcher at University of Pisa (2021-2023)
- Research interests: deep learning (explainable AI, automatic target recognition, object detection), signal processing, synthetic aperture radar

The authors represent a mix of experienced faculty and newer researchers, with expertise spanning radar/SAR signal processing, array processing, detection theory, and more recently deep learning applications for radar. Their affiliations are primarily with K. N. Toosi University of Technology in Iran, with Dr. Oveis now based in Italy. 

Figures and Tables

Based on the information provided in the abstract and introduction, here's a list of the figures and tables mentioned, along with their descriptions:

Figures:

1. Figure 1: Geometry of coprime array SAR
   - (a) Configuration of coprime array SAR
   - (b) Equivalent virtual arrays
   - (c) Geometry of the coprime array VSAR

2. Figure 2: Processing gain curves versus velocity (vy)
   - (a) Conventional DPCA filter
   - (b) GO-DPCA filter
   - (c) Third-order DPCA filter
   - (d) EGO-DPCA filter
   - (e) Comparison of processing gain between EGO-DPCA and GO-DPCA filter

3. Figure 3: Velocity images of detected moving targets
   - (a)-(b) Velocity images using VSAR method
   - (c)-(g) Comparisons of velocity images between CAA-VSAR and proposed method for different targets

4. Figure 4: Image of the strong clutter background from real SAR data

5. Figure 5: Image of detected moving targets using VSAR

6. Figure 6: Image of detected moving targets using CAA-VSAR method

7. Figure 7: Image of detected moving targets using proposed method in EGO-DPCA filter output

8. Figure 8: High azimuth resolution image of detected moving targets using proposed method

9. Figure 9: High azimuth resolution image of detected moving targets after relocation in EGO-DPCA filter output

10. Figure 10: High azimuth resolution image of detected moving targets after relocation in strong clutter background

11. Figure 11: Comparison of Improvement Factor (IF) between CAA-VSAR and proposed method
    - (a) Breezy condition
    - (b) Gale force condition

12. Figure 12: Flowchart of the improved coprime 2-D-VSAR joint EGO-DPCA filter

Tables:

1. Table I: Reduction of computational burden using the proposed method compared to conventional VSAR-based techniques

2. Table II: Comparison of moving targets' detection and parameter estimation between VSAR, CAA-VSAR, and the proposed methods

3. Table III: Comparison of moving targets' azimuth location estimation between VSAR, CAA-VSAR, and the proposed methods

These figures and tables are designed to illustrate the methodology, demonstrate the performance improvements, and provide comparative analyses between the proposed method and existing techniques for moving target detection and parameter estimation in SAR imagery.

 "Improved coprime 2-D-VSAR joint EGO-DPCA filter" algorithm

Figure 12 is a detailed flowchart illustrating the process of the "Improved coprime 2-D-VSAR joint EGO-DPCA filter" algorithm. The flowchart is divided into several steps, each corresponding to specific equations mentioned in the paper. Here's a detailed description:

1. The process starts with multiple channels (Channel 1 to Channel M-1) at the top.

2. The first major step is "Equation (3): Range compression" applied to all channels.

3. Next, there's a branch for "Equation (18): Azimuth time shift" instead of two-step phase compensation.

4. The process then splits into two main paths:

   a. Left path: Estimation of vy and x0 using CAA-VSAR joint EGO-DPCA filter
   b. Right path: Estimation of vx, vy, and x0 using CAA-2D-VSAR joint EGO-DPCA filter

5. The left path includes:
   - Equation (22): Applying EGO-DPCA filter
   - Equation (27): Azimuth compression and CFAR for moving target detection
   - Equation (28): Azimuth compression for detected moving targets
   - Equation (16) and (17): Estimation of vy and x0

6. The right path is more complex and includes:
   - Equation (30): Applying EGO-DPCA filter with new azimuth time shift
   - Equation (37): Phase compensation
   - Equation (38): Estimation of vx
   - Equation (39): Modified azimuth matched filter
   - Equation (44): Estimation of vy with more accuracy
   - Equation (45): Azimuth relocation

7. Both paths converge at the bottom for the final outputs: estimation of vx, vy, and x0 with high accuracy.

The flowchart uses color-coding and connecting lines to show the relationships between different steps and equations. It provides a comprehensive visual representation of the algorithm's workflow, emphasizing the improvements and additions to the conventional VSAR method.

Article

Published in: IEEE Transactions on Geoscience and Remote Sensing ( Volume: 62)

Article Sequence Number: 5219915

Date of Publication: 19 August 2024

ISSN Information:

DOI: 10.1109/TGRS.2024.3446046

Publisher: IEEE

 

SECTION I. Introduction

Mimo synthetic aperture radar ground-moving target indication (SAR-GMTI) systems, the combination of multichannel SAR and GMTI, can produce high-resolution images of stationary objects and detect moving targets simultaneously, and have been widely used in battle reconnaissance, maritime observation, traffic monitoring, and other industries [1], [2], [3], [4], [5], [6], [7], [8], [9]. In practice, GMTI is affected by two challenges. First, moving targets disappear in the presence of stationary objects and they must be distinguished from clutters. Thus, clutter suppression is an essential factor in moving target detection. Second, radial velocity estimation is needed for relocating the moving target and correcting its position. For GMTI and radial velocity estimation, different methods such as along track interferometry (ATI) [10], [11], [12], [13], [14], displaced phase center antenna (DPCA), and DPCA-ATI are utilized in multichannel SAR [14], [15], [16], [17], [18], [19]. These methods suppress clutters by the appropriate phase shift between the channels. After clutter suppression, the velocity and real position of the moving target are estimated using interferometry methods and, in some cases, by applying fractional Fourier transform (FrFT) to the azimuth linear frequency modulation (LFM) signal. The main problem of the interferometry methods is the phase ambiguity of noise degrading the accuracy of redial velocity estimation. Also, using FrFT to estimate the chirp rate and Doppler centroid of the azimuth LFM signal increases the computational complexity.

Another conventional method used in MIMO SAR GMTI is space-time adaptive processing (STAP). Theoretically, this method has more accuracy in suppressing strong clutter than non-adaptive methods [20], [21], [22], [23], [24], [25]. However, this method searches pixel by pixel in MIMO-SAR images to suppress clutter and detect moving targets. Since MIMO SAR images have so many pixels, the computational burden of the STAP algorithm is too expensive. Also, the clutter suppression accuracy depends on the precision of covariance matrix estimation. Thus, if the covariance matrix is not estimated accurately, the clutter will not be suppressed precisely, and the output signal-to-clutter ratio (SCR) of the moving target will decrease seriously.

The MIMO-velocity SAR (VSAR) algorithm is another method for MIMO SAR GMTI, which attempts to reconstruct the full 3-D image (range-azimuth-velocity) in a scene containing slow-moving targets. The VSAR system estimates the target velocity in every pixel of the image by applying array discrete Fourier transform (DFT) across the channels. Thus, this method has less computational burden than the STAP algorithm [26], [27], [28], [29], [30], [31]. One of the important applications of the VSAR system is imaging the dynamic backgrounds such as the sea and ocean surface. The knowledge of the target velocity makes it possible to undo the velocity blurring and approximately reconstruct the reflectivity image [32], [33]. After array DFT implementation in the VSAR method, the dc term of clutter appeared in the zero velocity image. So, for clutter suppression, the zeroth velocity image must be discarded. But, in wind-blown strong clutter environments, the spectrum of the ac term of clutter remains in other velocity images. Thus, the Doppler frequency of weak and slow-moving targets disappears into the strong clutter spectrum and these targets are not detected by the VSAR method. The adaptive implementation of processing VSAR (AIOP-VSAR) presented in [34] improved moving target detection. This method searches for moving target detection in every pixel of channel images and solves an optimization problem to suppress strong clutters. Also, the parameter estimation is performed using the maximum likelihood (ML) method to approach Cramér-Rao bounds (CRBs). This method like STAP is adaptive and has too expensive computational burden and complexity.

In recent years, the combination of the multichannel VSAR method and other methods, such as interferometry and VSAR, has been proposed [35]. This method uses multifrequency instead of enhancing element numbers to increase the velocity estimation accuracy of fast-moving targets. Another GMTI method using STAP and VSAR algorithms is proposed in [36]. Similar to the STAP algorithm, this method searches for moving targets in each pixel of all images and has the same computational burden. After moving target detection, this method estimates the target’s velocity by using a bank of parallel velocity frequency filters. Also, in this method, the accuracy of clutter suppression depends on the precision of the covariance matrix estimation. Another method is the combination of the coprime adjacent array VSAR (CAA-VSAR) and the multiple signal classification (MUSIC) algorithm. In the first step, the moving targets are detected by the VSAR method. In the second step, the sampling covariance matrix (SCM) of every detected moving target signal is vectorized and the unambiguous velocity is estimated via all elements based on the MUSIC algorithm [36].

A recent study involves combining the greatest of DPCA (GO-DPCA) method with the local STAP algorithm [37]. GO-DPCA has better processing gain than conventional DPCA. In this method, clutter suppression and moving target detection are performed using GO-DPCA. However, the velocity of the target is estimated by the STAP algorithm, which has more computational load and complexity than the array DFT in the VSAR algorithm. Also, the accuracy of velocity estimation depends on the precision of the covariance matrix estimation.

However, in all of the algorithms based on the VSAR system, the greater the distance between antenna arrays, the higher the accuracy of slow-moving target detection and velocity estimation. However, increasing the distance between the arrays increases the total length of the antenna, increases the effects of the grating lobe, and also reduces the unambiguity range of velocity estimation, so the system is not able to estimate fast-moving targets. To decrease the length of the antenna, decrease the grating lobe effects, and enhance the unambiguous range velocity for detecting fast-moving targets, the coprime arrangement with smaller array spacing can be used. However, due to the reduction of the distance between coprime arrays, the accuracy of weak and slow-moving target indication has decreased and these targets are not detected in wind-blown strong clutter environments. To solve this problem, we introduce the extended GO-DPCA filter and apply it to the VSAR system with the coprime arrangement, so that in addition to using the advantages of reducing the distance between virtual arrays and detecting fast-moving targets, we can increase the detection accuracy and estimate the velocity of weak and slow-moving targets in wind-blown strong clutter environments.

As mentioned before, in this article, we propose extended GO-DPCA (EGO-DPCA) as an extended filter applied across consecutive virtual arrays. The DPCA and GO-DPCA filters used in former studies are first-order filters with two filter coefficients ([1, −1]), and one image is obtained in the output of the filter. However, the EGO-DPCA filter has more order, filter coefficients, and freedom degree than the GO-DPCA filter. Also, the EGO-DPCA filter has several images in the output of the filter. In this article, we convolve the EGO-DPCA filter across the virtual arrays, and we have several images in the output of the EGO-DPCA filter. So, we can apply array DFT across the output images of the filter to obtain the velocity images in the output array of the EGO-DPCA filer. Thus, we have better processing gain, signal-to-noise ratio (SNR), and SCR than the GO-DPCA for clutter suppression and moving target detection. Therefore, weak and slow-moving targets are detected in wind-blown strong clutter environments and the improvement factor (IF) for moving target detection increases significantly.

Additionally, in this article, we propose two methods to reduce the computational burden of the VSAR algorithm. First, we utilize a specific condition for element spacing to replace azimuth time shift instead of two-step phase compensation for every pixel of the images and the computational load of conventional VSAR decreases considerably. Second, in this method, we can avoid searching pixel by pixel for moving target detection and all of the moving targets are detected in the output of the EGO-DPCA filter. Also, we estimate the range direction velocity just in the detected pixel by applying array DFT across the output images of the EGO-DPCA filter.

Furthermore, we utilize another form of the EGO-DPCA filter including appropriate azimuth time shift to obtain the azimuth direction velocity of the detected target, by applying DFT across the output images of the EGO-DPCA filter. Therefore, we introduce the 2-D-VSAR joint EGO-DPCA filter that estimates the target’s velocity in two dimensions (range and azimuth direction). Also, by estimating azimuth direction velocity and using the modified-azimuth matched filter, the accuracy of azimuth compression and azimuth relocation estimation of targets is increased considerably. However, in this method, all of the processes for 2-D velocity and position estimation have been performed in the detected pixel of the moving targets across the output images of the EGO-DPCA filter. Thus, the complexity and computational burden have been decreased seriously in comparison with the VSAR and adaptive methods. The article’s contributions can be summarized as follows.

1. Utilizing the coprime configuration for the VSAR method with smaller element spacing than the conventional VSAR array configuration to improve the unambiguous range velocity estimation, decrease the effects of the grating lobe, and estimate the velocity of fast-moving targets using array DFT.

2. Proposing a specific condition for element spacing to use azimuth time shift instead of two-step phase compensation for every pixel of the images, which reduces the computational burden of conventional VSAR.

3. Applying EGO-DPCA as an extended filter across the consecutive virtual arrays, for clutter suppression and moving target detection, resulting in increased detection of weak and slow-moving targets in the strong clutter background and improved IF.

4. Developing a 2-D-VSAR joint EGO-DPCA filter by adding appropriate azimuth time shift into the EGO-DPCA filter that estimates the target’s velocity in two dimensions (range and azimuth direction) and improves the accuracy of azimuth compression using a modified azimuth matched filter.

5. Decreasing the computational load significantly in comparison with the VSAR and adaptive methods by performing all of the processing for 2-D velocity and position estimation in the detected pixel of the moving targets across the output images of the EGO-DPCA filter.

The rest of the article is organized as follows. In Section II, we provide a brief introduction to the coprime VSAR configuration and review the conventional VSAR algorithm and its limitations. Section III introduces the proposed EGO-DPCA filter and explains how it combines with the coprime VSAR algorithm to detect weak and slow-moving targets in a strong clutter background. Section IV presents the results of acquired data to demonstrate the effectiveness of the proposed algorithm. Section V is the conclusion.

SECTION II. Conventional MIMO VSAR Algorithm With 2-D Velocity Target Using Coprime Array

In this section, we consider the geometry of the coprime array VSAR system described in [36] and [38]. Fig. 1(a) shows the configuration where two collinear uniform sub-arrays are arranged along the flight path in the azimuth direction. The first sub-array consists of 2P elements, and the second sub-array consists of Q elements, with the zeroth element common between the two sub-arrays, and we assume 1<P<Q . The total number of physical elements is 2P+Q−1 . The spacing between two adjacent elements in the first sub-array is Qd, and in the second sub-array, it is Pd. The number of consecutive virtual arrays M is 2PQ+2P−1 , with a spacing of d between two adjacent arrays. Fig. 1(b) shows the equivalent consecutive virtual arrays, and the geometry of the coprime array VSAR is shown in Fig. 1(c).

Fig. 1.

Geometry of coprime array SAR. (a) Configuration of coprime array SAR. (b) Equivalent virtual arrays. (c) Geometry of the coprime array VSAR.

Show All

The platform velocity and the flight height are denoted by Vs and h, respectively. The distance between the mth virtual element and the moving target located at (x0,y0) , considering t as slow time and, azimuth and range direction velocities are denoted by vx and vy , respectively, is given by the following equation:

Rm=h2+(x0+md−(Vs−vx)t)2+(y0+vyt)2−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√m=0,…,M−1.(1)

View SourceThe closest distance from the antenna beam center to the target is Rc=(h2+y20)1/2 ; thus, the following equation gives the approximation of Rm :

Rm=R2c+(x0+md−(Vs−vx)t)2+v2yt2+2y0vyt−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√≈Rc+(x0+md−(Vs−vx)t)22Rc+v2yτ2+2y0vyt2Rc.(2)

View SourceAfter range compression, the received signal of the mth channel (m=0,…,M−1) is expressed as follows:

Srcm(τ,t)=μ⋅sinc{B[τ−2(Rm)c]}⋅wa(t)⋅exp{−j2πλc(2Rc+(x0+md−(Vs−vx)t)2Rc+v2yt2+2y0vytRc)}(3)

View Sourcewhere μ is the amplitude of the received signal, τ , t, B, λ , and c denote fast-time, slow-time, bandwidth, wavelength, and speed of light, respectively, and wa(.) refers to the azimuth time window function. The amplitude of the range compressed signal can be denoted by A0 , which is a constant value. In the following, we explain the conventional MIMO VSAR algorithm for 2-D velocity moving targets. The first step of the conventional MIMO VSAR algorithm is phase compensation, which must be performed in each pixel for all the channel images. Gc1 shows the first step phase compensation term for the mth channel

Gc1=exp{+j2πλc((md)2Rc+V2st2−2mdVstRc)}.(4)

View Source

After phase compensation, ym(τ,t) is given by

ym(τ,t)=Srcm(τ,t)×Gc1≈A0⋅exp{−j2πλc(2Rc+v2yt2+2y0vytRc+x20+2mdx0−2x0(Vs−vx)tRc)}.(5)

View SourceAccording to (5), the phase terms that are independent of m and t can be considered constant as A′0

ym(t)=A0⋅A′0⋅exp{−j2πλc(2mdx0−2x0(Vs−vx)tRc+v2yt2+2y0vytRc)}.(6)

View SourceBy azimuth Fourier transforming (6), the focused image of each channel can be obtained

Im(x)Im(x)=1Ts∫Ts2−Ts2ym(t)exp{−j2πλc(2VsxRc)t}dt=A0⋅A′0⋅exp{−j4πdx0λcRcm}×sinc[2VsTsλcRc(x0−x0vxVs−y0vyVs−x)](7)(8)

View Sourcewhere Ts is the aperture time and the absolute value of Im(x) peaks at

argmaxx|Im(x)|x0=x0−x0vxVs−y0vyVs=x+x0vxVs+y0vyVs.(9)(10)

View SourceBy substituting (10) into (8), Im(x0) is

Im(x0)=A0⋅A′0⋅exp⎧⎩⎨⎪⎪−j4πd(x+x0vxVs+y0vyVs)λcRcm⎫⎭⎬⎪⎪.(11)

View SourceIn this step, the phase known term must be removed by Gc2=exp{+(j4πd(x)/λcRc)m} that is the second step of phase compensation

Icm(x0)=Im(x0).Gc2=A0⋅A′0exp{−j4πdVsλc(x0vx+y0vyRc)m}.(12)

View SourceAssuming y0≈Rc , x0≪Rc and vx≪Vs , (12) is approximated by

Icm(x0)≈A0⋅A′0exp{−j4πdVsλc(y0vyRc)m}.(13)

View SourceAccording to (13), the steering vectors for clutter (vy=0) and moving target (vy≠0) are given by

S––c1×M=[1,1,…,1]TS––t1×M=[1,exp{−j4πdy0λcVsRcvy},…,exp{−j4πdy0λcVsRc(m−1)⋅vy}]T.(14)(15)

View SourceNext, the velocity of moving targets can be estimated by applying channel DFT to the sequence of complex values of the M channel at each pixel in (13). The frequency of the channel sequence is approximated as fk=(2dy0(vy)/VsλcRc)k for k=0,…,M−1 , where −0.5≤fk≤0.5 , and the unambiguous velocity is −0.5(VsλcRc/2dy0)≤vy≤0.5(VsλcRc/2dy0) . So, the maximum unambiguity velocity can be estimated as approximately 0.5(Vsλc/2d) . Using a coprime array configuration with smaller element spacing (d) leads to an increased unambiguous velocity estimation range and enables the detection of fast-moving targets through the application of array DFT. Therefore, in the output of the array DFT, the clutter is suppressed, and moving targets are detected in the velocity image. Thus, the velocity of the moving target is estimated by the array DFT, and due to the approximation in (12), the estimation error of vy is Δvy≈(x0vx/Rc) . The position of the moving target is estimated as follows:

x^0x^0=x+v^yy0Vs=x+(vy+Δvy)y0Vs=x+x0vxVs+y0vyVs.(16)(17)

View Source

SECTION III. Proposed Method

A. Improved Coprime Array VSAR Algorithm

In this step, we propose a new condition for the VSAR method to obtain the distance between two adjacent virtual arrays based on the pulse repetition interval (PRI) as d=Vs×PRI . Based on this condition, we can replace azimuth time shift instead of two-step phase compensation in the conventional VSAR method for every pixel of channel images. This reduces the computation burden of the conventional VSAR method considerably. If the antenna phase center shifts between the mth channel and the first channel is Δtm=(md/Vs) . We will apply azimuth shift delay to (3), and the steering vector of moving targets will be obtained without using two-step phase compensation. According to (3) and considering Δtm=mΔt , we have

Srcm(τ,t+Δtm)≈Src0(τ,t)⋅exp{−j4πλc(x0vx+y0vyRc)mΔt}m=0,…,M−L′.(18)

View SourceAssuming y0≈Rc , x0≪Rc , vx≪Vs , and Δt=(d/Vs) , (18) is approximated by

Srcm(τ,t+Δtm)≈Src0(τ,t)⋅exp{−j4πdVsλc(y0vyRc)m}.(19)

View SourceAfter azimuth compression, (19) is given the same as (13), without using the two-step phase compensation performed in the conventional VSAR method. Therefore, the computational burden decreases significantly. Also, the velocity and position of the moving target are estimated by applying azimuth DFT to each pixel of channel images similar to the conventional VSAR algorithm.

B. Improved Coprime VSAR Joint EGO-DPCA Filter

In this section, we explain the EGO-DPCA filter and apply it to the coprime array VSAR. Assuming a filter order of L, the length and coefficient vector of the filter will be L+1 and B––1×(L+1)=[b0,b1,…,bL]T , respectively, where b0=1 and ∑Ll=0bl=0 . The filter coefficients are driven as follows:

bl=(Ll)=(−1)lL!(L−l)!l!.(20)

View SourceThe impulse response of the EGO-DPCA filter is driven by

hkL(m)=∑l=0Lblδ(m−kl),m=0,…,M−L′k=1,2,3,…, L′=L+(k−1)(L−1)(21)

View Sourcewhere k is the freedom degree of the EGO-DPCA filter operating as the up-sampler factor, (k−1) expresses the number of zeroes between two adjacent filter tabs, and L′ denotes the length of the EGO-DPCA filter with the freedom degree of k. In the following, by applying the EGO-DPCA filter to (19), the strong clutters are removed, and the weak moving targets are detected. The mth output of the EGO-DPCA filer is given by

ykmGO-DPCA(τ,t)=Srcm(τ,t+Δtm)∗hkL(m).(22)

View SourceAccording to (5) and (6), the phase terms that are independent of m and t can be considered constant and after substituting (18) and (21) into (22), we have

ykmGO-DPCA(t)=A0⋅A′0⋅exp{−j4π(y0vy)λcRcmΔt}×(∑l=0Lblexp{+j4πλc(y0vyRc)l⋅k⋅Δt})m=0,…,M−L′.(23)

View SourceAccording to (23), if the range velocity of the target (vy ) is zero, the output of the EGO-DPCA filter will be nearly zero. As a result, clutters are suppressed from the channel images, and the moving targets with vy≠0 are detected.

Notice that in (23), the processing gain of the EGO-DPCA filter is equal to

PG=∣∣∣∣∑l=0Lblexp{+j4πλc(y0vyRc)l⋅k⋅Δt}∣∣∣∣.(24)

View SourceAccording to (24), the processing gain depends on vy and k. Fig. 2 shows the processing gain curve of the filters versus target velocity. Fig. 2(a) shows the processing gain curve of the conventional DPCA filter with k=1,2,3,4,5 and b=[1,−1]T . As shown in this figure, some target velocities are detected by a certain value of k, while others are not. Fig. 2(b) shows the processing gain curve of the GO-DPCA filter with k=1,2,3,4,5 and b=[1,−1]T , such that by varying k, all of the moving targets with different velocities are detected. For example, for a moving target, if vy is in the range of 2(m/s) to 7(m/s) , it can be detected by k=5 . The moving target with vy=8(m/s) to 11(m/s) is detected by k=4 , with vy=12(m/s) to 16(m/s) is detected by k=3 , and with vy=16(m/s) to 20(m/s) is detected by k=2 . Fig. 2(c) shows the processing gain curve of the third-order DPCA filter with k=2,4,6,8,10 and b=[1,−3,3,−1]T . As shown in this figure, some target velocities are detected by a certain value of k, while others are not. Fig. 2(d) shows the processing gain curve of the EGO-DPCA filter with k=2,4,6,8,10 and b=[1,−3,3,−1]T , such that by varying k, all of the moving targets with different velocities are detected. For example, for a moving target, if vy is in the range of 2(m/s) to 3(m/s) , it can be detected by k=10 . The moving target with vy=4(m/s) to 6(m/s) is detected by k=6 , with vy=7(m/s) to 10(m/s) is detected by k=4 , with vy=13(m/s) to 15(m/s) is detected by k=8 , and with vy=19(m/s) to 20(m/s) is detected by k=2 . The compression between the processing gain of EGO-DPCA and GO-DPCA is shown in Fig. 2(e). The red line shows the processing gain of the third-order EGO-DPCA filter with k=2,4,6,8,10 and b=[1,−3,3,−1]T . The blue line shows the processing gain of the GO-DPCA filter with k=1,2,3,4,5 and b=[1,−1]T . As shown in Fig. 2(e), the processing gain of the EGO-DPCA filter is much greater than the Go-DPCA filter.

Fig. 2.

Processing gain curve versus vy . (a) Conventional DPCA filter with b=[1,−1]T . (b) GO-DPCA filter. (c) Third-order DPCA filter with b=[1,−3,3,−1]T . (d) EGO-DPCA filter. (e) Compression of processing gain between EGO-DPCA and GO-DPCA filter.

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In the first step, we calculate the first output of the EGO-DPCA filter as follows:

ykm=0GO-DPCA(t)≈A0⋅A′0⋅(∑l=0Lblexp{−j4πλc(y0vyRc)l⋅k⋅Δt})k=1,2,3,…(25)

View SourceNext, the azimuth LFM signal of the moving targets needs to be compressed, and the azimuth-matched filter is expressed as

h(t)=wa(t)⋅exp{+j2πRcλcV2st2}.(26)

View SourceAfter azimuth compression, we obtain

Ikm=0GO-DPCA(x)=ykm=0GO-DPCA(t)∗h(t)≈A0⋅A′0⋅(∑l=0Lblexp{−j4πλc(y0vyRc)l⋅k⋅Δt})×sinc[2VsTsλcRc(x0−x0vxVs−y0vyVs−x)]k=1,2,3,…(27)

View SourceAfterward, we apply the constant false alarm rate (CFAR) for (27) to detect all of the moving target pixels. In this article, we continue the rest of the processing for each of the moving targets in the same range gate and around the same pixel ([(x−(Ls/2)),(x+(Ls/2))]) as it has been detected in the previous step. Thus, the computation burden will be reduced considerably. (Notice that Ls is the aperture length of the SAR.)

As previously mentioned, each moving target has been detected using the EGO-DPCA filter with a certain value of “k.” In the following, we obtain the output of the EGO-DPCA filter in (23) for m=1,…,M−1 and with the same value of k (k=kt ) as each target has been detected in (27). Also, we detected pixels of each moving target, detected in the previous step. After applying azimuth compression to (23) for each of the detected moving targets, we obtain

IkmGO-DPCA(x)≈A0⋅A′0⋅exp{−j4πd(y0vy)VsλcRcmΔt}×sinc[2VsTsλcRc(x0−x0vxVs−y0vyVs−x)]×(∑l=0Lblexp{−j4πλc(y0vyRc)l⋅kt⋅Δt})m=0,…,M−L′.(28)

View SourceFinally, the range velocity of the target can be estimated by applying channel DFT only to the detected pixel of the moving target. According to (16) and (17), the position of the target can be estimated.

C. Estimation of the Moving Target Azimuth Direction Velocity

As stated in (3), the azimuth direction velocity of the moving targets (vx ) affects the chirp rate of the azimuth LFM signal and it is equal to ((Vs−vx)2/λcRc) . Since the chirp rate of azimuth matched filter is considered as (V2s/λcRc) , the resolution of azimuth compression and the accuracy of the moving target position estimation decrease. Furthermore, as previously mentioned, the estimation error of vy is Δvy=(x0vx/y0) and influenced by vx , making it crucial to estimate vx before azimuth compression.

However, there are two main challenges to estimating vx : a low SNR of the azimuth LFM signal before azimuth compression, and the need to suppress clutters and detect the azimuth LFM signal of moving targets to obtain a steering vector for vx . To address these challenges, this research proposes the application of a GO-DPCA filter with a k′≥kt to increase the processing gain, which corresponds to the moving targets detected in Section III-B, all subsequent processing is performed in the estimated pixel of the moving target (x=x0 ). In this section, we apply the EGO-DPCA filter to (3), but with a different azimuth time shift as expressed in (29), to obtain a steering vector versus vx

h′k′L(m,t)=∑l=0Lblδ(m+k′l)δ(t+k′l⋅Δt)m=0,…,M−L′.(29)

View SourceNow apply (29)-​(3), and the output of the EGO-DPCA filter with the new azimuth time shift is given by

y′k′=nktmGO-DPCA(τ,t)y′k′=nktmGO-DPCA(τ,t)=Srcm(τ,t)∗h′k′L(m,t)=∑l=0Lbl.Src(m+l.k′)(τ,t+(l.k′.Δt)).(30)(31)

View SourceNoticing (18) and (19), we have

Src(m+l.k′)(τ,t+(l.k′.Δt))=Srcm(τ,t)⋅exp{−j4π(y0vy)λcRc(l⋅k′⋅Δt)}m=0,…,M−L′L′=L+(k′−1)(L−1).(32)

View SourceBy substituting (32) into (31), we have

y′k′=nktmGO-DPCA(τ,t)=Srcm(τ,t)×(∑l=0Lblexp{−j4πλc(y0vyRc)l⋅k′⋅Δt})m=0,…,M−L′.(33)

View SourceIn (33), clutters are suppressed, and the processing gain of the EGO-DPCA is at its maximum for a given value of k=kt for each detected moving target. Thus, before azimuth compression, the SCR and SNR of the azimuth LFM signal are increased. By substituting (3) into (33), and considering the amplitude of the range compressed signal as A0 , we have

y′k′=nktmGO-DPCA(t)=A0⋅exp{−j2πλc(2Rc+(x0+md−(Vs−vx)t)2Rc+v2yt2+2y0vytRc)}×(∑l=0Lblexp{−j4πλc(y0vyRc)l⋅k′Δt})m=0,…,M−L′.(34)

View SourceNext,

y′k′=nktmGO-DPCA(t) is obtained for x=x0 , where its azimuth time is t0=(x0/Vs)

y′k′=nktmGO-DPCA(t0)=A0⋅exp{−j2πλc(2Rc+(Vs−vx)2⋅t20Rc+2md(x0−t0⋅Vs)Rc+m2d2+2mdt0⋅vxRc+v2yt20+2y0vyt0Rc)}×(∑l=0Lblexp{−j4πλc(y0vyRc)l⋅k′⋅Δt}).(35)

View SourceAccording to (35), by substituting x0=t0.Vs in the second term of the azimuth LFM signal phase and considering the other terms that are independent of m as A′0 , we have

y′k′=nktmGO-DPCA(t0)=A0⋅A′0⋅exp{−j2πλc(m2d2+2mdt0⋅vxRc)}×(∑l=0Lblexp{−j4πλc(y0vyRc)l⋅k′⋅Δt})m=0,…,M−L′.(36)

View SourceAfter phase compensation by Gc=(+j2π/λc)(m2d2/Rc) , (36) is given by

y′k′=nktmGO-DPCA(t0)×Gc=A0⋅A′0.exp{−j2πλc(2mdt0⋅vxRc)}×(∑l=0Lblexp{−j4πλc(y0vyRc)l⋅k′⋅Δt})m=0,…,M−L′.(37)

View SourceNotice that in (37), the steering vector of the moving target is obtained versus vx

S––t1×M=[1,exp{−j4πt0dλcRcvx},…,exp{−j4πt0dλcRc(m−1)vx}]T.(38)

View SourceBy applying array DFT to the detected pixel of the moving target at x=x0 in (37), the azimuth direction vx is estimated.

Moreover, by estimating vx , the azimuth chirp rate of the azimuth LFM signal of the moving target is obtained, and the azimuth-matched filter is modified as follows:

hmodified(t)=wa(t)⋅exp{+j2πRcλc(Vs−vx)t2}.(39)

View SourceThe modified azimuth-matched filter is then applied to (34) in the range gate and around the detected moving target pixel

I′k=ktmGO-DPCA(x)I′k=ktmGO-DPCA(x)=hmodified(t)∗y′k=ktmGO-DPCA(t)=A0⋅A′0⋅exp{−j4πdx0λcRcm}×sinc[2VsTsλcRc(x0−y0vyVs−x)].(40)(41)

View SourceAccording to (9) and (10), the absolute value of Im(x) peaks at x=x0−(y0vy/Vs) , and by replacing x0 in (41), Im(x0) is given by

Im(x0)=A0⋅A′0⋅exp⎧⎩⎨⎪⎪−j4πd(x+y0vyVs)λcRcm⎫⎭⎬⎪⎪.(42)

View SourceBy compensating for the known phase term, we have

Icm(x0)Icm(x0)=Im(x0)×exp{+j4πdxλcRcm}=A0⋅A′0⋅exp⎧⎩⎨⎪⎪−j4πd(y0vyVs)λcRcm⎫⎭⎬⎪⎪.(43)(44)

View SourceThen, vy is estimated by applying DFT to (44), and the estimation error of vy due to vx mentioned in (12) is removed. By estimating vx and using the modified azimuth-matched filter, the accuracy of position and range velocity estimation is considerably increased, leading to a more accurate azimuth relocation of the moving target. Thus, the azimuth relocation of the moving target can be obtained by

Δx=y0vyVs.(45)

View Source

D. Reduction of Computational Burden for VSAR-Based Algorithm

In this study, we propose two techniques to reduce the computational burden in VSAR-based algorithms such as conventional VSAR and CAA-VSAR methods. The first row of compensation reduces the computational burden. In the second method, we use the EGO-DPCA filter to further reduce the computational burden. The reduction in the number of real multiplications and real summations for both methods is shown in Table I. Variables M,Np,Nt , and NLs represent the number of channels, the number of pixels in each channel image, the number of moving targets, and the number of azimuth time samples, respectively, in the aperture time interval [−(Ts/2),−(Ts/2)] .

TABLE I Reduction of the Computational Burden Using the Proposed Method Compression to Conventional VSAR-Based Techniques

SECTION IV.

Simulation Results of Acquired Data

In this section, we consider 2-D movement for moving targets in the strong clutter background of the real SAR data acquired from the northern regions of Iran, which include fields and forests on the coast of the Caspian Sea where the wind speed is (20−60 mp/h) 13−26 m/s . The platform velocity, PRI, wavelength, and azimuth time shift are set to Vs=200 m/s, PRI=200 μs , λ=0.03 m . In Fig. 3, we intend to compare the performance of VSAR, CAA VSAR, and proposed methods together. For the VSAR method, the system has 16 channels and the distance between two adjustment channels is d=0.5 m . So, the total length of the antenna is 7.5 m. The maximum unambiguity velocity can be estimated as 3.75 m/s. In the CAA VSAR system, we consider the coprime array with P=3 and Q=7 equivalent M=47 consecutive virtual arrays with the spacing d=0.04 m . The total length of the antenna is equal to 1.88 and is smaller than the antenna length of the VSAR system. The maximum unambiguity velocity can be estimated as 37.5 m/s. In the proposed method, we consider Δt=400 μs and apply third-order EGO-DPCA filter k=2,4,6,8,10 and b=[1,−3,3,−1]T to the CAA-VSAR system. In this comparison, we consider five moving targets T1,T2,T3,T4 , and T5 that their SCRin is −22.17, 20, 20, 20, and −20 dB, respectively, as mentioned in Table II. Also, the velocities of the targets are 2,3,4,10 , and 20 m/s , respectively. Fig. 3 shows the velocity images in the output of DFT across the arrays for pixels including the spectrum of the moving target, spread clutter, and noise. Velocity image shows the normalized magnitude of signal spectrum in the output of array DFT versus Doppler frequency. Because the Doppler frequency is equal to (2vy/λ) , we multiply the frequency axis by (λ/2) and show the velocity image versus vy . In all these figures, the spectrum of the clutter signal is spread around the zero velocity due to the wind speed. Fig. 3(a) and (b) shows the velocity images of targets T1 and T2 , respectively, by the VSAR method. As shown in Fig. 3(a) and (b), the clutter signal spectrum is spread around zero velocity. In Fig. 3(a) and (b), the signal spectrum normalized magnitude of the targets T1 , T2 is smaller than the clutter spectrum and maximized at their velocities vy=2(m/s) , vy=3(m/s) , respectively. Because the velocities of targets T3,T4 , and T5 are not in the unambiguity velocity range of the VSAR system, they are not detected by the VSAR method. Fig. 3(c)–(g) shows the comparison of the velocity images of targets T1,T2,T3,T4 , and T5 , respectively, between the CAA-VSAR and the proposed method. In Fig. 3(c)–(g), the blue lines and the red lines show the velocity images of CAA-VSAR and the proposed method, respectively. As shown by the blue lines in Fig. 3(c)–(e), the clutter signal spectrum is expended around zero velocity, which causes the spectrum of the slow-moving targets T1,T2 , and T3 to disappear into the spread clutter spectrum, and they are not detected by the CAA-VSAR algorithm. In other words, using the CAA-VSAR method, the targets’ signal spectrum T1,T2 , and T3 are not separated from the clutter spectrum and are not maximized at their velocities. So, slow-moving targets T1,T2 , and T3 are not detected by the CAA-VSAR method. However, in Fig. 3(c)–(e), the red lines show the velocity images of targets T1,T2 , and T3 , respectively, by the proposed method. As it is clear in Fig. 3(c)–(e), the spectrum of the clutter signal is weakened and, on the other hand, the spectrum of the moving targets T1,T2 , and T3 is amplified and maximized at their velocities 2,3 , and 4 m/s , respectively. Therefore, in the proposed method, by using the EGO-DPCA filter, the slow-moving targets T1,T2 , and T3 are detected in wind-blown strong clutter environments.

TABLE II Comparison of the Moving Targets’ Detection and Parameter Estimation Between VSAR, CAA-VSAR, and the Proposed Methods

Fig. 3.

Velocity image of the detected moving target. (a) Velocity image of T1 using the VSAR method. (b) Velocity image of T2 using the VSAR method. (c) Comparison of the velocity image of T1 between the CAA-VSAR and the proposed method. (d) Comparison of the velocity image of T2 between the CAA-VSAR and the proposed method. (e) Comparison of the velocity image of T3 between the CAA-VSAR and the proposed method. (f) Comparison of the velocity image of T4 between the CAA-VSAR and the proposed method. Velocity image of the detected moving target. (g) Comparison of the velocity image of T5 between the CAA-VSAR and the proposed method.

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However, in Fig. 3(f) and (g), the targets T4 and T5 are detected by the CAA-VSAR method. As shown by the blue lines in Fig. 3(f) and (g), the signal spectrum normalized magnitude of the targets T4 and T5 is smaller than the clutter spectrum and maximized at their velocity vy_T4=10(m/s) and vy_T5=20(m/s) , respectively. The red lines in Fig. 3(f) and (g) show the velocity images of targets T4 and T5 , respectively, by the proposed method. Notice the red lines in Fig. 3(f) and (g), the spectrum of the clutter signal is weakened, and, on the other hand, the spectrum of the moving targets T4 and T5 are amplified and maximized at their velocities 10 and 20 m/s , respectively. As it is clear in Fig. 3(f) and (g), the normalized magnitude of the moving targets’ spectrum (T4 and T5 ) of the proposed method is greater than the normalized magnitude of the moving targets’ spectrum of the CAA-VSAR method. Also, as shown in Fig. 3(f) and (g), the weakening of the clutter spectrum in the proposed method is much higher than the CAA-VSAR method. Thus, using the proposed method, the slow-moving targets T1,T2 , and T3 are detected, and the SCR of the fast-moving targets T4 and T5 is increased.

In the continuation, five moving targets T1,T2,T3,T4 , and T5 are considered, and their vx , vy , and SCRin are presented in the second, third, and fourth columns of Table II. The SCRout and v^y , the estimation of vy , obtained by the VSAR are shown in the fifth and sixth columns of Table II, respectively. Also, the SCRout and v^y , the estimation of vy , obtained by the CAA-VSAR are shown in the seventh and eighth columns of Table II, respectively. However, the VSAR and CAA-VSAR methods do not estimate vx . The last four columns of Table II represent SCRout,kt,v^y , and v^x , the estimation of vx , obtained by the proposed method. As shown in Table II, two slow-moving targets T1 and T2 are detected by the VSAR method, but two fast-moving targets T4 and T5 are detected by the CAA-VSAR method. Thus, the VSAR method cannot detect three moving targets T3 , T4 , and T5 . Also, the CAA-VSAR method cannot detect three moving targets T1 , T2 , and T3 .

According to Table II, the SCRout for detected moving targets obtained by the VSAR and CAA-VSAR methods is considerably lower than the proposed methods. Also, the accuracy of vy estimation (v^y ) for the VSAR and CAA-VSAR methods is less than the proposed method, due to the estimation of vx in our method. In Table III, the first column shows the azimuth location of moving targets x0 , and the three last columns represent the estimation of target azimuth location x^0 by VSAR, CAA_VSAR, and the proposed method, respectively. As shown in Table III, the accuracy of the azimuth location estimation of the detected moving targets for the VSAR and CAA-VSAR methods is less than the proposed method significantly. Fig. 4 shows the image of the strong clutter background of the real SAR data acquired from the northern regions of Iran, which include fields and forests on the coast of the Caspian Sea, where the wind speed is (20−60 mp/h) 13−26 m/s. The moving targets T1,T2,T3,T4 , and T5 , disappear in the strong clutter background image, and their vx , vy , and SCRin are presented in the second, third, and fourth columns of Table II. Fig. 5 shows the result of the moving target detection using the conventional VSAR algorithm in the strong clutter background. As shown in Fig. 5, two slow-moving targets T1 and T2 are detected. The moving targets T3,T4 , and T5 are not detected by the VSAR method, because their velocities are greater than the maximum unambiguity that can be estimated by the VSAR method. Fig. 6 shows the result of the moving target detection using the CAA-VSAR algorithm in the strong clutter background. As shown in Fig. 6, two fast-moving targets T4 and T5 are detected, but the slow-moving targets T1,T2 , and T3 are not detected by the CAA-VSAR method. Also, the azimuth resolution of the detected moving targets in Figs. 5 and 6 is not sharp because the azimuth velocities of targets are not estimated by VSAR and CAA-VSAR methods. Fig. 7 shows the result of the moving target detection using the proposed algorithm in the wind-blown strong clutter environments. It should be noted that Fig. 7 shows the output image of the EGO-DPCA filter, and therefore the strong clutter background has been removed, and just detected moving targets are shown. As shown in Fig. 7, all of the five moving targets T1,T2,T3,T4 , and T5 , are detected by the EGO-DPCA joint VSAR method. Thus, the proposed method can detect both fast and slow-moving targets in wind-blown strong clutter environments. However, in Fig. 7, the azimuth resolution is not sharp due to the azimuth direction velocities of moving targets are not estimated by the EGO-DPCA VSAR proposed method yet. In the next step, we estimate the azimuth direction velocity using the EGO-DPCA joint 2-D-VSAR proposed method. The estimated value of the azimuth direction velocity is presented in the last column of Table II. In Fig. 8, we perform azimuth compression again, after the estimation of azimuth direction velocity. As shown in Fig. 8, the azimuth resolution of moving targets increases compared to Fig. 7, using the modified azimuth-matched filter proposed in (39). In the continuation, we estimate the Y-direction velocity (vy ) of the moving target again. As mentioned in the columns of v^y of Table II, the estimated value of the Y-direction velocity for T1,T2,T3,T4 , and T5 , using the proposed method compared to the VSAR and CAA_VSAR method is closer to the real values presented in the third column of Table II. After estimating the Y-direction velocity, we obtain the azimuth relocation of moving targets mentioned in (45), to correct the azimuth location of the moving target. In Fig. 9, we show the image of detected moving targets after azimuth relocation correction in the output of the EGODPCA filter. In Fig. 10, we show the detected moving target after azimuth relocation correction in the strong clutter background. Fig. 11 shows the IF curve versus the Y-direction velocity of two CAA-VSAR, and the proposed methods are shown for two conditions of weather, breezy, and gale force. The IF curves for breezy and gale force conditions are presented in Fig. 11(a) and (b), respectively. This comparison expresses that the proposed method has a greater IF in both weather conditions. Fig. 12 shows the flowchart of the proposed method. In the first step, we explain the processing for estimatingo vy and x0 using the CAA-VSAR joint EGO-DPCA filter, without estimating vx . In the next step, we utilize the CAA-2-D VSAR joint EGO-DPCA filter. In this section, we estimate vx and use the modified azimuth-matched filter to reestimate the vy and x0 with more accuracy. In Fig. 12, all of the processes are explained step by step with their corresponding equation.

TABLE III Comparison of the Moving Targets’ Azimuth Location Estimation Between VSAR, CAA-VSAR, and the Proposed Methods

Fig. 4.

Image of the strong clutter background of the real data.

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Fig. 5.

Image of the detected moving target using VSAR.

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Fig. 6.

Image of the detected moving targets using the CAA-VSAR method.

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Fig. 7.

Image of the detected moving targets using the proposed method in the output of EGO-DPCA filter.

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Fig. 8.

High azimuth resolution image of the detected moving targets using the proposed method in the output of EGO-DPCA filter.

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Fig. 9.

High azimuth resolution image of the detected moving targets using the proposed method after relocation in the output of EGO-DPCA filter.

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Fig. 10.

High azimuth resolution image of the detected moving targets using the proposed method after relocation in the strong clutter background.

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Fig. 11.

Comparison of the IF between CAA-VSAR and the proposed method under two conditions of weather. (a) Breezy condition. (b) Gale force condition.

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Fig. 12.

Flowchart of the improved coprime 2-D-VSAR joint EGO-DPCA filter.

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SECTION V.

Conclusion

In this article, we utilize a coprime configuration for the VSAR algorithm to reduce the element spacing and improve the unambiguous range velocity estimation, decrease the effects of the grating lobe, and estimate the velocity of fast-moving targets using array DFT. Furthermore, we propose the Improved coprime 2-D-VSAR algorithm joint EGO-DPCA filter that detects the slow targets in wind-blown strong clutter environments. Also, in the first step, we suggest the azimuth time shift instead of the two-step phase compensation used in the conventional VSAR algorithm. Thus, the computational burden decreases considerably. In the second step, we apply EGO-DPCA as a filter across the arrays and detect weak moving targets in the strong clutter background. Thus, the IF of coprime array VSAR increases considerably, and the Y-direction velocity of the moving target is estimated by DFT across the output arrays of the EGO-DPCA filter. In the third step, we estimate azimuth direction velocity using 2-D-VSAR joint EGO-DPCA as a filter. In this way, we utilize another azimuth time shift for the EGO-DPCA filter to obtain the azimuth direction velocity of the detected target by applying DFT across the output arrays of the EGO-DPCA filter. Thus, by estimating vx , the chirp rate of the moving target azimuth LFM signal will be obtained more accurately, and the azimuth resolution increases noticeably. Furthermore, all of the processing for 2-D velocity and position estimation has been performed in the detected pixel of the moving targets across the output images of the EGO-DPCA filter. Thus, the complexity and computational burden have been decreased seriously in comparison with the conventional VSAR and the adaptive methods.