Ling Wang,Zhenxiao Cao,Ning Li,Teng Jing,and Daiyin Zhu

1.Key Laboratory of Radar Imaging and Microwave Photonics,Ministry of Education, Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;

2.Departmentof Space Microwave Remote Sensing System,Institute of Electronics,Chinese Academy of Sciences, Beijing 100190,China

Optimalship imaging for shore-based ISAR using DCF estimation

Ling Wang1,*,Zhenxiao Cao1,Ning Li2,Teng Jing1,and Daiyin Zhu1

1.Key Laboratory of Radar Imaging and Microwave Photonics,Ministry of Education, Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;

2.Departmentof Space Microwave Remote Sensing System,Institute of Electronics,Chinese Academy of Sciences, Beijing 100190,China

The optimalimaging time selection of ship targets for shore-based inverse synthetic aperture radar(ISAR)in high sea conditions is investigated.The optimalimaging time includes optimalimaging instants and optimalimaging duration.A novelmethod for optimalimaging instants selection based on the estimation of the Doppler centroid frequencies(DCFs)of a series of images obtained over continuous short durations is proposed.Combined with the optimal imaging duration selection scheme using the image contrast maximization criteria,this method can provide the ship images with the highest focus.Simulated and realdata processing results verify the effectiveness of the proposed imaging method.

inverse synthetic aperture radar(ISAR),ship target, optimalimaging time selection,Dopplercentroid frequency(DCF).

1.Introduction

Inverse synthetic aperture radar(ISAR)can obtain two-dimensional(2D)high resolution images of noncooperative moving targets under all weather and all day [1,2].An ISAR system usually obtains high range resolution by transmitting large bandwidth signals combined with the pulse compression technique,and obtains high cross-range resolution by coherently integrating the echoes backscattered from differentaspectangles[1,2].

As compared with the ISAR imaging of aircraftand vehicles,the characteristic of the ship imaging is that the ship angularmotion(including yaw,pitch and roll)induced by the ocean waves can be used to achieve the desired cross-range resolution[3].However,the ship motion is three-dimensional(3D)and time-varying,which increases the difficulty of the ISAR imaging[4].

A number of ISAR imaging algorithms for ship targets have been proposed in literature[5–13],which mainly utilize the time-frequency analysis methods[5–8],cleanbased methods[9,10],and optimaltime selection methods [11–13].Moreover,the methods based on Markovian approach[14],parameter estimation[15],and match Fourier transform[16]also have been proposed.Time-frequency analysis methods are time-consuming and suffer from well-known cross-term interference[5–8].The methods using clean techniques need the searching of parameters and are also time-consuming[9,10].The methodsbased on optimaltime selection can achieve high-quality images for targetrecognition and allow a complete real-time imaging and surveillance operations in wide sea areas[11–13,17]. In[11],Doppler spread of ship ISAR images was used as an indicator to select good ship images,and this method can work in real time,but it needs to set a threshold to segmentthe target from the background which influences the accuracy ofthe estimates.Furthermore,Dopplerspread can only reflect the absolute value of the effective rotation vector(ERV)of the ship.In[12],the maximum contrast based time selection method was proposed,which can obtain high focused plane orship images automatically,however,the performance of this method will be decreased in high sea conditions.In[13],a slope-based time selection method was proposed,which is able to select the time instants better suited for top or side view image formation and estimate the rotation motion for image cross-range scaling.Nevertheless,this method needs to know geometricalrelation between radar and the targetpreviously.

In this paper,an optimal-time-selection based ship imaging method is proposed for shore-based ISAR.A novel method that relies on measuring the Doppler centroid frequency(DCF)of a sequence of sub-images gener-ated with successive sub-intervals is proposed to estimate the variations ofthe ERV.The optimalimaging instants are determined according to the change of the ERV.The optimalimaging duration centred with the chosen time instant is determined by maximizing the image contrast[12].The proposed method does notneed any priorknowledge about the target shape and geometrical relation.Furthermore,it can work automatically in high sea conditions.Processing results using simulated and real data demonstrate the effectiveness of the proposed method.

The organization ofthispaperis as follows.In Section 2, the received signal model is developed.In Section 3,the ERV variation estimation method is presented,which relies on the DCF estimation.In Section 4,the algorithm for optimal imaging time selection is presented.In Section 5, simulated and real data processing results are presented. Section 6 gives the conclusions.

2.Signalmodel

The shore-based ship ISAR imaging geometry is shown in Fig.1.(X,Y,Z)is an inertial reference system which acts as the absolute reference system with O being the origin.(XS,YS,ZS)is a local coordinate system embedded on the ship body.The XS,YSand ZSaxes represent the ship length,width and height,respectively.Without loss of generality,we assume that(XS,YS,ZS)coincides with (X,Y,Z)atthe starting time.(R,H,V)is anothercoordinate system defined from the perspective of radar.The R axis represents the vectorofthe radarline ofsight(RLOS). The H axis lies in the(X,Y)plane and is perpendicular to the direction of R.The V axis is perpendicular to the (R,H)plane.

Fig.1 Shore-based ship ISAR imaging geometry

For shore-based radar,the height is very low and the grazing angleψis approximately 0°.?is the angle between the RLOS and the X axis.θr,θpandθyrepresent the angles changed by ship roll,pitch and yaw motion,respectively.

The echo signalof the n th scatterer on the ship attime t is expressed as

where Rn(t)denotes the range between the n th scatterer and the radar,λis the transmitted wavelength and a(t)is the amplitude modulation function ofthe echo signalin the cross-range.

The relative motion between the targetand the radarcan be decomposed as a translational motion along the RLOS direction and a rotationalmotion around a reference point. Thus,Rn(t)can be expressed as where Ra(t)is the range between the centre of the target and the radar which represents the component of translational motion,rs,n(t)is the range between the centre of the targetand the n th scatterer,which represents the component of rotational motion.In what follows,we assume that the translational motion has been compensated,and therefore Ra(t)is removed from(2).The explicitform of rs,n(t)in(2)can be obtained by using the 3D rotation matrix ofthe ship[3]:

where(rs,n,0,hs,n,0,vs,n,0)is the coordinate of the n th scatterer in(R,H,V)at the starting time of the imaging interval.andθvrepresentthe angle decomposed by total rotation of the target along the R axis,H axis and V axis,respectively.Totalrotation of the targetrelative to the radar includes the ship own 3D sway and the tangentialtranslation relative to the radar.θhandθvhave the form:

whereΔ?is the aspectangle changed by the ship tangentialtranslation relative to the radar.

Sinceθhandθvare relatively small in a shortimaging interval,using(3),we obtain:

Substituting(5)into(2),and the result back into(1), and calculating the first derivative of the phase,we obtain the Dopplerfrequency of the n th scattererafter the motion compensation:

whereωeis the ERV,γis the angle betweenωeand V axis,ωhandωvare the first derivatives ofθhandθv, which representthe horizontalrotation vector and vertical rotation vector,respectively.The term in the parentheses,

hs,n,0cosγ?vs,n,0sinγ,is the cross-range coordinate of the n th scatterer in the image projection plane.We denote itwith xn,c.

3.ERV variation estimation

As shown in(6),in orderto obtain wellfocused ship ISAR images,time intervals during which the ERVs have large amplitude and are almost constant should be selected to form good ISAR images[3].Due to the non-cooperative characteristics ofthe target,ERV variation with time needs to be estimated from the received data.In this section,a method based on the DCF estimation in the range-Doppler (RD)image domain is presented to estimate ERVvariation. The DCF of ship ISAR images is calculated as follows:

where Fnis the 1D cross-range profile,PRF is the pulse repetition frequency and N is the number of cross-range bins.

The DCF of the RD image varies with the ERV.When the amplitude of ERV increases,the Doppler occupied by the targeton the image plane spreads wider.The DCF accordingly deviates from the zero Doppler further.

From(6),we see that the change of xn,calso induces the Doppler variation.However,in practice the pitch motion of the ship is much larger than roll and yaw and the yaw motion is weakest among the three rotations due to the control of the rudder[4].Furthermore,since the ship moves slow,the rotation induced by the ship tangential translation relative to radar is much small and can be neglected as compared to the ship own sway induced rotation. Thus,for shore-based ISAR,the verticalrotation is much weaker than the horizontal rotation.The resulting image plane varies little and is nearly the side-view of the ship during the observation and hence,xn,c(t)varies little.Note thatthis side-view is notthe complete side-view.The view angle of the radar?determines the projection.

As analysed above,the Doppler variation is mainly caused by the variation of ERV in shore-based ISARimaging.Thus,the DCF variation is consistentwith the trend of ERV and can be used to predictthe ERV variation.In this paper,successive sub-intervals are processed by the RD algorithm to obtain a series of images.Then,DCF is estimated in the image domain for each sub-image.Finally, DCF variation is estimated by interpolating and smoothing DCFs ofallsub-intervals.The steps of the DCF estimation in each image are given as follows:

Step 1Obtain the ship image via fastFouriertransform (FFT)in the cross range.

Step 2Select severalrange bins around the range bin with maximum energy.

Step 3Obtain the 1Dcross-range profile Fnofthe ship by adding up with selected range bins in Step 2.

Step 4Calculate DCF of the ship image using(7).

After the ERV variation is obtained,the instantaneous time corresponding to extreme values of ERV can be selected as the optimal imaging instants.Besides,optimal imaging duration must be determined for the trade-off between the blur effects due to the ERV variation and the loss of resolution due to shortcoherentprocessing interval (CPI).In this paper,the optimalimaging duration centred with the chosen time instantis determined by maximizing the image contrastbased on the fact thatwell-focused images have high contrast[12].

4.Algorithm for optimalimaging time selection

The algorithm for optimalimaging time selection is summarized below.Forthe sake ofclarity,a flow chartis given in Fig.2.

Step 1Perform translationalmotion compensation on the received data,which includes the range alignmentand phase compensation.In this step,a global minimum entropy technique is used to achieve the range alignment [18].The phase gradient autofocus(PGA)method combined with the rank one phase estimation(ROPE)is used forphase compensation[19,20].

Step 2Divide the received data into successive partially overlapped or non-overlapped sub-intervals.

Step 3Estimate the DCF in the image domain foreach sub-interval.

Step 4Interpolate and smooth DCFs ofallsub-intervals to obtain the trend ofthe ERV variation.

Step 5Determine the optimalimaging time instants by locating localextreme points of the DCF curve.

Step 6Search for the optimal duration centered with the chosen instantby maximizing the resulting image contrast[12].

Step 7Obtain the final ship images using the optimal time intervals selected above.

Fig.2 Flowchart of optimaltime selection for ship imaging

5.Simulated and realdata processing and analysis

5.1 Simulation results

The performance of the proposed method is demonstrated firstby using simulated data.The ship is modelled by 301 scatterers with identicalreflectivity,as shown in Fig.3.

Fig.3 Ship model

The size of the target is 150 m(length)×30 m (width)×60 m(height).The space between two scatterers is 5 m,exceptfor those atthe bow.

The geometry of radar imaging of the ship used in the simulation is shown in Fig.1.The radar works in X band with a bandwidth of 60 MHz.The pulse repetition frequency(PRF)is 1 000 Hz.The altitude of radar is 200 m. Atthe starting time,the slantrange between the targetcentre and the radar is 50 km and the aspectangle is 30°.The target motion parameters are listed in Table 1.Note that in practice the yaw motion tends to be damped by rudder control.Thus,yaw motion is usually very weak compared to pitch and rollmotion[4],as shown in Table 1.

Table 1 Target motion parameters

The data collection time is 15 s.Here,0.256 s is used as the duration of each sub-intervalwith 50%overlapping between adjacentsub-intervals.Fig.4 shows both the measured and smoothed DCF curves obtained by the presented DCF estimation method.The result is consistent with the trend of ERV.From Fig.4,we see that the DCF variation is periodical and the amplitude of DCF changes significantly,which indicates thatthe targetto be imaged has obvious angular motions.Fig.5 shows the theoretical ERV of the ship target computed using the known target motion parameters.Comparing Fig.4 and Fig.5,we see that the measured DCF follows the variations of the theoretical ERV.The imaging results are shown in Fig.6,which are obtained by applying the proposed optimal time selection method.Note thatthe horizontalaxis represents the range and the verticalaxis represents the Dopplerfrequency.Two optimal imaging instants tn(n=1,2)corresponding to the extreme values of the DCF curve are chosen as the optimal imaging time instants,which are indicated with arrows in Fig.4.The optimal durations Tn(n=1,2)centred with the chosen instants are determined by maximizing the contrast of the resulting image.The initial duration is set to 0.128 s and the step size is chosen to be 0.01 s.For the purpose of comparison,we reconstructed two other ship ISAR images:the first image is shown in Fig. 7(a)where the imaging instant t3is chosen corresponding to the zero DCF,which represents the worst case.We see that the resulting image has a very poor cross-range resolution and the ship mast cannot be identified.The second image is shown in Fig.7(b)where the imaging instant t4is randomly chosen.Note that the DCF varies around t4. Comparing Fig.7(b)with Fig.6(a)and Fig.6(b),we see thatthe image resolution of Fig.7(b)gets degraded due to the smaller DCF as expected and the image is defocuseddue to the variation of ERV around t4.The imaging durations of Fig.7(a)and Fig.7(b)are both setto 0.256 s.

Fig.4 Estimated results of DCF using simulation data

Fig.5 Theoretical ERV of ship target of simulation data

Fig.6 Ship imaging results of simulated data by choosing optimal time using the proposed method

Fig.7 Ship imaging results ofsimulated data corresponding to nonoptimal imaging time

As we analyzed in Section 3,all ship images shown in Fig.6 are approximately side-view.Furthermore,Fig.6(a) and Fig.6(b)are well focused.However,due to different norms and directions of the ERV of the two chosen instants,the resulting two ship images are with different heights of superstructures and reversed orientation in cross-range.

5.2 Realdata results

In this section,two real ISAR data sets are performed to demonstrate the performance of the proposed optimal time selection method.The data collection time is about 17.279 s.The radar works in X band with a bandwidth of 170 MHz.The pulse width of the transmitted signal is 30μs.The PRF is 1 250 Hz.

Each data setcontains 21 600 pulses.We chose 1.638 s corresponding to 2 048 pulses as the duration of each sub-interval with 75%overlapping between adjacentsubintervals.The estimated DCF variation is shown in Fig.8 and four typical ship images are shown in Fig.9 and Fig.10.The same with the simulated case,the optimal imaging instants tn(n=1,2)of Fig.9(a)and Fig.9(b)are obtained by the proposed method.The initial duration for the searching for the optimalduration determination is set to be 0.8 s and the step size is chosen to be 0.08 s.Forcomparison,two images formed corresponding to an imaging instant t3where the DCF is close to zero and a randomly chosen imaging instant t4,are presented in Fig.10(a) and Fig.10(b),respectively.The imaging duration for Fig.10(a)and Fig.10(b)are both setto be 1.638 s.

Fig.8 Estimated results of DCF variation with time for data sets

From Fig.9 and Fig.10,we can see that all resulting ship images are approximately side-view.Furthermore,we find out that the inclination angle of the ship long axis changes over the sub-images,which is more evident in Fig.9(a)and Fig.9(b).This is consistentwith the periodicity of ship 3D rotationalmotion as expected,which may lead to differentcross-range resolutions and reverses ofthe images in the cross-range direction.In Fig.10(a),there is almost no resolution in the cross-range.We just see the long axis of the ship,but we can not see other structures as Fig.9(a)and Fig.9(b).In Fig.10(b),the image is obviously blurred due to the change of ERV.The resolution of Fig.10(b)is notas good as thatof Fig.9(a)and Fig.9(b).

Fig.9 Ship imaging results of first real data set by choosing the optimaltime using the proposed method

Fig.10 Ship imaging results of first real data set corresponding to non-optimalimaging time

Four ship images reconstructed at four optimal imaging instants using the second real data set are shown in Fig.11.We see thatthe ship side-view is clearly shown in each image in Fig.11 and we can also see the ship pitch by observing the attitude change of the ship in the four continuous images.

Fig.11 Ship imaging results ofsecond realdata set by choosing optimaltime using the proposed method

6.Conclusions

ISAR imaging of ship targets is of great significance in practicalapplications,however,itis difficultto realize due to the complexity of the ship 3D rotational motion and the unpredictable sea state.In this paper,a noveloptimum imaging instants selection method based on DCF is proposed for shore-based ISAR imaging.This method does not have a high computational burden and can be potentially used in operational systems for real-time processing.Simulated and realradardata sets have been processed and the results verify the effectivenessofthe proposed ship imaging method.

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Biographies

Ling Wangreceived her B.S.degree in electrical engineering and her M.S.and Ph.D.degrees in information acquirement and processing from Nanjing University of Aeronautics and Astronautics,in 2000,2003,and 2006,respectively.She has been with Nanjing University of Aeronautics and Astronautics since 2003,where she is currently a professor with the Department of Information and Communication Engineering.From February 2008 to May 2009,she was a post-doctoral research associate with the Department of Mathematical Sciences and the Departmentof Electrical,Computer,and Systems Engineering,Rensselaer Polytechnic Institute,Troy,New York.Her current research interests include inverse scattering,wave-based imaging, radar imaging,and passive imaging.

E-mail:tulip wling@nuaa.edu.cn

Zhenxiao Caowas born in 1990.He graduated from Nanjing University of Information Science&Technology in 2012.Now he is a master student in Nanjing University of Aeronautics and Astronautics.His currentresearch interestis inverse synthetic aperture radar imaging.

E-mail:c522692522@gmail.com

Ning Liwas born in 1987.He is now pursuing his Ph.D.degree in the Institute of Electronics,Chinese Academy of Sciences,Beijing,China.His research interests include synthetic aperture radar(SAR)and inverse SAR(ISAR)imaging algorithms and autofocusing techniques,SAR polarmetric theory,and SAR image analysis of naturalhazards and extreme events.

E-mail:LiNing nuaa@163.com

Teng Jingwas born in 1989.He is a master student in College of Electronic and Information Engineering,Nanjing University of Aeronautics and Astronautics.Now,he is an engineer in China AeronauticalRadio Electronics Research Institute.His current research interest is inverse synthetic aperture radar imaging.

E-mail:jingteng nuaa@163.comDaiyin Zhuwas born in 1974.He received his B.S. degree in electronic engineering from the Southeast University,Nanjing,in 1996 and M.S.and Ph.D. degrees in electronics from Nanjing University of Aeronautics and Astronautics(NUAA),in 1998 and 2002,respectively.From 1998 to 1999,he was a guestscientistwith the Institute of Radio Frequency Technology,German Aerospace Canter,Germany, where he worked in the field of SAR interferometry.In 1998,he joined the Department of Electronic Engineering,NUAA,where he is currently a professor.He has developed algorithms forseveraloperational airborne SAR systems.His current research interests include radar imaging algorithms,SAR/ISAR autofocus techniques,SAR ground moving target indication(SAR/GMTI),and SAR interferometry.

E-mail:zhudy@nuaa.edu.cn

10.1109/JSEE.2015.00082

Manuscript received April 15,2014.

*Corresponding author.

This work was supported by the Innovation Foundation for Scientific Research Base(NJ20140008;NJ20150018),the Aeronautical Science Foundation of China(20132052035),and the NationalDefense Basic Scientific Research(B2520110008).