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1、ISAR Imaging of Small Craft With Roll,Pitch and Yaw Analysis*Victor C.Chen and Ronald Lipps Radar Division,Naval Research Laboratory,Washington D.C.,U.S.A.ABSTRACT In this paper,we analyze the effect of roll,pitch and yaw rotations on inverse synthetic aperture radar(ISAR)imaging of small craft.An i
2、deal ISAR image of a target with regular motion can be derived from the image projection plane and the radar line-of-sight(LOS)unit vector.Roll,pitch and yaw rotations can induce time-varying Doppler shifts that can be analyzed through the rotation matrix and the effective rotation vector.We use a c
3、ommercial small craft ISAR data accompanied with roll,pitch and yaw data collected by Trimbles Tans Vector system with 4 GPS antennas to study the effect of rotational motion on ISAR imaging.For a target with regular motion,perturbations of roll and pitch motions may make image blurring if conventio
4、nal motion compensation is used.In this case,advanced imaging algorithms,such as polar reformatting algorithm,that compensate the perturbations may improve the image.1.INTRODUCTION An ISAR image is formed by coherently processing retumed signals from a moving target at different aspect angles relati
5、ve to the radar.The change of the aspect angle is usually accomplished by the relative motion and rotations between the radar and the target.When the target is moving smoothly,conventional motion compensation algorithms that correct for any changes in the targets velocity vector can be applied to ge
6、nerate a clear image of the target.If the motion and rotations are accompanied by perturbations in the rotations,the phase of the returned signal may be corrupted and,thus,the image of the target may be degraded by using the conventional algorithms 1,2.In this case,to generate a clear image of the t
7、arget,information about perturbations must be tracked and incorporated into the motion compensation algorithms.However,in many cases information about the perturbations may not be available.It is important to analyze the effects of roll,pitch,and yaw and their disturbances on the ISAR image of the t
8、arget.We use a commercial small craft ISAR data accompany with itsroll,pitch and yaw data collected by Trimbles Tans Vector system with 4 GPS antennas to study the effect of rotations on ISAR imaging.Because of the targets rotation,the location of a scatterer of the target becomes a function of time
9、 t.The round trip time-delay of the radar signal reflected from the scatterer located at?,(t)is T,(t).When the target has a radial velocity v,and acceleration a,then the distance traveled by the radar signal before being reflected from the scatterer of the target becomes CZk(t)/2=I 6(t)-ii I+V,t&(t)
10、/2+U,Tk(t)/2?where c is the speed of wave propagation,is the vector from the rotation center to the radar as shown in Fig.1.In most cases where the second-order term is much smaller than the first-order term,then ctk(t)/2=1&(t)-kl+v,t,(t)/21,or rk(1)=The instantaneous position vector of the scattere
11、r k at time t can be derived form its position vector at time to and a rotation matrix Rot(B,B,B,),i.e.,where 8,8,and e,is the roll,pitch and yaw angle,respectively.(1)2 l&(j)-l-2 l&(t)-l -c-v,C F(t)=we,ep,e,)6(to)(2)2.CHARACTERISTICS OF SMALL CRAFT MOTION A small craft can be considered as a rigid
12、body with 6 degrees of freedom.They are three translational motions:surge,sway and heave along x,y,z direction,and three rotational motions:roll,pitch and yaw as shown in Fig.2.The tangential motion of the small craft relative to the radar is relatively small.However,the roll,pitch and yaw angular m
13、otion that is relatively large is the major source of Doppler shift in the ISAR range-Doppler image.A small crafts motion induced by sea wave is determined by the sea wave action as well as craft orientation and velocity.Because of the complexity and inaccuracy in predicting small craft motions,we u
14、se simplified approach to linearize the small crafts motions,and thus to analyze rotation effects on ISAR imaging.For the motion over a short time,the small craft can be modeled with a constant rotation rate.The rotation can produce differential Doppler frequencies for scatterers in the small craft
15、that are used to form a radar range-Doppler image of the small craft.Usually,the translational motion of the small craft can be decomposed into a component along the radar line-of-This work was sponsored by the Office of Naval Research.3-7803-5776-0/00/$10.00 0(2000 IEEE)493 IEEE INTERNATIONAL RADAR
16、 CONFERENCE Authorized licensed use limited to:IEEE Customer.Downloaded on April 17,2021 at 09:15:45 UTC from IEEE Xplore.Restrictions apply.sight and a component perpendicular to the line-of-sight.The component along the line-of-sight can induce Doppler frequencies.On the other side,the translation
17、al motion can also induce changes of the view angle from radar to the small craft,called the effective rotation.The view angles changes have the same effect as the crafts rotational motion.The effective rotation combined with the self-rotation of the craft will induce spatially dependent Doppler fre
18、quencies that can be used to discriminate scatterers.However,the combining is not simply the linear vector summation of the two rotation vectors.Complexity is expected especially for the small craft having complex roll,pitch and yaw motions.The assumption of constant rotations may be valid only for
19、a very short time interval.Thus,these formulations based on lower order approximation can be used.3.PROJECTION OF 3-D COMPOSITE TARGET ONTO 2-D IMAGE PLANE The phase of the returned radar signal from a point scatterer at the rotation center of the target is do=2a-2fc tR-Jy,(04(3)where f,is the carri
20、er frequency of the radar signal,R is the initial range of the rotation center of the target and V,is the targets line-of-sight(LOS)velocity that determines the Doppler frequency shift of the target.The LOS velocity is determined by where P(t)is the targets velocity vector and f is called the LOS un
21、it vector 3,41.The targets position with respect to the radar is dynamically computed.The ISAR image is displayed in slant-range versus Doppler-frequency coordinates.The Doppler frequency produced by a scatterer in the target can be expressed as vIOs(t)=J(r)0 i(4)fD(t)=-2fc I G(t)T(t)I(5)C where?(?)
22、is the scatterer velocity vector.If T is the position vector of the scatterer measured from the center of rotation,then the Doppler frequency shift of the scatterer becomes fD(t)=%(fi(t)x.)0 i(f)(6)C Assuming the angle between the actual rotation vector 6 and the LOS unit vector i at time f is=jjp(7
23、)exp-j-7*r)fi 47&(9)C where the translational motion has been compensated,and r=x,y,z is the location vector in the local x-y-z coordinate system,i is the unit vector along the radar line-of-sight,p(7)is the targets reflectivity at r.The reconstructed image can be expressed as-p()=jJ)expj-eQ&4 7&(10
24、)C The Doppler shift induced by the rotational motions becomes where v is the velocity vector of the scatterer at r.When the target is rotating,the scatterer at To is rotated to r by a rotation matrix,i.e.,-r=ROt(e,e,e,)%.Then,and the Doppler shift becomes where dRot(er*Y)5 determines the effect of
25、the roll,pitch and yaw on Doppler shift of the scatterer at the location 6.If roll,pitch and yaw are hctions of time,the Doppler frequency of the k-th point scatterer in the target at rk(to)becomes dt fm(Q=-2f,Rot(,(t),(t),ey(r)G(tJ c dt The Doppler frequency is determined by the initial position of
26、 the scatterer and the rotation angles in the rotation matrix.For the simplest case where the target has only yaw motion in a 2-D x-y plane,i.e.,e,=6,=0,0=R t+0,and 6=(x,yo),the Doppler shift induced by yaw can be derived as 3 YY f D,=-x,(-,2f sine,-r c o s ,)(14)C-y,(R,cos,-R:rsin,)When the target
27、has rotations in addition to its regular motions,the standard phase correction procedure is not suitable for correcting the additional phase errors.Auto-focusing algorithms cannot track this rotation change,then the range-Doppler cells will no longer be locked to the target,and the target may drift
28、out from one range-Doppler cell into another.Thus,the ISAR image may become smeared.To obtain a clear image,we must accurately predict the targets rotations and dynamically adjust the range tracking and the Doppler tracking such that the target will be stationary in range cells and Doppler cells.6.I
29、SAR IMAGING OF SMALL CRAFT The data of the small craft(Fig.4)was collected by a X-band radar operating at 9.25GHz and transmitting a linear FM waveform with 500 MHz bandwidth or 0.3m range resolution.The coherent image integration time is 0.64s with 128 pulses.Thus,the ISAR image consists of 256 ran
30、ge cells and 128 Doppler frequencies.The roll,pitch and yaw rotations were obtained by on-board global positioning systems.These rotations can be used to investigate how the attitude and dynamics of the small craft measured from on-board systems can affect ISAR images.In ISAR,if the target rotationa
31、l motion(roll,pitch and yaw)follows a deterministic path,the relative motion must be measured and compensated.These measurements can be carried out by a precise motion measurement system.Vibration or bending motion of the target causes space-variant image degradation,which the processor cannot remov
32、e,and the uncompensated relative motion will degrade image quality.From the corresponding GPS data,the actual roll,pitch and heading rotations are shown in Fig.5,where the heading angle change is wrapped around 360 degrees.The coherent image time is 0.64 sec,and the corresponding number of the GPS d
33、ata samples is 6 since a lOHz data rate was used.Fig.6(a)shows a reconstructed clear image fiom one segment of the radar data.Fig.6(b)is the result from another data segment.Because of the perturbations of rotations,the image for this data segment is smeared.The rotation-rate vector derived from the
34、 GPS data has smaller heading-rate vector that causes uncompensated phase errors by using conventional algorithms.The large perturbations of the roll,pitch and yaw angles cause image smearing.Image generated fiom segments near 320,266 GPS-sec is smeared where large perturbations in the roll,pitch,an
35、d yaw angles can be seen in Fig.6.For the clear images,changes of the roll,pitch and yaw angles are relatively smaller.Therefore,from the attitude measurements,we are able to tell whether images can be reconstructed by using conventional algorithms.As shown in Fig.7,these 495 IEEE INTERNATIONAL RADA
36、R CONFERENCE Authorized licensed use limited to:IEEE Customer.Downloaded on April 17,2021 at 09:15:45 UTC from IEEE Xplore.Restrictions apply.images reconstructed from segments having perturbation are smeared.In cases where conventional algorithms do not work well,more sophisticated advanced motion
37、compensation algorithms may help for achieving clear ISAR images.Fig.8 shows some improvements with advanced algorithms for small craft images.Images on the left column are reconstructed by the conventional algorithm.The right column are reconstructed by using ISAR polar reformatting algorithm 6.Pol
38、ar reformatting is an image formation technique based on tomographic reconstruction.Since radar signal is modulated on a carrier frequency,the Fourier transform of the radars pulse produce a line segment in 3-D Fourier Space that is offset from the origin by the carrier frequency at an angle determi
39、ned by the angle of the radar line-of-sight.As successive pulses are received and the aspect between the radar and the target changes,the line segment sweeps out a data surface in 3-D Fourier space.Once the data surface is formed,an image of the target can be reconstructed by taking the Inverse Four
40、ier Transform.The processing that is performed for ISAR image formation is similar to the processing that is done for Spotlight SAR imaging.However,in ISAR the target motion provides the change in aspect necessary for Doppler processing,whereas in spotlight SAR the change in aspect comes from the mo
41、tion of the radar itself.As a consequence of this difference,in ISAR the aspect change over time is unknown and uncontrollable.Therefore,the rotation of the target must be determined before polar reformatting can be used to form the data into imagery.In ISAR the target rotation can be measured direc
42、tly using only the returned data from the target.7.SUMMARY We have analyzed the effect of rotations on ISAR imaging based on an example of a small craft with roll,pitch yaw motions.In this case,a clear ISAR image of the target is generated mainly due to the yaw motion,and pitch or roll motion will c
43、hange the geometric view of the target that causes the image smearing if auto-focusing algorithms cannot compensate motions for each individual scatterer.The reconstructed images may be relatively clear if the rotation vector of the local coordinates has a larger yaw vector.For a smaller yaw vector
44、and relatively larger pitch and roll vectors,the image may be smeared by using conventional motion compensation algorithms.In these cases,more sophisticated algorithms such as polar reformatting that can compensate motions for each individual scatterer may help in reconstructing a clear ISAR image.R
45、EFERENCES l Chen,C.C.and Andrews,H.C.,“Target-Motion-Induced Radar Imaging,”ZEEE Trans.on AES,01.16,no.1,pp.2-14,1980.2 Haywood,B.and Evans,R.J.,“Motion Compensation for ISAR Imaging,”Proceedings of Australian Symposium on Signal Processing and Applications,pp.112-1 17,1989.3 Wehner,D.R.,High-Resolu
46、tion Radar(2nd ed.),Boston:Artech House,1994.4 Kirk,J.C.,“Motion Compensation for Synthetic Aperture Radar,”ZEEE Trans.on AES,vol.11,n0.3,5 Chen,V.C.and Miceli,W.J.,“Time-Varying Spectral Analysis for Radar Imaging of Maneuvering Targets,”IEE Proceedings-Radar,Sonar,and Navigation,01.145,no.5,pp.262
47、-268,1998.6 Lipps,R and Kerr,D.“Polar Reformatting for ISAR Imaging,”Proceedings of the 1998 IEEE Radar Conference,pp.275-280,1998.pp.338-348,1975.I i Fig.1 Radar and rotating small craft in 2-D.Fig.2 Six-degree freedom of small craft.496 IEEE INTERNATIONAL RADAR CONFERENCE Authorized licensed use l
48、imited to:IEEE Customer.Downloaded on April 17,2021 at 09:15:45 UTC from IEEE Xplore.Restrictions apply.Fig.3 0 Imogcpro/Mon plane iage projection plane.Fig.4 picture of the small craft.3 19 3 195 3 2 3 205 3 21 3 215 322 3 225-,U IO 5 0 5.3.19 3.195 3.2 3.205 3.21 3 215 3 22 3.225 x 1 6 GPS Time(se
49、c)Fig.5 Roll,pitch and yaw data collected by Tans Vector System.I 10 M.M 40 50 60 M 40 60 80 I L n I n,h p e Rm Fig.6(a)A clear small craft image with zooming and(b)a smeared image.497 IEEE INTERNATIONAL RADAR CONFERENCE Authorized licensed use limited to:IEEE Customer.Downloaded on April 17,2021 at
50、 09:15:45 UTC from IEEE Xplore.Restrictions apply.GPS Time(sec)Fig.7 Roll,pitch and yaw angles along with two corresponding images:Before polar-reformatting After polar-reformatting Fig.8 ISAR image using polar reformatting algorithm.498 IEEE INTERNATIONAL RADAR CONFERENCE Authorized licensed use li