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1. Journal iof iScience iand iTechnology i ISSN: i2456-5660, iVolume i4, iIssue i3, iMay-June i2019, iPP i01-13 www.jst.org.in Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications I. iHemalatha1*, iP. iV. iSridevi2 1Sir iC iR iReddy iCollege iof iEngineering, iEluru, iDepartment iof iECE, ihemacrr2006@gmail.com 2AndhraUniversity,College iof iEngineering(A),Visakhapatnam, iDepartment iof iECE, pvs6_5@yahoo.co.in *corresponding iauthor Abstract: iSynthetic iaperture iradar iis ian iactive iremote isensing iapproach ithat itransmits ithe iknown iwavelength isignal iand imeasures ithe ireflected iwave ifrom ithe iscene. iMoving itarget idetection, iimaging, iand ivelocity iestimation iusing iraw idata iare iactive iresearch ifields iwith icivilian iand imilitary iapplications. iThe isynthetic iaperture iradar iendures ifrom ithe iimage idegradation ibecause iof iphase ierrors ipresent iin ithe ireceived isignal. iThese iphase ierrors igive irise ito ipoor ifocus iquality, ispurious itargets, iloss iof iresolution iand ierroneous ivelocities. iThe iprimary iobjective iof ithe ipaper iis ito iproduce ia ihigh-resolution iimage iof ithe itargets iand ithe imoving itargets imotion iestimation ipresent iin ithe iscene iin ithe ipresence iof iphase ierrors. iThe imodified irange-Doppler ialgorithm iperforms ithe irange imigration icorrection iand ithe ifocus ifiltering iwith ithe iwavelet idecomposition ito iimprove ithe iresolution iof ithe itarget iimage. iThe iparameters iextracted ifrom ithe irange imigration icorrection iand iazimuth ifiltering iis iused ito iestimate ithe imoving itarget ivelocity. iThe imodified iRDA iusing iSym8 iwavelet idecomposition ilevels iwith iAOPM ifor imoving itarget ivelocity iestimation iof iSAR iimage ihave ithe iaverage ipercentage iof iaccuracy iis i1.99. iThis iproposed iRDA imethod igives ithe iclose iapproximation ito ithe iactual ivelocity ivalue iand ialso iimproves ithe ifocus iquality iof ithe itarget iimage iwhen icompared iwith ithe iconventional iRDA. i Keywords i: iSynthetic iaperture iradar, iRange iDoppler ialgorithm, iWavelet idecomposition. i I. Introduction Velocity iestimation iof imoving itargets iis ione iof ithe iimportant iresearch itopics iin iSAR iimaging. iThe imoving itarget iin ithe iscene iis ifirst ifocused iwell ibefore ivelocity iestimation. iThe irange iDoppler ialgorithm i[1], i[2] iis iused ito ifocus ithe imoving itargets iin iSAR iimaging. iThe irange imigration icorrection i[5] iand ifocus ifiltering i[4] iis iperformed iin iRDA. iFor ifurther iimproving ithe ifocus iquality iwe iproposed imodified irange iDoppler ialgorithm. iThe iwavelet idecomposition ilevels iare iused iin ithe imodified iRDA ifor iimprovement iof ithe ifocus iquality iafter iazimuth icompression. i i The imoving itarget ivelocity iin iSAR iimaging iis icomposed iof itwo icomponents ii.e. ithe icross-track ivelocity iand ithe ialong-track ivelocity. iThe icoefficient iextracted ifrom ithe irange imigration icorrection iis iused ito icalculate ithe iaccurate iDoppler icentroid. iThe iradial ivelocity iof ithe imoving itarget iis iestimated ifrom ithe iDoppler icentroid. iThe icoefficient iextracted ifrom ithe iazimuth ifiltering iis iused ito icalculate ithe imoving itarget ialong-track ivelocity. iThe iadaptive iorder ipolynomial imethod iand ithe iphase igradient imethod iare iused ifor iazimuth ifiltering. iThe iperformance iof ithe imodified iRDA iis icompared iwith ithe iperformance iof ithe iconventional iRDA. iThe ifocus iquality iof ithe imoving itarget iin ithe iscene iis imeasured iby iusing ithe iparameter ientropy. iThe ipaper iis iorganized ias ifollows: iSection i1 ideals iwith ithe iintroduction. iSection i2 ipresents iautomatic iimaging iof imoving itarget iin iSAR iimaging. iThe iradial ivelocity iand ithe icross-range ivelocity iestimation iis idiscussed iin isection i3. iSection i4 iand isection i5 icontains iresults iand iconclusions irespectively. 2. iAutomatic iimaging i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i1 i| iPage

2. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ i iproposed imodified iRange iDoppler iAlgorithm ifor iSAR iimaging iis ias ishown iin iFig. i1. i Motion iparameters iof imoving itarget iare iextracted ifrom iits iautomatic iimaging. iThe iflowchart iof Raw iData i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i Range iCompression i i i i i i i i i i i i i i i i i i i i i i i Azimuth iFFT i i i RCMC Azimuth iCompression Raw iData Azimuth iIFFT i Wavelet idecompositio Processed iimage Fig. i1 iBlock idiagram iof iModified iRange-Doppler ialgorithm. First, ithe ireceived iecho isignals ifrom ithe iscaterrers iare iresolved iin ifast itime iusing itheir idifferent itime idelays iand ithe irange iresolution iis iimproved iusing imatched ifiltering ithe ireceived isignals iwith irange ireference isignal. iSimilarly, ithe isignals ifrom iscaterrers iare iresolved iin islow itime ibased ion itheir idifferent iazimuths iand ithe iazimuth iresolution iis iimproved iusing ifocus ifilter. iTo iacquire iwell ifocused iand ia icorrect ipositioned iimage, irange imigration icorrection ibefore iazimuth ifiltering, iand iwavelet idecomposition iafter iazimuth ifiltering iis irequired. iThe irange imigration icorrection, iazimuth ifiltering iand iwavelet idecomposition iare iperformed iautomatically iduring iimaging iof ithe imoving itarget. 2.1 iRange icell imigration icorrection The irange ibetween ithe itarget iand ithe iradar iis ivaried ibecause ithe itarget iis imoving ithrough ithe iazimuth iantenna ibeam; ithe iechoes ifrom ithe isame itarget iare inot iplaced iin ithe isame irange ibin. iIt iexhibit ivery ipoor ifocus iquality iof ithe iimage. iThe irange imigration icorrection iis icarried iout iin ithe irange-Doppler idomain, ithe iechoes ireturned ifrom ithe iparticular itarget iare iplaced iat icorresponding irange ibin. iThe irange imigration icorrection iis iaccomplished iby ishifting ithe isamples iat ia iDoppler ifrequency iin ithe irange iDoppler idomain iup ito ithe iamplitudes iare iequal. iThis iis ireferred ito ias iautomatic irange imigration icorrection. 2.2 iFocus ifiltering i i The ifocus ifilter iminimizes ithe iphase ierrors ipresent iin ireceived isignal iand iimproves ithe ifocus iquality iof iimage iby imatched ifiltering ithe icolumns iof iFourier itransformed iRCMC isignal iwith ithe iazimuth ireference isignal iin iazimuth idirection. iThe idesign iof ithe iazimuth ifilter iis ibased ion ithe ireceived iecho isignal ifrom ithe imoving itarget. iThis iis iknown ias iautofocus. iThe iphase igradient imethod i[12] iis iused ito iestimate ithe iphase ierrors ipresent iin ithe ireceived isignal. iThe ifocus ifilter icoefficient iis iadjusted ito idesign ithe iphase iresponse; itherefore ithe isharpness iof ithe iimage iis ioptimized. i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i2 i| iPage

3. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ 2.3 iWavelet idecomposition i i After iazimuth icompression, ia ide-noised iazimuth icompression isignal iis iobtained iby iusing iwavelet icoefficients ithresholding iusing iglobal ipositive ithreshold iTHR i[10, i28-31]. i iHaar, iDb4, iand iSym8 iwavelets iwith i2, i4, i& i6 idecomposition ilevels iare iused ito ireduce ithe inoise. iNoise idue ito ithe iphase ierrors iare ifurther ireduced iby ithis iprocess. 3. iVelocity iestimation The ireceived ireflected iwave ifrom ithe iobject iis irepresented ias: i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i?(?) = ? ?exp (−?4??(?) ) i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(1) i i i i i i i i i i ? Where it iis islow itime, iw iis ithe iparameter iof iscattering, iλ iis ithe icarrier iwavelength iand i i?(?) iis ithe idistance ibetween ithe idetector iand ithe iobject. i iHere i?(?) iis iwritten ias: Fig. i i2 iGraphical irepresentation iof iSAR iimaging iplane 2+ (??+ ??? − ???)2 ?(?) =√(??+ ??? − ???) i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(2) and iit iis iderived ifrom ithe iSAR iimaging iplane ishown iin iabove iFig. i2. iLet ius iconsider ithe iy-axis iis ithe iradar ibore isight idirected itowards itarget. iThe iradar imoves iwith iradial ivelocity iVy iin iy-axis iand icross irange ivelocity iVx iin ix-axis. iLet ithe itarget ialso imoves iwith iradial ivelocity ivy iand iwith icross irange ivelocity ivx. iAt it=0, ithe itarget iis ilocated iat ipoint i(x0, iy0) iand ithe iradar iat ipoint i(0, i0). After isome itime? = ?? ithe iradar ibore isight iis idirected ito ithe itarget, itherefore: x − 0 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(3) ?s= V v x x and ir0 ibe ithe irange iof ithe iscatter ito ithe iradar iat i?s iis igiven iby: ??= ?? ? + ????? ?– ????? ? i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(4) i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i3 i| iPage

4. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ Then, iapproximating ithe ir(t) iby iits isecond iorder iTaylor iseries iat its i, iwe iobtain: − 2 ( ) V v − 2 x x ( ) t t ?(?) = ?? ?–(?? ?–??) ?(? ?–??) ? + ? s 2 r 0 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(5) substituting iabove iequation i(5) iinto iequation i(1) iyields: (??−??) 2?? ?(?) = ? ????{−?4? (? − ??)2]} i i i i i i i i i i i i i i i i i i i i i i i i i i(6) ?[??− (??− ??)(? − ??) + Differentiate ithe iphase iangle iof ix(t) i iwill iresults ithe iinstantaneous iDoppler ifrequency iof ithat ireceived isignal ii.e.: (??−??)2 ?? 4? ?[(??− ??) − (? − ??)] i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(7) ??= i i i iAn iimportant iparameter icalled iDoppler icentriod ican ibe idefined ias iDoppler ishift iof ia itarget; iit iis ilocated iin ithe iantenna ibore isight idirection. i Doppler icentriod iis iobtained iby isubstituting ??=?? i iin iabove ieq...(7): 4? ?(?? ?–??) ? ? ? i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(8) ??= ? ??? 4?(??−??)2(??− ??) i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(9) i i i i i i? − ??= − substituting iequation i(9) iinto i(5) iyields: ?2?? ???(??−??) 4?(??−??)2(??− ??) + 32?2(??−??)2(??− ??) i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(10) ?(?) = ??+ i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i Equation i(10) iexhibits ithe irelationship ibetween ithe idistance iand ithe iinstantaneous iDoppler ifrequency. iThis igives ithe iapproximate irelationship ibetween ispectral iDoppler ifrequency iand irange. iTherefore ithe ishifting iof ithe iDoppler islice iin ithe irange iis igiven ias i ?2?? ???(??−??) 4?(??−??)2(??− ??) − 32?2(??−??)2(??− ??) i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(11) ??− ?(?) = − Extending ithe iequation i(11) ito ithe ioriginal iinterval iand idiscretizing i i?Ω= ??− ?(?) i iand iΩi i, iwe iget: i ? ??[2 ? 2 ?=1 −∑ ?(? − ??)] [2 ?(? − ??− ?)] ,0 ≤ ? < ??+ 2 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(12) ?(?) = { ? ? 2≤ ? < ? 2 ?=1 ? ? ? ? ? ? − ∑ ?? ,??+ i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i4 i| iPage

5. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ ?ro(Vy−vy) 4??(??−??)2 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(13) i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i?1= i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i ?2?? 32??2(??−??)2 ? ? ? i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(14) i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i?2= where iindex iof iinstantaneous iDoppler ifrequency iΩi i iis ik, ifast itime isampling iperiod iis id, ithe ishifting iof ithe isamples iat ia iDoppler ifrequency ik iis i?(?) iand inormalized iby id. ithe icoefficients iof irange icell imigration iare i?1 iand i?2. i i i i i i iThe iazimuth ifilter iphase iresponse iis iproperly idesigned ito iimprove ithe isharpness iof ithe iimage. iFor iazimuth icompression, ithe idesign iof ithe iazimuth ifilter iphase iresponse iwith ithe iparameters, ithat idepends iupon ithe iradar ivelocity, ithe ipulse irepetition ifrequency i(PRF), iand ithe iabsolute irange. i i The iazimuth ifilter iphase iresponse iis iderived ias ifollows, i i The iFourier itransform iof ithe ireceived iecho isignal ix(t) iis iapproximately i iequal ito: i 2(??−??)2 ???? [−?? ??? 4− ?4? ??? 8?(??−??)2(??− ??)2] i i i i i i i i i i i i(16) ?(??) = ?√ ???− ?????+ ? The iazimuth ifilter iphase iresponse ishould ibe: ??? 8?(??−??)2(??− ??)2 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(17) i i i i i i?(??) = − i i i i i i i i i i i i i i i i i   ( ) iExtending ithe iequation i(16) ito ithe ioriginal iperiod iand idiscretizing i , iΩi iand imodel ias ipolynomial i ii.e.: i i ? ?? (?−?? ? ? ?=2 −∑ ?) ,0 ≤ ? < ??+ 2 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(18) ?(?) = { ? (?−??−? ? ? 2≤ ? < ? ? ?=2 ? ? ? ? ? ? − ∑ ?? ) ,??+ i i i i i i i i i i i i i i i i i i i i i i i i i i i i i ??? 2?2(??−??)2 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(19) i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i? = i i i i i i i i i i i i i i iThe iphase iresponse i?(?) iof iazimuth ifilter iwith ik ias iindependent iparameter iand iβ iis icalled ithe iparameter iof iazimuth ifilter. i Focus ifilter iparameter iβ iis iadjusted ito iminimize ithe iphase ierrors ipresent iin iazimuth icompression isignal ito iimprove ithe isharpness iof ithe ifocused iimage iand iit iis ireferred ito ias ithe iautofocus. iMinimum ientropy iautofocus iusing iphase igradient imethod icarried iout iin ithe ifollowing iway. Focus ifiltering iis iachieved iby: i i 1 ?∑ ?−1 ?=0 ???(??(?)) i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(20) i i i i i i i i i i i i i i i i i i i i i?(?,?) = ??(?,?) Doppler irate, iazimuth, iand ifast itime iare iindexed iby ik, im iand in, irespectively. iThe irange icell imigration icorrected isignal iis i i??(?,?) i, iand ithe iphase iresponse iof iazimuth ifilter iis iΦ(k). iP i(m, in) iis ithe icomplex iimage. iThe ifocus iquality iof icomplex iimage iP i(m, in) iis iimproved iby ireducing iphase ierrors iof ifocus ifilter. iThe iphase iresponse iΦ(k) iof iazimuth ifilter iis ioptimized iuntil ithe ientropy iof i i| iP(m,n)|2is iminimized. i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i5 i| iPage

6. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ i iThe ientropy iof i|?(?,?)|2 iis idefined ias: |?(?,?)|2 ? i i i i i i i i i i i i i iƐ[|?(?,?)|2] = ∑ ?−1 ?=0 ?−1 ?=0 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(21) ∑ ?? |?(?,?)|2 ? ?−1 ?=0 ?−1 ?=0 |?(?,?)|2 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iWhere i i? = ∑ i i i i i i i i i i i i i ∑ In iSAR iimaging, ithe ientropy ican ibe iused ito imeasure ithe ismoothness iof ia idistribution ifunction, iusing ithis icharacteristic iof ientropy, isharpness iof ian iimage ito ibe icalculated i[9-14].The ientropy iof i| i iP(m,n)|2is iminimized iimplies iphase ierrors iof ifocus ifilter iare ireduced, iand ifocus iquality iof icomplex iimage iis iimproved. i i i iLet ithe ifocus ifilter’s iamplitude iresponse iis iassumed ito ibe ia iunit iand iS iis ia iconstant. iTherefore ithe ientropy iof iimage ican ibe idetermined iby: i i i i i i i i i i i i i i i iƐ[|?(?,?)|2] = −∑ ?−1 ?=0 ?−1 ?=0 |?(?,?)|2??|?(?,?)|2 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(22) ∑ iThus, ithe ientropy iof iimage ihas ito ibe iminimized iby iestimating ithe iphase iresponse iof ithe iazimuth ifiler i i 3.1 iEstimation iof iΦ(k) iusing iphase igradient imethod i iEstimation iof iΦ(k) iis idepending iupon ithe iparameter iβi. iTo iimprove ithe icomputational iefficiency, ithe isignal iis ifocused iusing iconventional ifocus ifilter iand ide-noised iusing iwavelet idecomposition. iFrom ithe ide-noised isignal, ithe iparameter iβ iis iadjusted ias ifollows. i i i Phase iestimation iand icorrection i i i i i i iPhase iGradient imethod iis iused ito iestimate iphase ierrors ipresent iin ithe iazimuth icompression isignal. i iThe ifirst istep iin ithe iPGM iis ito iselect istrongest iscatter ifrom ieach irange ibin iand ishift iit ito ithe iorigin, ito iremove ithe ifrequency ioffset idue ito ithe iDoppler iof ithe itarget. iCircular ishifting iis iused ifor ithis iprocess. iThe inext iimportant istep iis iwindowing ithe icircularly ishifted iimage idata. iThe igradient iof iphase ierror iestimation ifrom icircularly ishifted iand iwindowed iimage idata iis igiven iby: i i i   = N u G 0 filter icoefficient iβ i irelation iwith i iDoppler irate iwhere ig(u) iis ithe igradient iof ithe i iphase ierror, iGn(u) iis ithe iinverse iFourier itransform iof ithe icircularly ishifted iand iwindowed iazimuth icompression iimage idata. iThe islope irate iof ithe igradient iof iphase ierrors iis iestimated iand ithen ithe ivariance iof iDoppler irate idfr iis icalculated. i iTherefore ithe  N * Im ( G ) ( ) G u u n n 0 n i i i i i i i i i i i i i i i i i i i i i ig(u)= i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(23) i i i i  = n 2 ( ) n 1 iDoppler irate ifr iis iequal ito ifr i+ idfr iand ithe iazimuth ifilter icoefficient iβ i= . iAccording ito iphase ierrors iin T2 rf iazimuth icompression isignal, iβ iis iadjusted ito iget ifine ifocused iSAR itarget iimage. i 3.2 iEstimation iof iΦ(k) iusing iAdaptive-order ipolynomial iautofocus imethod i iEstimation iof i?(?) idepends iupon ithe iparameter ? ???. iThe iconventional ifocus ifiltering iis itaking iplace ibefore iautofocus ito iimprove icomputational iefficiency. i iFirst i?2 iis iincreased istep iby istep iuntil ientropy iƐ i[.] iis i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i6 i| iPage

7. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ iminimized. iIf iƐ i[.] icannot ibe iminimized i?2 iis ivaried iin ithe iopposite idirection iuntil ithe ientropy iof iimage iƐ i[.] iis iminimized. iThis iprocess iis irepeated ifor ? ??3, i?4 iand iso ion iuntil iƐ i[.] iis iminimized. iThe iphase iresponse i?(?) iis iadjusTABLE, iif ifurther iincrease iin iorder, ithe iestimate iof i?? iapproaches ito izero iand itherefore ithe ihigher iorder iterms iare inot iconsidered, ibecause ithe iestimates iof itwo isuccessive i?? iare iequal ito izero. The ifocus iquality iof iimage iis imeasured iby ientropy. iBetter ifocus icorresponds ito ismaller ientropy. iAfter icalculating iβ, ithe iRCMC icoefficient iis idetermined iby idividing iequations i13 iby i19: i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i?1= (??− ??)?? i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(24) i i i i i i i i i 2? iRCMC, ifocus ifiltering iand iwavelet idecomposition iis icarried iout iautomatically iuntil ientropy iis iminimized. iFrom ithese icoefficients ithe iradial iand icross-range ivelocities iare iestimated. iThe iradial ivelocity iis irepresented iby 2??1 ?? 1 ?√ ??? 2? i iand ithe icross-range iis igiven iby i??= ??− i i. i iThe itotal ivelocity iof imoving itarget iis i i??= ??− iestimated iby iusing ithe iparameters icross-track ivelocity i‘vy’ iand ithe ialong-track ivelocity i‘vx’ iis iwritten ias: i i i i i i i i i i i i i i i i i i i i i 2 + ??2 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(25) i i i i 4. i iResults ?? i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i? = √[ cos(?)] The idetector imoves iat ia icross-track ivelocity iof i0.262m/s iand ialong-track ivelocity iof i7125m/s. i0.56ms iis ithe iradar ipulse irepetition iperiod. iThe ibeam ihas ian iangle iof i0 irad iin iazimuth. iThe iwavelength iof ipulses ihas i5.67 icm iand i15.5MHz ibandwidth. i1.896 iMHz iis ithe isampling ifrequency, iand i1024 ipulses iwith i512 ifast itime isamples ieach iare irecorded. iWhen ithe iazimuth itime iis i0, ithe idetector iis ilocated iat i(0, i0) iand ithe icenter iof ithe iobject ilocated iat i(0, i1547300km). i iFig. i3 ishows ithe imoving icar iwith ivelocity iabout i5m/s iat ithe iairport i[23]. iThe iimage iof ithe icar iin ithe iscene iis iblurred ibecause iof iits imotion. iThe icar iimage iis iisolated ifrom ithe istationary ibackground iusing iMATLAB icommand i‘roipoly’ iand iconverted iinto isignal. iThis isignal iis iprocessed ifor iautomatic iimage iformation iand ifor ivelocity iestimation iusing imodified iRDA iand iconventional iRDA. Fig. i3 iMoving icar iimage iat iairport TABLE-1 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i7 i| iPage

8. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ Car ivelocity iestimation iusing iconventional iRDA True ivelocity iof icar i= i5m/s Radial ivelocity (m/s) S. iNo Method Cross-range ivelocity (m/s) Estimated ivelocity (m/s) Velocity ierror (m/s) 1 Conventional iRDA PGA -1.4860 -4.3564 4.6028 0.3972 AOPM -1.4860 -4.7528 4.9796 0.0203 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i 6 4 2 1 Convention al RDA PGA 1 Convention al RDA AOPM 0 (m/s) (m/s) (m/s) (m/s) -2 Radial velocity Cross-range velocity Estimated velocity Velocity error -4 -6 Fig i4 iEstimation iof icar ivelocity iusing iconventional iRDA iwith iPGA iand iAOPM. i TABLE-1 iand iFig i4 ishow ithe icar ivelocity iestimation iusing iconventional iRDA iwith iPGA iand iwith iAOPM. i0.3972m/s iand i0.0203m/s iare ithe ivelocity ierrors iusing iPGA iand iAOPM irespectively. iAccording ito ithe iobservations, i7.94% iand i0.4% iaccuracy iis iobtained ifor iPGA iand iAOPM irespectively. iAOPM iperforms ibetter iwhen icompared iwith iPGA. i i i TABLE-2 Car ivelocity iestimation iusing imodified iRDA iwith iHaar ide-composition True ivelocity iof icar i= i5m/s Modified iRDA Radial ivelocity (m/s) PGA -1.4060 S. iNo Cross-range ivelocity (m/s) -5.0435 Estimated ivelocity (m/s) 5.2518 Velocity ierror (m/s) 0.2518 Haar-2L decomposition 1 AOPM -1.4660 -4.7565 4.9956 0.0043 PGA -1.4660 -5.0435 5.2522 0.2522 Haar-4L decomposition 2 AOPM -1.4060 -5.1453 5.3497 0.3497 PGA -1.4060 -5.1287 5.4371 0.4371 Haar-6L decomposition 3 AOPM -1.4660 -4.9491 5.1793 0.1793 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i8 i| iPage

9. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ i i i i i i i i i i i i i i i i i i i i i i i 6 4 Radial velocity (m/s) Cross-range velocity (m/s) Estimated velocity (m/s) Velocity error (m/s) 2 0 PGA AOPM PGA AOPM PGA AOPM -2 Haar-2LdecompositionHaar-4LdecompositionHaar-6Ldecomposition 1 2 3 -4 -6 Fig i5 iEstimation iof icar ivelocity iusing imodified iRDA iwith iHaar idecomposition ilevels i TABLE-2 iand iFig i5 ishow ithe iestimation iof icar ivelocity iusing imodified iRDA iwith iHaar idecomposition ilevels iusing iPGA iand iAOPM. i6.3% iand i3.5% iaverage iaccuracy iis iobtained ifrom iPGA iand iAOPM irespectively. iAOPM iwith iHaar idecomposition iperforms ibetter iwhen icompared iwith iPGA. i i TABLE-3 Car ivelocity iestimation iusing imodified iRDA iwith iDb4 ide-composition True ivelocity iof icar i= i5m/s Modified iRDA Radial ivelocity (m/s) S. iNo Cross-range ivelocity (m/s) Estimated ivelocity (m/s) Velocity ierror (m/s) PGA -1.4060 -5.1287 5.3337 0.3337 Db4-2L decomposition 1 AOPM - i1.4660 -4.6546 4.8987 0.1012 PGA -1.4860 -4.4713 4.7316 0.2683 Db4-4L decomposition 2 AOPM -1.4660 -5.2509 5.4684 0.4684 PGA -1.4060 -3.8435 4.1130 0.8869 Db4-6L decomposition 3 AOPM -1.4860 -4.0509 4.2452 0.7547 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i9 i| iPage

10. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ 8 6 4 2 Radial velocity (m/s) Cross-range velocity (m/s) Estimated velocity (m/s) Velocity error (m/s) 0 PGA AOPM PGA AOPM PGA AOPM -2 Db4-2L decomposition Db4-4L decomposition Db4-6L decomposition 1 2 3 -4 -6 Fig i6 iEstimation iof icar ivelocity iusing imodified iRDA iwith iDb4 idecomposition ilevels. TABLE-3 iand iFig i6 ishow ithe iestimation iof icar ivelocity iusing imodified iRDA iwith iDb4 idecomposition ilevels iusing iPGA iand iAOPM. i9.9% iand i8.8% iaverage iaccuracy iis iobtained ifrom iPGA iand iAOPM irespectively. iAOPM iwith iDb4 idecomposition iperforms ibetter iwhen icompared iwith iPGA. TABLE-4 Car ivelocity iestimation iusing imodified iRDA iwith iSym8 ide-composition True ivelocity iof icar i= i5m/s Modified iRDA Radial ivelocity (m/s) PGA -1.4860 S. iNo Cross-range ivelocity (m/s) -4.7861 Estimated ivelocity (m/s) 4.9516 Velocity ierror (m/s) 0.0483 Sym8-2L decomposition 1 AOPM -1.4860 -4.7454 4.9914 0.0085 PGA -1.4660 -5.0139 5.2412 0.2412 Sym8-4L decomposition 2 AOPM -1.4260 -4.8509 5.0732 0.0732 PGA -1.4060 -4.8713 5.0867 0.0867 Sym8-6L decomposition 3 AOPM -1.4060 -4.5528 4.7825 0.2174 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i10 i| iPage

11. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i 6 4 Radial velocity (m/s) Cross-range velocity (m/s) Estimated velocity (m/s) Velocity error (m/s) 2 0 PGA AOPM PGA AOPM PGA AOPM Sym8-2L Sym8-4L Sym8-6L -2 1 2 3 -4 -6 Fig i7 iEstimation iof icar ivelocity iusing imodified iRDA iwith iSym8 idecomposition ilevels. TABLE-4 iand iFig i7 ishow ithe iestimation iof icar ivelocity iusing imodified iRDA iwith iSym8 idecomposition ilevels iusing iPGA iand iAOPM. i2.5% iand i1.99% iaverage iaccuracy iis iobtained ifrom iPGA iand iAOPM irespectively. iAOPM iwith iSym8 idecomposition iperforms ibetter iwhen icompared iwith iPGA. 5. iConclusions Modified iand iconventional iRDA iwith iPGA iand iAOPM iis iused ifor icar ivelocity iestimation iin iSAR iimaging. i1.99% iaverage iaccuracy iis iobtained iby iusing imodified iRDA iwith iSym8 idecomposition ilevels iusing iAOPM. iThis ivalue iis iless ithan iwhen icompared ito ithe iremaining imethods. iTherefore iAOPM iwith iSym8 iperforms ibetter ifor iSAR ireal idata iwhen icompared iwith ithe iother iexisting imethods. i i i References [1] i iCurlander, iJ.C., iand iMcDonough, iR.N.,“ iSynthetic iAperture iRadar: isystems iand isignal iprocessing”. i iNew iYork, iNY: iJohn iWiley i& iSons, i1991. [2] iR.K.Raney, iH.Runge, iR.Bamler, iG.Cumming,, iand iF.H.Wong., i‘Precision iSAR iProcessing i iUsing iChirp iScaling’,IEEE iTransactions ion iGeoscience, iremote iSens., ivol.32, ino.4,pp.786-799 i,july. i1994 [3] iR.Bamler, i“Acomparison iof irange-doppler iand iwave inumber i domain iSAR ifocusing ialgorithms”. iIEEE iTransactions ion iGeosci, iremote iSens., ivol.30, ino.4,pp.706- i713,jul.1992 [4] iWang,J., iand iLiu,X., i i“SAR iminimum-entropy iautofocus iusing ian iadaptive i– iorder i iPolynomial i imodel”. iIEEE iGeoscience iand iRemote iSensing iLetters, i3, i4(oct,2006),512-516 [5] iWang,J., iand iLiu,X.,“Automatic icorrection iof i irange imigration iin iSAR iImaging”.IEEE iGeoscience iand iRemote iSensing iLetters,7. i i2(Apr,2010),256-260. [6] i iWang,J., iand iLiu,X., i“ iVelocity iestimation iof i imoving itargets iin iSAR iimaging”.IEEE iTransactions ion iAerospace iand iElectronic iSystem,50. i i2(Apr,2014),1543-1548. i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i11 i| iPage

12. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ [7] iCaner iOzdemir, i“Inverse iSynthetic iAperture iRadar iImaging iWith i iMatlab i iAlgorithms”. iWiley iSeries iIn iMicrowave iAnd iOptical i i iEngineering. [8] iY.K.Chan iand iV.C.Koo i, i“An iIntroduction iTo iSynthetic iAperture iRadar i(SAR)”. i i[9] iBhuvan, iIndian iGeo-platform iof iISRO [10] iMichel i iMisiti., iYves i iMisiti., iGeorges iOppenheim., iJean-Michel i iPoggi i iWavelet iToolbox, i iFor iUse iWith iMATLAB [11] iP. iH. iEichel, iD. iC. iGhiglia, iand iC. iV. iJakowatz, i“Speckle iprocessing imethod ifor isynthetic iaperture iradar iphase icorrection,” iOpt. iLett., ivol. i14, ino. i1, ipp. i1–5, iJan. i1989. i[12] iD. iE. iWahl, iP. iH. iEichel, iD. iC. iGhiglia, iand iC. iV. iJakowatz, i“Phase igradient iautofocus—A irobust itool ifor ihigh iresolution iSAR iphase icorrection,” iIEEE iTrans. iAerosp. iElectron. iSyst., ivol. i30, ino. i3, ipp. i827–835, iJul. i1994. i[13] iS. iBarbarossa iand iA. iFarina, i“A inovel iprocedure ifor idetecting iand ifocusing imoving iobjects iwith iSAR ibased ion ithe iWigner-Ville idistribution,” iin iProc. iIEEE iInt. iRadar iConf., i1990, ipp. i44–50. i[14] iY. iG. iNiho, i“Phase idifference iauto ifocusing ifor isynthetic iaperture iradar iimaging,” iU.S. iPatent i4999635, iMar. i12, i1991. i[15] iE. iA. iHerland, i“Seasat iSAR iprocessing iat ithe iNorwegian iDefense iResearch iEstablishment,” iin iProc. iEARSeL-ESA iSymp., i1981, ipp. i247–253. [16] iR. iP. iBocker, iT. iB. iHenderson, iS. iA. iJones, iand iB. iR. iFrieden, i“A inew iinverse isynthetic iaperture iradar ialgorithm ifor itranslational imotion icompensation,” iProc. iSPIE, ivol. i1569, ipp. i298–310, i1991. i[17] iX. iLi, iG. iLiu, iand iJ. iNi, i“Autofocusing iof iISAR iimages ibased ion ientropy iminimization,” iIEEE iTrans. iAerosp. iElectron. iSyst., ivol. i35, ino. i4, ipp. i1240–1251, iOct. i1999. i [18] iD. iKasilingam, iJ. iWang, iJ. iLee, iand iR. iJensen, i“Focusing iof isynthetic iaperture iradar iimages iof imoving itargets iusing iminimum ientropy iadaptive ifilters,” iin iProc. iIEEE iInt. iGeosci. iand iRemote iSens. iSymp., i2000, ipp. i74–76. i[19] iJ. iR.Fienup iand iJ. iJ. iMiller, i“Aberration icorrection iby imaximizing igeneralized isharpness imetrics,” iJ. iOpt. iSoc. iAmer. iA, iOpt. iImage. iSci., ivol. i20, ino. i4, ipp. i609–620, iApr. i2003. i[20] iJ. iWang, iX. iLiu, iand iZ. iZhou, i“Minimum-entropy iphase iadjustment ifor iISAR,” iProc. iInst. iElect. iEng., iRadar, iSonar iNavigat., ivol. i151, ino. i4, ipp. i203–209, iAug. i2004. i[21] iJ. iWang iand iX. iLiu, i“SAR iminimum-entropy iautofocus,” iin iProc. iInt. iRadar iConf., i2004. i i i [22] iI. iHemalatha, iP. iV. iSridevi., i“Optimization iof iphase iresponse iof ifocus i ifilter iin isar iimaging”. iIJAERD, iVol. i5, ino. i4, iApril i-2018. [23] iX. iWang, iR. iWang, iN. iLi, iH. iFan, iand iY. iWang, i“A imethod iof iestimating ithe ivelocity iof imoving itargets ifor iuse iin ihigh-resolution iwide-swath iSAR iimaging,” iRemote iSens. iLett., ivol. i9, ino. i4, ipp. i305–313, iApr. i2018. [24] iT. iJin, iX. iQiu, iD. iHu, iand iC. iDing, i“An iML-Based iRadial iVelocity iEstimation iAlgorithm ifor iMoving iTargets iin iSpaceborne iHigh- Resolution iand i i i i i i i i iWide-Swath iSAR iSystems,” iRemote iSens., ivol. i9, ino. i5, ip. i404, iApr. i2017. [25] iW. iWeiwei, iZ. iShengQi, iZ. iJie  iJie, iand iL. iGuisheng, i“Compressive isensing-based iground imoving itarget iindication ifor idual-channel isynthetic iaperture iradar,” iIET iRadar iSonar iNavig., ivol. i7, ino. i8, ipp. i858–866, iOct. i2013. [26] iMin iLei, iYu iYang, iXiaoMing iLiu, iMingZhi iCheng, iand iRui iWang, i“Audio izero-watermark ischeme ibased ion idiscrete icosine itransform-discrete iwavelet itransform-singular ivalue idecomposition,” iChina iCommun., ivol. i13, ino. i7, ipp. i117–121, iJul. i2016. [27] iH. iDemirel iand iG. iAnbarjafari, i“IMAGE iResolution iEnhancement iby iUsing iDiscrete iand iStationary iWavelet iDecomposition,” iIEEE iTrans. iImage iProcess., ivol. i20, ino. i5, ipp. i1458–1460, iMay i2011. i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i12 i| iPage

13. Performance icomparison ibetween iconventional iand imodified iRange iDoppler iAlgorithm iin ireal itime iapplications __________________________________________________________________________________________ [28] iT. iCelik iand iT. iTjahjadi, i“Image iResolution iEnhancement iUsing iDual-Tree iComplex iWavelet iTransform,” iIEEE iGeosci. iRemote iSens. iLett., ivol. i7, ino. i3, ipp. i554–557, iJul. i2010. [29] iH. iDemirel, iC. iOzcinar, iand iG. iAnbarjafari, i“Satellite iImage iContrast iEnhancement iUsing iDiscrete iWavelet iTransform iand iSingular iValue iDecomposition,” iIEEE iGeosci. iRemote iSens. iLett., ivol. i7, ino. i2, ipp. i333–337, iApr. i2010. [30] iM. iZ. iIqbal, iA. iGhafoor, iand iA. iM. iSiddiqui, i“Satellite iImage iResolution iEnhancement iUsing iDual-Tree iComplex iWavelet iTransform iand iNonlocal iMeans,” iIEEE iGeosci. iRemote iSens. iLett., ivol. i10, ino. i3, ipp. i451–455, iMay i2013. i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i iwww.jst.org.in i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i13 i| iPage