Adaptive Processing of SAR Data for ATR

Transcription

1 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Mehrdad Soumekh M. Soumekh Cosultat & Departmet o Electrical Egieerig 33 Boer Hall SUNY-Bualo Amherst NY 46 Phoe: 76) msoum@eg.bualo.edu. Itroductio I this presetatio we outlie a ramework or Automatic Target Recogitio ATR) i Sthetic Aperture Radar SAR) that is based o a adaptive processig o the digitall-spotlighted phase histor data o idividual targets. I the covetioal SAR- ATR algorithms the magitude ol or the comple SAR image o a test target chip is aalzed ad compared with a set o reerece target chips to determie the test target tpe or class. Depedig o the relative coordiates o a test target i the imagig scee ad the light path o the radar-carrig aircrat the SAR image chip) o the test target possesses a spatial warpig with respect to the reerece target chips that should be blidl icorporated ad/or compesated i the ATR algorithm. Furthermore the ormed SAR images ehibit certai slat plae) parametric variatios ad erroeous shits that deped o the tpe o the SAR imagig algorithm that is used. For the success o a SAR- ATR algorithm the spatial warpig ad slat plae parameters o the SAR imagig algorithm should be available to the user. I practice these parameters o the ormed SAR image are ot eactl kow to the SAR-ATR user. Moreover a compariso betwee the test ad reerece target chips requires uderstadig ad icorporatig the sesor ad platorm variatios i the correspodig SAR data acquisitios. The sesor variatios are caused b various subtle chages imperectios) i the radar sstem circuitr e.g. waveorm geerator cables etc.) ad udesirable amplitude/phase luctuatios i the radiatio patter o the phsical radar betwee the reerece ad test data collectios; these are ukow ad result i dieret D Image Poit Respose IPR) or Poit Spread Fuctio PSF) i the reerece ad test SAR images. The above-metioed ambiguities result i ukow subtle geometric distortios ad comple PSF variatios i the recostructed SAR image that have adverse eects o the perormace o a SAR-ATR algorithm. Soumekh M. 5) Adaptive Processig o SAR Data or ATR. I MMW Advaced Target Recogitio ad Idetiicatio Eperimet pp. - -). Meetig Proceedigs RTO-MP-SET-96 Paper. Neuill-sur-Seie Frace: RTO. Available rom: RTO-MP-SET-96 - UNCLASSIFIED/UNLIMITED

2 Report Documetatio Page Form Approved OMB No Public reportig burde or the collectio o iormatio is estimated to average hour per respose icludig the time or reviewig istructios searchig eistig data sources gatherig ad maitaiig the data eeded ad completig ad reviewig the collectio o iormatio. Sed commets regardig this burde estimate or a other aspect o this collectio o iormatio icludig suggestios or reducig this burde to Washigto Headquarters Services Directorate or Iormatio Operatios ad Reports 5 Jeerso Davis Highwa Suite 4 Arligto VA -43. Respodets should be aware that otwithstadig a other provisio o law o perso shall be subject to a pealt or ailig to compl with a collectio o iormatio i it does ot displa a curretl valid OMB cotrol umber.. REPORT DATE MAY 5. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE Adaptive Processig o SAR Data or ATR 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHORS) 5d. PROJECT NUMBER 5e. TASK NUMBER 5. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAMES) AND ADDRESSES) M. Soumekh Cosultat & Departmet o Electrical Egieerig 33 Boer Hall SUNY-Bualo Amherst NY PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAMES) AND ADDRESSES). SPONSOR/MONITOR S ACRONYMS). DISTRIBUTION/AVAILABILITY STATEMENT Approved or public release distributio ulimited 3. SUPPLEMENTARY NOTES See also ADM5. The origial documet cotais color images. 4. ABSTRACT 5. SUBJECT TERMS. SPONSOR/MONITOR S REPORT NUMBERS) 6. SECURITY CLASSIFICATION OF: 7. LIMITATION OF ABSTRACT UU a. REPORT uclassiied b. ABSTRACT uclassiied c. THIS PAGE uclassiied 8. NUMBER OF PAGES 58 9a. NAME OF RESPONSIBLE PERSON Stadard Form 98 Rev. 8-98) Prescribed b ANSI Std Z39-8

3 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR I this work we provide a two-stage SAR-ATR algorithm that is ot sesitive to the above-metioed problems. I the proposed approach the SAR-ATR user applies a relativel ast CFAR detectio algorithm with a high probabilit o alse alarm as well as a high probabilit o detectio to ideti the coordiates o suspected targets i a SAR imagig scee. Net the coordiates o each suspected target is passed to what we reer to as the digital-spotlightig algorithm that etracts the SAR phase histor data o a eighborhood withi the iput coordiates. The resultat database is the comple SAR sigature phase histor) o the chip area at the desired coordiates that carries iormatio o the variatios o the target's comple radar sigature with respect to the ast-time radar) requec ad aspect agle. This database is the compared with a set o reerece phase histor models to ideti the target at the iput coordiates where the origial ATR algorithm detected a suspected target. A D adaptive method or the above-metioed matchig o test ad reerece phase histor data is utilized a algorithm that we call sigal subspace matched ilterig that is ot sesitive to the calibratio errors o the SAR sstem i.e. variatios o the radar radiatio patter rom oe eperimet to aother). Such calibratio errors that could drasticall alter the phase iormatio o a target's SAR sigature are oe o the major obstacles i eploitig the comple SAR sigature o a target i the classiicatio/recogitio problems. The sigal subspace processig method perorms a blid calibratio o variatios o the IPRs o the reerece ad test SAR phase histor data usig D adaptive ilterig methods. This calibratio also compesates or variatios i the IPRs that are due to imperect errors i) motio data ad required D autoocusig to compesate or them amog other SAR sstem phase errors such as ragegate slip) that ever results i the theoretical ideal) SAR image.. Sources o Calibratio Errors SAR sigature o a target depeds o the radar sesor characteristics beam patter sigal geerator etc.) as well as the phsical properties o the target. Figure shows the overall sstem diagram or geeratio o a target sigature i SAR. I SAR-ATR compariso betwee the test ad reerece target chips requires uderstadig ad icorporatig the sesor ad platorm variatios i the correspodig SAR data acquisitios. The sesor variatios are caused b various subtle chages imperectios) i the radar sstem circuitr e.g. waveorm geerator cables etc.) ad udesirable amplitude/phase luctuatios i the radiatio patter o the phsical radar betwee the reerece ad test data collectios; see Figures a ad c. These are ukow ad result i dieret D Image Poit Respose IPR) or Poit Spread Fuctio PSF) i the reerece ad test SAR images. These ambiguities result i ukow subtle geometric distortios ad comple PSF variatios i the recostructed SAR image that have adverse eects o the perormace o a SAR-ATR algorithm. Variatios i the target ma also eist; e.g. rotatio i the gu o a tak opeig or closig o driver/commader/turret hatch etc.; see Figure d. - RTO-MP-SET-96 UNCLASSIFIED/UNLIMITED

4 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Figure. Model or Geeratio o SAR Sigal RTO-MP-SET-96-3 UNCLASSIFIED/UNLIMITED

5 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Variatios i Radar Trasmit-Mode Beam Patter Variatios i Motio & Autoocus Figure a. SAR Calibratio Errors: Trasmit Mode Variatios i Target Coheret SAR Sigature Figure b. SAR Calibratio Errors: Variatios i Target - 4 RTO-MP-SET-96 UNCLASSIFIED/UNLIMITED

6 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Variatios i Radar Receive-Mode Beam Patter Variatios i Motio & Autoocus Figure c. SAR Calibratio Errors: Receive Mode 3. Adaptive Calibratio o Dual SAR Imager via Sigal Subspace Processig I SAR-ATR the task o a sigal processor is to blidl compesate or the abovemetioed calibratio errors. For this purpose we utilize a D adaptive method or the matchig o test ad reerece target chips is utilized []. This algorithm that we call sigal subspace matched ilterig is ot sesitive to the calibratio errors o the SAR sstem i.e. variatios o the radar radiatio patter etc. rom oe eperimet to aother) as well as small variatios i the target. The mathematical oudatio o this approach is the same as a adaptive ilterig algorithm that we have developed or coheret chage detectio [] [ ch. 8] ad movig target detectio [ ch. 8] [3] [4] i SAR sstems. The ollowig outlies the oudatio o the adaptive sigal subspace algorithm usig irst a oe-dimesioal sigal space. The results are the eteded to the twodimesioal problems o SAR. RTO-MP-SET-96-5 UNCLASSIFIED/UNLIMITED

7 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Sigal Subspace Processig: A D Eample ) h) out ) e) ) We wat to determie h) such that ) ) i.e. e) ) or the eample this meas that we must determie hi) or i -. The equatios or the output o h) are: ) h ) ) h ) ) h ) M ) h ) ) h ) ) h ) ) h ) ) h) ) h) ) h) ) h) ) h) 3) h) ) h) 3) h) 4) h) ) h ) ) h) ) h) ) h) M M M M out out out out ) ) ) ) This ca be represeted i vector orm as show o the et slide. This ca be represeted i vector orm as show o the et slide. ) ) ) ) ) ) ) ) ) 3) h ) h ) h) h) h) M M M M M ) ) ) ) ) out ) ) M ) out out v - v - v v v v out The vector represetatio shows that the output resides i the sigal subspace spaed b V {v i i i - }. We ca create a orthoormal basis or this subspace via Gram-Schmidt) ad obtai modiied ilter coeiciets based o these ew basis vectors. That is: v h ) v vˆ hˆ ) vˆ h ) v h) v hˆ ) vˆ h) v h) hˆ) vˆ hˆ) vˆ hˆ) Where the otatio vˆ i idicates that the vector is part o the orthoormal basis ad the otatio h ˆ i ) idicates that the coeiciet has bee adjusted appropriatel or the orthoormal basis vector). - 6 RTO-MP-SET-96 UNCLASSIFIED/UNLIMITED

8 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR We ca solve or each o the ilter coeiciets b calculatig the ier product with the correspodig orthoormal basis vector: hˆ i) vˆ hˆ ) vˆ vˆ v i out hˆ ) vˆ hˆ) vˆ hˆ) vˆ hˆ) vˆ i These coeiciets ca the be used to calculate the projectio o ) sigal ito the sigal subspace o ). These coeiciets ca the be used to calculate the projectio o ) sigal ito the sigal subspace o ). The resultig output o h) the estimate o )) is simpl the projectio o ) ito the sigal subspace o )!! The dierece betwee the reerece sigal ad the projected test sigal becomes: e which also shows how much the test sigal diers rom the reerece. ˆ RTO-MP-SET-96-7 UNCLASSIFIED/UNLIMITED

9 ) ) ) ) ) j i k m k m j i k m h Etesio to D ] [ ); ) ) j i k k m m L L Φ Liear Filter: Sigal Subspace: h) ) ) e) out ) ] [ ma mi mi ma mi mi ); ) ) k k k j k k k i m m j i k k K K L L Θ θ The orthoormalized Sigal Subspace: ) ˆ ) ˆ ) ) ) j i k m k m j i k m h The ilter output or the ormalized subspace): Aalogous to the D case the output o the ilter is simpl the projectio o k) ) ito Θ k). Adaptive Processig o SAR Data or ATR - 8 RTO-MP-SET-96 UNCLASSIFIED/UNLIMITED UNCLASSIFIED/UNLIMITED

10 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR 4. Adaptive SAR-ATR: Ka Bad Turtable ISAR) Data We et eamie the applicatio o the SSP algorithm i SAR-ATR usig a Ka bad turtable ISAR database. Figure 3a shows a portio o the measured ISAR data i the radar requec ad aspect agle domai. The irst issue that we otice or this database is the irregular vertical lies. Figure 3b shows the cumulative spectrum o the data. This idicates irregular trasmitter power variatios i the ISAR data. This is also a calibratio error source that ca be easil compesated or usig the iverse o the distributio i Figure 3b as a ilter to be applied to the measured ISAR data. Note that this is magitude ol calibratio. Oe ma also perorm phase calibratio provided a omi-directioal target had bee put i the imagig scee.) Figure 3c shows the magitude-calibrated ISAR data. Figure 3a. Measured ISAR Data RTO-MP-SET-96-9 UNCLASSIFIED/UNLIMITED

11 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Figure 3b. Cumulative Spectrum o Measured ISAR Data We use two SAR/ISAR recostructio algorithms to orm images rom the magitudecalibrated data. The irst method is the polar ormat algorithm that is based o approimatios; the secod method is the waverot recostructio algorithm that is error-ree [ ch. 7]. Figures 4a ad 4b are the resultat images usig 6 degrees o itegratio agle; similar results or a 3-degree itegratio agle are show i Figures 5a ad 5b. Note that the waverot recostructio algorithm provides better images. For our SAR-ATR stud the waevrot images are used. For the SAR-ATR stud we cosider two o the ISAR databases o a T-7 tak: T6.rq ad T7.rq. The dierece betwee the two databases is the orietatio o the gu o the vehicle: or the T6.rq data the gu is at the azimuth agle o - degrees; the azimuth agle o the gu is zero or the T7.rq data. Thus the recogitio algorithm should match the structure o the T-7 tak ecept or the gu i the two databases. - RTO-MP-SET-96 UNCLASSIFIED/UNLIMITED

12 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Figure 3c. Calibrated ISAR Data A simple dierecig or correlatio o the two ISAR images would ot idicate a match. Figures 6a ad 6b respectivel show the icomig ad outgoig sigal subspace dierece SSD) images. Note that the T-7 compoets are matched ecept or the gu ad a area ear the upper hatch. The latter might be a uiteded chage that occurred while movig the tak o ad o the turtable. This ca also be see i Figure 7a ad 7b that are the close ups o the origial ISAR images ad SSD images. RTO-MP-SET-96 - UNCLASSIFIED/UNLIMITED

13 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Figure 4a. Polar Format Recostructio: Itegratio Agle 6 Degrees - RTO-MP-SET-96 UNCLASSIFIED/UNLIMITED

14 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Figure 4b. Waverot Recostructio: Itegratio Agle 6 Degrees RTO-MP-SET-96-3 UNCLASSIFIED/UNLIMITED

15 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Figure 5a. Polar Format Recostructio: Itegratio Agle 3 Degrees - 4 RTO-MP-SET-96 UNCLASSIFIED/UNLIMITED

16 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Figure 5b. Waverot Recostructio: Itegratio Agle 3 Degrees RTO-MP-SET-96-5 UNCLASSIFIED/UNLIMITED

17 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Figure 6a. Icomig Coheret Sigal Subspace Dierece - 6 RTO-MP-SET-96 UNCLASSIFIED/UNLIMITED

18 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Figure 6b. Outgoig Coheret Sigal Subspace Dierece RTO-MP-SET-96-7 UNCLASSIFIED/UNLIMITED

19 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Figure 7a - 8 RTO-MP-SET-96 UNCLASSIFIED/UNLIMITED

20 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR Figure 7b RTO-MP-SET-96-9 UNCLASSIFIED/UNLIMITED

21 UNCLASSIFIED/UNLIMITED Adaptive Processig o SAR Data or ATR 5. Summar Sesor calibratio is a critical problem that has to be dealt with though igored) i ocoheret ad coheret imagig sstems such as SAR. Simple modiicatio ad/or reormulatio o eistig D adaptive blid) ilterig methods eist or D calibratio problems o SAR-ATR SAR-Coheret Chage Detectio CCD) SAR-MTI etc. This paper ehibited a eample o the applicatio this method i the SAR-ATR problem. 6. Reereces. Soumekh SAR Sigal Processig Wile 999. Dilsavor Mitra Hesel Soumekh GPS-Based Spatial ad Spectral Registratio o Delta-Headig Multipass SAR Imager or Coheret Chage Detectio Proc. U.S. Arm Workshop o Sthetic Aperture Radar Techolog Redstoe Arseal October 3. Soumekh Movig Target Detectio ad Imagig Usig a X Bad Alog-Track Moopulse SAR IEEE Tras. O Aerospace ad Electroic Sstems Jauar 4. Soumekh Himed SAR-MTI Processig o Mutli-Chael Airbore Radar Measuremet MCARM) Data Proc. IEEE Radar Co. Ma - RTO-MP-SET-96 UNCLASSIFIED/UNLIMITED

22 Adaptive Processig o SAR Data or ATR Mehrdad Soumekh M. Soumekh Cosultat & Departmet o Electrical Egieerig 33 Boer Hall SUNY-Bualo Amherst NY 46 Phoe: 76) msoum@eg.bualo.edu

23 Outlie Sources o Calibratio Errors i SAR Radar Calibratio Errors Target Sigature Variatios Model or Geeratio o SAR Sigal Adaptive Calibratio o Dual SAR Imager via Sigal Subspace Processig SSP) Eample: Ka Bad Turtable ISAR) Data Summar

24 Sources o Calibratio Errors i SAR

25 Sources o Calibratio Errors SAR sigature o a target depeds o the radar sesor characteristics beam patter sigal geerator etc.) as well as the phsical properties o the target I SAR-ATR compariso betwee the test ad reerece target chips requires uderstadig ad icorporatig the sesor ad platorm variatios i the correspodig SAR data acquisitios

26 Sources o Calibratio Errors Cot. The sesor variatios are caused b various subtle chages imperectios) i the radar sstem circuitr e.g. waveorm geerator cables etc.) ad udesirable amplitude/phase luctuatios i the radiatio patter o the phsical radar betwee the reerece ad test data collectios These are ukow ad result i dieret D Image Poit Respose IPR) or Poit Spread Fuctio PSF) i the reerece ad test SAR images

27 Sources o Calibratio Errors Cot. These ambiguities result i ukow subtle geometric distortios ad comple PSF variatios i the recostructed SAR image that have adverse eects o the perormace o a SAR-ATR algorithm Variatios i the target ma also eist; e.g. rotatio i the gu o a tak opeig or closig o driver/commader/turret hatch etc.

28 Model or Geeratio o SAR Sigal

29 Overall SAR Sstem Sigal Model

30 Variatios i Radar Trasmit-Mode Beam Patter Variatios i Motio & Autoocus

31 Variatios i Target Coheret SAR Sigature

32 Variatios i Radar Receive-Mode Beam Patter Variatios i Motio & Autoocus

33 Adaptive Calibratio o Dual SAR Imager via Sigal Subspace Processig

34 Adaptive SAR-ATR Solutio A D adaptive method or the matchig o test ad reerece target chips is utilized This algorithm that we call sigal subspace matched ilterig is ot sesitive to the calibratio errors o the SAR sstem i.e. variatios o the radar radiatio patter etc. rom oe eperimet to aother) as well as small variatios i the target

35 Sigal Subspace Processig: A D Eample ) h) out ) e) ) We wat to determie h) such that ) ) i.e. e) ) or the eample this meas that we must determie hi) or i -. The equatios or the output o h) are: ) h ) ) h ) ) h ) M ) h ) ) h ) ) h ) ) h ) ) h ) M ) h) ) h) ) h) ) h) ) h) ) h) 3) h) ) h) ) h) 3) h) 4) h) M M ) h) out out out out ) ) ) M ) This ca be represeted i vector orm as show o the et slide. This ca be represeted i vector orm as show o the et slide.

36 Sigal Subspace Processig: A D Eample Cot. ) ) ) ) ) 3) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) h h h h h out out out M M M M M M v - v - v v v v out The vector represetatio shows that the output resides i the sigal subspace spaed b V {v i i - }. We ca create a orthoormal basis or this subspace via Gram-Schmidt) ad obtai modiied ilter coeiciets based o these ew basis vectors. That is: The vector represetatio shows that the output resides i the sigal subspace spaed b V {v i i - }. We ca create a orthoormal basis or this subspace via Gram-Schmidt) ad obtai modiied ilter coeiciets based o these ew basis vectors. That is: ˆ) ˆ ˆ) ˆ ˆ) ˆ ) ˆ ˆ ) ˆ ˆ ) ) ) ) ) h h h h h h h h h h v v v v v v v v v v Where the otatio idicates that the vector is part o the orthoormal basis ad the otatio idicates that the coeiciet has bee adjusted appropriatel or the orthoormal basis vector). Where the otatio idicates that the vector is part o the orthoormal basis ad the otatio idicates that the coeiciet has bee adjusted appropriatel or the orthoormal basis vector). i vˆ ) ˆ i h

37 Sigal Subspace Processig: A D Eample Cot. We ca solve or each o the ilter coeiciets b calculatig the ier product with the correspodig orthoormal basis vector: hˆ i) vˆ hˆ ) vˆ hˆ ) vˆ hˆ) vˆ hˆ) vˆ hˆ) vˆ i vˆ i v out These coeiciets ca the be used to calculate the projectio o ) sigal ito the sigal subspace o ). These coeiciets ca the be used to calculate the projectio o ) sigal ito the sigal subspace o ). The resultig output o h) the estimate o )) is simpl the projectio o ) ito the sigal subspace o )!! The dierece betwee the reerece sigal ad the projected test sigal becomes: which also shows how much the test sigal diers rom the reerece. e ˆ

38 Etesio to D ) ) ) ) ) j i k m k m j i k m h Liear Filter: ] [ ); ) ) j i k k m m L L Φ Sigal Subspace: h) ) ) out ) e)

39 Etesio to D Cot. The orthoormalized Sigal Subspace: ] [ ma mi mi ma mi mi ); ) ) k k k j k k k i m m j i k k K K L L Θ θ ) ˆ ) ˆ ) ) ) j i k m k m j i k m h The ilter output or the ormalized subspace): Aalogous to the D case the output o the ilter is simpl the projectio o k) ) ito Θ k).

40 Sigal Subspace Matchig or Chage Detectio Gram- Schmidt Image chips Chip Vectors Create small local image chips or both reerece ad test Shit each reerece chip to create a basis or each grid square Create Reerece Image Basis Vectors rom Basis Chips Orthoormalize Reerece Image Basis Vectors dierece chage o chage Threshold dierece test reerece test Reerece plae Decide i target has etered or eited scee Subtract Reerece rom projectio Project test vector ito reerece subspace

41 Adaptive SAR-ATR: Ka Bad Turtable ISAR) Data

42 Measured SAR Data Aspect Agle deg Radar Frequec GHz

43 . Cumulative Relative Magitude..9 Magitude Radar Frequec GHz

44 Magitude Calibrated SAR Data Aspect Agle deg Radar Frequec GHz

45 Polar Format Recostructio: Itegratio Agle 4 o 6 4 Azimuth m Rage m 4 6

46 Waverot CSAR Recostructio: Itegratio Agle 4 o 6 4 Azimuth m Rage m 4 6

47 Polar Format Recostructio: Itegratio Agle 8 o 6 4 Azimuth m Rage m 4 6

48 Waverot CSAR Recostructio: Itegratio Agle 8 o 6 4 Azimuth m Rage m 4 6

49 Polar Format Recostructio: Itegratio Agle 6 o 6 4 Azimuth m Rage m 4 6

50 Waverot CSAR Recostructio: Itegratio Agle 6 o 6 4 Azimuth m Rage m 4 6

51 Polar Format Recostructio: Itegratio Agle 3 o 6 4 Azimuth m Rage m 4 6

52 Waverot CSAR Recostructio: Itegratio Agle 3 o 6 4 Azimuth m Rage m 4 6

53 Block Partitioig o Recostructio

54 Reerece Image: T6 Test Image: T7 Azimuth m Azimuth m Rage m Rage m Icomig CSSD Outgoig CSSD Azimuth m Azimuth m Rage m Rage m

55 Reerece Image: T6 Test Image: T7 Azimuth m - Azimuth m Rage m Rage m Icomig CSSD Outgoig CSSD Azimuth m - Azimuth m Rage m Rage m

56 Icomig Coheret Sigal Subspace Dierece: T6-T7 6 4 Azimuth m Rage m 4 6

57 Outgoig Coheret Sigal Subspace Dierece: T6-T7 6 4 Azimuth m Rage m 4 6

58 Summar Sesor calibratio is a critical problem that has to be dealt with though igored) i ocoheret ad coheret imagig sstems such as SAR Simple modiicatio ad/or reormulatio o eistig D adaptive blid) ilterig methods eist or D calibratio problems o SAR-ATR SAR-Coheret Chage Detectio CCD) SAR-MTI etc.

59 Reereces Soumekh SAR Sigal Processig Wile 999 Dilsavor Mitra Hesel Soumekh GPS-Based Spatial ad Spectral Registratio o Delta- Headig Multipass SAR Imager or Coheret Chage Detectio Proc. U.S. Arm Workshop o Sthetic Aperture Radar Techolog Redstoe Arseal October Soumekh Movig Target Detectio ad Imagig Usig a X Bad Alog-Track Moopulse SAR IEEE Tras. O Aerospace ad Electroic Sstems Jauar Soumekh Himed SAR-MTI Processig o Mutli-Chael Airbore Radar Measuremet MCARM) Data Proc. IEEE Radar Co. Ma