Spatially-Varying Calibration of Along-Track Monopulse Synthetic Aperture Radar Imagery for Ground Moving Target Indication and Tracking

Transcription

1 Spatially-Varying Calibration o Along-Track Monopule Synthetic Aperture Radar Imagery or Ground Moving Target Indication and Tracking Uttam Majumder 1 Mehrdad Soumekh Michael Minardi 1 John Kirk 3 1: Air Force Reearch Laboratory 41 Avionic Circle Wright-Patteron AFB OH : Soumekh Conulting Betheda Maryland : Goleta Star LLC 4085 Garnier Street Torrance CA Abtract In thi reearch we have developed an algorithm to reduce the reidual artiact o the background clutter (that i tationary ) that appear in the imagery that are generated by Global Signal Subpace Dierence (GSSD) o the monotatic and bitatic image o an along-track monopule ynthetic aperture (SAR) data We have alo etablihed the theoretical oundation or etimating the motion track and parameter o the detected moving We will how the reult o thee algorithm on meaured SAR data I INTRODUCTION In recent year the United State Air Force Reearch Laboratory at Wright Patteron Air Force bae ha conducted nonlinear SAR data collection with an X-band ytem [1][5] Thi platorm i capable o making bitatic meaurement in the along-track domain a well a monotatic meaurement The data were collected over an urban area that contained high tationary clutter (building vegetation etc) The radiated cene alo included variou road with dierent type o moving vehicle Due to the heavy clutter in the imaging cene the ignature o mot the moving all below the clutter ignature We have developed a nonlinear ubaperture-baed coherent proceing o dual receiver channel o the Gotcha platorm to detect the moving [4] Thi approach utilize the D adaptive proceing that we propoed in []- [4] to blindly calibrate the two receiver channel o an alongtrack monopule SAR ytem Furthermore a pre-proceing o the nonlinear ubaperture data enure the two channel are coherently calibrated with repect to the variation o the light path The current paper i concerned with calibration o the two along-track monopule SAR image via a global patially-varying D adaptive ilter that provide more accurate inormation not only or ground moving indication (G) but alo tracking data that could be exploited to etimate the motion parameter o a moving The baic principle behind extracting moving indication () rom two monotatic and bitatic alongtrack receiver channel o a SAR platorm i that ater compenating/calibrating or known determinitic dierence o the two channel the SAR image can be contructed via the ollowing: x y x y x y m b ( ) where m and ( x b are repectively the monotatic and determinitically-calibrated monotatic and bitatic SAR image In practice due to unknown variation o the electronic antenna etc o the two receiver channel there are unknown phae and gain variation in both range and Doppler domain that are unknown to the uer The implet way to model thi i to aume that thee variation are invariant in range and Doppler In that cae under the null hypothei that i there i no moving the monotatic and bitatic image are related via the ollowing: where m and ( x b h ( x u y v) h( u v) du dv b repreent two-dimenional convolution h i an unknown two-dimenional ilter Under the null hypothei thi ilter can be determined uing the leat mean quare (LMS) algorithm; thi approach i called adaptive iltering A practical implementation o thi method or the two-dimenional problem wa decribed in our previou work []-[4] and wa reerred to a Signal Subpace Proceing (SSP) A more realitic micalibration model or the two receiver channel i baed on the act that the ilter i patially-varying In thi cae the relationhip between the monotatic and bitatic image can be expreed via the ollowing: Correpondence POC: Uttam Majumder Uttammajumder@wpabamil /10/$ IEEE 00045

2 Report Documentation Page Form Approved OMB No Public reporting burden or the collection o inormation i etimated to average 1 hour per repone including the time or reviewing intruction earching exiting data ource gathering and maintaining the data needed and completing and reviewing the collection o inormation Send comment regarding thi burden etimate or any other apect o thi collection o inormation including uggetion or reducing thi burden to Wahington Headquarter Service Directorate or Inormation Operation and Report 115 Jeeron Davi Highway Suite 104 Arlington VA Repondent hould be aware that notwithtanding any other proviion o law no peron hall be ubject to a penalty or ailing to comply with a collection o inormation i it doe not diplay a currently valid OMB control number 1 REPORT DATE MAY 010 REPORT TYPE 3 DATES COVERED to TITLE AND SUBTITLE Spatially-Varying Calibration o Along-Track Monopule Synthetic Aperture Radar Imagery or Ground Moving Target Indication and Tracking 5a CONTRACT NUMBER 5b GRANT NUMBER 5c PROGRAM ELEMENT NUMBER 6 AUTHOR(S) 5d PROJECT NUMBER 5e TASK NUMBER 5 WORK UNIT NUMBER 7 PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Air Force Reearch Laboratory41 Avionic CircleWright-Patteron AFBOH PERFORMING ORGANIZATION REPORT NUMBER 9 SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10 SPONSOR/MONITOR S ACRONYM(S) 1 DISTRIBUTION/AVAILABILITY STATEMENT Approved or public releae; ditribution unlimited 11 SPONSOR/MONITOR S REPORT NUMBER(S) 13 SUPPLEMENTARY NOTES See alo ADM003 Preented at the 010 IEEE International Radar Conerence (9th) Held in Arlington Virginia on May 010 Sponored in part by the Navy 14 ABSTRACT In thi reearch we have developed an algorithm to reduce the reidual artiact o the background clutter (that i tationary ) that appear in the imagery that are generated by Global Signal Subpace Dierence (GSSD) o the monotatic and bitatic image o an along-track monopule ynthetic aperture (SAR) data We have alo etablihed the theoretical oundation or etimating the motion track and parameter o the detected moving We will how the reult o thee algorithm on meaured SAR data 15 SUBJECT TERMS 16 SECURITY CLASSIFICATION OF: 17 LIMITATION OF ABSTRACT a REPORT unclaiied b ABSTRACT unclaiied c THIS PAGE unclaiied Same a Report (SAR) 18 NUMBER OF PAGES 6 19a NAME OF RESPONSIBLE PERSON Standard Form 98 (Rev 8-98) Precribed by ANSI Std Z39-18

3 m b ( x u y v) hxy ( u v) du dv where in thi model the ilter ( u v) patial coordinate that i ( h xy varie with the x While the above model i a more uitable one however it i computationally prohibitive to implement the LMS or SSP method or thi cenario A practical alternative i to aume that the ilter i approximately patially-invariant within a mall area in the patial domain In thi cae we can divide the SAR cene into ubpatche within which the ilter can be approximated to be patially-invariant The reultant model i given by: m b h ( x u y v) h ( u v) du dv b where repreent an index or the ubpatche In the approach that we call Local Signal Subpace Proceing (LSSP) the LMS/SSP method i ued to etimate the local unknown calibration ilter h Ater thi ilter i etimated or each ubpatch an approach that we call Global Signal Subpace Proceing (GSSP) i ued to etimate the original patially-varying ilter ( u v) II h xy MATHEMATICAL PRELIMENARIES The baic oundation o our work i the ue o ubaperture proceing to not only detect but alo geolocate and track moving The imple and mot prominent rational or exploiting ubaperture proceing i that the ignature o a moving appear airly localized in ubaperture SAR imagery though it i lightly meared (Note that the ignature o a moving in a ull-aperture image appear a a everely meared tructure in the ormed image) We hould however point out that the ubaperture image o a moving may not be viible in the ormed image In act the coherent proceing o the monotatic and bitatic image i the key in uppreing the background clutter and revealing the ignature o the moving in the imaging cene We hould alo point out that ubaperture proceing ha alo merit in the cae o SAR data that are collected over a nonlinear light path The reaon or thi i not jut or imaging purpoe or waveront recontruction It turn out that a nonlinear ubaperture that reult in interrogating (imaging) the cene at dierent lant plane actually add to the inormation bae that i exploited to etimate the parameter o a moving Thi will be dicued later Thi ection i intended to outline the baic equation that model the ignature o a moving in a ubaperture Thi model i the oundation o our approach to geolocate and track moving We denote the low-time domain with τ We divided the SAR data into ubaperture that overlap The ize o a ubaperture i choen uch that the baic aumption that the ubaperture image o a moving i relatively localized Thi clearly depend on the SAR ytem parameter (requency band platorm peed etc) and the anticipated maximum peed o the ground moving In the cae o the Gotcha platorm a uitable ubaperture ize i about 104 PRI In our implementation we ue 51 PRI or the overlap region between two adjacent ubaperture Conider the -th ubaperture o the light path In the ubaperture waveront proceing a patially-varying motion compenation i ued to convert the meaured data over the nonlinear path every ubaperture into a conventional linear SAR with a contant platorm velocity or that ubaperture; we call thi the yntheized linear SAR ubaperture (We hould emphaize that thi approach motion compenate the meaured SAR data or every individual point in the 3D patial domain; that i it i a accurate a the backprojection imaging) We denote the coordinate at the midpoint o the reultant linear SAR or the -th ubaperture by ( X Y Z ) We alo denote the contant velocity o the yntheized linear SAR ubaperture by ( v v v ) x y z Note that the yntheized platorm velocity doe vary rom one ubaperture to another Next we identiy the lant-plane where the image i ormed or the -th ubaperture We denote the 3D patial domain by ( x y z) (Thi i equivalent to what i called PCS coordinate ytem by General Dynamic) The waveront proceor orm a lant-plane image with motion compenation that incorporate variation in terrain (uing Digital Elevation Map DEM) The inal output o the waveront proceor i a D image on the plane that i interpolated rom the lant-plane SAR image For convenience we reer to the D ground domain a the UTM domain (though the true UTM domain i a rotated verion o the PCS coordinate ytem); we alo call the two variable a the Northing and Eating coordinate; thi terminology i ued to identiy the UTM domain The lant-plane where the image i ormed i denoted x where lant-plane range with y x x g ( Z Z ) (1) Slant-plane cro-range x inθ y coθ () Slant-plane ground range x coθ y in (3) y x g θ /10/$ IEEE

4 Target area mean elevation i deined by yntheized light path motion angle i θ Z and We hould point out that the D lant-plane ( x y ) varie with each ubaperture and hould be denoted with x For notational implicity we drop the y upercript to identiy the D lant-plane The waveront proceor produce two SAR image on the lant-plane uing monotatic and bitatic data or each Subaperture We denote thee via mono( x y ) and bit ( x y ) Furthermore the coherent ignal ubpace proceing o thee two imagery reult in the GSSD that i the inormation; we deine thi by ( ) x y Uing the invere o the tranormation in equation (1)- (3) thee lant-plane image are tranormed into the ground plane o the PCS coordinate ytem; we reer thee a III mono ( x y ) gmono ( x y ) g ( x RESIDUAL CLUTTER SIGNATURE SUPPRESSION The coherent ignal ubpace proceing yield an in which the background inormation bae ( x y ) clutter i motly uppreed Thi lant-plane image however doe contain ome reidual clutter ignature Since the lant-plane vary with each ubaperture the reidual clutter ignature do not appear at the ame coordinate in the ubaperture image (though they correpond to the eect o tationary ) Meanwhile when the ubaperture image are tranormed into the UTM domain that i g the tranormed reidual clutter ignature do co-regiter in the UTM coordinate Thi property can be exploited to urther reduce the clutter ignature in the UTM domain imagery For thi purpoe we contruct a reerence image via a ubaperture domain median iltering o the image or every point in the UTM coordinate We denote the reultant by g re Thi image i baically a repreentative o the common reidual clutter ignature in all the imagery; it contain almot no moving ignature Next we ue thi reerence image in the adaptive iltering method o ignal ubpace proceing to reduce the reidual clutter ignature in We denote the each ubaperture image g inal image by g -R IV MOVING TARGET SIGNAL MODEL AND IMAGE SIGNATURE WITHIN A SUBAPERTURE Our next tak i to examine the iue that are aociated with tracking a detected moving and etimating it motion parameter To do o we irt develop a ignal model or the ignature o a moving and it image ignature within a ubaperture In our model we aume the velocity o a moving i contant within a ingle ubaperture Conider a moving that i located at the coordinate ( X Y Z ) at the low-time τ 0 that i at the midpoint o the ubaperture Furthermore the 3D velocity o thi moving i denoted with ( v v v ) x y z Thu the radial ditance o the rom the a a unction o the low-time i 1/ ( X v ) xτ X vx τ - R τ ( Y v ) y τ Y v τ (4) y ( ) Z vz τ Z vz τ We denote the angular Doppler requency o thi via the ollowing: ( τ ) φ - Uing SAR ignal theory the - ditance and the angular Doppler requency are related via the ollowing: inφ d dτ () τ R ( τ ) - ( vx vx )( X vx τ X vx τ ) ( vy vy )( Y vy τ Y vy τ ) ( v v )( Z v τ Z v τ ) z z - R z ( τ ) - z A we mentioned earlier the principal aumption in our ubaperture-baed approach i that the ignature o a moving appear airly localized in ubaperture image Thi location in the polar coordinate o the lant-plane are the - radial ditance and the angular Doppler requency at the midpoint o the ubaperture (that i the low-time τ 0 ): ( ) ( [ φ 0 ) () - R- 0 ] (6) Thu the lant-plane coordinate o the moving in the ubaperture image are x y R-() 0 coφ-( 0) ( ) ( ) ( 0 ) in ( R φ ) ( 0 ) - - (5) /10/$ IEEE

5 Uing the mapping rom the lant-plane to the UTM domain the lant-plane coordinate o the moving can be converted to it ground UTM (PCS) coordinate: [ x y ] [ x y ] The ditance o thi ignature rom the location o the platorm at the mid-point o the aperture in the UTM domain i: R X x Y y ( ) ( ) [ R ( 0) ] ( Z Z ) - V RESULTS The overall ignal proceing ued in our approach i hown in Figure 1 and Figure 3 i the UTM domain recontruction o the interrogated or Subaperture 1 Figure 4 how the image or the ame cene uing the coherent GSSP Figure 3: UTM Recontruction: FP-18; Subaperture 1 Figure 1 Waveront Recontruction and Coherent Clutter Suppreion with Monotatic and Bitatic Data o Along-Track Monopule SAR Figure 4: Coherent via GSSP in UTM Domain: FP-18; Subaperture 1 Figure : Slant-Plane to UTM (Ground-Plane) Tranormation o Image and Reidual Clutter Suppreion Figure 5 i the reerence image that i contructed rom the median iltering o the UTM domain -GSSD imagery; ee the block diagram in Figure Figure 6 i the reultant image or Subaperture 1 uing non-coherent LSSP proceing o the -GSSD image o Figure 6 and the reerence image o Figure 5 We have generated movie o thee reult or a et o the ubaperture /10/$ IEEE

6 Figure 5: Reerence Image Ued or Reidual Clutter Suppreion Figure 6: Ater Reidual Clutter Suppreion FP-18; Subaperture 1 Figure 7a: Detected Moving Target in Recontruction and FP-18; Subaperture 1 Figure 7b: Detected Moving Target in Recontruction and FP-18; Subaperture 1 (zoomed verion) /10/$ IEEE

7 VI CONCLUSION In thi paper we have preented an algorithm to reduce the reidual artiact o the background clutter that appear in the imagery Thi wa accomplihed by Global Signal Subpace Dierence (GSSD) o the monotatic and bitatic image o an along-track monopule SAR data We have decribed the theoretical oundation or etimating the motion track and parameter o the detected moving The reult preented here were generated uing Gotcha data Thi reearch will continue to detect geolocate and tracking multiple moving in SAR imagery in realtime Figure 8a: Radial Location o Detected Moving Target ACKNOWLEDGMENT The author would like to thank Mr LeRoy Gorham or decription o the Gotcha data Mr Steven Scarborough and Mr Edmund Zelnio or valuable technical dicuion on the merit o thi algorithm REFERENCES [1] U Majumder M Minardi E Blach L Gorham K Naidu T Lewi and R William Radar Signal Dimount Data Production Proc SPIE Deene and Security Conerence Orlando April 006 [] M Soumekh Signal Subpace Fuion o Uncalibrated Senor with Application in SAR and Diagnotic Medicine IEEE Tranaction on Image Proceing vol 8 no 1 pp January 1999 [3] M Soumekh Moving Target Detection and Imaging Uing an X Band Along-Track Monopule SAR IEEE Tranaction on Aeropace and Electronic Sytem vol 38 no 1 pp January 00 [4] U Majumder et al SAR- Proceing o Along-Track Monopule Nonlinear SAR GOTCHA Data Proc IEEE Radar Conerence Paadena May 009 [5] S Scarborough C Cateel Jr L Gorham M Minardi U Majumder M Judge E Zelnio M Bryant H Nichol and D Page A Challenge Problem or SAR-baed G in Urban Environment Proc SPIE Vol G (009) Figure 8b: Radial Location o Detected Moving Target (zoomed verion) /10/$ IEEE