A Novel Approach for Multiple Moving Target Localization Using Dual-Frequency Radars and Time-Frequency Distributions

Transcription

1 A Novel Approah for Multple Movng Target Loalzaton Usng Dual-Frequeny Radars and Tme-Frequeny Dstrbutons Ymn Zhang, Moeness Amn, and Fauza Ahmad Radar Imagng Lab, Center for Advaned Communatons Vllanova Unversty, Vllanova, PA E-mal: {ymn.zhang, moeness.amn, Abstrat - Aurate range estmaton and trakng of movng targets s an mportant task n urban sensng applatons. A dual-frequeny radar, whh estmates the range of a target based on the phase dfferene between two losely spaed frequenes, has been shown to be a ost-effetve approah to aomplsh both range-to-moton estmaton and trakng. Ths approah, however, suffers from two drawbaks: t annot deal wth multple movng targets, and has poor performane n nosy envronments. To overome these drawbaks, we propose, n ths paper, the use of tmefrequeny sgnal representatons. Hgh sgnal-to-nose rato (SNR) s obtaned by fousng on the movng target nstantaneous Doppler frequeny law provded by the power loalzaton propertes of tme-frequeny dstrbutons. The ase of multple movng targets s handled by separatng the dfferent Doppler sgnatures pror to phase estmaton. I. INTRODUCTION Through-the-wall radar magng (TWRI) and sensng s an emergng tehnology supportng a range of vlan and mltary applatons [1-6]. TWRI has been reently sought out for survellane and reonnassane n urban envronments, requrng not only the layout of the buldng, nludng types and loatons of walls, but also deteton and loalzaton of both movng and statonary targets wthn enlosed strutures. Ths tehnology an also be used by frefghters to detet and loate survvors, by rmnal juste offers for enhaned stuatonal awareness and talored tatal operatons, and n searh and resue operatons n natural dsasters. There are many hallenges fang the development of a suessful TWRI system to meet the needs of urban sensng. The system should be low ost, lght weght, relable, portable, and user-frendly. It should be able to detet, loate, and lassfy a varety of ndoor targets, nludng both movng and statonary objets, enlosed n small spaes and n the presene of sgnfant multpath propagaton and heavy lutter. Doppler radars satsfy all of the above ondtons, spefally when the loaton of movng targets, rather than target resolutons, are of prmary nterest. Ths work was supported n part by ONR under grant N and n part by DARPA under ontrat no. HR C The ontent of the nformaton does not neessarly reflet the poston or the poly of the Government, and no offal endorsement should be nferred. Approved for Publ Release, Dstrbuton Unlmted. In ths paper, we onsder Doppler radars for both target moton deteton and rangng. Doppler radars typally use a sngle frequeny and, as suh, suffer from large range ambguty. In urban sensng applatons, range ambguty may be elmnated f the dfferene between onseutve range estmates s larger than the buldng dmensons. Due to restrtons on antenna sze and frequeny alloaton management, lowerng the radar frequeny to redue the range ambguty s not a vable opton for urban sensng applatons. A smple and low ost alternatve s the dualfrequeny ontnuous-wave (CW) radar based approah, whh employs two dfferent frequenes and smultaneously measures the phase hange wth respet to tme, for eah of the two frequenes, separately [7-9]. It uses phase omparson of the refleted sgnals to estmate the range, whereas the target veloty s dretly obtaned from the Doppler shft. The two arrer frequenes, and hene ther respetve wavelengths, determne the maxmum unambguous range of the target. The method an detet movng targets up to a maxmum range orrespondng to 360 phase dfferene of the radar returns for two dstnt arrer frequenes. Ths an sgnfantly nrease the unambguous range ompared to that of sngle frequeny operaton. The performane of the dual-frequeny radar tehnque rapdly degrades when operatng n a nosy luttered envronment [10], whh s ommonly enountered n urban sensng applatons, and when dealng wth multple targets. In the latter, the reeved sgnal s the superposton of returns from dfferent targets and, therefore, phase nformaton orrespondng to ndvdual targets annot be obtaned from the raw data. Smlarly, when there are strong multpaths of a sngle or multple targets, the phase s dstorted and the phase nformaton from raw returns does not yeld orret range estmates. In ths paper, we propose the use of tme-frequeny representaton of the target return sgnals for mproved range estmaton and trakng of one or more movng targets. The proposed tehnque has three major advantages. Frst, the tme-frequeny representaton allows onentraton of the sgnal energy around the nstantaneous Doppler frequeny and thus enhanes the sgnal-to-nose rato (SNR) [11-1]. Seond, tme-frequeny representatons provde a platform to obtan enhaned phase nformaton as well as the Doppler sgnatures of the targets. Thus, range estmaton and trakng an be mproved through the fuson of Doppler sgnature and the phase nformaton, whh s most effetve, partularly n low

2 SNR senaros. Thrd, separaton of multple target sgnals an be aomplshed n the tme-frequeny doman. II. RANGE ESTIMATION USING DUAL- FREQUENCY CW RADAR Consder a dual-frequeny CW radar operatng at frequenes f 1 and f. The baseband radar return at frequeny f, 1,, an be expressed as, s ( ρ ( exp( jφ ( ), 1,, (1) where ρ ( and φ ( are, respetvely, the range- dependent ampltude and the phase of the return orrespondng to the -th frequeny of operaton. If R( s the law of moton of the target, then 4 fr( φ ( π, 1,. () The Doppler frequeny shft, f D, (, s the dfferental of the orrespondng phase, φ (, and s gven by 1 dφ ( f dr( f D, (, π dt dt 1,. (3) If both phases are measured modulo π, then 4πf 1R( 4πf R( φ1( t ) + nπ, φ ( + mπ, (4) where m and n are unknown ntegers. Aordngly [8, 10] R( [( φ( ) π ( m n)] 4π ( f f1) (5) ( m n) ( φ( ). 4π ( f f ) ( f f ) 1 The seond term n the above equaton ndues ambguty n range. For the same phase dfferene, the range an assume nfnte values separated by /[(f f 1 ) ]. Therefore, the maxmum unambguous range s gven by Rmax. (6) ( f f1) Dependng on the applaton, suffent unambguous range an be aheved by properly seletng the frequeny dfferene between the two arrers. For example, when frequenes of 1GHz and 990MHz are employed, the 10MHz dfferene n the arrer frequenes yelds a 15m unambguous range. In urban sensng, ths unambguous range may be suffent to unquely solve for the target range, gven pror knowledge of the struture bounds on target loaton. The bounds determne the nteger value m n orrespondng to the possble target range. The hoe of the spef values of f 1 and f an be made based on RF wall penetraton and desgn ssues of the radar unts. III. TIME-FREQUENCY REPRESENTATION A. Short-Tme Fourer Transform It s lear from the prevous seton that the key to determnng the range of a target s the estmaton of the phase dfferene of the return sgnals orrespondng to the two frequenes, f 1 1 and f. The suessful applaton of the dual-frequeny approah for range estmaton of a sngle movng target has been demonstrated n [8, 10]. However, as we dsussed earler, ths method suffers from two fundamental problems, namely, poor performane n a nosy envronment and the strt lmtaton that only a sngle movng target an exst n the sene. In ths Seton, we propose the use of tmefrequeny representaton of the target return sgnals n onjunton wth the dual-frequeny approah to overome these lmtatons. In the followng, we explot the short-tme Fourer transform (STFT) to demonstrate the effetveness of tmefrequeny analyss to provde range estmates for multple targets usng a dual-frequeny radar. The STFT of a sgnal x( an be defned as j τ F t f x τ h τ t e π f x (, ) ( ) ( ) dτ, (7) where h( s the wndow funton. When no wndow s used, the STFT redues to ordnary Fourer transform. The use of dfferent wndows allows tradng-off the tme and frequeny resolutons. A larger wndow sze provdes hgher frequeny resoluton at the expense of redued tme-resoluton. In our analyss, we assume that the wndow span s suffently small suh that eah return sgnal has a lnear phase (.e., onstant Doppler frequeny) over the wndow tme-duraton. On the other hand, the wndow span s assumed to be large enough to aheve reasonable frequeny resoluton. Satsfatory tme and frequeny resolutons requre proper seleton of the samplng rate and wndow funton. Multple target returns wth dstnt Doppler sgnatures an be separated n the tme-frequeny doman. Effetve tme-frequeny representaton tools, suh as the magntude square of (7), known as spetrogram, loalze the sgnal power n the tme-frequeny doman. The target Doppler sgnature an, therefore, be obtaned by loatng the hgh power tmefrequeny peaks. It an be shown that, the phase nformaton of a sgnal s preserved at the orrespondng peak of the STFT sgnature [13]. Wth the ablty to apture eah Doppler sgnature of the movng targets n the sene, one an proeed to alulate the respetve phase nformaton and subsequently estmate the target range. B. Multpath Consderaton Multpath s a ommon ourrene n a typal urban sensng envronment. It s noted that the effet of multpath s very smlar to the presene of another target. Wth a propagaton envronment wth two or more paths, the phase of the reeved sgnal orresponds to nether the target (dret path), nor that of the ndret path. The effet of multpath dffers dependng on the strength and loaton of the refleton. Beause the phase of the ombned sgnal s hghly nonlnear wth respet to the multpath strength, the phase of the ombned sgnal s lose to that of the target return sgnal f the multpath sgnal s weak ompared to dret path return. Otherwse, the phase wll be hghly dstorted and thus annot render meanngful range nformaton.

3 IV. RANGE ESTIMATION A. Range Estmaton Based on STFT Phase Informaton As dsussed earler, ths phase nformaton, and thereby the range estmate, obtaned from the tme-frequeny representaton at the Doppler sgnatures s muh more robust ompared to that obtaned from the raw data. Ths s due to the enhanement of the SNR when measured at the target nstantaneous Doppler frequeny. The seleton of the Doppler sgnatures n the tmefrequeny doman, n general, an be done usng smple peak deteton. Wth multple movng targets, some addtonal work to trae dfferent pees of the Doppler sgnature to the same target s requred. Separaton of non-overlappng and rossng Doppler sgnatures an be effetvely performed by observng the phase ontnuty [14], often desrbng motons of ndoor anmate or nanmate target. B. Range Estmaton Based on Doppler Sgnatures In addton to the phase nformaton, the Doppler sgnature of eah target an also be obtaned from the tme-frequeny representatons. As a target moves, the phase progresson an be obtaned from the ntegral of the Doppler frequeny, f D, (. As suh, the phase nformaton of the return sgnals and, subsequently, the ranges of movng targets, an be obtaned from the Doppler sgnatures up to an ntal value as follows, t ˆ φ ( π f ( dt + φ (0), 1,, (8) 0 D, where φ (0) s an unknown ntal phase at t0. The unknown ntal phase dfferene between the two arrer frequenes, denoted as φ(0)φ (0) φ 1 (0), an be obtaned by mnmzng the overall dstane between the Doppler sgnature based phase dfferene estmaton ˆ φ ( t ) ˆ φ ( ) ˆ t and that obtaned at the seleted STFT ponts ~ ~ ~ φ ( φ (. That s, ~ φ( 0) arg mn ˆ( φ φ ( dt, (9) φ (0) where the ntegral s evaluated over the entre observaton perod. Smulatons and experment results have shown that the range estmaton based on the Doppler sgnature s muh more robust to varous perturbaton fators aused by noses, refleton, and ross-omponent nterferene. A Doppler sgnature bas may aumulate over tme to yeld a large error n the range estmate. Therefore, hgh resoluton fast Fourer transform (FFT) operaton n the STFT omputaton s desrable. C. Range Estmaton Based on Blnear Tme-Frequeny Representatons The proposed method an also be straghtforwardly extended to blnear tme-frequeny representatons, suh as the Cohen s lass of tme-frequeny dstrbutons. For blnear tme-frequeny dstrbutons, the phase dfferene between the two frequenes an be omputed by examnng the phase of the ross-omponent tme-frequeny dstrbuton of s 1 ( and s ( [13]. In general, blnear tme-frequeny representatons provde hgher frequeny resoluton, but suffer from the wellknown ross-term ssue. For blnear tme-frequeny dstrbutons, areful desgn of data-dependent or fxed kernels for ross-term reduton should be performed so that the true auto-term ponts an be seleted. V. SIMULATION RESULTS We frst onsder a sngle target senaro. The target swngs around a enter whh s 5 m away from the radar wth a maxmum dsplaement of 1 m. The observaton perod s one seond. The two arrer frequenes are 900 MHz and 1 GHz, respetvely. The refleton oeffent s assumed to be a onstant, regardless of the range. The nput SNR s 0 db. Fgure 1(a) shows the magntude of the STFT of s 1 (. Due to the frequeny resoluton lmtaton, the STFT of s ( approxmately ondes wth that of s 1 (. The samplng frequeny s 1 khz, and a 101-pont Hannng wndow s used. As shown n Fg. 1(a), despte the low SNR level, the Doppler frequeny sgnatures an be learly dentfed n the STFT dstrbutons. Fgs. 1(b)-(d) show the range estmates usng raw data, STFT phase, and the Doppler sgnature. It s evdent from Fg. 1(b) that, beause of the nose, the raw data based approah fals to provde meanngful range estmaton. Sgnfant mprovement s aheved when usng the phase nformaton from the STFT. The best results are, however, obtaned when applyng the Doppler sgnature based approah. In ths ase, the range estmate error s very small. Next, we onsder two-target senaros. We frst onsder a senaro where the Doppler frequenes of the two targets do not overlap. In ths senaro, one person walks towards the radar, and the other walks away from the radar, at the same speed of v1 m/s. The targets were at the same ntal range of 5 m. The samplng frequeny s 1 KHz. No nose s onsdered n ths example. Fgure (a) shows the STFT magntude at the arrer frequeny 900 of MHz. A 501-pont Hannng wndow s used, and the STFT s obtaned usng a 104-pont FFT transform. It s evdent that the Doppler frequenes are separated n the tme-frequeny doman. From Fg. (b), t s observed that the raw data provdes a onstant range estmate, as the phase hanges due to the movement of one target are anelled by that of the other. On the other hand, as shown n Fgs. ()- (d), STFT-based methods provde range estmates well mathed to the true results, exept small errors toward the edges due to the edge effet n Fg. (). In the next senaro, the Doppler frequenes of the two targets overlap. In ths senaro, one walks away from the radar at a onstant speed of 0.5 m/s, whereas the other walks away at a tme-varyng speed aeleratng from 0 m/s to m/s n the 5 se perod. The ntal ranges of the two targets are 4.5 m and 4 m, respetvely. Fg. 3(a) shows the STFT results at the arrer frequeny of 900 MHz. The Doppler frequenes of the two targets are separated n the tme-frequeny doman for most of the observaton perod, but they overlap at around t 0.15 se. As a result, poor range estmates our around ths moment when the STFT phase nformaton s used, as seen n Fg. 3(). Ths problem s overome by usng the Doppler

4 sgnature, as deomnstarted by the range estmate n Fg. 3(d). For omparson, the use of raw data only yelds a sngle range estmate n the mddle poston of the two targets (Fg. 3(b)). VI. EXPERIMENTAL RESULTS To demonstrate the effetveness of the proposed method n a real envronment, laboratory experments were onduted at Vllanova Unversty s Radar Imagng Lab (RIL). An I/Q dual-frequeny radar wth operaton frequenes of MHz and MHz was employed. A 10-element Welded Yag antenna was used for sgnal transmsson and reepton. The walls of the Lab were lned wth eletromagnet absorbers to redue ambent refletons. The reeved baseband data s preproessed to remove lutter omponent near the DC frequeny before the tme-frequeny analyss and range estmaton are performed. In the frst experment, two ondutng spheres of 10" and 8" dameter are mounted on separate lnear postoners. One sphere remans statonary at the far end whereas the other moves bak and forth over a 10 ft (3.05 m) range wth a speed of 5 nh/s (0.635 m/s). Thus, t takes approxmately 4.8 se for the sphere to travel the 10 ft dstane n one dreton. The samplng frequeny s 1 khz and the tme duraton of olleted data s 0 se. Fg. 4(a) shows the magntude of the STFT of the baseband sgnal orrespondng to arrer frequeny of MHz, where a 001-pont Hannng wndow s used. To obtan a hgh resoluton n the frequeny doman, the STFT s omputed for 819 frequeny bns and only the frequeny band of nterest s shown n the fgure. The estmated range usng raw data s shown n Fg. 4(b), whereas that estmated from the STFT phase dfferene s shown n Fg. 4(). Note that n ths example the SNR s relatvely hgh. As a result, the estmaton result based on the raw data s relatvely good, although some loal varane s observed n the result. Suh varane s not observed n Fgs. 4()-(d) for the result based on tme-frequeny representatons. Interestngly, range estmaton results n Fgs. 4(b)-() are affeted by a phase dstorton due to weak refleton from a omputer rak near the antenna. Suh effet s mtgated when the Doppler sgnature based approah s exploted, as shown n Fg. 4(d). The seond experment has the same settngs as the frst one, but now both ondutng spheres move wth the same speed but n opposte dretons. Fg. 5(a) shows the STFT magntude of the baseband sgnal. When the raw data s used, as shown n Fg. 5(b), only the range of the sphere loser to the radar at a tme s obtaned as ts return sgnal has domnate effet to the phase of the reeved sgnal. Tme-frequeny analyss based methods allow separaton of the two targets. The STFT phase based method provdes relatvely good range estmaton for the 10" sphere, but the result for the 8" s not onsstent. The Doppler sgnature based approah yelds very robust range estmaton for both targets. VII. CONCLUSIONS We have presented a dual-frequeny radar based tmefrequeny proessng method for range-to-moton estmaton n urban envronments. The dual-frequeny approah estmates the range of a movng target by estmatng the phase dfferene of the sgnal returns at two losely spaed frequenes of operaton. The performane of ths sheme degrades sgnfantly n hgh nose power level and wth multple movng targets. To overome these shortomngs, we proposed the use of tme-frequeny sgnal representatons where power an be loalzed n the tme- frequeny doman. Both smulaton and expermental results were provded whh learly demonstrate the apablty of the proposed method to aurately estmate the phase dfferene, thereby provdng robust range-to-moton estmates n nosy envronments as well as n the presene of multple movng targets. ACKNOWLEDGEMENT The authors would lke to thank Mr. Pawan Setlur at Vllanova Unversty for hs assstane wth real-data olleton experments. REFERENCES [1] Dgest of the 007 URSI North Ameran Rado Sene Meetng, Speal Sesson on Through-Wall Imagng, July 007. [] Proeedngs of the 007 IEEE Workshop on Sgnal Proessng Applatons for Publ Seurty and Forenss, Speal Sesson on Through-the-Wall Imagng and Urban Sensng, Aprl 007. [3] S. E. Borek, An overvew of through the wall survellane for homeland seurty, Appled Imagery and Pattern Reognton Workshop, Ot [4] Proeedngs of the 005 IEEE AP-S Internatonal Symposum, Speal Sesson on Through-Wall Imagng and Sensng, vol. 3B, pp , July 005. [5] Proeedngs of the 004 IEEE AP-S Internatonal Symposum, Speal Sesson on Through-Wall Imagng, vol. 3, pp , July 004. [6] D. D. Ferrs, Jr. and N. C. Curre, A survey of urrent tehnologes for through-the-wall survellane, Pro. SPIE Sensors, and Command, Control, Communatons, and Intellgene (C3I), Informaton, and Tranng Tehnologes for Law Enforement, vol. 3577, pp. 6-7, San Dego, CA, Nov [7] W. D. Boyer, A dplex, Doppler, phase omparson radar, IEEE Trans. on Aerospae and Navgatonal Eletrons, vol. ANE-10, no. 3, pp. 7-33, [8] F. Ahmad, M. Amn, P. Setlur, Through-the-wall target loalzaton usng dual-frequeny CW radars, SPIE Symposum on Defense and Seurty, vol. 601, Orlando, FL, Aprl 006. [9] A. Ln and H. Lng, Three-dmensonal trakng of humans usng very low-omplexty radar, Eletrons Letters, vol. 4, no. 18, pp , Aug [10] F. Ahmad, M. G. Amn, and P. D. Zemany, Performane analyss of dual-frequeny CW radars for moton deteton and rangng n urban sensng applatons, Pro. SPIE Symposum on Defense and Seurty, Orlando, FL, Aprl 007. [11] Y. Zhang, W. Mu, and M. G. Amn, Subspae analyss of spatal tmefrequeny dstrbuton matres, IEEE Trans. Sgnal Proessng, vol. 49, no. 4, pp , Aprl 001. [1] M. G. Amn, Y. Zhang, G. J. Frazer, and A. R. Lndsey, Spatal tmefrequeny dstrbutons: Theory and applatons, n L. Debnath (ed.), Wavelets and Sgnal Proessng, Boston, MA: Brkhauser, 003. [13] Y. Zhang, M. G. 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5 (a) STFT magntude of s 1 ( (b) Range estmate based on raw data () Range estmate based on STFT phase (d) Range estmate based on Doppler sgnature Fgure 1 STFT and range estmaton results of a sngle target ase n the presene of nose (SNR0 db). (a) STFT magntude of s 1 ( (b) Range estmate based on raw data () Range estmate based on STFT phase (d) Range estmate based on Doppler sgnature Fgure STFT and range estmates of two targets n the absene of nose. The targets have non-overlappng Doppler sgnatures n the tme-frequeny doman. (a) STFT magntude of s 1 ( (b) Range estmate based on raw data () Range estmate based on STFT phase (d) Range estmate based on Doppler sgnature Fgure 3 STFT and range estmates of two-targets n the absene of nose. The targets have overlappng Doppler sgnatures n the tme-frequeny doman. (a) STFT magntude of s 1 ( (b) Range estmate based on raw data () Range estmate based on STFT phase (d) Range estmate based on Doppler sgnature Fgure 4 STFT and range estmaton results of the frst experment where one ondutng sphere moves bak and forth. (a) STFT magntude of s 1 ( (b) Range estmate based on raw data () Range estmate based on STFT phase (d) Range estmate based on Doppler sgnature Fgure 5 STFT and range estmates of the seond experment where both ondutng spheres move wth the same speed but n opposte dretons.