Automatic Target Recognition with Unknown Orientation and Adaptive Waveforms

Transcription

1 Automatic Target Recognition wi Unknown Orientation and Adaptive Waveform Junhyeong Bae Department of Electrical and Computer Engineering Univerity of Arizona 13 E. Speedway Blvd, Tucon, Arizona 8571 Naan A. Goodman Department of Electrical and Computer Engineering Univerity of Arizona 13 E. Speedway Blvd, Tucon, Arizona 8571 Abtract In previou work, we have demontrated e utility of a feedback loop for enabling optimized tranmit pule haping in radar target recognition. Thi previou work wa baed on low-fidelity target model, but in i paper, we demontrate e cloed-loop, adaptive-waveform approach applied to highfidelity target model ignature generated by commercial electromagnetic FDTD oftware. We alo incorporate e radar equation into our model for u in e waveform deign procedure. Becaue SNR varie wi range, o do our optimized waveform for target recognition. Contant-modulu waveform contraint are enforced, and a template-baed claification trategy i ued. I. INTRODUCTION Cognitive radar [1] ue an adaptive tranmitter to tranmit cutomized waveform. At each tranmiion, e adaptive tranmitter update it waveform baed on e radar objective, a probability model for previou meaurement, and oer prior information. Waveform cutomization can refer to bo e temporal tructure of e waveform a well a e tranmit beampattern. Becaue e adaptive tranmitter exploit previou meaurement, we can view cognitive radar a having a feedback loop between e radar receiver and tranmitter. Thi feedback loop deliver analyzed information from previou radar meaurement to e radar tranmitter in e form of updated prior information. In i paper we focu on e cutomization of a waveform temporal tructure in order to perform automatic target recognition (ATR) wi reduced tranmit power and/or at longer range. The goal of ATR i to identify an object at i oberved by e radar ytem. In our earlier work [], an adaptively haped temporal waveform wa applied to a target identification cenario. Thi work howed at a radar performing ATR according to cognitive radar principle ue fewer radar reource (i.e., reduced power or energy) and make a fat deciion wi low error rate. Cognitive radar can alo be applied to make better ue of e radar timeline in detection and tracking cenario. In [3], a cognitive-radarbaed technique for adaptive beamteering wa implemented. Thi cloed-loop approach to beamteering ha been demontrated to improve detection time. In [4], cognitive tracking radar wa implemented. The tranmit waveform wa elected from a precribed library according to information collected by e receiver, and e cognitive tracking radar wa hown to outperform conventional radar. In [5], cognitive radar wi knowledge-aided (KA) proceing wa propoed. We extend our previou work in e area of ATR wi two contribution in i paper. Firt, we ue new high-fidelity target ignature. In previou work, our target ignature were generated from imple arbitrary target outline and handplaced catterer, which allowed e ignature to vary wi rotation of e target. In i paper, we ue commercial EM oftware (XFdtd, by Remcom) and publicly available target CAD model to calculate target ignature veru angle. Second, e radar equation i incorporated directly into e target ignature to model propagation lo. Therefore, e radar equation affect e target ignature pectral treng. Becaue optimized waveform deign i SNR-dependent, uing e radar equation in e target ignature model affect our waveform deign procedure. The performance of cloed-loop radar can en be conidered a a function of target range. Thi paper i organized a follow. In Section II, we preent e problem tatement and ignal model. In Section III, we decribe e target ignature model. In Section IV-A, we how e waveform deign technique and incorporation of e radar equation to e deign technique. In Section IV-B, we ummarize contant-modulu waveform contraint. In Section V, we decribe e deciion-making procedure and probability update baed on Baye Theorem. In Section VI, we how imulation reult, and in Section VII, we make our concluion. II. PROBLEM STATEMENT AND SIGNAL MODEL A monotatic radar ytem wi a matched illumination waveform i applied to e target recognition cenario in e preence of additive white Gauian noie (AWGN). The baic problem formulation i imilar to our previou work [6] /11/$6. 11 IEEE 1

2 and ummarized below. It i aumed at a target ha already been detected and i known to be one of M poible target type. The target ha a continuum of target ignature a a function of azimu and elevation angle. For implicity, here we hold e elevation angle fixed and conider only azimu rotation. Conider a linear target model a follow. When e radar waveform ( i tranmitted, e radar received ignal y ( i denoted a y ( = g( * + n( (1) where g ( i e azimu-varying target ignature of e unknown target, * i e convolution operator, and n ( i AWGN wi power σ n. A dicrete-time verion of e ignal model i neceary to implement a a computer imulation. In dicrete-time notation, e target ignature i repreented by a leng- L g vector g, e waveform i denoted a a leng- L vector, e noie i defined a a leng-l n vector n, and e received ignal i repreented by a leng-l y vector y. To implement e convolution between waveform and target impule repone in e dicrete-time model, a ignal matrix S i defined a [7] 1) ) S = L ) L 1) 1) L ) L 1) L ) 1). () 1) ) L ) Uing e ignal matrix and above definition, e dicretetime ignal model i y = Sg + n. (3) To handle target ignature at vary wi azimu angle, e azimu angle i divided into N g uniformly ized angular ector. Multiple target ignature are generated for angle wiin each ector, and e ignature are averaged to acquire a mean template for at ector. The mean template of all M target type are defined a g i ( t ), i = 1,..., N g,..., MN g. When e number of ector N g i large, e ize of each ector i mall, and e mean-template for each ector i a good repreentation of e target ignature acro e ector. However, computational complexity increae when we mut conider many ector, epecially in cognitive radar where probabilitie aociated wi each ector will be updated after each tranmiion. Thu, e ector ize hould be baed on bo required accuracy and ytem complexity. To employ prior information about e target orientation (derived, for example, from target bearing information), e target orientation at e beginning of e recognition phae i aumed known to wiin a few angular ector. To et up e target recognition problem in term of hypoei teting, we define a ingle hypoei a correponding to a ingle angular ection wiin a ingle target type. Thu, for e ake of feeding information back to e tranmitter and optimizing e waveform deign, each angular ector i treated a a different hypoei. A meaurement are received, e probabilitie aociated wi each target/ector combination are updated to reflect what ha been learned. But to do i, we need to define a probability denity function (pdf) of e radar received ignal for each target/ector hypoei. One potential ditribution i Gauian, which might be able to capture bo e mean template for a ector a well a e variation of e ignature around e mean for at ector. Unfortunately, a multivariate normality tet applied to e XFdtd target ignature [8] over a ector howed at Gauian wa not repreentative, even a an approximate ditribution. Thu, intead of making a Gauian aumption for e target ignature, e ignature are treated a contant acro a ector, reulting in a determinitic model wi e mean-template g i for each ector. Since e waveform and target template (given a particular target and ector) are determinitic, and e noie n i AWGN, e received ignal y i Gauian. The pdf of e complex received ignal given e i target/ector hypoei i defined a 1 1 H p( y H i ) = exp( ( y μ, ) (, )) N y i y μ y i (4) ( πσ ) σ n where μ y, i = Sgi i e mean of e received ignal under e i target/ector hypoei and tranpoe operator. The mean ignal n H ( ) i e conjugate μ y, i i waveformdependent and mut be updated a e tranmit waveform change. III. TARGET MODEL In prior work [6], our target model conited of arbitrary target outline wi cattering center placed at variou location along e outline. Thi model allowed e rotation of e target to affect e reulting target ignature. However, e model were admittedly low-fidelity. Here, we ue a 3D commercial electromagnetic (EM) imulator, XFdtd, to calculate high-fidelity target ignature. The XFdtd oftware wa provided by Remcom. The etup for generating e ignature i a follow. We ued caled 3D target CAD model in e XFdtd imulation. A monotatic radar wa located in far-field. A broadband waveform wa tranmitted to e target and e reflected ignal wa tored. The procedure wa repeated at many different apect angle to create a received ignal library. Wi each reflected ignal, we calculated frequency-domain target tranfer function according to G ( f ) = Y ( f ) / S( f ) (5) /11/$6. 11 IEEE 11

3 Figure 1. Head-on target ignature of F-16 aircraft. where G ( f ), Y ( f ), and S ( f ) are e Fourier tranform of target ignature, e radar received ignal, and e wideband tranmitted waveform, repectively. The bandwid of e tranmitted pule in i ignature generation phae wa ignificantly larger an e maximum waveform bandwid for any of e ATR imulation at ued e ignature. For e cognitive-radar ATR imulation, a ection of e target tranfer function correponding to e radar tranmiion band wa extracted from e wideband function in (5). The timedomain target ignature wa en generated from e invere Fourier tranform of e reulting bandlimited target tranfer function. Two example of target ignature generated by XFdtd are hown in Figure 1 and. A monotatic radar i located lightly above e target horizontal plane at elevation. A wideband pule wi 5 GHz bandwid wa imulated via XFdtd. Figure 1 how e head-on target ignature for an F- 16. The leng of F-16 CAD model i m (approximately a 1:1 cale model). The peak of e target ignature correpond to e location of catterer in e CAD model. The firt peak correpond to e tip of e noe and e econd peak correpond to e canopy of aircraft. The two larget peak correpond to e larget under-wing miile. The lat peak i from e tail of e aircraft. The leng of target ignature between e firt peak and e lat peak i lightly maller an e CAD leng, becaue e radar i above e target and e reflection from e tail happen at e leading edge of e tail. Figure how e target ignature of an A-1 CAD model at 3 azimu. The leng of A-1 CAD model i.817 m. The firt and e lat mall peak correpond to e noe and tail of e A-1, repectively. The four big peak are generated by e two Figure. Azimu angle 3 target ignature of A-1 aircraft. under-wing landing-gear houing and two engine. In XFdtd, e propagation of e EM wave in pace i calculated according to Maxwell equation, which provide much more repreentative target ignature an we have ued previouly. IV. RADAR WAVEFORM DESIGN A. Waveform deign and e radar equation The waveform deign technique at we ue here i baed on maximization of mutual-information. The technique i adapted from e analyi in [9] and ummarized below. We aume at an enemble of target impule repone exit. We alo aume at e radar waveform ha everal contraint (energy, time, and frequency). For a Gauian target enemble, e waveform at maximize e mutual information between e radar received ignal and e (Gauian) enemble of target impule repone can be found according to [9] 1 σnt y f max, A T S( f ) = G( f ) 1 σ (6) f > T where e enemble pectral function i defined a σ ( f ) = E{ G( f ) E{ G( f )} }, G ( f ) i e Gauian target G tranfer function, and T i e ampling interval of e ignal. The total energy in e waveform i controlled by e calar value A, uch at /11/$6. 11 IEEE 1

4 E = 1 TS 1 TS σ nty max, A df. (7) σ G ( f ) A mentioned, e above deign technique i baed on a Gauian enemble, which we do not have. Fortunately, e pectral variance function can be extended for a finite number of dicrete target hypoee according to [] G MN g MN g Pi Gi ( f ) i= 1 i= 1 σ ( f ) = P G ( f ) (8) where G i ( f ) i e Fourier tranform of e i mean target template. Thi pectral variance can be ubtituted in (6), and e waveform pectrum i found according to e waterfilling technique [9]. In i technique, e deired waveform energy pectrum i acquired by inverting e function A σ n Ty / σ G ( f ) and pouring energy into e lowet part of e inverted function until e allowable energy i gone. The amount of energy at i poured into each pectral component determine e waveform magnitude pectrum. The phae of e waveform i an additional deign variable at may be ued to meet oer deign contraint, uch a a contant modulu contraint. A een in (6), e optimum waveform depend on e noie power a well a e treng of e target enemble (rough e pectral variance). When SNR i low, e waveform defined by (6) will tend to have energy in only a couple narrow pectral band. When SNR i high, e waveform become diverified and pread it energy over e allowable band. Becaue e waveform deign i SNRdependent, it i important to factor e radar equation into e ignal model. The power, P r, of e return ignal from e target at e radar receiver can be calculated by e radar equation according to [1] PG T aλσ Pr = = P 3 4 TσC = PTσeff (9) (4 π ) R where P T i e radar tranmit power, G a i e antenna gain, λ i e operating waveleng, σ i radar cro ection, and R i e range between radar and target. The variable C can be incorporated into σ to repreent an effective radar cro ection at varie wi range, and i effective radar cro ection can be ued to properly cale e target ignature library. Therefore, propagation lo i factored into e pectral variance function above, which en affect e waveform deign. In i work, we cale e target template librarie uch at e average level of e magnitude of all target tranfer function for a particular target i equal to e average quare root of RCS for at target. In oer word, uppoe at a target ha an RCS of σ, en we et e target tranfer function caling uch at ( ) = E G f C σ. (1) i i Thi normalization enure at for a narrowband waveform centered around frequency f, we have a contant-valued tranfer function over e waveform bandwid wi average magnitude equal to ( ) E = The received waveform will en be () G f CE σ. (11) G a λ ( 4π ) ( ) ( ) y t = E σ t R c + n t 3 4 R. (1) Wi e caling of e radar range equation incorporated into e target ignature, e ignal model now fit e form of (1) a required by e mutual information waveform deign meod. B. Waveform contraint Any practical radar ytem ha a peak power limitation, o e temporal radar waveform hould be deigned and operated under i limitation. Thu, a contant modulu [11] contraint on e radar waveform i neceary to operate e radar ytem efficiently. The technique ued here to contruct a contant-modulu ignal wi a precribed Fourier tranform magnitude i baed on iterative magnitude and amplitude projection. The technique i preented in [11] and ummarized below. The et of function { v ( } wi equal Fourier tranform magnitude F(w) over e frequency et Ψ i denoted a D M. Then, we can define a magnitude projection operator P M at project an arbitrary function x ( to nearet point on D M. Auming jω( w) e Fourier tranform of x ( i X ( w) = X ( w) e, e magnitude projection procedure i repreented by jω( w) F( w) e, w Ψ PM x( =. (13) X ( w), w Ψ' The et of function { v ( over e temporal duration T i repreented by } wi poitive contant value B D A. Then, P at we can alo define an amplitude projection operator A project an arbitrary function x ( to cloet point on D A. Auming x ( i equal to a( e i defined a j B e PA x( = x(, φ ( jφ(, e amplitude projection, t T. (14) oerwie The above magnitude and amplitude projection i performed iteratively according to xk + 1( = PA PM xk ( (15) where x k ( i e arbitrary function after k projection. After many iteration, e function x ( maintain exact contant modulu amplitude, but ha a Fourier tranform magnitude at approximate e deired Fourier magnitude /11/$6. 11 IEEE 13

5 V. FIXED NUMBER OF ITERATIONS AND BAYES THEOREM We adopt a procedure whereby a claification deciion i made after tranmitting a fixed number of optimized waveform. Therefore, e number of tranmiion i fixed in advance. At each tranmiion, e likelihood are formed and e probabilitie aociated wi each target/ector combination are updated. The expreion of e i hypoei likelihood after e k tranmiion depend on joint pdf of e received ignal on all tranmiion. However, ince e radar waveform and target ignature are modeled a determinitic, and e white Gauian noie ample are uncorrelated and independent, e meaurement data are tatitically independent. Then, e joint pdf of e data on all tranmiion can be accumulated to update e likelihood of e i hypoei according to p ) P (16) ( Hi yk ) pi1( y1) pi( y) pik ( yk where p y ) i e pdf of e k received ignal for e ik ( k i hypoei, y k i e received ignal due to tranmiion, and P i i e probability of e i k i hypoei prior to any tranmiion. The final deciion i made after e number of tranmiion reache e pre-defined iteration limit. The hypoei H i correponding to e highet likelihood i e final deciion. In e cloed-loop radar ytem, e waveform are updated at each tranmiion. To update e waveform, e hypoei probabilitie are update by Baye eorem according to (16) (except for a caling factor at enure e probabilitie um to unity). The updated probabilitie are ubtituted into (8) to update e radar waveform. VI. RESULTS We performed a computer imulation of a radar target recognition cenario baed on e technique above. We have two plane target (F-16 and A-1). We aume at e elevation angle between e horizontal plane of e target and e radar line of ight i, uch at e monotatic radar i a little above e target. We conider azimu angle over a 9 range from head-on to broadide of each target. We generated target ignature at every.1 interval. Since we know e actual ize of ee target from e literature, we ue a caling factor to adjut e ampling interval and bandwid of e original CAD-baed XFdtd target ignature to e actual target ize, approximately. Table I how e leng and caling factor. The target ignature are grouped into 1 ector. The target ignature wiin each uniform angular ector are averaged to generate a mean-template. We aume at we have prior knowledge about e velocity and bearing information of a target. Thu, for a given trial of e ATR imulation, we can narrow down e poible target angular ector to two adjacent mean-template for each target. We treat each ector a a hypoei, o we have four hypoee in total for a given trail. For randomly elected Error rate Error rate TABLE I. TARGET LENGTHS AND SCALING FACTORS Target Actual leng(m) CAD leng(m) Scaling factor F A Waterfilling(R=km) Waterfilling(R=3km) Impule(R=km) Impule(R=3km) Tranmit power (db) Figure 3. Error rate veru tranmit power for fixed number of tranmiion Waterfilling Impule Range (Km) Figure 4. Error rate veru range for fixed number of tranmiion. target angle at do not fall on e.1 increment, we generate e true target ignature by a weighted average of e two adjacent target ignature. We compare e performance of two waveform: e information-baed waveform realized via e pectral variance trategy over a 5-MHz bandwid, and a 5-MHz wideband impule. We ue e radar equation to compare e performance of e waveform baed on e range between radar and target. The radar parameter ued were an antenna gain of 3dB at S band, a noie temperature of 9 K, and an average total RCS for each target of 1 m. Five waveform were tranmitted before making a deciion. We ran, Monte Carlo trial (over noie realization and orientation angle), and counted e number of incorrect deciion to compute error rate /11/$6. 11 IEEE 14

6 Figure 3 how e error rate veru tranmit power. The information-baed waveform perform better an e wideband waveform for e ame range becaue e information-baed waveform put energy into e frequency band where pectral dicrimination i trong. The radar return ignal from farer range ha lower ignal-to-noie (SNR), o e error rate are higher. The two waterfilling waveform (for R = km and 3 km) at error rate.1 are hift by approximately 7 db. Becaue e ratio between ee ditance i 3/ = 1.5, and e received power ha a 1/R 4 4 relationhip to target range, 1*log1 (1/(1.5) ) = dB, and e 7 db hift i expected. The information-baed waveform require about 5 db le power an e wideband waveform at e ame range. Figure 4 how e error rate veru range when e tranmit power i 6 db. In i cae, e information-baed waveform can achieve e ame error rate a e wideband waveform, but at an approximately 3% increae in range. VII. CONCLUSIONS We have imulated a cloed-loop radar ytem for target recognition uing high-fidelity target model calculated via commercial EM oftware and publicly available target CAD model. We alo incorporated e radar equation into e target ignature a part of e waveform deign proce. The information-baed waveform wi a contant modulu contraint wa compared to a flat-pectrum wideband waveform in a target recognition cenario. The two target being claified were an F-16 and an A-1. The reult how at e information-baed waveform provide approximately 5 db improvement in tranmitted power for e ame error rate, which tranlated to a more an 3% increae in recognition range. ACKNOWLEDGMENT The auor acknowledge upport from e ONR via grant #N We are alo very grateful to Remcom for providing eir XFdtd oftware. REFERENCES [1] S. Haykin, Cognitive radar: a way of e future, IEEE Sig. Proc. Mag., vol. 3, no. 1, pp. 3-4, Jan. 6. [] N.A. Goodman, P.R. Venkata, and M.A. Neifeld, Adaptive waveform deign and equential hypoei teting for target recognition wi active enor, IEEE J. Selected Topic in Signal Proceing, vol. 1, no. 1, pp , June, 7. [3] P. Nielen and N.A. Goodman, Integrated detection and tracking via cloed-loop radar wi patial-domain matched illumination, in Proc. 8 International Conference on Radar, Adelaide, Autralia, pp , Sept. 8. [4] S. Haykin, A. Zia, I. Araaratnam, and Y. Xue, Cognitive tracking radar, 1 IEEE Radar Conference, pp , Wahington DC., May 1. [5] J.R. Guerci, Cognitive radar: a knowledge-aided fully adaptive approach, 1 IEEE Radar Conference, pp , Waington DC., May 1. [6] J. Bae, N. A. Goodman, Evaluation of modulu-contrained matched illumination waveform for target identification, 1 IEEE Radar Conference, pp , Wahington DC., May 1. [7] D.A. Garren, M. K. Oborn, A. C. Odom, J. S. Goldtein, S. U. Pillai, and J. R. Guerci, Enhanced target detection and identification via optimized radar tranmiion pule hape, Proc. IEEE, vol. 148, no. 3, pp , Jun. 1. [8] S.P. Smi and A. K. Jain, A tet to determine e multivariate normality of a dataet,. IEEE Tranaction on Pattern Analyi and Machine Intelligence, vol. 1, no. 5, pp , Sep [9] M.R. Bell, Information eory and radar waveform deign, IEEE Tran. Info. Theory, vol. 39, no. 5, pp , Sept [1] D.R. Wehner, High-reolution radar, Artech Houe Publiher, Boton, [11] S.U. Pillai, K.Y. Li, and H. Beyer, Contruction of contant envelope ignal wi given Fourier Tranform magnitude, 9 IEEE Radar Conference, Paadena, California, USA, May 4-8, /11/$6. 11 IEEE 15