Continuous Transmission Frequency Modulation Detection under Variable Sonar-Target Speed Conditions

Transcription

1 Sensors 3, 3, ; doi:.339/s Aricle OPEN ACCESS sensors ISSN Coninuous Transmission Frequency Modulaion Deecion under Variable Sonar-Targe Speed Condiions Yang Wang, and Jun Yang,, * Key Laboraory o Noise and Vibraion Research, Insiue o Acousics, Chinese Academy o Sciences, Beijing 9, China; wangyang@mail.ioa.ac.cn The Sae Key Laboraory o Acousics, Insiue o Acousics, Chinese Academy o Sciences, Beijing 9, China * Auhor o whom correspondence should be addressed; jyang@mail.ioa.ac.cn; Tel.: ; Fax: Received: December ; in revised orm: 5 February 3 / Acceped: 5 March 3 / Published: 3 March 3 Absrac: As a ranging sensor, a coninuous ransmission requency modulaion (CTFM) sonar wih is abiliy or range inding and range proile ormaion works eecively under saionary condiions. When a relaive velociy exiss beween he arge and he sonar, he echo signal is Doppler-shied. This siuaion causes he oupu o he sensor o deviae rom he acual arge range, hus limiing is applicaions o saionary condiions only. This work presens an approach or correcing such a deviaion. By analyzing he Doppler eec during he propagaion process, he sensor oupu can be correced by a Doppler acor. To obain his acor, a convenional CTFM sysem is slighly modiied by adding a single one signal wih a requency ha locaes ou-o-sweep range o he ransmied signal. The Doppler acor can be exraced rom he echo. Boh veriicaion experimens and perormance ess are carried ou. Resuls indicae he validiy o he proposed approach. Moreover, ranging precision under dieren processing seups is discussed. For adjacen muliple arges, he discriminaion abiliy is inluenced by displacemen and velociy. A discriminaion boundary is provided hrough an analysis. Keywords: CTFM; ulrasonic ranging sensor; Doppler shi; deviaion; correcion; range proile

2 Sensors 3, Inroducion Ulrasonic ranging sensors have been widely used in collision avoidance [], navigaion [,3], mapping [4,5], arge classiicaion [6,], and in ravel aid devices or visually impaired individuals [7,8]. The ulrasonic ranging sensor, which is low cos, accurae in posiioning, and easy o operae, is considered as a compeiive choice or implemening arge deecion and recogniion. Sensors ha work in pulse-echo mode, which is he mos common mode, have been applied in various orms [9,]. However, mos pulse-echo sensors only reain he reurn o he neares arge and neglec he res o he echo signals. A more sophisicaed ulrasonic sensor, a coninuous ransmission requency modulaion (CTFM) sonar, has been exensively developed in he pas several decades. Wih is advanages o high precision, broadband, high signal-o-noise raio, and high quaniy o inormaion, he CTFM sonar is capable o deecing muliple arges, classiying primiive indoor arges [], and even recognizing complex arges such as rough suraces [], leay plans [3], and human aces [4]. However, mos o he applicaions o a CTFM sonar are carried ou under saionary condiions. When one or boh o he sonar and he arge are moving, he echo signal is Doppler-shied. Aer demodulaion, he oupu o he sysem is deviaed rom he acual arge range. This siuaion limis he applicaion o a CTFM sonar o saionary plaorms and moionless-arge sensing. An early sudy o a CTFM sonar provided an analysis o how he sysem oupu changes wih a moving arge [5]. In a more recen work, a CTFM sonar was mouned on a mobile agen o classiy dieren rough suraces [6]. The specrum o he demodulaion oupu signal was averaged o reduce he inluence o Doppler shi o he range proile. However, he oupu range value deviaion was no considered. Unil now, no eecive soluion has been provided o eliminae he aoremenioned deviaion. This work presens an approach or correcing CTFM oupu under non-saionary condiions wih a sligh modiicaion o he sysem. Wih his approach, he sysem sill works wih high precision, and is now capable o generaing he range proile o complex arges. The modiied sysem can be urher applied o non-saionary scenarios such as robo navigaion and moving-arge deecion. In he ollowing secion, a descripion is provided on how a convenional CTFM sonar sysem works. A dual-sweep demodulaion approach is inroduced o eliminae he blind ime in he oupu signal o a convenional CTFM sonar sysem. Noise and inererence ha may aec he sysem are discussed. In Secion 3, a general condiion o he propagaion procedure o he ulrasonic signal beween a moving sonar and a moving arge is analyzed. A Doppler acor is inroduced o correc he sysem oupu. Secion 4 presens experimenal sudies or veriicaion and perormance ess or he proposed approach. A deailed discussion o he experimen resuls and he sysem perormance is given in Secion 5. Finally, conclusions and uure research consideraions are summarized in Secion 6.. CTFM Sysem Descripion.. Basic CTFM Sysem A basic CTFM sysem ransmis a cyclic linear sweep signal S T (). In one sweep period, S T () can be described as:

3 Sensors 3, S A m T sin T H sw () S T () sweeps rom H down o L during a period o T sw. The sweep bandwidh is B = H L, and he sweep rae is m = B/T sw. A is he signal ampliude. The echo signal is a replica o S T wih a ime delay o: where R is he range o he arge, and c is he sound speed. The echo signal can be described as: where β(λ,r,θ) is an aenuaion acor relaed o he wavelengh λ, he range R, and he inciden angle θ. The ampliude o he echo also depends on he surace characerisic o he relecor [6,]. To ocus on he range inding uncion o he sysem, i is assumed ha he arges are srong relecors and are wihin he observable area. The requency o S T () is: R c,, S A R S where Φ T () = π( H m/) is he insananeous phase o S T (). Similarly, he requency o S R () is: The demodulaion procedure includes mixing and ilering operaions. When S T () is mixed wih S R (), a sum requency and a dierence requency componen are included in he produc signal. The sum is ilered ou by a low-pass iler (LPF), he dierence requency componen α is le as he demodulaion oupu signal: Thereore, he measured range value can be wrien as: R dt m T d T H sw m R T H Rm m c c R m A specrogram explanaion is shown in Figure. The componen α is obviously proporional o range R. A relecor can be seen as a peak in he specrum o he demodulaion oupu signal. I he echo comes rom muliple relecors, corresponding peaks can be ound in he specrum. In a CTFM sonar sysem, signal requency is concerned wih arge range. Thereore, all he analyses in his paper ocus only on he requency domain. T () (3) (4) (5) (6) (7)

4 Sensors 3, Figure. The signal specrogram o he demodulaion procedure. T () sum τ dierence sop band o LPF oupu signal R () blanks.. Dual Sweep Demodulaion The oupu o a basic CTFM sysem includes a blank in every sweep period. The blank appears a he sar o a sweep period wih a lengh o τ. Such blanks are called blind ime, hey make he oupu disconinuous and decrease oupu signal energy. A dual demodulaion mehod has been brough ou o eliminae blind ime [7]. An addiional sweep signal, wih a sweep rae equal o m and a band nex o he band o S T (), is inroduced in he demodulaion procedure. The addiional sweep signal is described as: S A m T sin A L sw (8) Similar o Equaion (4), he requency o S A () is: d A m T d A L sw where Φ A () = π( L m/) is he insananeous phase o S A (). The echo signal mixes wih he sum signals o S T () and S A () insead o S T () only. Oupu signal requency can be wrien as: R A R T Tsw S A () can be considered as an exension o S T () in he specrogram. In such a manner, S A () orms a sweep signal wih a period long enough o cover he echo signal; hereore, blind ime gaps are illed. In pracice, T' sw is se o be equal o T sw, hus S A () shares he same rigger signal wih S T () o reduce he complexiy o signal generaion (Figure ). (9) ()

5 Sensors 3, Figure. Signal specrogram o a dual demodulaion sysem. T () A () R () R () mixed wih T () R () mixed wih A () Noe ha he maximum value o he dierence requency beween R () and T () is B/, which corresponds o a range value o ct sw /4. A relecor arher han his value will make R () demodulaed wih T () in he nex sweep period. Targes around ct sw /4 cause range ambiguiy or phanom arges. To avoid his siuaion, irsly he sop band o he LPF is usually se lower han B/ o eliminae range ambiguiy. Furhermore, he inensiy o he ransmied signal can be adjused o an appropriae value, so ha he echo releced rom arher han ct sw /4 dies ou beore i reaches back o he sonar. Acually, in mos airborne ulrasonic uses, phanom arge seldom appears due o he rapid aenuaion o he ulrasonic signal. Thereore only he irs sep is needed o be done in he sysem design, and only arges ound wihin he region o ~ ct sw /4 are meaningul..3. Noise and Inererence Dieren rom he pulse-echo sonar, he CTFM sonar operaes in a coninuous manner, which provides a much higher power oupu. Meanwhile, he dual sweep demodulaion operaion ills he blind ime o he oupu signal, which urher enhances he energy o he oupu. The demodulaion procedure ransers he echo signal in ime domain o requency domain or indicaion. The arge can be seen in he specrum o he oupu signal generaed using Fourier Transorm. The Fourier Transorm also provides an averaging process ha reduces he noise. A band-pass iler (BPF) applied o he echo signal can eliminae he noise ou o he sweep band. The pass band o he BPF should be designed wider han he sweep band o he ransmied signal. The margins on boh sides o he pass band are le or he Doppler shied echo signal. Alhough CTFM sonar has he abiliy o noise suppression, crossalk beween he ransmission and he recepion channel sill exiss. The ransmied signal may mix ino he received echo signal, which appears as a large relecor very close o he sonar. The impac o his inererence can also be eliminaed by ilering. Insead o a LPF, anoher BPF can be applied ollowing he mixing operaion in he demodulaion procedure o iler ou he inererence and he sum requency. The ilers guaranee a high qualiy o he oupu signal in mos pracical uses. However, under harsh signal condiions, he sysem migh be disurbed by unknown noise ha canno be ignored. Figure 3 shows he specrum o he oupu signal when he echo signal is aeced by addiive whie Gaussian noise. These resuls are obained under assumpions ha he relecor is m away rom he sonar, and he echo signal is ampliied o he same magniude o he sum signals o S T () and S A (). The

6 Normalized Ampliude Normalized Ampliude Normalized Ampliude Normalized Ampliude Sensors 3, peak corresponding o he arge sill can be seen clearly, even when he echo signal has a signal-o-noise-raio (SNR) o db. In he sysem described below, he BPFs are also applied, and he signal condiion is considered o be good enough o generae a clear indicaion o he arge. Figure 3. Oupu signal specrum under echo SNR o (a) db; (b) 3 db; (c) db; and (d) db Frequency (khz) (a) Frequency (khz) (b) Frequency (khz) (c) Frequency (khz) (d) 3. Deecion under Non-Saionary Condiions Range deecion can be quie accurae when he sonar and he arge are boh saionary. However, when a relaive movemen occurs beween he arge and he sonar, he echo is Doppler-shied. As a resul, he requency o he demodulaion oupu signal α deviaes rom he acual arge range value. The deviaion increases along wih relaive velociy. In his case, deecion resul may easily become unaccepable. 3.. Analysis o Ulrasonic Propagaion In general, he sonar and he arge are boh moving a dieren velociies and oward dieren direcions. When he arge is wihin he beam o he sonar, he Doppler eec occurs a hree momens in he enire procedure o ulrasonic signal propagaion, namely: (a) a ransmission, (b) a relecion, and (c) a recepion, as shown in Figure 4.

7 Sensors 3, Figure 4. The propagaion o he ulrasonic signal. vs sonar (a) v (c) (b) arge Supposing ha an arbirary signal wih an insananeous requency o () is ransmied by he sonar, hen, only he ulrasonic beam ha his he arge and is releced back o he sonar is considered. The sonar is moving a a velociy vecor o v s () a he momen o ransmission. The angle beween v s () and he beam is θ. Aer ransmission, () is shied o ˆ () because o he Doppler eec (a) [8]: ˆ c c v cos Aer raveling or a ime o ligh (TOF) o τ (), he signal his he arge. The arge is moving a a velociy vecor o v (), wih an angle o θ rom he beam, a he momen o relecion. Because o he Doppler eec (b), he requency o he echo becomes: ˆ ˆ Aer raveling once more or τ (), he signal reurns o he sonar. A he momen o recepion, he oal TOF o he signal is he sum o τ ()and τ (): τ() = τ () + τ (). Assuming ha τ() is shor enough o neglec he displacemen and he velociy change o he sonar, hen he angle beween v s () and he echo beam is sill θ. As a resul o he Doppler eec (c), he received signal requency can be described as: By subsiuing Equaion () ino Equaion (), and hen ino Equaion (3), ˆ() can be described by (), ha is: Examining Equaion (4) shows ha aer he enire propagaion in a period o τ(), he signal is shied rom he ransmied signal (-τ()) o he received signal ˆ() by a Doppler acor D(), which is he oal shi raio, ha is: s c v c v ˆ ˆ c vs c ˆ c v s cos cos cos cos cos c v cos c v cos s ˆ D c v () () (3) (4) (5)

8 Disance (m) Disance (m) Sensors 3, According o Equaions (4) and (5), D() is: D c vs cos c v c v cos c v s cos cos (6) I a single one signal wih a known requency ST is ransmied, D() can be easily acquired by: where ˆ ST () is he received signal requency o he single one signal. 3.. Correcion o he CTFM Oupu D The received signal requency T is a replica o he ransmied signal requency shied by D(), ha is: ˆT T ˆST ST D (7) (8) According o Equaion (), he requency o he demodulaion oupu signal is: ˆ A ˆ T ˆ T T T sw (9) Obviously, ˆ α no longer ollows Equaion (6). Figure 5 demonsraes wo moving condiions, deviaions occur beween he CTFM oupu and he acual arge range. The CTFM oupu exhibis an oblique, sawooh shape because higher velociy makes he Doppler acor D() larger, hus is conribuion o he deviaion is also greaer, according o Equaions (8) and (9). A he same ime, a higher ransmied requency also conribues more o he deviaion. Figure 5. The CTFM oupu vs. he acual arge disance. (a) A arge approaching he sonar a m s ; (b) A arge acceleraing away rom he sonar a.5 m s..8 CTFM oupu Acual Range.8.6 CTFM oupu Acual Range (a) (b) To obain a correc oupu, a single one componen S ST () wih a requency o ST is added o he ransmied sweep signal S T (). A blank requency gap should be le beween ST and he sweep range

9 Sensors 3, o S T. This gap should be wide enough so ha ST and T () will no inerere wih each oher aer Doppler-shiing. The acual ransmied signal becomes: S S S T ST T Because ˆ ST, which is he requency o Doppler-shied S ST in he received signal, can be easily obained, he Doppler acor D() is also obained by using Equaion (7). To acquire he acual range o he arge, he aim is o deermine he value o α () ha ollows Equaion (6). Thus, Equaions (5), (8), and (9) are combined: D ˆ A A T D T Tsw () () When Equaion () is reorganized, α () can be wrien as: A D T D ˆ D ˆ D T sw () The arge range can be solved using an equaion similar o Equaion (7): r c m (3) Noe ha in Equaion (), all he componens are available excep or he oal TOF τ(), which acs as a dividing poin o he equaion. τ() can be calculaed using τ = r/c. The range value a he end o a sweep period can be calculaed using he second sage o Equaions () and (3). In low-velociy condiions, τ() can be approximaely calculaed by τ r()/c. In higher-velociy condiions, velociy or even acceleraion can be inroduced in esimaing τ(). Velociy and acceleraion can be esimaed using he previously acquired nearby range values. In his manner, all componens ha describe α () are available. By inegraing Equaion () wih Equaion (3), he range value r( τ()) can be acquired. 4. Experimen The approach described in he previous secion is veriied and esed hrough experimenal analysis. Firs, he equipmen and he seup o he experimens are inroduced below. 4.. Experimen Seup The pieces o equipmen used in he experimen consised o:. The sonar head is composed o a SensComp 6 insrumenal ransducer as he ransmier and a G.R.A.S. 46BE microphone as he receiver. The SensComp 6 is an elecrosaic ransducer wih a beam angle o 5 a 6 db.

10 Sensors 3, The arge is made up o boxes. One box only or a simple arge, or more han one box pu ogeher o creae a complex arge wih muliple relecors. 3. Two idenical slide rails are marked as A and B. The sonar head and he arge are respecively ixed on he slider o slide rails A and B. The slider is driven by a sepper moor mouned on he end o he rail hrough a conveyor bel. The slider can reach a maximum speed o.6 m s. The maximum ravel lengh o he slide rails is m. 4. Two ampliiers are used. One is or ampliying he echo signal received by he microphone; he oher is or ampliying he ransmied signal and or driving he ransducer. 5. An ADLINK MXC-6 expandable compuer is used. The compuer is embedded wih an ADLINK DAQ- daa acquisiion card. Picures o he movemen mechanism and he sonar head used in he experimens are shown in Figure 6. Figure 6. Picures o he experimenal apparaus. (a) The enire moion sysem; (b) The sonar head. (a) (b) The connecions among he apparauses are shown in Figure 7. The daa acquisiion card is conrolled by he compuer hrough MATLAB soware. Two o he analog oupu (AO) channels are used o expor pulse rains o he sepper moors hrough wo moor drivers. Anoher AO channel is used o expor he ransmied signal o he sonar head. An analog inpu channel collecs he echo signal rom he sonar head. All he aoremenioned signal operaions are perormed under a sample rae o MS s. Transmied signal parameers are lised in Table. Figure 7. The conrol diagram o he experimenal apparaus. Moor driver Slide rail or sonar PC DAQ Card Moor driver AMP Slide rail or arge Transducer Sonar Head AMP Receiver

11 Sensors 3, H Table. Signal parameer seup o he experimens. L T sw m ST 8 khz 4 khz. s 4 khz/s khz Transmission and recepion o he CTFM signal and he moor conrol signal are perormed a he same ime. All inpu and oupu signals are sored in he compuer. The demodulaion operaion is perormed oline aerwards. Firs, signals are ilered o eliminae noise rom he useul band. Signals are processed in rames. The specrum o each rame is obained by as Fourier ransorm (FFT) analysis. The parameers ˆ ST () and ˆ α () can be deermined by searching he peak in he specrum o he echo signal and he demodulaed signal. Thus, he Doppler acor D() and α () can be deermined using Equaions (7) and (), respecively. The arge range can be obained by subsiuing α () ino Equaions (3). The processing procedure can be described as a block diagram, as shown in Figure 8. Figure 8. A block diagram o he sysem. Single Tone Transducer Driver Convenional CTFM Sysem Transmied Sweep Addiional Sweep Oupu R Peak Deecion FFT Ampliier D Peak Deecion Doppler Correcion FFT The insananeous posiions o he sliders can be deermined by he pulse number o he moor conrol signal. The iniial geomeric relaionship beween he wo slide rails are measured manually. Acual range o he arge a any momen can be acquired by rigonomeric calculaion. 4.. Veriicaion Experimens In he ollowing experimens, a large rame wih 6,384 samples and a shor rame shi wih 5, samples are se up. This seup produces a high rame rae o allow veriicaion o he approach wih dense daa. Veriicaion experimens are perormed in wo condiions: () he sonar is moving while he arge remains sill; he slide rail and he arge are arranged as shown in Figure 9(a); () boh he sonar and he arge are moving, he wo slide rails are arranged as shown in Figure 9(b).

12 Disance (m) Disance (m) Doppler Facor Relaive Velociy (m/s) Doppler Facor Relaive Velociy (m/s) Sensors 3, Figure 9. The seup or he wo esed condiions. (a) The sonar head is moving while he arge remains sill; (b) Boh he sonar head and he arge are moving. Sonar Head Slide Rail Targe v s (a) Targe Slide Rail A Sonar Head v v s Slide Rail B (b) In boh condiions, he slider is conrolled o speed up irs, and hen o slow down. The speeds o he sonar head and he arge ollow dieren acceleraion curves o creae various moions. In condiion, he arge is ixed close o he end o slide rail A. The sonar moves oward or away rom he arge. Figure show experimen resuls when he speed o he sonar head ollows a linear and an exponenial curve, respecively. Figure. Experimen resuls o condiion, he speed o he sonar head changes (a) linearly; and (b) exponenially Doppler Facor Relaive Velociy Doppler Facor Relaive Velociy Demodulaion Oupu Correced Oupu Acual Disance. Demodulaion Oupu Correced Oupu Acual Disance....4 (a).. (b)

13 Disance (m) Disance (m) Doppler Facor Relaive Velociy (m/s) Doppler Facor Relaive Velociy (m/s) Sensors 3, In condiion, he wo slide rails make he same movemen a he same ime. As can be seen in Figure 9(b), an angle is ormed beween rail slides A and B. Thereore, he arge is wihin he sonar beam only or a shor ime. Figure shows wo experimenal resuls in which he sliders move a a linear velociy curve and an exponenial curve. Figure. Experimen resuls o condiion, he speeds o boh he sonar head and he arge change (a) linearly; and (b) exponenially Doppler Facor Relaive Velociy Doppler Facor Relaive Velociy Demodulaion Oupu Correced Oupu Acual Disance (a) (b) Demodulaion Oupu Correced Oupu Acual Disance 4.3. Perormance Tess A series o consan speed experimens is perormed o es he perormance o he approach. The experimenal seup is he same as ha in condiion, which is described in he previous subsecion. The eec o correcion is esed a dieren velociies and rame sizes. CTFM oupu range daa ake he shape o a sep because o he discree oupu o FFT analysis. Aer correcion, daa ake a minor sawooh shape. Higher velociy causes larger sep dierence, which leads o higher oscillaion o he correced range value. By conras, a larger rame size produces smaller inervals beween FFT oupus, hus leading o a higher range resoluion. These inerences are suppored by he experimenal resuls shown in Figure. Figure (a) indicaes how he mean square error (MSE) o correced range value changes wih he velociy o he sonar movemen. Thireen velociy values rom.3 m/s o.5 m/s are esed, wih an inerval o.5 m/s. Figure (b) indicaes he relaionship beween he MSE o he correced range and daa rame size, under he velociy o m/s. Five rame sizes,,48, 4,96, 8,9, 6,384, and 3,768, are esed. Frame shi is equal o hal he rame size. In he aoremenioned es resuls, each value poin is an average o six ess a a corresponding velociy, wih hree approaching movemens and hree backing-away movemens.

14 Magniude Range MSE (m ) Magniude Range MSE (m ) Sensors 3, Figure. Resuls o perormance ess (a) variance o correced range vs. velociy and (b) variance o correced range vs. rame size. x Velociy (m/s) (a) Frame Size (b) 4.4. Complex Targe Tess Muliple relecors disribued in dieren ranges produce a more complex specrum. Such specrum can be seen as a range proile ha represens he geomeric inormaion o he arge [3]. In his subsecion, several iniial complex arge experimens are perormed o suppor he discussion in Subsecion 5.. Two boxes are placed side by side in ron o he sonar, which orms a wo-relecor arge. The sides acing he sonar are misaligned by 5 cm, hus creaing wo relecors. The seup o he es is he same as ha in condiion in Subsecion 4.. The velociy o he sonar is m s. Four rame sizes are chosen o be esed. The correcion approach is applied o he whole range proile. Correcion resuls are shown in Figure 3. The magniude o he range proiles is normalized. The shied and correced range proiles are ploed in dashed and solid lines, respecively. In a saionary condiion, he wo relecors orm wo corresponding peaks wih a dip beween hem. In moving condiions, however, he wo peaks may merge wih each oher or may become vague. Figure 3. Resuls o range proile correcion using dieren rame sizes: (a) 8,9; (b) 6,384; (c) 3,768; and (d) 65, Range (m) (a).. Range (m) (b)

15 Magniude Magniude Sensors 3, Figure 3. Con Range (m) (c) Range (m) (d) 5. Discussion 5.. Resul Analysis As discussed in Secion 3, he deviaion o he CTFM oupu is caused by Doppler shi when relaive movemen occurs beween he sonar and he arge. Supposing ha he simulaneous moion inormaion o he sonar and he arge is available, hen he requency shi o he echo signal can be esimaed hrough geomeric calculaion. Unorunaely, his inormaion is unavailable in pracice. Even i he moion o he mobile agen ha carries he sonar can be obained using velociy measuremen devices such as encoders, angle values o he ulrasonic beam during he propagaion will remain unknown. In his case, Doppler shi inormaion obained rom he echo signal isel is he bes mach or he propagaion procedure. However, in a CTFM sysem, signal requency is changing all he ime, hus Doppler shi is also hard o obain. An idea ha inspired he proposed approach is o combine he conceps o a CTFM sonar and a Doppler sonar. The sweep signal o a CTFM sonar and he single one signal o a Doppler sonar go hrough he same requency shi during he propagaion. Thereore, hey share he same Doppler acor. The acor can be easily acquired by he Doppler sonar, and hen used o correc CTFM oupu. As shown in he veriicaion experimen resuls, he velociy o he movemen keeps on changing, and he Doppler acor value keeps ollowing he speed curve. The correced range remains very close o he value obained rom he pulse coun o he sepper moor, hus proving he validiy o he proposed approach. Sample rae and rame size are se a high values in he veriicaion experimens o yield a dense daa oupu. Some oher sample rae and rame size values are se in he perormance ess. Resuls show ha oupu precision decreases when velociy is higher. Mos mobile agens or indoor arges move a a speed o m/s or lower, wih an oupu range variance reaching 6 4 m. This value is accepable in mos pracical applicaions. As rame size goes larger, oupu precision goes higher. However, rame size canno be se oo high because he specral peak o a CTFM sonar oupu may become vague as a resul o he movemen.

16 Sensors 3, Complex Targe Analysis In a moving condiion, he range proile is aeced by Doppler shi and displacemen. Doppler shi does no only cause deviaion in he range value, bu i also sreches or compresses he range proile. The inluence o Doppler shi can be reduced by applying he correcion approach o he enire proile daa. The experimenal resul o range proile correcion can be seen in Figure 3. However, he inluence o displacemen sill needs o be solved. In his scenario, he rame size should be careully chosen. A larger rame size provides higher range resoluion bu makes he range proile uzzy because o he movemen. Assuming ha he sonar moves a a cerain speed, hen a displacemen Δd is produced wihin he rame duraion: vl d where L is he rame size. Frequency resoluion o specrum Δ is he sample rae divided by he rame size. However, a 3 db dip beween wo adjacen peaks is required o make hem disinguishable [7]. Thereore, he range resoluion o he range proile Δr is calculaed rom Equaion (7) using Δ such ha: s (4) c r s ml By combining he wo equaions above, a relaionship beween Δd and Δr can be wrien as: cv dr m (5) (6) Obviously, Δd and Δr are inversely proporional o each oher. To mainain an opimized perormance, he sysem needs o adjus rame size L o balance beween Δd and Δr, according o v. For a cerain velociy value v and a sysem wih a ixed sample rae, he heoreical minimum disinguishable range inerval ΔR beween wo arges is he sum o Δd and Δr. According o Equaions (4) and (5): vl cs R d r ml Curves o R on several velociy values are shown in Figure 4. The op one is or v =.5 m s and he boom one is or v =.5 m s, wih an inerval o. m s. For his resul, he signal sample rae is se o MS s, which is he same as in he previous experimens. According o Equaion (7), a minimum value o ΔR exiss or a single velociy value. The parial derivaive o ΔR wih respec o L is: R v c L ml When Equaion (8) is se o zero, he value o L or he minimum ΔR can be wrien as: s s s (7) (8) c L round min R s vm (9)

17 R (m) Sensors 3, Figure 4. Minimum disinguishable range inerval vs. rame size L=3594 R=.7 L=5344 R=.66 L=755 R=.6 L=3459 R=.55 L=34538 R=.48 L=4866 R= Frame Size x 4 The minimum poins o ΔR on each curve are marked as black dos in Figure 4. These minimum values are he ines ha he sysem can reach or he corresponding velociy value. Curves in Figure 4 demonsrae ha ΔR decreases very as beore reaching he minimum poin. Aer reaching his valley poin, ΔR increases more slowly. The variaion rend o ΔR can also be seen in Figure 3. Noe ha he higher sample rae does no improve disinguishing abiliy, and only produces a larger L value o reach he minimum ΔR. This resul can be seen in Equaion (9). For a cerain velociy, a corresponding boundary o ΔR is ound: R b cv m (3) This inding implies ha or a CTFM sonar sysem on a mobile plaorm, discriminaion abiliy decreases as movemen speed goes higher. 6. Conclusions Alhough a convenional CTFM sonar is compeiive as a ranging sensor, he shorcoming o is erroneous deecion under moving condiions resuls in a grea limiaion. This work presens an approach o compensae or his law and o broaden he applicaion scope o a CTFM sonar. A single one signal ouside he sweep band is added o he CTFM ransmied signal. A Doppler acor can be acquired by exracing he requency o he single one componen in he echo. Acual arge range can be obained using his Doppler acor and he deviaed CTFM oupu. Experimenal resuls veriy his approach. In his work, daa is sampled, ramed densely, and hen processed in an oline manner. In his manner, oupu daa can be presened wih beer coninuiy and higher resoluion. A high sample rae and rame rae are acually no necessary in pracical applicaions. Lower sample raes may cause lower resoluion o he Doppler acor and he range oupu. However, as long as i saisies Nyquis sampling heorem, he proposed approach sill does no lose is validiy. A low rame rae does no aec he perormance o he approach. I can only cause

18 Sensors 3, he oupu o he sysem o be sparse; however, accuracy is no aeced. Thereore, he enire sysem can be buil as an embedded sysem. The key requiremens are a sample rae high enough or ulrasonic signal acquisiion and he abiliy o he processor or FFT analysis. These requiremens are he same or a convenional CTFM sysem. Addiional uncions are a single one signal generaion and anoher FFT analysis o he echo signal. These uncions do no increase sysem complexiy oo much. Wih regard o complex arges, he discriminaion abiliy o adjacen relecors is discussed. Doppler shi and displacemen boh aec range proile. The choice o rame size is a key poin o allow beer separaion o adjacen arges. This research provides a basic idea or applying a CTFM sonar in deecions involving moving condiions. Furher research will include he ollowing aspecs: () implemenaion o he approach as a real-ime sysem; () moving arge recogniion using he range proile daa obained hrough he approach described in Subsecion 5.; ranslaion-invarian eaure exracion mehods and suiable recogniion mehods should also be invesigaed; and (3) he developmen o a muliple arge deecion abiliy; he maching problem beween Doppler acors and CTFM oupus needs o be solved. Acknowledgmens The auhors would like o acknowledge he inancial suppor by he Naional Naural Science Foundaions o China under Gran No and Gran No Reerences. Fox, D.; Burgard, W.; Thrun, S. The dynamic window approach o collision avoidance. IEEE Robo. Auom. Mag. 997, 4, Burguera, A.; Gonzalez, Y.; Oliver, G. Sonar sensor models and heir applicaion o mobile robo localizaion. Sensors 9, 9, Raner, D.; McKerrow, P.J. Navigaing an oudoor robo along coninuous landmarks wih ulrasonic sensing. J. Robo. Auon. Sys. 3, 45, Chong, K.S.; Kleeman, L. Sonar Based Map Building or a Mobile Robo. In Proceedings o IEEE Inernaional Conerence on Roboics and Auomaion, Albuquerque, NM, USA, 5 April 997; Volume, pp Kao, G.; Prober, P. Feaure exracion rom a broadband sonar sensor or mapping srucured environmens eicienly. In. J. Robo. Res., 9, Marinez, M.; Bene, G. Wall-corner classiicaion using sonar: A new approach based on geomeric eaures. Sensors,, Kay, L. Audiory percepion o objecs by blind persons, using a bioacousics high resoluion air sonar. J. Acous. Soc. Am., 7, Ulrich, I.; Borensein, J. NavBel and he Guide-Cane obsacle-avoicance sysems or he blind and visually impaired. IEEE Robo. Auom. Mag. 3,, Kuc, R. Biomimeic sonar recognizes objecs using binaural inormaion. J. Acous. Soc. Am. 997,,

19 Sensors 3, Kleeman, L.; Kuc, R. An Opimal Sonar Array or Targe Localizaion and Classiicaion. In Proceedings o IEEE Inernaional Conerence on Roboics and Auomaion, San Diego, CA, USA, 8 3 May, 994; Volume 4, pp Poliis, Z.; Prober, P. Percepion o An Indoor Robo Workspace by Using CTFM Sonar Imaging. In Proceedings o IEEE Inernaional Conerence on Roboics and Auomaion, Leuven, Belgium, 6 May 998; Volume 4, pp Poliis, Z.; Prober, P. Modeling and Classiicaion o Rough Suraces Using CTFM Sonar Imaging. In Proceedings o IEEE Inernaional Conerence on Roboics and Auomaion, Deroi, MI, USA, 5 May, 999; Volume 4, pp McKerrow, P.J.; Harper, N. Plan acousic densiy proile model o CTFM ulrasonic sensing. IEEE Sens. J.,, Zhenwei, M.; Wei, J.; Yong, X.; Jun, Y. Human ace classiicaion using ulrasonic sonar imaging. Jpn. J. Appl. Phys. 9, 48, doi:3/jjap.48.7gc. 5. Do, M.A. New dual-sweep receiver or CTFM sonar. Ulrasonics 986, 4, McKerrow, P.J.; Krisiansen, B.E. Classiying surace roughness wih CTFM ulrasonic sensing. IEEE Sens. J. 6, 6, Gough, P.T.; Roos, A.D.; Cusdin, M.J. Coninuous ransmission m sonar wih one ocave bandwidh and no blind ime. IEE Proc. Commun. Radar Signal Process. 984, 3, Morse, P.M.; Ingard, K.U. Theoreical Acousics; McGraw-Hill: New York, NY, USA, by he auhors; licensee MDPI, Basel, Swizerland. This aricle is an open access aricle disribued under he erms and condiions o he Creaive Commons Aribuion license (hp://creaivecommons.org/licenses/by/3./).