VEHICLE detectors (VDs) are widely used to gather traffic

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1 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO., APRIL Estimating Speed Using a Side-Looking Single-Rada Vehile Deteto Shy-Long Jeng, Wei-Hua Chieng, and Hsiang-Pin Lu Abstat This pape pesents a side-looking single-beam miowave vehile deteto (VD) system fo estimation of pe-vehile speed and length. The poposed VD system is equipped with a -D ange Dopple fequeny-modulated ontinuous-wave (FMCW) ada using a squint angle. The assoiated Fouie poesso uses an invese syntheti apetue ada (ISAR) algoithm to extat ange and speed data fo eah vehile using a single-beam FMCW ada. The simulation and expeimental esults show auate estimations of vehile speed and length. The measuement eos of speed and length wee appoximately ±4 km/h and ±1 m, espetively. The poposed method has exellent detetion apability fo small moving tagets, suh as bikes and pedestians, at speeds down to 5 km/h. A ommeial 10.6-GHz ada with signal poessing modifiations was used in the expeiments. Index Tems Fequeny-modulated ontinuous wave (FMCW), intelligent tanspotation system (ITS), syntheti apetue ada (SAR), vehile deteto (VD). I. INTRODUCTION VEHICLE detetos (VDs) ae widely used to gathe taffi infomation in an intelligent tanspotation system (ITS). The objetive of a VD is to obtain taffi infomation, suh as the speed and length of vehiles passing on a oad. A wide ange of senso tehnologies ae available fo VDs, suh as indutive loops, video, ultasoni detetos, and miowave detetos. The advantage of ada-based detetos is that they ae a matue tehnology beause of past militay appliations. Rada-based detetos ae unintusive and an opeate day o night in any weathe onditions. A fequeny-modulated ontinuous-wave (FMCW) ada is widely used fo taffi data olletion. It tansmits a ontinuous-wave (CW) signal and ompaes the fequeny diffeene between the tansmitted and efleted signals to estimate the vehile ange and its speed. The installation methods of ada-based detetos an be lassified as fowad-looking and side-looking (o oadside). Fowad-looking detetos have an illuminative dietion paallel to the dietion of taffi and ae applied only to a single lane Manusipt eeived May 17, 013; evised July 9, 013 and Septembe 17, 013; aepted Septembe 19, 013. Date of publiation Otobe 17, 013; date of uent vesion Mah 8, 014. This wok was suppoted by the National Siene Counil of Taiwan unde Contat NSC E The Assoiate Edito fo this pape was F. Zhu. S.-L. Jeng is with the Depatment of Eletial and Eletoni Engineeing, Ta Hwa Univesity of Siene and Tehnology, Hsinhu 307, Taiwan ( aetsl@tust.edu.tw). W.-H. Chieng and H.-P. Lu ae with the Depatment of Mehanial Engineeing, National Chiao Tung Univesity, Hsinhu 300, Taiwan ( wh@.ntu.edu.tw; hamp.lu@gmail.om). Colo vesions of one o moe of the figues in this pape ae available online at Digital Objet Identifie /TITS Fig. 1. Conventional side-looking vehile detetion systems. [1]. Convesely, Fig. 1 shows that side-looking ada detetos illuminate the dietion pependiula to taffi. A single-ada deteto in a side-looking onfiguation an ove multiple lanes if it is popely plaed and if appopiate signal poessing tehniques ae used. In this ase, miowave sensos an eplae a lage numbe of loops, whih ae usually installed in the tavel lanes. Pependiula side-looking installation is the most popula appoah fo uent ITS appliations. The woking theoy of a side-looking VD is the same as that of a single loop in eah lane. When the vehile length and vehile speed ae unoelated, vehile speed v and vehile length l ae elated by v = l t. (1) IEEE. Tanslations and ontent mining ae pemitted fo aademi eseah only. Pesonal use is also pemitted, but epubliation/edistibution equies IEEE pemission. See fo moe infomation.

2 608 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO., APRIL 014 These paametes annot be independently measued in a single loop. A single loop an only detet dwell time t. Vehile length l is typially set to a onstant value, and (1) is used to estimate speed fom single-loop measuements. Howeve, this appoah does not onside vaying vehile lengths. Duing a low flow, a long vehile an skew statistial data beause it equies moe time to pass the deteto. Many studies [] [4] have addessed this poblem. Most side-looking adas an measue only the dwell time of a vehile passing though the ada sensing zone. A singlebeam ada seved as a single indued loop to estimate speed based on the dwell time. Although dual-ada detetos an povide moe auate speeds and vehile lassifiations by measuing the time diffeene between two ada beams, they enounte a numbe of poblems. Fist, they equie a highly peise installation to ensue pependiulaity to the dietion of taffi; othewise, mathing the deteted signals between two adas is diffiult. The seond poblem is that the pefomane an be inhibited when one of the ada signals is bloked by neaby vehiles in taffi jam senaios. The onventional installation of a side-looking ada does not use the advantage of deteting the Dopple effet of miowave detetos beause the etuned Dopple fequeny geneated by the vehile is weak. Pio studies [5], [6] have deteted the weak Dopple shift fo measuing eal-time speed by using wide beam antennas. The disadvantage of this appoah is degadation in ange auay. Many othe studies [7], [8] have used vaious wavefoms and fequenies to obtain ange and speed infomation. Beause of the weak Dopple effet, the pependiula side-looking VD annot apply the typial FMCW speed detetion method by ompaing beat fequenies of up and down sweeps [9] o the displaement diffeene [10]. Theefoe, it is uial to develop an appopiate method with a naow-beam single-ada deteto to povide auate ange, speed, and vehile lassifiation estimates. This pape poposes a novel ada system to detet multiple vehiles in multiple lanes. The following setion pesents the assoiated FMCW ada measuement sheme and the assoiated -D ange Dopple FMCW ada Fouie poessing method. The ange and Dopple fequeny wee obtained using the -D fast Fouie tansfom (FFT) tehnique [11] widely used in invese syntheti apetue ada (ISAR) signal poessing [1] [15]. Vehile detetion was pefomed by using a highspeed digital signal poesso (DSP) and a 10.6-GHz FMCW font end. This pape also pesents an algoithm to measue the speed and vehile length by using a fixed single-ada module. The emainde of this pape is oganized as follows. Setion II biefly desibes the deivation of the poposed method and Setion III pesents the measuement esults to illustate the apability of the poposed method. Finally, Setion IV onludes the study. II. PROPOSED METHOD Fig. shows an FMCW-based VD installed on a oadside with a squint angle. In this onfiguation, the Dopple fequeny etuned fom the moving vehile is enhaned ompaed with that fom the pependiula VD. Fig. 3 shows a typial FMCW Fig.. Fig. 3. Poposed VD installation. Typial FMCW-based ada ahitetue. ada setup. Fo a side-looking FMCW VD, the ange data etieved fom up and down sweeps ae almost the same exept fo a little phase diffeene. In addition, a tiangula wavefom doubles the time span on a sweep; it edues the pulse epetition fequeny (PRF) and downgades the Dopple fequeny detetion. Theefoe, a sawtooth wavefom is used instead of a tiangula wavefom. The CW signal is modulated in the fequeny to podue a linea hip, whih adiates towad a taget though an antenna. The eho s x (t) eeived τ(t) seonds late is mixed with a potion of the ontinuous tansmitted signal s tx (t) to podue a beat signal at fequeny s b (t), whih is popotional to the oundtip time-of-flight (RTOF) τ(t) between the ada and the taget. The tansmitted signal an be expessed as s tx (t) =A tx os (φ tx (t)) () whee the instantaneous phase tem is φ tx (t) =ω 0 t + α t + φ tx0. The aie fequeny in whih the modulation stats is denoted by ω 0 = πf 0. Sweep ate α = π(b/t) is equal to the quotient of ada signal sweep bandwidth B and sweep duation T. t is the time vaiable in the ange 0 <t<t. Signal s x (t), whih is efleted by the taget and eeived by the ada, is a eplia of the tansmitted signal; howeve, it is delayed by the RTOF. The signal eeived fom the taget is delayed and attenuated, i.e., s x (t) =A x s tx (t τ(t)). (3)

3 JENG et al.: ESTIMATING SPEED USING A SIDE-LOOKING SINGLE-RADAR VEHICLE DETECTOR 609 The eeived and tansmitted signals, i.e., s x (t) and s tx (t),ae multiplied in the mixe. A low-pass filte is used to suppess the signal omponents loated at the double aie fequeny. By solving the multipliation and onsideing () and (3), a beat signal was obtained as s b (t) =A b os (ω 0 τ(t)+ατ(t)t 1 ) ατ(t). (4) Conside a taget loated at distane d at time t = 0 and moving at speed v. The taget eflets the FMCW signal tansmitted by the ada unit. Vehile distane d(t + kt ) is defined as the ange fom the senso to the vehile at the kth sweep. d(t + kt ) is deived by d(t + kt )=d 0 + v (t + kt ), k = 0, 1,,...,N 1 Fig. 4. Measuement sheme. TABLE I PARAMETERS USED IN SIMULATION whee v denotes the adial omponent of the vehile speed at squint angle θ. T denotes the pulse epetition inteval (PRI). Duing NT, the oheent poessing inteval (CPI), the speed is assumed to be onstant, and the RTOF τ(t + kt ) between the ada and the taget is defined as τ(t + kt ) d(t + kt ) = (d 0 + v (t + kt )) = τ 0 + v (t + kt ) (5) whee τ 0 is the RTOF when the vehile is at the initial ange d 0. Replaing τ(t) in (4) with (5) deives a -D beat signal, i.e., whee s b (t, kt )=A b os(φ b ) (6) φ b (t, kt ) = ω 0 τ(t + kt )+ατ(t + kt )t 1 ατ(t + kt ) v = ω 0 τ 0 + ω 0 (t + kt )+ατ 0 t + α v (t + kt )t 1 [ α τ0 v ( + 4τ 0 (t + kt v ) ] )+4 (t + kt ) ( v = ω 0 τ 0 + ω 0 + ατ v ) 0 ατ 0 t ( v + ω 0 ατ v ) 0 kt 1 ατ 0 + α v ( 1 v ) t + α v ( 1 v ) tkt ( v ) α (kt ). Without a loss of geneality, this disussion assumes (v /) 1, and the tem α(v /) (kt ) is ignoed. Equation (6) an be ewitten as φ b (t, kt ) ( ) ( ) ( v = ω 0 +ατ v 0 t+ ω 0 kt + ω 0 τ 0 1 ) ατ 0 = ω R t + ω D kt + φ 0 (7) whee the taget fequeny vaiables fo the ange and Dopple dietion, i.e., ω R and ω D, espetively, ae defined as v ω R = ω 0 + ατ 0 (8) v ω D = ω 0. (9) The FMCW measuement was peiodially epeated, and a set of a numbe of N signals was eoded. Fig. 4 depits the measuement sheme. The omplex analyti signal in (6) was used fo the desiptions to simplify the following mathematial expessions: s b (t, kt )=A b e j(ω D kt +ω R t). (10) The omplex amplitude A b ompises all onstant phase tems. The -D FFT of this signal an be deived by applying the Fouie modulation theoem. With the spatial fequeny vaiables and v in the ange and Dopple dietion, the spetum of s b (t, kt ) is deived as F {s b (t, kt )} = S b (, v). (11) The VD poedue an be summaized as follows. Step 1) Estimate the ange by applying the ange FFT: Fo eah PRI, sample beat signals fom the font end and obtain the beat fequeny by applying FFT. The ange is popotional to the fequeny. Step ) Estimate the dwell time of the vehile in the sensing egion: An appopiate theshold must be set fo a patiula ange bin. Step 3) Estimate vehile speed v by applying the Dopple FFT: At a patiula ange bin, sample ange data fom the fist FFT and obtain the Dopple fequeny by applying the seond FFT. Step 4) Identify the vehile length.

4 610 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO., APRIL 014 Fig. 6. VD setup. (a) VD setup at a height of m and at a bak-off distane of 3 m to the fist lane. (b) VD setup with 10 squint angle. Fig. 7. Deteted dwell time of a vehile passing though the detetion zone. Fig. 5. Simulated -D spetum of thee moving vehiles. (a) Range speta of thee vehiles. (b) Range/speed speta of thee vehiles. () Range/speed speta of thee vehiles in 3-D. The simulation used a data set fo thee vehiles simultaneously taveling distanes of 10, 0, and 30 m though the detetion zone at speeds of 10, 60, and 40 km/h, espetively. Table I shows the senso paametes. The taget ange and speed an be unambiguously detemined by evaluating the positions of the thee -D impulses based on (8) and (9). Fig. 5(a) shows that the ange infomation fo the vehiles was obtained by applying the ange FFT fo all sweep data. The speed infomation of eah vehile an be aquied duing eah CPI by applying a seond FFT at eah fixed ange, beause only one vehile is at eah fixed ange. The speed measuement poblem equies a peak seah on the seond FFT spetum. By applying a single-tone fequeny estimation method [16], the fine speed esolution an be obtained. This method addesses seveal uial issues. As shown in (8), the ange esponse was shifted by the Dopple effets egading the tue position. Howeve, the shifted ange is substantially lowe than the ange esolution. The poposed appoah equies a Dopple shift within the Nyquist limit detemined by the PRF, i.e., whee PRF f D = v f <f D < PRF = v sin(θ)f. (1) The PRF must be suffiiently high to sample the instantaneous bandwidth. Equation (1) effetively ontols the Dopple shift by adjusting the squint angle.

5 JENG et al.: ESTIMATING SPEED USING A SIDE-LOOKING SINGLE-RADAR VEHICLE DETECTOR 611 TABLE II MEASURED SPEED FOR DIFFERENT SPEEDS AT A SQUINT ANGLE OF 10 TABLE III ESTIMATED VEHICLE LENGTH FOR VARIOUS SPEEDS AT A SQUINT ANGLE OF 10 The fist test ase onfimed that the -D FFT esults enabled auate speed measuements. The seond test ase futhe onfimed that the poposed method an simultaneously measue the speeds of multiple vehiles. Fig. 8. Two-dimensional ange/dopple speta measued at diffeent speeds. (a) v = 10 km/h. (b) v = 30 km/h. () v = 50 km/h. III. EXPERIMENTAL RESULTS This setion pesents expeimental esults to demonstate the pefomane of the poposed method in side-looking speed measuement. The data wee olleted using a 10.6-GHz FMCW VD, as shown in Fig. 3. Fig. 6 shows the ada was mounted on a tipod beside the oad at a height of m and at a distane of 3 m to the fist lane. Both lanes of the oad wee 3.5 m wide, and the ada beams wee plaed at a 10 squint angle faing the oad. Table I shows the VD paametes. Beause of the PRF limitations, the maximal unambiguous speed was 50 km/h. High pefoming hadwae would be needed to measue highe speeds. A. Test Case A: Vaious Speeds at a Squint Angle of 0 The fist expeiment showed the ability of the poposed -D FFT appoah to detet the speed and length of a vehile. A vehile with a length of 4.6 m was diven at speeds fom 10 to 50 km/h in the fist lane. The eho signal poessed by the fist FFT onvets to ange infomation. The dwell time fo a vehile in the detetion zone an be measued by setting a suitable theshold at a speified ange bin fom onseutive fames. Fig. 7 shows the deteted dwell time as the vehile passed though the detetion zone. Duing the dwell peiod, the ange FFT data of a taget ae olleted fo the Dopple spetum afte a seond FFT. The Dopple speta diffe fo vaious vehile speeds. Fig. 8 shows that the -D ange-dopple speta measued at vaious vehile speeds had stonge peak signals at low speeds than at high speeds. These haateistis an solve the poblem of impeise speed measuement in most side-looking VD appliations. Table II shows that the measuement eo between atual and estimated speed was limited to ±4km/h. Fom the measued dwell time and speed, the vehile length an be deived using (1). The length must be alibated by subtating the beamwidth at Lane 1. Table III shows that the measuement eo in the deived vehile length at vaious speeds was limited to 1 m.

6 61 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO., APRIL 014 Fig. 9. Senaio of vehiles moving in opposite dietions. (a) Snapshot of the senaio. (b) Range/speed spetum. B. Test Case B: Multiple-Taget Detetion Thee senaios wee used to demonstate the effetiveness of the poposed method fo simultaneous detetion of multiple tagets at vaious anges and taveling at vaious speeds. The fist senaio was two tagets moving in opposite dietions at appoximately the same speed (30 km/h). Both moving objets enounteed eah othe in the detetion zone. Fig. 9(a) shows a photogaph of the enounte. Although the eho powe of the bike was lowe than that of the a, Fig. 9(b) shows that both wee distinguishable in the ange-dopple spetum. The seond senaio was one a and one pedestian moving in the same dietion at low speeds. The spetum in Fig. 10(b) shows that, although the pedestian was walking at a slow speed (appoximately 5 km/h), the eho powe was suffiient fo auate detetion. The thid senaio was two small as moving in the same dietion at 15 km/h. Fig. 11(b) shows that the spetum fo this senaio had two distinguishable peaks. Figs show that, although the etun signals of fathe objets wee often patly obstuted by neae objets, the poposed method oetly extated the ange and speed infomation. The poposed single-ada detetion method auately measued the speeds of slow-moving and obstuted objets even when powe substantially diffeed between zones, whih limits the auay of speed estimation in the dual-ada and multiple-zone appoahes. The seond advantage is that the speed oheent poess in the seond FFT auately detets tagets with a small ada oss setion, i.e., vehiles, bikes, and pedestians. Fig. 10. Senaio of a a and a pedestian moving in the same dietion. (a) Snapshot of the senaio. (b) Range/speed spetum. Fig. 11. Senaio of two as moving in the same dietion at 15 km/h. (a) Snapshot of the senaio. (b) Range/speed spetum.

7 JENG et al.: ESTIMATING SPEED USING A SIDE-LOOKING SINGLE-RADAR VEHICLE DETECTOR 613 Fig. 1. Sequential Dopple speta and taked speed of a van taveling at 0 km/h. (a) Tested van. (b) Sequential Dopple speta. () Taked speed. C. Test Case C: Signals fo Diffeent Vehile Types This expeiment ompaed sequential -D FFT speta between a van and a tuk. The pupose of the expeiment was to measue signal quality in a sequential -D FFT. The van (length, 4.9 m) and the tuk (length, 1 m) wee both diven at a onstant speed (appoximately 0 km/h). Fig. 1(b) shows that the -D FFT was applied to the signal fo 1.15 s, whih was the time when the van was in font of the sensing aea. The 115 sweeps obtained by the FFT at a 1-kHz sweep ate wee equally divided into nine time sequenes. Fig. 1(b) also shows the sequential esults of Dopple speta. Equation (1) was used to alulate the speed of the van based on the spetum peak in eah segment [see Fig. 1()]. The same poedue was used to deive the speed of the tuk. Notably, the shapness of the Dopple speta in Fig. 13(b) is lowe than that of the speta Fig. 13. Sequential Dopple speta and taked speed of a tuk taveling at 0 km/h. (a) Tested tuk. (b) Sequential Dopple speta. () Taked speed. in Fig. 1(b) beause the wide Dopple bandwidth yielded a wide vaiation in speed estimates. IV. CONCLUSION Estimating and lassifying vehile speed ae uial poblems in VDs used to gathe taffi data in an ITS. Howeve, as noted in Setion I, pe-vehile speed estimation by sidelooking single-beam miowave detetion is geneally inauate o unsuppoted. In addition, olleting eliable length data fom these detetos is impossible beause of the noisy speed estimates povided by onventional data aggegation fo singlebeam detetos. The poposed algoithm enables auate detetion of pevehile speed and length by using side-looking single-beam miowave detetos. Unlike onventional side-looking ada sensos, the poposed method uses a squint angle to obtain

8 614 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO., APRIL 014 stonge Dopple signals ompaed with onventional sensos. Sine the poposed sheme ouples speed and ange measuements fo the lane in whih a vehile is moving, estimates of vehile loation and movement ae unambiguous and eliable. The dietions of moving vehiles ae also detemined aoding to negative- o positive-displaement Dopple shifts, egadless of the diving lane. The length of a vehile an be also deived fom its speed and the duation of time in the sensing zone. Theefoe, a single ada an effiiently measue speed and monito all lanes of a taffi oute. Simulations onfimed that the theoetial ange-dopple FMCW piniple deived in this study an be used to detet multiple vehiles simultaneously. A ommeially available 10.6-GHz ada and modified signal poessing softwae wee used fo expeimental tests. The expeimental esults show that the poposed algoithm is highly auate, patiulaly at low speeds. The measuement eo was less than 4 km/h. In addition to deteting vehiles, the expeiments showed that the poposed method an detet weak moving tagets, suh as bikes and pedestians. Although the poposed algoithm exhibited aeptable pefomane at low speeds, futhe studies ae needed to inease the appliable vehile speed ange fo the algoithm. Reduing the squint angle an edue adial speed but would also weaken the Dopple signal and speed esolution. The solution is using a DSP with highe pefomane apability to impove the obustness and auay of the poposed algoithm. ACKNOWLEDGMENT The authos would like to thank U&U Engineeing, In. fo suppoting VDs and failities to aomplish the expeimental wok and C.-M. Yang, H.-J. Hsu, and C.-Y. Hsu fo implementing the expeiments. REFERENCES [1] I. S. Kim, K. Jeong, and J. K. Jeong, Two novel ada vehile detetos fo the eplaement of a onventional loop deteto, Miow. J., vol. 44, no. 7, pp. 69, 001. [] Y. H. Wang and N. L. Nihan, Can single-loop detetos do the wok of dual-loop detetos? J. Tansp. Eng., vol. 19, no., pp , Ma [3] B. Coifman, S. Dhoojaty, and Z. H. Lee, Estimating median veloity instead of mean veloity at single loop detetos, Tansp. Res. C, Emeging Tehnol., vol. 11, no. 3/4, pp. 11, Jun. Aug [4] B. Coifman and S. B. Kim, Speed estimation and length based vehile lassifiation fom feeway single-loop detetos, Tansp. Res. C, Emeging Tehnol., vol. 17, no. 4, pp , Aug [5] S. J. Pak, T. Y. Kim, S. M. Kang, and K. H. Koo, A novel signal poessing tehnique fo vehile detetion ada, in Po. IEEE MTT-S Int. Miow. Symp. Dig., Philadelphia, PA, USA, Jun. 003, vol. 1, pp [6] P. J. Wang, C. M. Li, C. Y. Wu, and H. J. Li, A hannel awaeness vehile deteto, IEEE Tans. Intell. Tansp. Syst., vol. 11, no., pp , Jun [7] H. Rohling, Some ada topis: Wavefom design, ange CFAR AND taget eognition, in Advanes in Sensing with Seuity Appliations. New Yok, NY, USA: Spinge-Velag, 006, pp [8] I. Uazghildiiev, R. Ragnasson, and A. Rydbeg, High-esolution estimation of anges using multiple-fequeny CW ada, IEEE Tans. Intell. Tansp. Syst., vol. 8, no., pp , Jun [9] M. Skolnik, Intodution to Rada Systems., 3d ed. Boston, MA, USA: MGaw-Hill, 001. [10] A. G. Stove, Linea FMCW ada tehniques, Po. Inst. Elet. Eng. F, Rada Signal Poess., vol. 139, no. 5, pp , Ot [11] A. Wojtkiewiz, J. Misiuewiz, M. Nałez, K. Jedzejewski, and K. Kulpa, Two-dimensional signal poessing in FMCW adas, in Po. XX KKTOiUE, Kołobzeg, Poland, 1997, pp [1] M. Vossiek, T. vonkessenbok, and P. Heide, Signal poessing methods fo millimetewave FMCW ada with high distane and Dopple esolution, in Po. 7th Eu. Miow. Conf., 1997, pp [13] A. Meta, P. Hoogeboom, and L. P. Ligthat, Signal poessing fo FMCW SAR, IEEE Tans. Geosi. Remote Sens., vol.45,no.11,pp , Nov [14] P. Maques and J. Dias, Veloity estimation of fast moving tagets using a single SAR senso, IEEE Tans. Aeosp. Eleton. Syst., vol. 41, no. 1, pp , Jan [15] N. Webe, S. Moedl, and M. Hakne, A novel signal poessing appoah fo miowave Dopple speed sensing, in Po. IEEE MTT-s Int. Miow. Symp., 00, pp [16] C. F. Huang, H. P. Lu, and W. H. Chieng, Estimation of single-tone signal fequeny with the speial efeene to fequeny-modulated ontinuous wave system, Meas. Si. Tehnol., vol. 3, no. 3, pp , Ma. 01. Shy-Long Jeng was bon in Taiwan in He eeived the Ph.D. degee in mehanial engineeing fom National Chiao Tung Univesity, Hsinhu, Taiwan, in Fom 1996 to 1998, he was with an eletial moto design ompany. He is uently an Assoiate Pofesso with the Depatment of Eletial and Eletoni Engineeing, Ta Hwa Univesity of Siene and Tehnology, Hsinhu. His eseah inteest inludes miopoesso-based ontol and appliations. Wei-Hua Chieng was bon in Taiwan in He eeived the B.S. degee in mehanial engineeing fom National Tsing Hua Univesity, Hsinhu, Taiwan, in 198 and the M.S. degees in mehanial engineeing and in eletial engineeing and the Ph.D. degee in mehanial engineeing fom Columbia Univesity, New Yok, NY, USA, in 1986, 1987, and 1989, espetively. Fom 1987 to 1989, he was awaded an IBM Manufatuing Fellowship. He is uently a Pofesso with the Depatment of Mehanial Engineeing, National Chiao Tung Univesity, Hsinhu. His eseah inteests inlude automated ontol, mehatonis, and mioeletomehanial systems. Hsiang-Pin Lu was bon in Taiwan in He eeived the B.S. degee in ompute siene fom Chung Cheng Institute of Tehnology, Taoyuan, Taiwan, in 1988 and the M.S. degee in omputing fom Impeial College London, London, U.K., in He is uently a Reseah Assistant with National Chiao Tung Univesity, Hsinhu, Taiwan. Fom 1988 to 006, he was a Reseahe with Chung- Shan Institute of Siene and Tehnology, Taoyuan. His eseah inteests inlude signal poessing in fequeny-modulated ontinuous-wave sensos, musi ognition, and algoithmi omposition.