Fast and Accurate Positioning Technique Using Ultrasonic Phase Accordance Method

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1 Fast ad Accurate Positioig Techique Usig Ultrasoic Phase Accordace Method Hiromichi Hashizume Natioal Istitute of Iformatics -- Hitotsubashi, Chiyoda-ku, Tokyo -8, Japa Ayumu Kaeko, Yusuke Sugao, Koji Yatai ad Masaori Sugimoto Graduate School of Frotier Scieces The Uiversity of Tokyo 7-- Hogo, Bukyo-ku, Tokyo -, Japa {ayumu, sugao, yatai, Abstract A iovative measuremet techique for use by positioig systems usig ultrasoic sigals was developed. The advatage of this techique is that it ca accurately idetify the relative distace ad orietatio betwee devices by usig a oe- ultrasoic packet. It is therefore especially useful for ubiquitous computig applicatios where people with mobile devices cotiuously chage their positios i idoor eviromets. The techique, which is amed phase accordace method, uses two or more carriers i ultrasoic commuicatio. A special ultrasoic burst sigal, called syc patter i the header part of the commuicatio packet gives the base poit of the measuremet. The whole differece calculatio is the carried out usig this base poit. A experimet based o the proposed method proved that the techique attais remarkable performace, amely, errors of less tha ± mm i three meter distace measuremets ad less tha. degree errors i the zero, te, twety, ad thirty degree measuremets. Idex Terms Ultrasoic measuremet, sigal processig, positioig system, of arrival, agle of arrival. I. INTRODUCTION Estimatig the positio of people ad mobile devices is a critical issue i the fields of ubiquitous computig [7], locatioaware computig [], ad mixed reality []. I the ope air, GPS sigals ca easily provide positio iformatio; however, iside buildigs they ca be blocked ad become uusable. Cosequetly, the estimatio of the positio of multiple people s or devices idoor is a active research issue. Positioig systems for idoor use were based o, for example, ifrared sigals [], weight-sesitive floors [], radiofrequecy (RF) sigals [], [6], ad computer visio []. A major problem with these methods is accuracy, i.e., estimatio errors rage from several ceters to a doze or so meters. Ultrasoic positioig systems provide more accurate i measuremets tha the above systems. Active Bat [], usig ultrasoic sigals ad radio waves, measures distaces from multiple referece poits (ultrasoud receivers) ad estimates the D positio of a ultrasoud trasmitter. The serious drawback, however, of ultrasoic systems is related to their istallatio. I Active Bat, for example, umerous receivers must be placed o the ceilig; thus, set up is expesive ad ivolves laborious tasks. We believe that ubiquitous computig eviromets must be developed effortlessly ad costlessly. I additio, they should be deployed i offices ad homes as well as i laboratories. To reduce the umber of ultrasoud receivers, [8] proposed a positioig system based o iterative multilateratio. However, reducig the quatity of positioed refereces cosiderably degraded the estimatio accuracy of the system. A more precise estimatio method for ultrasoic positioig is therefore required. I respose to this eed, we have developed a iovative techique for measurig distaces ad orietatios that improves the estimatio performace of positioig systems. This techique amed phase accordace method uses two or more carriers i ultrasoic commuicatio. A special ultrasoic burst, a syc patter, is placed i the header of a commuicatio packet ad gives the base poit, which is called epoch for measuremet. This epoch is the used for a precise calculatio of the propagatio delay. This techique is especially useful whe there are few referece objects at kow positios ad multiple mobile devices (e.g., PDA) which mout both ultrasoud trasmitters ad receivers. It ca also be used to accurately determie relative positios of mobile devices without the eed of referece objects. The proposed techique has several advatages: The syc patter ot oly gives a precise mark for distace measuremet, it also provides a exact phase ad amplitude sychroizatio of carriers. Usig a syc patter eables arbitrary digital commuicatio by phaseshift keyig or multi-value QAM with ultrasoud chaels. Whe a trasmitter seds out its estimated positioal coordiate ad a stamp o the ultrasoud chael, eighborig receivers that ca detect the data packet ca modify their estimated positios accordig to the distace measured with of arrival method, provided that all odes are -sychroized usig, e.g., NTP (Network Time Protocol). I this maer the odes i a system ca maitai relative coordiates without havig to set up special beacos i the room. The proposed techique showed a remarkable accuracy i estimatig the distace ad orietatio of odes: less tha ± mm i three-meter measuremets, ad less tha. degrees i zero-, te-, twety-, ad thirty-degree measuremets. This meas that the techique is more accurate tha existig systems such as [9] ad [] that use ultrasouds for positio estimatio.

2 II. LOCATION MEASUREMENT USING ULTRASOUND A. Time of Arrival Method The most popular techique used by of ultrasoic locatio systems is the of arrival (TOA) method. Whe the trasmitter (TX) ode ad receiver (RX) odes are sychroized, ad if the RX kows whe a TX ode seds out a ultrasoud packet, it ca calculate the trasmissio delay of the packet. By dividig the delay value by the velocity of soud, the RX kows the distace betwee the TX ad itself. The key issue with this algorithm is maitaiig the sychroizatio amog the odes ad determiig the exact arrival s of ultrasoud packets. The mai cause of errors i measuremets by a TOA locatio system is the estimatio error of the arrival s of ultrasoud packets. Ultrasoic trasmitter ad receiver devices resoate sharply to a specific frequecy, i.e., khz, for the most popular devices. Wave packets commuicated via those resoators get deformed from their origial shape, which makes determiig the TOA difficult at a RX. A. ms ambiguity i receivig, for example, makes a cm error i the distace measuremet. B. Agle of Arrival Method Aother techology for ultrasoic locatio measuremet is the agle of arrival (AOA) method which became well kow after it was used i Cricket Compass[9]. I those systems, RXs use two or more ultrasoic microphoes i parallel to estimate the D or D positios of TXs usig triagulatio. The sigal reaches the two idividual microphoes at differet momets. The differece δt is calculated as cδt= L si θ () where c is the soud velocity ad L is the distace betwee the two microphoes, the baselie of the triagulatio. Ad θ is the agle as show i Fig.. (N.B. () is approximately correct whe the distace to the odes R>>L.) From () the agle θ is estimated as θ =si cδt/l. () I the usual settig baselie L is relatively small compared to the speed of soud c, which reders the differece δt a very small so the differece is oly observed from the phase differece betwee wave-packet carriers. For this reaso almost all AOA systems seds a fairly log ultrasoic carrier wave to make phase detectio ad compariso easy. Give phase differece δφ () ca be rewritte as: cδφ θ =si () πfl where f is the carrier frequecy. However, the difficulty of solvig () lies i the fact that the phase φ ca oly be retrieved from the siusoidal fuctio represetig carrier which is a π-periodic fuctio. If the observed phase differece is δφ the true value may be δφ, π δφ, π + δφ, etc. I most cases multiple cadidates of δφ give differet, reasoable solutios of () hece the choice of the correct solutio is difficult. (If L<c/f = λ/ there is o such cofusio, but for khz ultrasoud λ/ is about mm which is too short for a triagulatio.) To cope with the π-phase ambiguity the Criket Compass system, for example, employs three microphoes for a D measuremet or five microphoes for a D measuremet i order to make simultaeous triagulatios with the differet baselies. Aother difficulty of the phase-orieted measuremets of locatios is the existece of a multipath. The objects aroud the ultrasoic wave chael reflect, or scatter the soud wave, ad they spoil the phase accuracy. III. PHASE ACCORDANCE METHOD A. Basic Idea The authors propose a ew method amed phase accordace method for measurig ultrasoic distaces. This method uses a burst of ultrasoic waves, as with burst-pulse systems. However, it does ot use the evelope of the burst to determie the -start iformatio. Istead, the burst cosists of two or more frequecy sub-carriers f,f,f,..., ad the carriers phases accord at a sigle marker epoch. For simplicity s sake we explai this method with a dual carrier system f +f, e.g., f = 9.7kHz ad f =.khz (Fig. ). The superpositio of the two frequecy sigals makes a beat, which shows a distictive patter o the evelope. We, however, do ot pay attetio to the shape; istead we look the phase differece of the compoet carriers. We call this beat patter a syc patter. Mathematically the syc patter is described as si πf t +siπf t = siω t +siω t. () If the duratio of a syc patter legth is equal to the iverse of frequecy distace, i.e., /(f f )=/ = ms, the phase differece φ φ sweeps from π to π, ad the specific phase distace, e.g., φ φ = Fig.. Dual carrier wave

3 occurs oly oce i the patter. We use this matchig poit of the phases as the epoch. The algorithm explaied i the followig sectio ca determie the epoch very precisely, withi a few microsecods, uder experimetal coditios. As a result, this techique provides distace measuremets withi a error rage of a few millimeters. The required for a measuremet is the duratio of a syc patter, i.e., ms. The aalysis of the syc patter also gives the base poit ad amplitude iformatio which are useful for subsequet data commuicatio usig ultrasouds. B. Phase Detectio Whe the syc patter is received by the receiver, the compoet carriers f ad f should be extracted, ad the phase iformatio of the carriers φ ad φ should be precisely determied. To do this, we use the followig mathematical process. We defie the ier product of two domai fuctios f(t) ad g(t) by <f(t),g(t) >= T T/ T/ f(t) g(t)dt where g(t) is the complex cojugate of g(t). The ier product of si(ωt+φ) ad the complex expoetial fuctio e jωt =cosωt + j si Ωt yields < si(ωt + φ),ɛ jωt >= T = = = Tj = j = j T/ T/ T/ T/ T/ si(ωt + φ) e jωt dt (e j(ωt+φ) e j(ωt+φ) )e jωt dt (e j(ω Ω)t+jφ e j(ω+ω)t jφ )dt Tj T/ (e jφ ej(ω Ω)T/ e j(ω Ω)T/ Tj j(ω Ω) e jφ ej(ω+ω)t/ e j(ω+ω)t/ j(ω +Ω) ( jφ si(ω Ω)T/ e (ω Ω)T/ ( e jφ sic ω Ω ) e jφ si(ω +Ω)T/ (ω +Ω)T/ T e jφ sic ω +Ω T ) where sic x =six/x is the samplig fuctio. The receiver captures the syc patter () from the trasmitter ad it ca be writte as s(t) = a si(ω t + φ )+ a si(ω t + φ ), where φ ad φ are the iitial phase of the compoet carriers. We estimate them by calculatig the ier products of the sigals with stadard sigals e jωt ad e jωt. From the above formula, the ier product of s(t) with e jωt is give as ) <s(t),e jωt > = ( a (e jφ sic ω ω T e jφ sic ω + ω T ) j +a (e jφ sic ω ω T e jφ sic ω + ω T ) ) observig the relatios sic( x) =sicx ad sic = = ( a (e jφ e jφ sic ω T ) j +a (e jφ sic ω ω T e jφ sic ω + ω T ) ).() Similarly the ier product of s(t) ad e jωt is <s(t),e jωt > = ( a (e jφ sic ω ω T e jφ sic ω + ω T ) j +a (e jφ e jφ sic ω T ) ). (6) Equatios () ad (6) ca be combied to a matrix equatio where a e jφ ad a e jφ are the ukows. sic ω ω T ( ) sic ω a e jφ ω T a e jφ sic ω T sic ω + ω T ( ) sic ω a e jφ + ω T sic ω T a e jφ =j ( <s(t),e jω t > <s(t),e jωt > ). (7) This equatio ca be strictly solved by examiig the real part ad the imagiary part idividually. Whe the itegratio iterval T is chose to make ω T, ω T ad (ω ± ω )T/ as iteger multiples of π, the terms with sic ω T =simπ/mπ, etc will be equal to zero. The direct solutios ca thus be derived from (7) as a e jφ =j<s(t),e jωt > a e jφ =j<s(t),e jωt >. The above expressios are also approximately true whe T is large eough compared to the period of carrier frequecies. I ay case, phase ad amplitude iformatio of f ad f compoets ca be obtaied from a syc patter by the multiplicatio ad the itegratio of the received sigal with e jωt ad e jωt. The multiplicatio of the received sigal of carrier agular frequecy ω with cos ωt ad si ωt is called quadrature detectio, ad is widely used for demodulatio of phase modulated sigals. The above equatio shows that the same method ca be applied to obtai precise phase iformatio from multiple carrier sigals. The itegratio iterval T is called a widow. Note that whe the received sigal f(t) is coverted to discrete- series f, the ier product is approximately <f(t),g(t) > (/N ) N i= f i g i.

4 C. Fidig Phase Accordace With the above-metioed algorithm, we ca obtai carrier phases φ ad φ at the ceter of the widow, ad set it as t =.Asω <ω, φ icreases faster tha φ. As passes, φ catches up with φ ad the two phases become idetical agai. This happes at t = φ φ = φ φ ω ω π(f f ). This is the epoch retrieved from the received sigal. Fig. shows the head part of a actual received sigal. This is stored i the waveform memory after beig digitized by a AD coverter, so the decodig process is carried out with digital processig Fig.. patter Commuicatio packet with leadig syc Fig.. A 8PSK diagram D. Other Properties of Phase Accordace Method The beefit of this techique is the short measuremet of a operatio. It oly requires a burst of two millisecods. Whe the system is adopted i the full mobile eviromet i which oly a itermittet commuicatio is possible for a pair of odes, a good cosequece is expected. Aother beefit is that the syc patter sychroizes the receiver s local oscillator to a certai trasmitter s carrier phase. Usig subsequet ultrasoic commuicatio, we ca commuicate data by phase shift keyig or phase amplitude modulatio. Fig. shows the phase diagram whe we processed the received 8-PSK ultrasoic sigal. It shows that the eight phase positios ca be clearly discrimiated. This techology is therefore applicable for geeral digital commuicatio usig the modulated bit fields trailig the header syc patter. We expect the maximum data rate of the ultrasoic trasmissio to be close to a telephoe modem s, e.g., a few to a few tes of kilobits per secod. Trasmissio ode ID, trasmissio stamp, trasmitter coordiate positio ad eve etwork ca be set with a ultrasoic chael. Ultrasoic-oly positioig system (i which odes do ot use IR, wireless or other commuicatio methods) is therefore theoretically possible. Because this method is based o the mechaism of phasetrackig systems, we expect the measuremet accuracy to be up to their level, i.e. a few millimeters. I additio, this system may be more tolerat to multipath errors, which were somes critical i phase-trackig systems. The syc patter is placed at the head of trasmissio packets so that it reaches the receiver first. The spatial legth of a syc patter is about 7 cm, so the multipath sigals should arrive after the real syc patter has bee received ad processed, provided that the reflectio paths are loger tha 7cm. E. Itegratio of TOA ad AOA methods Followig the priciples of the phase accordace method both the TOA ad AOA locatio systems ca be costructed, ad eve more, they ca be itegrated i a sigle system. Fig. (a) shows the basic orgaizatio of a TOA system usig phase accordace. Each ode i the system is sychroized ad exchages stamps ad coordiates by usig the digital commuicatio capability of the system. The distace betwee a pair of odes is determied whe a RX ode received a packet from a TX ad compares the TX stamp ad the receivig by usig the epoch. (As demostrated later the accuracy of a measuremet is expected to be withi a few millimeters.) Time sychroizatio is achieved, for example, via NTP (etwork protocol) usig the secodary wireless LAN chael, or eve usig the ultrasoic chael which is primarily devised for distace measuremet, as it ca commuicate geeral data. The odes i the system have to maitai their estimated positios as well as a estimated system. This algorithm is already utilized i the GPS system. Fig. (b) shows the AOA measuremet. Whe a RX ode detects the directio to the TX ode usig AOA method, sychroizatio betwee the odes is ot eeded. I the covetioal AOS systems the RX ode receives carrier-wave from the TX ode usig least two microphoes for a D positioig, or three or more for a D positioig ad compares the phase betwee the received (a) d sigals. The drawback of this TX d method, however, is the difficulty of choosig sigle a- d RX TX gle value form multiple cadidates of the solutio; we explaied this effect as the TX π ambiguity i the previous (b) sectio. Phase accordace method TX ca also be applicable to AOA measuremet. By t RX receivig a syc patter (c) with two microphoes, the differece betwee d the arrival s ca be so TX d precisely determied that the agle is calculated by t RX solvig equatio () with differece, rather tha Fig.. Three differet positioig methods. (a) TOA (b) AOA solvig equatio () with (c)itegratio of TOA ad AOA phase differece. Equatio () gives a sigle, direct

5 solutio without the π-phase ambiguity problem which is hardly avoided whe we use phase-orieted methods. With phase accordace method TOA ad AOA measuremet ca be itegrated to a sigle system as schematically show i Fig. (c), sice both the distace ad the agle ca be aalized from differece of epoch i the syc patters. The odes are sychroized to the etwork, ad coduct the distace ad the agle measuremets at the same. This meas that the positio determiatio (estimatio of the coordiates) of a RX ode is possible just by perceptig a sigle packet from the TX ode whose coordiates are kow. IV. EXPERIMENTAL SYSTEM To cofirm the feasibility ad expected properties of the phase accordace method, we have carried out the experimet described below. Fig.. A ultrasoic trasmitter Fig. 6. L =86mm A ultrasoic receiver A. Trasmitter ad Receiver Fig. shows the trasmitter. It has a waveform ROM which cotais the trasmissio waveform, ad a subsequet DA coverter ad a ultrasoic trasducer which sed out the soic waveform. The dual carrier frequecies are 9.7kHz ad.khz which compose a ms burst of a syc patter. It also has a coector that provides a electrical pulse. To examie the trasmissio delay, a receiver compares the epoch retrieved from the ultrasoic microphoe with the electric pulse. (N.B. It is just for the experimet purposes. I the case of a practical system we will make sychroizatio amog odes usig NTP or other methods.) Fig. 6 shows the receiver. To coduct the AOA measuremet of a plaar agle, the receiver uses two microphoes. They are placed at a distace L of 86 mm, which is the baselie for the triagulatio. The receiver is very sesitive to evirometal electric oise, so the etire settig is covered with copper foil as shieldig. The sigal is coverted to a digital form, ad the detectio process is implemeted as software i the CPU. The AD coverter operates at speed of Msps (samplig per secod), ad the resolutio is 8bit liear with 6 levels. B. Evaluatios We evaluated the developed method by placig the TX at six differet positios, ad coducted te idepedet measuremets at each positio (Fig. 7). The physical distace betwee the TX ad RX was kept to three meters. Fig. 7. [deg] trasmitter receiver mm Trasmitter ad receiver arragemet Fig. 8 shows the results of the agle measuremets. The retrieved agles of zero-, te-, twety- ad thirty-degree positios. These results show that the phase accordace method improved measuremet accurtcy compared with former methods i which the accuracy was usually a few ceters or a few degrees. The retrieved agles, however, are showig errors at the agles of degrees ad beyod. We presume this error comes from the diffractio of the ultrasoic wave at the corer of the receiver trasducer, ad ca be avoided by choosig a wider aperture device. The estimated agles still show a small distributio for these positios. This meas the receiver still sees the ultrasoic source as a poit i space eve after the wave is deflected. Fig. 9 shows the result of distace measuremets. Calculated distaces of all the measuremets are close to their true values ( mm or meters) ad the distributios are also small. Note that the positioal accuracy of the sigal source i the experimet was ot particularly high. The few-millimeter shift of the average distace value from mm is due to the error of the phase accordace method. We thus eed to do more experimets to examie the total accuracy. I the beig, we oly state that the distributio of the measuremet values is withi a millimeter for these distaces ad agles. V. CONCLUSIONS We developed a ew techique for positioig systems usig ultrasouds. The ew techique uses multiple ultrasoic waves (two, i this study) of differet frequecies to correctly idetify TOA ad accurately estimate distaces ad orietatios betwee trasmitters ad receivers. We built a experimetal system ad ackowledged the performace of the proposed techique is satisfactory, amely the error i estimated distace is withi ± mm whe measurig a three meter distace ad the orietatio estimatio error is less tha. degrees whe measurig zero-, te-, twety- or thirty-degree agles. I additio to the accuracy, the proposed method ca estimate distaces ad orietatios betwee devices by usig a oe ultrasoic burst wave. A positioig system based o the proposed techique is therefore especially useful for ubiquitous computig applicatios where people with mobile devices cotiuously chage their positios i a idoor eviromet.

6 [deg] ceter:.[deg] [deg] ceter:.[deg] [deg] ceter:.[mm] [deg] ceter: 8.[mm] ~ ~ ~ ~ Distributio of measuremets [deg] Distributio of measuremets [deg] [deg] ceter:.[deg] [deg] ceter:.[deg] [deg] ceter: 998.[mm] [deg] ceter: 98.[mm] ~ ~ ~ Distributio of measuremets [deg] Distributio of measuremets [deg] ~ 6 [deg] ceter: 7.[deg] [deg] ceter: 6.[deg] [deg] ceter: 997.[mm] [deg] ceter:.[mm] ~ ~ ~ ~ Distributio of measuremets [deg] Distributio of measuremets [deg] Fig. 8. Error distributio (agle) Fig. 9. Error distributio (distace) Several issues still eed to be ivestigated, for example, whe measurig a agle of degrees ad beyod, the estimatio is ot accurate. We will try several methods for estimatig correct orietatios, such as choosig a wider perceptio agle device. We have ot yet coducted itesive evaluatios o how effective the proposed techique is for solvig the multipath problem. We also pla to develop ubiquitous computig applicatios by usig a positioig system based o the proposed techique. A example of the applicatios is Toss-It which allows people with a mobile device to trasfer data by a toss ad a swig actio []. REFERENCES [] Addlesee, M., et al: The ORL Active Floor, I IEEE Persoal Commuicatios, Vol., No., pp.- (997). [] Bahl, P., Padmaabha, V.: RADAR: A I-Buildig RF-Based User Locatio ad Trackig System, I Proceedigs of IEEE Ifocom, pp (). [] Brumitt, B., et al: EasyLivig: Techologies for Itelliget Eviromets, I Proceedigs of Iteratioal Symposium o Hadheld ad Ubiquitous Computig, pp.-9 (). [] Foxli, E., Harrigto, M., Pfeifer, G.: Costellatio TM : A Wide-Rage Wireless Motio-Trackig System for Augmeted Reality ad Virtual Set Applicatios I Proceedigs of ACM SIGGRAPH98, pp.7-78 (998). [] Hightower, J., Borriello, G.: Locatio Systems for Ubiquitous Computig, IEEE Computer, Vol., No.8, pp.7-66 (). [6] Ladd, A., et al.: Robotics-based Locatio Sesig Usig Wireless Etheret, I Proceedigs of ACM MobiCom, pp.7-8 (). [7] Lyytie, K., Yoo, Y.: Issues ad Challeges i Ubiquitous Computig: Itroductio, Commuicatios of the ACM, Vol., No., pp.6-6 (). [8] Miami, M. et al.: Implemetatio ad Evaluatio of a Distributed Ultrasoic Positioig System, I Proceedigs of INSS, pp (). [9] Priyatha, P., Miu, A., Teller, S.: The Cricket Compass for Cotext-Aware Mobile Applicatios, I Proceedigs of ACM MobiCom, pp.- (). [] Wat, R. et al: The Active Badge Locatio System, ACM Trasactios o Iformatio Systems, Vol., No., pp.-7 (99). [] Ward, A., Joes, A., Hopper, A.: A New Locatio Techiques for the Active Office, IEEE Persoal Commuicatios, Vol., No., pp.-7 (997). [] Yatai, K., Tamura, K., Sugimoto, M., Hashizume, H.: Iformatio Trasfer Techiques for Mobile Devices by Toss ad Swig Actios, I Proceedigs of IEEE WMCSA, pp. - ().