Simulation of Microphone Array for Sound Localization using Human Binaural Hearing Model

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1 Simulatio of Microphoe Array for Soud Localizatio usig Huma Biaural Hearig Model Viktor Hristov, Sejaa Pleshkova Abstract Ivestigatio of the huma hearig system ad attempts for its simulatio are oe the most popular themes owadays. If the soud sigals are received from a perso it is easy to determiate the proper directio oly with the help of the huma ears ad huma brai. But if the huma is replaced with mobile robot - combiatio of a proper microphoe array structure ad the correspodig soud localizatio algorithm is eeded. Both workig together are importat to achieve the appropriate accuracy of directio of soud arrival ad the correspodig soud source localizatio. There are proposed may microphoe array structures ad algorithms, which are tested ad ca be characterized with advatages ad disadvatages i some cocrete applicatios. Here i this article is proposed to apply ad test a combiatio of a simple two microphoe array structure ad algorithm for modellig ad simulatig biaural huma perceptio. The most importat thig i this proposal is the simulatio of huma ears with two microphoes ad to choose their type to have the beam formig diagram of sesitivity similar each other. Also i simulatio algorithm is proposed to apply the elemets of huma biaural hearig to as much as is possible to ow the complex ad ot fully uderstad the processes i the huma brai o auditory perceptio ad i particular huma perceptio of the directio from which soud waves arrive. The results from simulatios are preseted to show the characteristics of soud source localizatio achieved with propositio to apply huma biaural hearig model for the purposes of soud directio of arrival ad soud source localizatio. Keywords Huma biaural hearig model, Soud source localizatio, Microphoe arrays. I. INTODUCTION Soud source localizatio is a powerful approach of fidig directio of soud arrival from soud source to a target. Usually it could be a perso, but there are also the applicatios, the target ca be a mobile robot, a video coferecig audio system or somethig other like artificial audio perceptio system. If the souds from the source are received from a perso, the huma hearig system is capable to determie properly directio of soud arrival from soud source. This is doe ot oly with the help of the huma ears, but with the leadig role of the huma brai, the received from the two huma ears biaural audio iformatio is processed to form i huma mid the impressio of soud Viktor Hristov is with the Faculty of Telecommuicatios at Techical Uiversity of Sofia, 8 Kl. Ohridski Blvd, Sofia, Bulgaria, hristov.viktor@gmail.com Sejaa Pleshkova is with the Faculty of Telecommuicatios at Techical Uiversity of Sofia, 8 Kl. Ohridski Blvd, Sofia, Bulgaria, segpl@tu-sofia.bg directio of arrival. Ufortuately, for mobile robots or for other auditory perceptio systems this is ot possible. easo for this is the absece i them of similar system as the huma brai with such capabilities to aalyze the received audio iformatio ad to determie the soud directio of arrival. Therefore, there is a eed to develop some appropriates methods ad algorithms to fid the proper soud arrival directio without the presece of a system similar to the huma brai. Soud source localizatio ca be separated ad described i three mai groups: depedig o the time of arrival, fixed beamformig ad adaptive beamformig usig correlatio fuctios []. There are two scearios depedig o the place, experimets was doe. It could be i ope space, without ay reflectios ad i closed space, also called multipath propagatio, because each reflectio from the wall or object ca be treated as a separate source []. A microphoe array cosist of a umber of acoustic sesors positioed o the proper distace betwee each other i a way that spatial iformatio ca be captured [3]. As a result, the array outputs cotai sigal of iterest, oise, iterferece ad also propagatio iformatio that is represeted by the acoustic impulse respose from the radiatig sources to the microphoes. The combiatio of a microphoe array ad the correspodig soud localizatio algorithm ca be used to simulate the huma hearig system [4]. Both microphoe array structure ad chose algorithm workig together are importat to achieve the appropriate accuracy of directio of soud wave arrival ad the correspodig soud source localizatio. A umber of factors affect the spatial aspects of how a soud is perceived. The Duplex theory was the first comprehesive aalysis of the physics of biaural perceptio [5]. There is a differet time of arrival of the soud sigals to the receivig microphoes (huma ears) as illustrated i Fig.. Fig.. Iteraural differeces of time ad itesity of impigig soud wave o a ideal spherical head from a distat source Uless a soud source is located directly i frot of or behid the head, soud arrives slightly earlier i time at the ear that is physically closer to the source, ad with somewhat greater itesity [6]. This iteraural time differece (ITD) is produced because it takes loger for the soud to arrive at the

2 ear that is farther from the source [7]. The iteraural itesity differece (IID) is produced because the shadowig effect of the head prevets some of the icomig soud eergy from reachig the ear that is tured away from the directio of the source [8]. The estimatio of ITD is the most critical aspect of the biaural processig. May models are based o the crosscorrelatio of the sigals to the two ears after processig by the auditory periphery [9]. Several series of measuremets have bee performed the time differece i receivig of the soud source []. If the imagiary or artificial head as model of the huma head i a mobile robot huma hearig model of mobile robot microphoe array had completely spherical ad uiform surface, as Fig., the iteraural time differece (ITD) produced by a soud source that arrives from a azimuth of θ radias ca be approximately described with the followig equatio usig diffractio theory [, ad 3]: a τ = siθ, () c τ is the iteraural time differece (ITD); a - the radius of the imagiary or artificial model of huma head; c = 343 m/s - the speed of soud waves i the air. There are proposed may microphoe array structures ad algorithms, which are tested ad ca be characterized with advatages ad disadvatages i some cocrete applicatios. The goal of this article is to propose, apply ad test a combiatio of a simple two microphoe array structure ad algorithm for modellig ad simulatig biaural huma perceptio. The most importat i this proposal is the arragemet of two microphoes i such a way like the huma ears ad to choose their type with the proper sesitivity. Also, i the simulatio algorithm, it is proposed to apply the elemets of huma biaural hearig to as much as is possible to ow the complex ad ot fully uderstad the processes i the huma brai o auditory perceptio ad i particular huma perceptio of the directio from which soud waves arrive. II. DEVELOPMENT OF GEOMETICAL MODEL FO SOUND SOUCE LOCALIZATION The geometrical model of microphoe array based o the huma biaural hearig is proposed i Fig.. It is based o the huma hearig aid ad biaural soud source localizatio. It cosists of two microphoes M ad M, with the idetical parameters. They are situated o the short distace d betwee them, with the value similar to the distace of the ears i the huma head. The positios of the two microphoes are show i Fig. as coordiates x m, y m ad x m, y m, respectively (assumig x as horizotal, y as vertical coordiate ad the origi of coordiate system i the left upper corer i Fig.). Soud source, producig correspodig soud source sigal S, (usually a speakig perso or speaker producig soud waves from a audio system) is positioed o the other ed of the room. It is be described (for the proposed i Fig. plaar case of geometric model) with the coordiates (x src ad y src ). I Fig. are show also the model of the imagiary or artificial head (as the circle i dark) as model of the huma head ad also two circles presetig the microphoe beamformig diagrams. Usually the umber of soud waves arrivig to the huma ears or to each of the microphoes i the microphoe array is also ifiite i real situatios, but it is very difficult or impossible to describe the summary soud wave arrivig to each of microphoes i the microphoe array. Therefore, i this article based o huma hearig model, a simplified geometric model (Fig. ) is proposed for soud waves propagatio to each of two microphoes i a microphoe array, assumig the existece oly of oe direct ad two reflected soud waves arrivig to each the left ad to right microphoes, respectively. I Fig. are show for simplicity oly the trajectories of direct ad two reflected soud waves arrivig from the soud source to the left stadig microphoe M i microphoe array. The correspodig trajectories legths of the direct, two reflected soud waves arrivig to each the left microphoe M ad reflectio agles are idicated i Fig. i the followig way: l direct soud wave trajectory legth; - d L L L - l l + l = first reflected soud wave trajectory legth with two parts L L l ad l ; - θ reflectio agle for first reflected soud wave; - = l + l l secod reflected soud wave l + 3 trajectory legth with three parts l, l ad l 3 ; - θ agle of the for secod reflected soud wave. The direct ad two reflected soud waves with the L legths l d, l ad l produce the correspodig soud sigals S d, S ad S at the positio of the left microphoe M, arrivig from the soud source S. The explaied above simplified geometric model (Fig. ) ca be cosidered also for the right stadig microphoe M, assumig, that it is ecessary oly to chage the idex L with the idex for the correspodig idicatio of trajectories legths of the direct, two reflected soud waves arrivig to each the right microphoe M ad reflectio agles. Needed geometric parameters, show i Fig., are room dimesios (legth r l ad width r w ), distace betwee microphoes d, soud source coordiates (x src ad y src ) ad positios of the two microphoes (x m, y m, x m ad y m ). Some of these geometric parameters, for example x m ad y m, ca be calculated i the followig way from x m ad y m, if they are defied: xm = xm + d, () y = m = ym y, (3) m x m ad x m are x-coordiates of two microphoes M ad M ; y m ad y m - y-coordiates of two microphoes M ad M ;

3 d - distace betwee them. Fig.. The proposed geometrical model of microphoe array based o the huma biaural hearig L For the calculatios of the values of the legths l d, l ad l of direct ad two reflected soud waves, is ecessary to ow the followig additioal geometric parameters: L = y y (4) per i m m src src d = x x (5) L per is the vertical compoet of the distace betwee soud source S ad microphoes M ad M if it is assumed the placemet of the two microphoes M ad M i a horizotal lie, i.e. the equatio (3) is satisfied; d i - the horizotal compoet of the distace betwee soud source S ad microphoe M. Usig equatios (4) ad (5) is possible to calculate the distace L di (for i=,) betwee soud source S ad each of microphoes M ad M as follow: L di = d i + 4L for i=, (6), per The agle of arrival θ of the direct soud wave, for example to the microphoe M, ca be calculated usig equatios (4) ad (6): Lper θ = arcsi( ) (7) Ld I the similar way, usig the ordiary geometric relatios is possible to calculate also each of the agles of arrival θ to the microphoes M or M of reflected soud waves after =,,3. umber of reflectios from the walls of the room (Fig. ). Therefore, the resultat sigals S M ad S M, received from microphoes M ad M, respectively are the sum of correspodig sigals produced by the arrived direct ad reflected soud waves to each of them, after =,,3. umber of reflectios: S M = ksd + ks + ks S S M = k Sd + k S + ks S, (8) k,..., ad k are the atteuatio idexes of the correspodig parts (direct ad reflected) soud sigals produced by direct ad reflected soud waves arrived to each of the microphoes M ad M. The atteuatio idexes are importat for descriptio of the iteraural itesity differece (IID) i algorithms of soud S ad S localizatio. Idirectly i the resultat sigals M M i equatio (8) exist as the legths of the reflected soud wave trajectories ad correspodig time differece of arrival, as estimatio of iteraural time differece (ITD). The values of the defied i equatio (8) atteuatio idexes k,..., ad k ca be determied (i decibels) from microphoe beamformig diagram (Fig. 3) of chose type of microphoes M ad M, for the correspodig values of agles of arrival θ to the microphoes M or M of direct ad reflected soud waves after =,,,3. umber of reflectios from the walls of the room. For simplificatio, i the determiatio of the values of the atteuatio idexes k k,..., k ad, k, is assumed to igore the losses i reflectio ad absorptio i the walls of the room.

sesitivity ad with appropriate orietatio like i the huma ears o huma head.

4 Matlab class of microphoes as elemets of basic class Microphoe array. I this case is chose to use the class Custom Microphoe Elemet as the type of microphoes M ad M, which allow to defie their beamformig diagram of the type cardioid, similar to the huma ear hearig sesitivity ad with appropriate orietatio like i the huma ears o huma head. These coditios are ivolved i the followig module of Matlab program ad the defiitio of beamformig diagram of the left (microphoe M ) ad the right (microphoe M ) orietatio is prepared with chose + or - i the lies 4 ad 5 i the module of Matlab program: Fig.3. Microphoe beamformig diagram h = phased.custommicrophoeelemet; h.polarpatterfrequecies = [5 ]; h.polarpatter = magdb([....5±.5*cosd(h.polarpatteragles);....6±.4*cosd(h.polarpatteragles)]); resp = step(h,[5 5 ],[ ;4 5]'); plotespose(h,5,'espcut','az','format','polar'); The resultat sigals S M ad S M of microphoes M ad M, derived by equatio (8) ca be used as iput audio iformatio i developmet ad testig the algorithms of soud source localizatio. Simulatig the appropriate situatios ad scearios of positios for differet cases for soud waves reflectios from the room walls ad i room costructios ad dimesios is possible. The proposed simplified plaar geometrical model of soud waves propagatio from soud source to the correspodig microphoes i microphoe array To evaluate the characteristics of the proposed simplified plaar geometrical model of soud waves propagatio from soud source to the correspodig microphoes M ad M i microphoe array based o the huma biaural hearig model, i this article, the ecessary simulatios are carried out. III. SIMULATION OF THE GEOMETICAL MODEL FO SOUND SOUCE LOCALIZATION The simulatios proposed to test the proposed simplified plaar geometrical model of soud waves propagatio from soud source to the correspodig microphoes M ad M i microphoe array preseted i Fig.4. It is based o the huma biaural hearig model, arraged followig the algorithm ad the realized as the correspodig Matlab program. I the first part of the algorithm ad the correspodig Matlab program are defied some ecessary iput parameters for room dimesios - legth r l ad width r w, also the distace betwee microphoes d, coordiates of soud source (x src ad y src ) ad positios of the two microphoes (x m, y m, x m ad y m ). With these defied parameters the differet agles of arrival are calculated depedig o the situatios if there is o reflectio, there is oe reflectio or there are two reflectios. The geeratio of microphoe beamformig diagram (Fig. 3) of microphoes M ad M is doe usig the existig i Fig.4. Simulatio model is arraged as a appropriate algorithm.

The correspodig beamformig diagrams of the left microphoe M ad the right microphoe M with their achieved ecessary orietatio are preseted i Fig.5.

mm mm 5 mm Fig.5. Beamformig diagram of the used microphoes From the geerated beamformig diagrams of the left microphoe M ad the right microphoe M, show i Fig.

5 The correspodig beamformig diagrams of the left microphoe M ad the right microphoe M with their achieved ecessary orietatio are preseted i Fig.5. Mic Y coordiate ym Mic X coordiate Xm Mic Y coordiate Ym 5 mm mm 5 mm Fig.5. Beamformig diagram of the used microphoes From the geerated beamformig diagrams of the left microphoe M ad the right microphoe M, show i Fig. 5 is possible to obtai the iformatio about the values of atteuatio idexes k,..., ad k i the correspodece of calculated from equatio (7) agles of arrival θ to the microphoes M or M of direct ad reflected soud waves after =,,,3. umber of reflectios from the walls of the room. The values of atteuatio idexes k,..., ad k are ecessary i the equatio (8) for defiitio of the resultat sigals S M ad SM received from microphoes M ad M as the sum of correspodig sigals produced from the arrived to each of two microphoes direct ad reflected soud waves. IV. EXPEIMENTAL ESULTS Experimetal results after the simulatios carried out with the proposed ad developed simplified plaar geometrical model of soud waves propagatio from soud source to the correspodig microphoes M ad M i microphoe array based o the huma biaural hearig model are preseted i the followig way. The iitial parameters, eeded for the calculatios with equatio (7) of the agles of arrival θ to the microphoes M or M of direct ad reflected soud waves after =,,,3. umber of reflectios from the walls of the room are collected i Table I. For example, i cocrete simulatio the values of the calculated agle of arrival of direct soud wave, i.e. without reflectio, is θ = 89 degree (marked with red arrow i Fig.6), which correspod to the idex of atteuatio k = 6. db (Fig.6). TABLE I INITIAL ENVIONMENT S PAAMETES oom legth rl oom width - rw Source X coordiates - xsrc Source Y coordiates - ysrc Mic X coordiate xm 4 mm 6 mm mm 5 mm 9 mm Fig.6. Experimetal results I the similar way, the agle of arrival of soud wave after oe reflectio is θ = 49 degree (correspodig to 3 degree i Fig. 6 ad marked with gree arrow i Fig. 6) with atteuatio idex k =. 7dB (Fig.6). Also the agle of arrival of soud wave after two reflectios is θ = degree (ot marked i Fig.6), which correspod to the atteuatio idex k = 8. db (Fig.6). The used above values of the agles of arrival θ, θ, θ ad the atteuatio idexes k are calculated executig the developed for these simulatios Matlab program, based o the proposed algorithm, show i Fig.4. The results i Table II are for these calculated from Matlab program agles of arrival θ, θ, θ (theta, theta ad theta i Table II) ad the atteuatio idexes k, k k, ( k, k i Table II). The values of the atteuatio idexes calculated by the Matlab program k ( k, k i Table II) are substituted i the equatio (8) for determie the resultat sigal S M received from microphoe M as the sum of correspodig sigals produced by the arrived to the microphoe M direct soud wave ad reflected soud waves after =,,3. umber of reflectios: S M.Sd.57S 8. = 6 S (9) The similar equatio to the equatio (9) ca be achieved for the right microphoe M usig the similar results from Matlab program of the atteuatio idexes k substituted i the equatio (8) for determie the resultat sigal S M received from microphoe M as the sum of correspodig sigals produced by the arrived to the microphoe M direct soud wave ad reflected soud waves after =,,3. umber of reflectios.

TABLE II THE CALCULATED IN MATLAB POGAM ANGLES OF AIVAL AND ATTENUATION INDEXES waves propagatio with a two microphoe array o the base of huma biaural hearig model.

6 TABLE II THE CALCULATED IN MATLAB POGAM ANGLES OF AIVAL AND ATTENUATION INDEXES waves propagatio with a two microphoe array o the base of huma biaural hearig model. The results, derived as equatios ad simulatios, will be used for further deep aalyses ad will be exteded ad complicated for the differet positios of soud source, icreasig the umber of soud waves reflectios. ACKNOWLEDGEMENT This paper was supported by Techical Uiversity Sofia ier program to support PhD research projects uder Cotract 4 PD 8-7: Developmet of methods ad tools to locate audio sources i iformatio ad commuicatio etworks. EFEENCES V. CONCLUSION The aim of the proposed i this article geometrical model of soud waves propagatio from soud source with combiatio of a simple two microphoe array based o the huma biaural hearig model is fully achieved. The equatios derived from the proposed geometrical model lead to achieve the importat descriptios of direct ad reflected soud waves propagatio after the defied simple cases of two umbers of reflectios from the walls of the room, especially the resultat sigals received from two microphoes i the i the microphoe array. These equatios hold the iformatio of iteraural itesity differece (IID) as defied atteuatio idexes ad iformatio of iteraural time differece (ITD) as the legths of the reflected soud wave trajectories. Both, the iteraural itesity differece (IID) ad iteraural time differece (ITD) are used i the popular algorithms to achieve the soud source localizatio with the appropriate precisio. The derived from the proposed geometrical model equatios are applied i the developed algorithm for simulatig the microphoe array as the model of biaural huma perceptio ad soud source localizatio. Used microphoes are with similar receivig characteristics like the huma ears ad their type is chose to have the beam formig diagram of sesitivity similar to huma ears beam formig diagram of sesitivity. The results from simulatios are preseted ad show the ability to use i tasks of soud source localizatio the proposed geometric model as combiatio from descriptios of direct ad reflected soud [] Yog ui ad Diei Florecio, New direct approaches to robust soud source localizatio, Multimedia ad Expo, 3. ICME '3. Proceedigs. 3 Iteratioal Coferece,Volume:, 3, pp. I-737-I-74. [] Iai McCowa, Microphoe Array, April, pp [3] J. Beesty, ad J. Che, Study ad Desig of Differet Microphoe Arrays, 3, pp [4] Muller,.S., Howe,.T., Seturia, S.D., Smith,.L., ad White, Microsesors,.M, IEEE Press, New York, 99, pp [5] J. W. Strutt, O our perceptio of soud directio, Volume 3, pp. 4 3, 97. [6] C. Trahiotis, L.. Berstei,. M. Ster, ad T. N. Buell, Iteraural correlatio as the basis of a workig model of biaural processig, Soud Source Localizatio, Spriger Hadbook of Auditory esearch, Chapter 7, Spriger-Verlag, Heidelberg, 5, pp [7] DeLiag Wag, Guy J. Brow, Biaural soud localizatio, Chapter 5, Book Computatioal Auditory Scee Aalysis: Priciples, Algorithms, ad Applicatios, Joh Wiley & Sos, September 9, 6, [8] M. Bodde, Modellig huma soud-source localizatio ad the cocktail party effect. Acta Acustica, Volume, 993, pp [9] M. Wu, D. L. Wag, ad G. J. Brow, A multipitch trackig algorithm for oisy speech, IEEE Trasactios o Speech ad Audio Processig, volume (3), 3, pp [] C. Faller ad J. Merimaa, Soud localizatio i complex listeig situatios: Selectio of biaural cues based o iteraural coherece. Joural of the Acoustical Society of America, Volume6 (5), 4, pp [] G. F. Kuh. Model for the iteraural time differeces i the azimuthal plae. Joural of the Acoustical Society of America, Volume 6, 977, pp [] G. F. Kuh, Physical Acoustics ad Measuremets Pertaiig to Directioal Hearig". I W. A. Yost ad G. Gourevitch, editors, Directioal Hearig, Chapter, Spriger-Verlag, New York, 987, pages pp [3] E. A. G. Shaw, Acoustical features of the huma exteral ear. I. H. Gilkey ad T.. Aderso, editors, Biaural ad Spatial Hearig i eal ad Virtual Eviromets, Chapter, Lawrece Erlbaum Associates (Mahwah, New Jersey), 997, pp

APPLICATION NOTE UNDERSTANDING EFFECTIVE BITS

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