A BSS-BASED APPROACH FOR LOCALIZATION OF SIMULTANEOUS SPEAKERS IN REVERBERANT CONDITIONS

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1 A BSS-BASED AROACH FOR LOCALIZATION OF SIMULTANEOUS SEAKERS IN REVERBERANT CONDITIONS Hamid Reza Abutalebi,2, Hedieh Heli, Danil Korchagin 2, and Hervé Bourlard 2 Seech rocessing Research Lab (SRL), Elec. and Com. Eng. Det., Yazd University, Yazd, Iran 2 Idia Research Institute, Martigny, Switzerland hone: + (98) , ax: + (98) , habutalebi@yazduni.ac.ir web: htt://ee.yazduni.ac.ir/srl, htt:// ABSTRACT In this aer, we address the localization o simultaneous seakers by means o Blind Source Searation (BSS) based algorithms. Considering BSS demixing ilters as some blind null beamormer and roducing an acoustical ma rom them, source localization can be achieved by identiying the local minima o this acoustical ma. To imrove the erormance o this method in reverberant environments, we have roosed to relace the demixing ilter with one, corresonding to the direct ath only. This is done by keeing only the largest coeicient in each demixing ilter and neglecting the other coeicients. Besides, the roosed method reduces the comutational comlexity. To urther imrove the comutational eiciency o the localization method, we have also roosed the limitation o the reuency range within averaging rocedure. The exerimental results demonstrate imroved accuracy and eiciency o the roosed method in the localization o multile simultaneous sound sources in reverberant environments.. INTRODUCTION Automatic seaker localization is an imortant task in several alications such as acoustic scene analysis, hands-ree video conerences, hearing aids, and seech enhancement. It is also rereuisite or other rocesses like steering beamormer or ointing camera towards the sound sources. In this aer, we concentrate on the category o multileseaker (sound source) localization methods that are based on Blind Source Searation (BSS). Generally these methods are divided in two grous: In the irst grou, by considering the relations between BSS roblem and blind adative Multile-Inut-Multile-Outut (MIMO) system identiication, BSS demixing ilters are emloyed to estimate Time Dierence O Arrival (TDOA) in reverberant environments []; this can also be extended to the multi-dimensional case as well [2]. The second grou o the BSS-based localization methods is based on the interretation o BSS algorithms as a set o blind adative beamormers. To steer a beamormer toward a desirable source, the inormation o source location is necessary, while BSS algorithm recovers the original signals without any exlicit inormation about source ositions; This means that BSS demixing ilters contain some useul and imortant inormation or localization o sound sources. In this grou o methods, a directivity attern is introduced based on the BSS demixing ilters; then, the beam attern is used to extract Direction O Arrival (DOA). Some o the rimary methods in this category used to extract location inormation o each source in each reuency bin searately. However, this causes a ermutation roblem seciic to narrowband BSS [3, 4] which should be treated someway. Alternatively, [5] roosed an averaging rocedure over all reuency bins and BSS oututs. The so-called BSS Averaged Directivity attern (BSS-AD) rovides useul inormation rom a large range o reuencies, including the higher reuency regions which are otentially corruted by satial aliasing. In this aer we concentrate on BSS-AD and roose some modiications or imroving the erormance in (highly) reverberant environments and reducing comutational comlexity. The rest o this aer is organized as ollows. We review BSS algorithms and BSS-AD method in Section 2. The roosed method is exlained in Section 3. Section 4 exlains the exerimental evaluations. Finally, some concluding remarks are resented in Section SEAKER LOCALIZATION USING THE BSS-AD 2. Searation o convolutive mixtures Fig. shows the general BSS setu. In real-lie environments, due to the reverberation, source signals are iltered by a MIMO mixing system, H, deined as: h L h H M M M, () hq L hq which contains the Finite Imulse Resonse (FIR) ilters h (,2,..., Q,,2,..., ). Suose that Q source signals s (... Q) are mixed and observed at sensors as: where, k Q M x h, k s ( n k), (2) k h reresents the k-th coeicient o the FIR ilter rom -th source to -th sensor (o length M). We assume that Q. The demixing (searatio system, W, is deined as:

2 w L w Q W M M M, (3) w L wq consisting a set o FIR ilters w (o length L) that roduce Q searated signals: L y w, k x ( n k), (4) k where w, k reresents the k-th coeicient o the demixing ilter between -th sensor to -th outut and it should be obtained blindly, i.e. without knowing s ( n ) or h. To searate the source signals, s, without any inormation about the mixing system H, BSS algorithms orce the outut signals, y (, 2,..., Q), to be statistically indeendent. This is done by suitably adating the weights o BSS demixing system W. The general orm o ideal searating ilter matrix is shown in the reuency domain as ollows [5]: Wideal ( ) Adj{ H( )} Λ, (5) where Adj{.} oerator comutes the adjoint o a suared matrix. Matrix shows the ermutation and diagonal matrix Λ describes scaling o BSS oututs. The erect searation will be achieved i the BSS demixing system converges to (5). This can be justiied by considering the act that in case o convergence, the overall mixing-demixing system would be reduced to a diagonal matrix: Cideal ( ) H( ) Wideal ( ) Η( ) Adj{ H( )} Λ (6) det{ H( )} Λ, where det{.} comutes the determinant o a suare matrix. Figure BSS setu [6] 2.2 DOA extraction using averaged BSS directivity atterns In this sub-section, we exlain the BSS-AD method roosed in [5] or a linear array o microhones and ar-ield assumtion. Convolutive blind source searation and adative beamorming have similarities in concet and structure. Both attemt to extract selected source signals rom observed sensor mixtures by a ilter array. Due to this simililarity, BSS demixing ilters can also be interreted as a set o blind adative null beamormers [7]. Considering Fig. and alying E. (4) in reuency domain, the resultant outut signals are obtained as Y ( ) w ( ) X ( ) ; (7) Then, at each reuency bin the directivity attern or -th outut can be calculated using w ( ) [4]. The directivity attern o each BSS outut is deined as the magnitude suared resonse o a Multile-Inut-Single-Outut (MISO) system o ilters to lane waves coming rom all ossible directions, and is given by: 2 j 2πd sin( θ ) c B ( W, θ, ) w ( ) e, (8) where,2,..., Q, θ is the direction o lane waves, c is the sound velocity, and d is the distance rom -th sensor to the reerence sensor o the assumed linear array. This euation shows that the -th directivity attern, B ( W, θ, ), is roduced to extract the -th source signal. Actually, these directivity atterns reresent Q null beamormers, each o them creates Q- satial nulls in the direction o Q- undesirable sources. When the BSS null beamormers are considered in each reuency bin and each outut, searately, the ermutation roblem is encountered. In order to solve this roblem, [5] roosed to aly an averaging rocedure beore extracting the source locations. It consists o summing the BSS directivity atterns over the reuencies and over the - best BSS oututs, as: * ( θ, ) arg B ( W, θ, ), (9) (, θ) ( C min, θ, ) * ( θ, ) BW B W d, () where C is an arbitrary constant. In ractice, integral is relaced with a summation over a inite number o reuency oints rom min to. It is known that in high reuencies, satial aliasing may occur. This will result in some errors in individual beam atterns. However, in averaging rocedure o directivity atterns [5], only true satial nulls add u coherently when summing over all BSS oututs and all reuencies; this artially decreases the eect o satial aliasing at high reuencies. So the averaging rocedure lets to collect useul location inormation rom a large range o reuencies, even including those high reuency regions that are otentially corruted by satial aliasing in large microhone arrays. Source localization can then be achieved by identiying local minima in averaged directivity attern diagram.

3 3. ROOSED METHOD In this section we roose some modiications to imrove the erormance o BSS-AD method in reverberant environments and to reduce the comutational comlexity. The deinition (8) or BSS directivity attern ignores the resence o relection aths. As a result, the directivity attern does not comletely show the behaviour o the BSS algorithms under reverberant environments. The idea behind the roosed modiication is the considering direct ath o sound roagation. According to the dominance o the direct roagation ath in the acoustic imulse resonse, they can be very useul or source localization. In other words, the direct roagation aths deliver some meaningul location inormation. In reverberant environment, demixing ilters would contain several coeicients with medium to large amlitude, where the largest one is considered as the direct ath. For instance, consider the case with 2 sources and 2 microhones. I there is no reverberation in the environment, i.e., under ree ield assumtion, the single ath ilters o the mixing system H in reuency domain are in the orm o: j 2πτ ( θ ) h ( ) e, () where τ ( θ ) d sin( θ ) c is the TDOA between the -th sensor and the reerence sensor or the -th source with DOA θ and d is the distance rom -th sensor to the reerence sensor o the linear array. Clearly, this ilter is reresented by only one coeicient in time domain, which is corresonding to the direct ath between the -th source and -th sensor. Under real-lie conditions, due to the relection aths (reverberatio, the mixing ilters contain more than one coeicient in time domain. Nevertheless, the largest one (i.e. with the largest amlitude) corresonds to the direct ath between the source and the sensor which is imortant in source localization. Moreover, exanding (5) or the case o 2 sources and Λ I, we get: h22 ( ) h2 ( ) W ( ), (2) ideal h2( ) h( ) Thereore the ideal searation solution allows us to identiy the ilters o the acoustical demixing system. Considering (2) in time domain, we have: w( h22, w2 h2, (3) w 2( h2(, w 22 h( This euation clearly shows the corresondence between the largest coeicients in mixing and demixing ilters, which is in turn corresonds to the direct ath. Here, we roose to neglect all but only one (the largest) coeicient o the demixing ilter and comute the directivity attern (E. (8)) based on only the largest coeicient. For simlicity, hereater, we reer to the roosed (modiied) method as BSS-AD Direct ath (or, briely, BSS-AD-D). It is noted that similar idea has been already alied in the roblem o TDOA estimation [], however, we use it here to comute directivity atterns o BSS oututs. Furthermore, reducing the demixing ilters to those with only one coeicient decreases the comutational comlexity drastically. Similar to what mentioned in Section 2.2, the BSS-AD-D emloys an averaging over the reuency range o min to. To imrove the comutational eiciency o the algorithm, we also roose the limitation o the reuency averaging range by reduction o. In turn, this may decrease the eect o satial aliasing and imrove the localization accuracy (as it is shown in Section 4). 4. EXERIMENTAL EVALUATIONS To demonstrate the erormance o the BSS-AD-D in a reverberant situation, we have comared its localization accuracy with that o baseline BSS-AD method (by considering the whole ilter coeicients). In our simulations, we have considered a linear microhone array that contains two omnidirectional microhones as shown in Fig. 2. The imum length o microhone array is 2 cm and the sources are laced on a circle o 2 meters ar rom the center o array. Room Imulse Resonses (RIRs) were simulated by an imlementation o the Image method [8] at the samling reuency s 6kHz. Microhone signals were then generated by convolving source signals with the comuted RIRs. The length o BSS ilters is L 24 samles. Also, the reuency range or averaging rocedure is min Hz to 8 Hz. Figure 2 microhone array and sources setu In the exeriments, we assumed the case with two sources and two microhones. At irst, we considered two microhones at the ositions shown in Fig. 2 and two sources with DOA o ( θ, θ 2) ( 65,25). The exeriment was done under a highly reverberant situation, where the reverberation time was eual to T6 s. Fig. (3-a) shows the directivity attern or the baseline BSS- AD. As shown, the method is not able to resent a attern with reliable nulls at the desired angles ( θ, θ 2) ( 65,25). Then the localization rocess was done via the roosed BSS-AD-D method. The resulted directivity attern has been shown in Fig. (3-b). As shown, there are two distinct o nulls within ± 2 rom exact DOAs.

4 deg db deg db deg -.68 db deg db (a) (a) deg db deg db deg db deg -2.5 db (b) Figure 3- Directivity attern o the (a) BSS-AD, (b) BSS-AD-D, or the irst exeriment in a simulated room with T6. s In the second exeriment, we ket two microhones at the same ositions (as shown in Fig. 2), while consider two other sources at DOAs o ( θ, θ 2) ( 2,55). The oututs o the second exeriment (the directivity atterns o BSS-AD and BSS-AD-D) have been shown in (4-a) and (4-b). Obviously, the roosed method outerorms the baseline BSS- AD in localization o two sources. To comare the erormance o the modiied and baseline methods in a more objective manner, we reeated the localization rocedure or 5 times with dierent (random) o ( θ, θ 2) (each angle in the range o [ 9 o, + 9 ] ). In this exeriment, no minimum angle was ket between two sources, so the sources may all very close. These tests were done or ive dierent reverberant conditions ( T6.2,.5,.7,.9,. s). In each case, the DOA error was comuted as the absolute value o the dierence o the resulted DOA and the exact one, summed over two sources. The results were averaged over 5 cases. Table shows average DOA error values o two mentioned methods in dierent reverberant conditions and or 8Hz. Clearly, the roosed modiication has resulted in a suerior method or the localization o multile simultaneous sound sources in highly reverberant environments (b) Figure 4- Directivity attern o the (a) BSS-AD, (b) BSS-AD-D, or the second exeriment in a simulated room with T6. s To examine the eect o lower, we reeated the tests on BSS-AD-D considering 5Hz and 6Hz (instead o 8Hz). As exected, our (inormal) measurements showed the reduction o rocessing runtime. Also, Table 2 shows average DOA error values or the case o dierent values. As shown, desite the reduction o reuency range within averaging rocedure, the localization error remains in the same order (and even decreases in some cases, like the case o 6Hz ). This can be justiied by the reduction o the otential satial aliasing.

5 Table - Average DOA error values or BSS-AD and BSS-AD- D methods (or 8Hz) BSS-AD BSS-AD-D T6.2 s 2.2 o 4.74 o T6.5 s 6.82 o 7.38 o T6.7 s.6 o 7.65 o T6.9 s 5.35 o 8.28 o T6. s 6.96 o 8.42 o Table 2- Average DOA error values or BSS-AD-D in dierent values 5 Hz 6 Hz 8 Hz T6.2 s 3.77 o 3.89 o 4.74 o T6.5 s 6.88 o 6.7 o 7.38 o T6.7 s 7.95 o 7.4 o 7.65 o T6.9 s 8.37 o 7.48 o 8.28 o [3] M. Ikram, D. Morgan, A beamorming aroach to ermutation alignment or multichannel reuency-domain blind seech searation, in roc. ICASS, 22, vol., [4] S. Kurita, H. Saruwatari, S. Kajita, K. Takeda and F. Itakura, Evaluation o blind signal searation method using directivity attern under reverberant environments, in roc. ICASS, Istanbul, Turkey, 2, vol. 5, [5] A. Lombard, T. Rosenkranz, H. Buchner, and W. Kellermann, Exloiting the sel-steering caability o blind source searation to localize two or more sound sources in adverse environments, in roc. ITG Conerence on Seech Communication, Aachen, Germany, 28. [6] H. Buchner, R. Aichner and W. Kellermann, TRINICON: a versatile ramework or multichannel blind signal rocessing, in roc. ICASS, Montreal, Canada, 24, vol. 3, [7] S. Araki, S. Makino, Y. Hinamoto, R. Mukai, T. Nishikawa and H. Saruwatari, Euivalence between reuency-domain blind source searation and reuencydomain adative beamorming or convolutive mixtures, EURASI Journal on Alied Signal rocessing, vol. 23, no., , 23. [8] E. Habets, Room imulse resonse generator. [online]. available: htt://home.tiscali.nl/ehabets/rir_generator.html T6. s 8.75 o 7.95 o 8.42 o 5. CONCLUSION In this aer, we used the ability o BSS algorithms to blindly identiy the MIMO acoustical system. Using the roosed method, we could comute new BSS demixing ilters which are ormed by only the largest coeicient (corresonding to direct roagation ath). Then, we used these ilters to comute the averaged directivity attern o [5]. We also limit the reuency range o the averaging to imrove the comutational eiciency o the roosed method (called BSS-AD- D). The method was evaluated or the case o two microhones and two sensors. The simulation results show the accuracy imrovement o the method in multile-seaker localization. In the uture, we lan to extend the BSS-AD- D to localizing more sources and to nonlinear microhone arrays. REFERENCES [] H. Buchner, R. Aichner, J. Stenglein, H. Teutsch, and W. Kellermann, Simultaneous localization o multile sound sources using blind adative MIMO iltering, in roc. ICASS, hiladelhia, A, USA, 25. [2] A. Lombard, H. Buchner, and W. Kellermann, Multidimensional localization o multile sound sources using blind adative MIMO system identiication, in roc. MFI, Heidelberg, Germany, 26.