Successful localization of sound sources in reverberant enclosures is an important prerequisite for many spatial signal processing algorithms. We investigate the use of a weighted fuzzy-means cluster algorithm for robust source localization using location cues extracted from a microphone array. In orderto increase the algorithm's robustness against sound reflections, we incorporate observation weights to emphasize reliable cues over unreliable ones. The weights are computed from local feature statistics around sound onsets because it is known that these regions are least affected by reverberation. Experimental results illustrate the superiority of the method when compared with standard fuzzy clustering. The proposed algorithm successfully located two speech sources for a range of angular separations in room environments with reverberation times of up to 600 ms

Kuhne, M.

Nordholm, Sven

Togneri, R.

English

espace@Curtin

©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.IEEE SIGNAL PROCESSING LETTERS, VOL. 16, NO. 2, FEBRUARY 2009 85Robust Source Localization in ReverberantEnvironments Based on Weighted Fuzzy ClusteringMarco Kühne, Roberto Togneri, Senior Member, IEEE, and Sven Nordholm, Senior Member, IEEEAbstract—Successful localization of sound sources in rever-berant enclosures is an important prerequisite for many spatialsignal processing algorithms. We investigate the use of a weightedfuzzy  -means cluster algorithm for robust source localizationusing location cues extracted from a microphone array. In orderto increase the algorithm’s robustness against sound reflections,we incorporate observation weights to emphasize reliable cuesover unreliable ones. The weights are computed from local featurestatistics around sound onsets because it is known that theseregions are least affected by reverberation. Experimental resultsillustrate the superiority of the method when compared withstandard fuzzy clustering. The proposed algorithm successfullylocated two speech sources for a range of angular separations inroom environments with reverberation times of up to 600 ms.Index Terms—Fuzzy clustering, microphone array, reverbera-tion, source localization.I. INTRODUCTIONA COUSTIC source localization by means of a microphonearray is still an active field of research. It is the taskof extracting the localization information of one or severalsound sources by sampling the sound field through a numberof spatially distinct microphones. One important applicationfor source localization algorithms can be found in the field ofblind source separation (BSS). Specifically, under-determinedBSS strategies that rely on source sparseness frequently exploitlocalization information, such as directions-of-arrival (DOA),for segmenting the time-frequency (T-F) plane into disjoint re-gions each assigned to a particular source [1], [2]. For example,Araki et al. [2] use the -means algorithm to perform thepartitioning of the T-F plane into a number of clusters, whichis assumed to be known a priori. For stationary sources, eachof the cluster centers corresponds to the location parameter of aparticular source. Each cluster membership matrix indicates towhich degree a T-F point belongs to a particular source and canbe interpreted as a T-F mask. Individual sources are separatedfrom the mixture by selecting all T-F points belonging to thesource’s cluster as indicated by its membership mask. Locationcues are most reliable in anechoic environments, where almostall T-F points contribute observations that are effective forclustering. However, for reverberant mixtures, the location cuesbecome increasingly corrupted. This often leads to incorrectManuscript received August 02, 2008; revised October 09, 2008. Current ver-sion published January 08, 2009. The associate editor coordinating the reviewof this manuscript and approving it for publication was Prof. Jen-Tzung Chien.M. Kühne and R. Togneri are with the School of Electrical, Electronic, andComputer Engineering, The University of Western Australia, Crawley 6009,Australia (e-mail: marco@ee.uwa.edu.au; roberto@ee.uwa.edu.au).S. Nordholm is with the Western Australian Telecommunications ResearchInstitute, a Joint Venture Between The University of Western Australia andCurtin University of Technology, Crawley 6009, Australia (e-mail: sven@watri.org.au).Digital Object Identifier 10.1109/LSP.2008.2009833localization and partitioning results, mostly due to falselydetected cluster centers, e.g., source locations.In this letter, we address this issue by presenting a robustsource localization technique based on a weighted fuzzy-means algorithm. Contrary to [2], where every observation istreated as equally important, we deal with imperfect locationcues by indicating their usability for the clustering process.The observation weights are obtained prior to the clustering byscanning the T-F plane around sound onsets for regions withlow DOA fluctuations. This was motivated by a number of pre-vious studies which have shown that in echoic enclosures, onlya small fraction of the location cues correspond to the correctsource locations. For example, Faller and Merimaa [3] showedthat binaural source localization remains feasible, even inhighly reverberant conditions by selecting cues consistent withan interaural coherence measure. Huang et al. [4] emulated theprecedence effect by concentrating on location cues extractedfrom sound onsets, a concept that is known to be exploited bythe human auditory system [5]. Through computer simulations,we show that the proposed algorithm is successful in locatingtwo speech sources for a range of angular separations in roomenvironments with reverberation times ( ) of up to 600 ms.The remainder of this letter is organized as follows. Section IIdescribes the proposed localization algorithm in more detail andillustrates the importance of observation weighting for rever-berant mixtures. Section III describes the experimental protocoland presents the results for a number of simulated source local-ization experiments. Finally, the letter concludes with a shortsummary in Section IV.II. ROBUST SOURCE LOCALIZATION ALGORITHMA. Mixing Model and Sparseness AssumptionConsider sources in a reverberant enclosure impingingon a uniform linear microphone array (ULA) made up ofidentical, omnidirectional sensors with inter-element spacing(Fig. 1). The source positions are assumed to be stationary inthe median plane at azimuth angles . It is further as-sumed that each microphone observation can be represented inthe frequency domain as an instantaneous mixing model(1)where represents a time index, is a frequency index, andis the room impulse response from source to sensor. and are the short-time Fourier transforms(STFTs) of the th microphone observation and th source de-fined on a T-F grid by the lattice spacing parameters . Acommon assumption for speech signals [1], [2] is that for each1070-9908/$25.00 © 2009 IEEEAuthorized licensed use limited to: University of Western Australia. Downloaded on November 24, 2009 at 00:46 from IEEE Xplore.  Restrictions apply. 86 IEEE SIGNAL PROCESSING LETTERS, VOL. 16, NO. 2, FEBRUARY 2009Fig. 1. Uniform linear microphone array with         sensor pairs   and two sources  ,  located at azimuth angles  and  .T-F point, only one arbitrary source will be active, such that(1) simplifies to(2)Note that assumptions (1) and (2) become increasingly unre-alistic for short STFT window lengths and long reverberationtimes due to strong reflections from preceding sound events.B. Spatial Feature ExtractionThe most commonly adopted location feature is based on theestimation of the time delay between two microphones usingthe generalized cross-correlation or cross-power spectrum phase[6]. However, within the BSS framework of T-F masking, it ismore common to use level ratios and/or phase differences whichproduce instantaneous location estimates for each T-F cell [1],[2]. According to [7], for sparse sources in echoic environments,the longer the distance is between a sensor pair(Fig. 1), the better the DOA localization performance will be.Hence, the instantaneous DOA at T-F point is computedas the normalized phase difference(3)where denotes the index of the sensor pair with the longestdistance and is the propagation velocity of sound [2],[7]. However, when , with being thesignal’s maximum frequency, the sensor pair violates the spatialaliasing theorem and the phase values in (3) become ambiguous.To avoid this problem, we employ the SPIRE algorithm [7]which utilizes the smaller non-aliased distance pairs to restorethe aliased values of the longer distance pairs. SPIRE is appli-cable when multiple microphone pairs are available and at leastone sensor-pair distance is shorter than the aliasing distance.Note that can be converted to its equivalent azimuth angle via. The frequency normalization in (3) avoids thepermutation problem usually encountered in frequency domainBSS and ensures that for short data, enough DOA measurementsare available for clustering [2].C. Fuzzy Clustering of DOA ValuesA weighted fuzzy -means (wFCM) algorithm [8] is thenused for grouping the extracted features into clusters. InwFCM, clustering is achieved by minimizing the cost function(4)where represents the membership of inthe th cluster, is the observation weight for ,is the th cluster center, and is a distance metric, such asthe norm. The parameter controls the softness of theclustering and is fixed here to . Starting from a randompartitioning, the cost function (4) is iteratively minimized byalternating the updates for centers and memberships(5)(6)until an appropriate termination criterion is met. While the finalcentroids correspond to the DOA estimates, the membershipmatrices can be used as soft T-F masks in BSS applications [1],[2]. Note that wFCM defaults to the standard FCM clustering ifthe weights are chosen to be unity.D. Observation WeightsThe observation weights are used to emphasize sound on-sets and regions with low DOA fluctuations. The steeper anonset and the lower the local variance for a DOA measurement,the more weight should be given to this observation during clus-tering. In particular, the weights are computed as(7)where denotes the onset component and are theweights based on the local DOA variance around . Themotivation for (7) is that reliable DOA measurements are oftenfound at echo-free sound onsets [4] and single source areas withlow local DOA variances [9]. High variances, however, indicateregions where sources overlap or where reflections contaminatethe DOA measurements. The additional term gives moreweight to high frequencies because the localization accuracyin low frequencies is often severely degraded by reverberation.The weighting mechanism is particularly helpful in reverberantconditions because it favors T-F points that better satisfy thesparseness assumption (2).To determine , a simple onset weighting scheme is im-plemented. Let the instantaneous power be defined as in [1](8)and let its first-order time difference on the log-scale be(9)After smoothing with a 5 5 median filter, the onset weightsare determined via the sigmoid compression(10)where is the sigmoid slope and is the sigmoid center. Bothparameters can be tuned, such that sound offsets with small ornegative values are suppressed and onsets with large pos-itive are emphasized. The second weight component isAuthorized licensed use limited to: University of Western Australia. Downloaded on November 24, 2009 at 00:46 from IEEE Xplore.  Restrictions apply. KÜHNE et al.: ROBUST SOURCE LOCALIZATION IN REVERBERANT ENVIRONMENTS 87derived from local DOA statistics gathered in a small neighbor-hood around each DOA measurement. Let the local DOAmean around be(11)and the local DOA variance around be(12)where the neighborhoodis chosen in this study as a nine-point window of adjacentfrequency bins, e.g., . The variances are then mapped tothe [0, 1] interval using the sigmoid function(13)where and are the sigmoid slope and center parameter, re-spectively. Again, both parameters can be tuned, such that T-Fpoints with large DOA variances are suppressed and areas withlow DOA fluctuations are emphasized. Optimal selection of thesigmoid parameters is beyond the scope of this letter, and there-fore, all parameters are empirically derived through a series oftuning experiments (see Section III).Fig. 2 illustrates the importance of the proposed observationweighting for a two-source configuration. For anechoic con-ditions, as shown in Fig. 2(a), almost all of the observationsin the T-F plane are reliable for clustering. The cor-responding azimuth histogram with unity weights in Fig. 2(b)clearly shows two distinctive peaks close to the true DOA an-gles. However, as evident from Fig. 2(c), in reverberant con-ditions, only a small fraction of the DOA observations remainwithin a localization error of 5 . Consequently, the azimuth his-togram with unity weights in Fig. 2(d) fails to identify the twosources. Only when the observations are weighted according totheir reliability do the two sources become visible again[Fig. 2(e) and (f)].III. EXPERIMENTAL EVALUATIONA. SetupMultipath sound propagation was simulated for asmall rectangular room of dimensions 6 m 4 m 3 m(length width height). Wall reflections were estimatedusing the image model method for simulating small-roomacoustics [10]. Room impulse responses for different reverber-ation times were generated for each sensor of a six-channelULA with inter-element spacing of at a samplingfrequency of 8 kHz. The array was positioned in the middle ofthe room at a height of 2 m. Two speech sources with equal gainwere placed at different horizontal angles facing array broad-side and a distance of 1.5 m from the array center. A total of 240different speech mixtures were constructed for testing with ut-terances from the TIMIT and TIDIGIT databases. Simulationswere run for three different DOA configurations with azimuthsof and threeroom reverberation times .The STFT frame size was 25 ms with a shift of 10 ms. Fol-lowing a range of tuning experiments on a cross-validationset, the sigmoid slope parameters were fixed to andFig. 2. Example of reliable localization information for two sources located at   and 10 under (a)-(b) anechoic and (c)-(f) reverberant conditions with   . (a) Anechoic DOA observations  	  with max. of 5localization error (black points). (b) Anechoic azimuth histogram with unityweights. (c) Reverberant DOA observations  	  with max. of 5 localiza-tion error (black points). (d) Reverberant azimuth histogram with unity weights.(e) Estimated DOA weights 	 . (f) Reverberant azimuth histogram withweights from (e).. For each utterance, the sigmoid center was fixedto be the 98th percentile of the set . Similarly,the center parameter was set to be the th percentile of. The value of was tuned for each con-figuration. The stronger the reverberation and the smaller theazimuth separation between sources, the lower the percentilewas chosen. The localization performance of the fuzzy -meansalgorithm was then measured with and without the proposedobservation weighting.B. Results and DiscussionAs expected, for anechoic conditions (Fig. 3, left column)the localization performance using the standard fuzzy clusteringwas sufficient for all azimuth separation angles. The observationweighting had little effect in these cases as almost all T-F obser-vations produced DOA values close to the true azimuth angles.However, for 300-ms and 600-ms reverberation times (Fig. 3,middle and right column) the standard clustering failed to lo-cate the two sources correctly. Too many observations have be-come unreliable and have consequently started to bias the clus-tering towards incorrect solutions. On the other hand, the pro-posed weighting scheme successfully located both sources formost tested configurations, even for the challenging case of only10 angular separation and 600-ms reverberation time (Fig. 3,right column, bottom row).In terms of limitations, our current implementation is basedon a linear array which is restricted to azimuth angle estima-tion and is subject to front-back confusions. However, for fullthree-dimensional localization, the outlined approach can easilyAuthorized licensed use limited to: University of Western Australia. Downloaded on November 24, 2009 at 00:46 from IEEE Xplore.  Restrictions apply. 88 IEEE SIGNAL PROCESSING LETTERS, VOL. 16, NO. 2, FEBRUARY 2009Fig. 3. DOA localization performance for a two-source configuration with different reverberation times (columns) and azimuth separations (rows). Results arepresented for the standard FCM method and the proposed   algorithm with observation weighting. The true DOA angles for speaker   and  are indicated by horizontal dashed lines.be extended to nonlinear array geometries [2], [7]. The majordrawback of the current approach is the rather ad-hoc deter-mination of the weighting factors which requires prior knowl-edge about the environment. Ideally, the sigmoid parametersshould be automatically adapted by the algorithm itself. Fur-ther research is needed to address these issues and to extend themethod to cases with moving speakers and sources with smoothor no onsets.IV. CONCLUSIONWe have presented a weighted fuzzy clustering algorithm fortackling multisource localization in reverberant environments.In order to increase the algorithm’s robustness, observationweights were incorporated to emphasize reliable over unreliableDOA cues. The weights were derived from local DOA statisticsaround sound onsets because it is known that these regions areleast affected by reverberation. Our experimental evaluationshowed that the proposed method produces superior localiza-tion results when compared with standard fuzzy clustering,particularly in reverberant conditions. As a consequence, it isexpected that the resulting cluster partitions will also lead tobetter T-F separation masks. In subsequent work, we thereforeintend to investigate reverberant BSS problems by integratingour robust source localization scheme into T-F masking andspatial filtering techniques.REFERENCES[1] Ö Yilmaz and S. Rickard, “Blind separation of speech mixtures viatime-frequency masking,” IEEE Trans. Signal Process., vol. 52, no. 7,pp. 1830–1847, Jul. 2004.[2] S. Araki, H. Sawada, R. Mukai, and S. Makino, “Underdeterminedblind sparse source separation for arbitrarily arranged multiple sen-sors,” Signal Process., vol. 87, no. 8, pp. 1833–1847, 2007.[3] C. Faller and J. Merimaa, “Source localization in complex listeningsituations: Selection of binaural cues based on interaural coherence,”J. Acoust. Soc. Amer., vol. 116, no. 5, pp. 3075–3089, 2004.[4] J. Huang, N. Ohnishi, and N. Sugie, “Sound localization in reverberantenvironment based on the model of the precedence effect,” IEEE Trans.Instrum. Meas., vol. 46, no. 4, pp. 842–846, Aug. 1997.[5] R. Litovsky, H. Colburn, W. Yost, and S. Guzman, “The precedenceeffect,” J. Acoust. Soc. Amer., vol. 106, no. 4, pp. 1633–1654, 1999.[6] C. Knapp and C. Carter, “The generalized correlation method for esti-mation of time delay,” IEEE Trans. Acoust., Speech, Signal Process.,vol. ASSP-24, no. 4, pp. 320–327, Aug. 1976.[7] M. Togami, T. Sumiyoshi, and A. Amano, “Stepwise phase differencerestoration method for sound source localization using multiple micro-phone pairs,” in Proc. IEEE ICASSP, Honolulu, HI, 2007.[8] S. Miyamoto, R. Inokuchi, and Y. Kuroda, “Possibilistic and fuzzyc-means clustering with weighted objects,” in IEEE Fuzzy Syst. Conf.,Vancouver, BC, Canada, 2006.[9] F. Abrard and Y. Deville, “A time-frequency blind signal separationmethod applicable to underdetermined mixtures of dependent sources,”Signal Process., vol. 85, pp. 1389–1403, 2005.[10] E. Lehmann and A. Johansson, “Prediction of energy decay in roomimpulse responses simulated with an image-source model,” J. Acoust.Soc. Amer., vol. 124, no. 1, pp. 269–277, 2008.Authorized licensed use limited to: University of Western Australia. Downloaded on November 24, 2009 at 00:46 from IEEE Xplore.  Restrictions apply. 

Robust Source Localization in Reverberant Environments Based on Weighted Fuzzy Clustering

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Robust Source Localization in Reverberant Environments Based on Weighted Fuzzy Clustering

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