Source Localisation Mapping using Weighted Interaural Cross-Correlation

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1 ISSC 27, Derry, Sept 3-4 Source Localisation Mapping using Weighted Interaural Cross-Correlation Gavin Kearney, Damien Kelly, Enda Bates, Frank Boland and Dermot Furlong. Department of Electronic and Electrical Engineering, Trinity College Dublin, IRELAND. Abstract Computational sound localisation using binaural microphones requires accurate Interaural Time Difference (ITD) estimation in order to infer an angle of incidence. The Phase Transform weighting function, used in generalized cross correlation calculations for microphone arrays is investigated here for application to ITD estimation in binaural head recordings. Empirical measurements using the method allow for the derivation of a theoretical ITD to angle of incidence mapping function for use with binaural microphones. The corresponding results for estimation of ITDs in a reverberant environment are presented. These results are pertinent to an entire audience area, and not just a single listener position. This objective analysis is then confirmed by the results of real audience listening tests. Keywords Sound localisation, Distributed Audience, IACF, Phase Transform I INTRODUCTION Current trends in computational sound source localisation utilise large numbers of microphones for direction of arrival estimation [, 2, 3]. At the heart of these computations is the estimation of the relative time of arrival of the source wavefront at the microphones. This is commonly achieved by cross-correlation of the received signals at the microphone array in order to determine their relative time delays. Several frequency domain weighting functions have been explored which aim to enhance this estimation technique [4, 5]. Such a weighting function, or processor, acts as a pre-filter to the cross-correlation so as to accentuate the signals at frequencies where the signal to noise ratio is highest, whilst suppressing the noise components. However, the use of such processors for estimation of Interaural Time Differences (ITDs) from binaural recordings has not been sufficiently explored. In the domain of binaural recording studies, the Interaural Cross-Correlation Function (IACF) or simply, normalized cross correlation, is the standard measure for interaural time difference estimation. It provides a measure of ITD estimation that is crucial to the design and testing of sound systems and concert halls, as well as the enhancement of virtual 3-Dimensional acoustic environments [6, 7, 8]. Throughout this paper, we use the terms ITD and time delay estimation interchangeably. In this paper we derive a theoretical head model for ITD to angle of arrival mapping based on empirical measurements. These measurements are accomplished through binaural computations employing the Phase Transform (PHAT) weighting function to Interaural Cross-Correlation. We begin by reviewing the generalized cross-correlation and the PHAT processor as described by Knapp and Carter [4] and the application of the Phase Transform. We then derive empirical ITD to angle of arrival mapping functions with and without the PHAT weighting. A theoretical model is then constructed based on these measurements and the accuracy of this model is verified in a reverberant environment. II GENERALIZED CROSS-CORRELATION AND THE INTERAURAL CROSS-CORRELATION FUNCTION The received signals at the ear points of a binaural head can be sufficiently modelled by, x (t) = s(t) + n (t) x 2 (t) = αs(t + T) + n 2 (t) (a) (b) where s(t) is the source signal, n (t) and n 2 (t) are the noise components associated with x (t) and x 2 (t) respectively and T is the relative time delay between the received signals. The value of α is used to represent signal attenuation. The IACF or normalized cross-

2 correlation function may be defined as, IACF(τ) = t2 x t (t)x 2 (t + τ)dt t2 x 2 t (t)dt (2) t 2 x 2 t 2 (t)dt Essentially the IACF is a function in the range [-,] which gives a measure of the correlation between the received signals in the integration limits t to t 2 as a function of the time delay τ. Therefore the function yields its maximum where τ equals the true delay between x (t) and x 2 (t), i. e., T = arg (max τ [IACF(τ)]) (3) Prior to the normalization of (2) pre-filters may be applied in the frequency domain so as to enhance the observed peak at the true time delay. This defines the generalized cross correlation (GCC) approach [4] where the GCC function is defined as, R x x 2 (τ) = + Φ(ω)G x x 2 (ω)e jωτ dω (4) where G x x 2 (ω) is the cross-power spectrum of signals x (t) and x 2 (t) and Φ(ω) is a weighting function. In the case of the white and independent noise components n (t), n 2 (t) and multiple delays T i with corresponding attenuation factors α i, the GCC function can be interpreted as, R x x 2 (τ) = R s s (τ) α i δ(τ T i ) (5) i where R s s (τ) is the autocorrelation of the source signal s(t). From this, it can be seen that a sharp peak at the delays T i is desirable so as to avoid spreading of the delta functions making individual peaks indistinguishable from one another. The use of a weighting function Φ(ω) attempts to reduce this spreading. One such weighting is that of the Phase Transform (PHAT), Φ(ω) = G x x 2 (ω) (6) This particular weighting function has been shown to be the most suitable choice of processor for use in reverberant environments with microphone arrays [9]. However, one consequence of using a binaural mannequin as opposed to a microphone array is that the mapping of time delay estimates versus source angle is difficult to derive due to the complex shape of the head. Thus, we will first obtain an empirically measured mapping function for the weighted and non-weighted cross-correlation approaches. In the context of this paper the non-weighted cross-correlation approach refers to the use of the IACF in ITD estimation and the weighted cross-correlation approach refers to the use of the IACF with pre-filtering through the PHAT processor. It is then attempted to explain the mapping function attained using a theoretical head model. This model is then used to compare the weighted and nonweighted cross-correlation approaches in reverberant rooms. III DERIVATION OF ITD TO ANGLE OF ARRIVAL MAPPING FUNCTION Binaural recordings were taken in a controlled studio environment using the setup in Figure. The micro- Fig. : Studio setup for binaural recordings. phone used was the Neumann KU dummy head with a Genelec 29A loudspeaker at m from the head as the reference source. The ITDs were calculated using weighted and unweighted IACF at 5 head rotation increments. The source stimuli used were second unfiltered samples of male speech, female speech, white noise and music. Knowledge of the source position in a hemispherical space was used in post-processing in order to avoid the cone of confusion, where a single time delay estimate can result in multiple possible angles. The calculated time delay estimates to source angle mappings for both normalized cross correlation and weighted IACF can be found in Figure 2. These cross-correlograms show the magnitude of the cross correlation coefficient at the delays corresponding to each possible source angle. Gray-scale levels are used to visualise the magnitude of the coefficients increased from black to white in the images. We can clearly see here how the use of the PHAT processor tightens the estimation of the delay as opposed to the smearing shown in the standard cross correlation. IV THEORETICAL BASIS FOR ITD MAPPING The theoretical derivation of the angle of incidence for a given ITD was implemented using an elliptical model of the head. The ear points were set at ± from the azimuth as recommended by Blauert []. The model allows us to compensate for the diffraction effects of the head in the estimate of the time delay. The ear points E and E 2 can be expressed in Cartesian form as, [ hw E = E 2 = 2 cos(θ + ), hw 2 2 ] sin(θ + ) [ hw 2 cos(θ + 26), hw 2 sin(θ + 26) 2 ] (7a) (7b)

3 Time Delay 96khz) Time Delay 96khz) IACF Angle of Rotation (Degrees) Weighted IACF Angle of Rotation (Degrees) where c = 343m/s is the speed of sound. It is useful to examine how this model compares to that of a circular head model without compensating for the funnelling effect of the ears. This corresponds to the case where hw = hw 2 and ρ =. The resultant theoretical mapping function obtained using this model is shown superimposed over the empirical measurements in Figure 4. Interaural Time Difference (msec) Empirical Data Theoretical Model Fig. 2: Cross correlograms for simple cross-correlation and weighted cross-correlation using the Phase Transform. S Head Angle (Degrees).8 Empirical Data Theoretical Model d ET d o T T 2 d ET 2 2 d E E 2 Interaural Time Difference (msec) d ET 2 Fig. 3: Elliptical model of head. d ET 2 where hw = 9cm and hw 2 = 2cm correspond to the length of the elliptical head minor and major axes, respectively. When the source is in the shadow region of the head the distance from the source to the ears E, E 2 is given by, d se = d + min(d E T, ρd E T 2 ) (8a) d se2 = d + min(ρd E T, d E T 2 ) (8b) where the propagation path weighting ρ is used to model the funneling effect of the ears which will be explained later. When the ear is in the non-shadow region of the head in relation to the source these values are taken to be, d se = S E, (9a) d se2 = S E 2 (9b) The theoretical time delay is then determined as, T = d S E d S E2 c () Head Angle (Degrees) Fig. 4: Comparison of circular (top) and elliptical (bottom) mapping functions to empirically derived data. We see that the time delay estimates match well for angles between 8 and +8. However, localisation accuracy breaks down around the contra-lateral points between 8 to 5 and 245 to 28. This is attributed to the shadowing effect of the dummy head outer ear with respect to the ear canal affecting the intensity levels at the microphones, thus highlighting the need for the weight ρ in Equation (8b). Because the shortest propagation path has a smaller intensity at the ear, the dominant peak in the cross-correlation function corresponds to the longer path to the ear. At approximately ±5 the ear canal is no longer shadowed and the time delay estimate drops significantly. The resultant theoretical mapping function obtained using the elliptical head model with weighting ρ = 2 is shown in Figure 4 overlaying the empirically derived mapping function. The elliptical head model can be seen to explain well the empirical data particularly at the contra-lateral points through the use of the path weighting ρ. What remains to be seen is the ability of the PHAT approach using this theoretical mapping function to determine

4 the correct angle of localisation in a reverberant environment in comparison to the use of the IACF. V ITD ESTIMATION ACCURACY IN A REVERBERANT ENVIRONMENT As a precursor to studies by the authors for testing the localisation accuracy of various spatial enhancement systems [, 2], a series of experiments were set up in a small sized concert hall in Trinity College Dublin for the purposes of evaluating monophonic localisation in a real listening environment. The aim of this study is to show the objective and subjective localisation of monophonic sources through both binaural recordings and real listening tests. The setup, shown in Figure 5 incorporates a 6 loudspeaker array of Genelec 29A loudspeakers. Again, the Neumann KU- dummy head microphone was used and a MOTU 896HD interface was employed to route the audio to a PC. 8 o 9 o 2 27 o o Fig. 5: Geometry of loudspeaker array and audience area for monophonic listening tests. Each loudspeaker was calibrated to 8dBA at m from the on-axis tweeter position and their axis lines were coincident with the centre listener position. The reverberation time (RT6) was measured at four different points (equidistant from the centre listening position) in the hall, using 8kHz maximum length sequence noise and the spatially averaged values against frequency are shown in Figure 6. The dummy head was RT6 RT6 (Seconds) Frequency (Hz) x 3 Frequency (Hz) x 3 Fig. 6: Spatially averaged RT6 reverberation time for hall placed at each listener position and monophonic presentations of male speech, female speech, white noise and music were recorded. Time delay estimates were made over the full lengths of the recordings. These objective results for frontal, front-lateral, rear-lateral and rear localisation for male speech are shown in Figure 7(a) and (b). It is important to note that in this set of plots the error bar ( ) does not correspond to angular deviation ±σ θ, but rather to the accepted tolerance of localisation in the direction of a particular loudspeaker, before the source is localised at the another loudspeaker. This tolerance is set by the angles corresponding to the halfway points between the loudspeakers on either side of the target location. It was found that the localisation accuracy for both the weighted and unweighted cross-correlation did not change with the source stimulus. This was attributed to the large window lengths (full signal duration) used. It can be seen that weighted cross correlation performs to a higher accuracy than standard IACF, in particular at seat positions where the reflection levels can be significantly higher than the direct sound. This can be seen for presentations from loudspeaker 2 at seat positions 8 and 9, loudspeaker 6 at position 7, and loudspeaker at positions and 2. We also see that the PHAT significantly improves the localisation accuracy at the contralateral points. This can be seen at loudspeaker 6 at listener positions, 2 and 3, and loudspeaker 4 at listener positions 8 and 9. We also note that all results using the PHAT method are within the tolerance limits for loudspeaker localisation in the array. VI COMPARISON OF WEIGHTED IACF TO REAL LISTENING TESTS The objective results obtained with the theoretical model are also compared to the results of real audience listening tests. For this, an audience of nine test subjects were presented with monophonic sound from pseudo-random (pre-determined) positions located about the loudspeaker array and were then asked to identify the location of the sources via a questionnaire running concurrently with the tests. This randomised method was used to negate any order effects during the tests. The same source signals and source locations used for the binaural measurements were presented to the audience. Each sample was presented twice, followed by a short interval before the next presentation and the listeners were asked to keep their heads in the forward direction. Each of the listeners answers were weighted, depending on the confidence level of the listener with their choice, with weightings of /n, where n is the number (or range) of speakers that a listener felt the sound originated from. From this, the histogram {h(θ i )} i [:6] collecting all the listeners answers is computed for each seat. The angular mean θ and the unbiased standard deviation σ θ at each listener position are computed as: 6 i= θ = h(θ i) θ i 6 i= h(θ () i) σ θ = 6 i= h(θ i)(θ i θ) 2 ( 6 i= h(θ i)) (2)

5 8 Simple Cross Correlation, Loudspeaker 2, Stimulus: MaleSpeech PHAT Weighted Cross Correlation, Loudspeaker 2, Stimulus: MaleSpeech 8 8 Loudspeaker 2, Stimulus: Male Speech Simple Cross Correlation, Loudspeaker 6, Stimulus: MaleSpeech PHAT Weighted Cross Correlation, Loudspeaker 6, Stimulus: MaleSpeech 35 Loudspeaker 6, Stimulus: Male Speech Simple Cross Correlation, Loudspeaker, Stimulus: MaleSpeech PHAT Weighted Cross Correlation, Loudspeaker, Stimulus: MaleSpeech 3 3 Loudspeaker, Stimulus: Male Speech Simple Cross Correlation, Loudspeaker 4, Stimulus: MaleSpeech PHAT Weighted Cross Correlation, Loudspeaker 4, Stimulus: MaleSpeech 8 8 Loudspeaker 4, Stimulus: Male Speech (a) (b) (c) = θ IT D, = θ T, = Tolerance. = θ IT D, = θ T, = Tolerance. = θ, = θ T, = ±σ θ. Fig. 7: (a) Objective front, front lateral, rear and rear-lateral localisation using mapping function and ITD estimation using the IACF. (b) Objective front, front lateral, rear and rear-lateral localisation using mapping function and ITD estimation using the weighted IACF. (c) Subjective front, front lateral, rear and rear-lateral localisation.

6 The results of these tests can be found in Figure 7(c) for sources at speakers 2, 6, and 4. The plots show the mean θ (circle), deviation σ θ (whiskers) and presented localisation angle, or ground truth (square) from the perspective of each listener position. These results validify the use of PHAT weighting for ITD measurements. They also indicate that monophonic sources can be reasonably well localised by a distributed audience under reverberant conditions. They also confirm the findings of the PHAT weighted cross correlation that, for this loudspeaker configuration, localisation accuracy is greatest for frontal and frontally-biased lateral sources. The results for rear and rear-biased lateral sources are also comparable to the binaural measurements. It was found from the subjective results that localisation for music, white noise and female speech were similar, whilst the best localisation was achieved for male speech. These results match the findings of other localisation studies [] which also indicate that localisation accuracy is greater for speech than for broadband noise. It is important to note that the subjects were tested using a forced-choice, speaker identification method which explains the high degree of correlation between the mean results and presented angle, and in general, a higher accuracy over the objective results. The deviation varies considerably for different listening and source positions, which is unsurprising considering the non-ideal listening conditions. A number of studies [3, 4], have shown that localisation accuracy decreases with increasing levels of reverberation. These findings are supported by our results which show wider angular deviations than reported in similar studies [5] carried out under anechoic conditions. VII CONCLUSIONS Empirically derived mapping functions were created for both simple and weighted cross correlation for the angle of incidence inferred from a given ITD. A theoretical mapping function was derived based on the elliptical shape of the head and was shown to improve the mapping to the empirical data over a circular head model. The shadowing effect of the ear on the ear canal was found to play a significant role in this mapping. It was shown that the PHAT processor significantly improves the estimation of the delay and the results complement the subjective listening tests. Further work is required to investigate the effect of shorter window lengths with varying source stimuli and to extend the model to a 3-Dimensional oval shape to accommodate elevating sources. Examination into the relationship between the weight ρ and ear prominence, as a function of the Interaural level differences, is also required. This theoretical model can now be used with the PHAT processor to obtain estimates of source locations at any given azimuthal position and can be used to verify the accuracy of horizontal phantom source images created with spatialisation systems at the equivalent acoustic positions of the monophonic sources. VIII ACKNOWLEDGEMENTS This research is supported by Science Foundation Ireland. Damien Kelly also gratefully acknowledges the support of the Irish Research Council for Science Engineering and Technology (IRCSET). REFERENCES [] M. Omologo and P. Svaizer, Acoustic Event Localization Using a Crosspower-Spectrum Phase Based Technique, in Proc. ICASSP 94, Adelaide, Australia, 994, pp. II 273 II 276. [2] M. Omologo and P. Svaizer, Talker Localization and Speech Enhancement in a Noisy Environment using a Microphone Array based Acquisition System, in Proceedings Eurospeech, Berlin, September 993, pp [3] H. F. Silverman, W. R. Patterson III, and J. L. Flanagan, The Huge Microphone Array (HMA), Journal of the Acoustical Society of America, vol., no. 5, pp , 997. [4] C. H. Knapp and G. C. Carter, The Generalized Correlation Method for Estimation of Time Delay, IEE Transactions on Acoustics, Speech and Signal Processing, vol. 24, pp , 976. [5] J. Stuller, Maximum-likelihood estimation of time-varying delay Part I, Acoustics, Speech, and Signal Processing, IEEE Transactions on,, vol. 35, no. 3, pp. 3 33, March 987. [6] T. Okano, L. L. Beranek, and T. Hidaka, Relations among interaural cross-correlation coefficient (IACC), lateral fraction (LF), and apparent source width (ASW) in concert halls, Journal of the Acoustical Society of America, vol. 4, no., pp , 998. [7] T. Hidaka, L. L. Beranek, and T. Okano, Interaural crosscorrelation, lateral fraction, and low- and high-frequency sound levels as measures of acoustical quality in concert halls, Journal of the Acoustical Society of America, vol. 98, no. 2, pp , 995. [8] D. R. Begault, 3-D Sound for Virtual Reality and Multimedia, Academic Press Cambridge MA, 994. [9] T. Gustafsson, D. R. Bhaskar, and M. Trivedi, Sound Localization in Reverberant Environments: Modeling and Statistical Analysis, IEEE Transactions on Speech and Audio Processing, vol., pp , November 23. [] J. Blauert, Spatial Hearing, MIT Press Cambridge MA, 23. [] E. Bates, G. Kearney, D. Furlong, and F. Boland, Localization Accuracy of Advanced Spatialization Techniques in Small-Sized Concert Halls, in 53rd Meeting of the Acoustical Society of America, June 27. [2] G. Kearney, E. Bates, D. Furlong, and F. Boland, A Comparative Study of the Performance of Spatialization Techniques for a Distributed Audience in a Concert Hall Environment, in 3st International Conference of the Audio Engineering Society, June 27. [3] W. M. Hartmann, Localization of sound in rooms, Journal of the Acoustical Society of America, vol. 74, pp , Nov [4] C. Giguere and S. M. Abel, Sound localization: Effects of reverberation time, speaker array, stimulus frequency, and stimulus rise/decay, Journal of the Acoustical Society of America, vol. 94, pp , 993. [5] G. Theile and G. Plenge, Localization of lateral phantom sources, Journal of the Audio Engineering Society, vol. 25, pp. 96 2, 977.

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