The recently proposed subspace pseudointensity method for direction of
arrival estimation is applied in the context of Tasks 1 and 2 of the LOCATA
Challenge using the Eigenmike recordings. Specific implementation details are
described and results reported for the development dataset, for which the
ground truth source directions are available. For both single and multiple
source scenarios, the average absolute error angle is about 9 degrees.Comment: In Proceedings of the LOCATA Challenge Workshop - a satellite event
  of IWAENC 2018 (arXiv:1811.08482 

Moore, Alastair H.

English

arXiv

The recently proposed subspace pseudointensity method for direction of arrival estimation is applied in the context of Tasks 1 and 2 of the LOCATA Challenge using the Eigenmike recordings. Specific implementation details are described and results reported for the development dataset, for which the ground truth source directions are available. For both single and multiple source scenarios, the average absolute error angle is about 9 degrees

Moore, AH

Spiral - Imperial College Digital Repository

LOCATA Challenge Workshop, a satellite event of IWAENC 2018 September 17-20, 2018, Tokyo, JapanMULTIPLE SOURCE DIRECTION OF ARRIVAL ESTIMATION USING SUBSPACEPSEUDOINTENSITY VECTORSAlastair H. MooreImperial College LondonDepartment of Electrical and Electronic EngineeringLondon, SW7 2AZABSTRACTThe recently proposed subspace pseudointensity method for direc-tion of arrival estimation is applied in the context of Tasks 1 and 2of the LOCATA Challenge using the Eigenmike recordings. Spe-cific implementation details are described and results reported forthe development dataset, for which the ground truth source direc-tions are available. For both single and multiple source scenarios,the average absolute error angle is about 9◦ degrees.Index Terms— direction of arrival estimation, spherical micro-phone array, multiple sources, array processing1. INTRODUCTIONIn recent years many direction of arrival (DOA) estimation methodsoperating in the spherical harmonic (SH) domain have been pro-posed [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. These methods transform thesignals captured by a spherical microphone array into a represen-tation in which the steering vectors are independent of the specificarray geometry and of frequency. In practice, the size of the sphere,the number of microphones and their arrangement affect the signal-to-noise ratio (SNR) as a function of frequency, limiting the usablefrequency region.The subspace pseudointensity vector (SSPIV) method [11]uses frequency smoothing [3, 8], in addition to conventional time-smoothing, to estimate the SH covariance matrix of the sound fieldover a range of frequencies. This reduces the coherence causedby multipath progation and allows DOA estimates to be obtainedfrom shorter observation intervals, i.e. with less time-smearing,than those based on a single frequency bin.Exploiting window-disjoint orthogonality (WDO) [12], it hasbecome common to estimate the DOA of a single source in eachtime-freqeuncy (TF) region before combining these estimates to es-timate the number of sources and their directions. Some methods[8, 9, 10] specifically test each TF region for the validity of thisassumption before deciding whether to include it in the overall es-timation. However, this can lead to relatively few DOA estimatesbeing retained. In contrast the SSPIV method includes all the localestimates on the assumption that, on average, even erroneous localestimates will tend to cluster around the true DOAs.The SSPIV method is fully described in [11] and so will notbe repeated in this work. Rather we focus on a block-level descrip-tion of the overall system in Section 2 and specific implementationissues in Section 3. In Section 4 results are reported for Tasks 1This work was supported by the Engineering and Physical Sciences Re-search Council [grant number EP/M026698/1].Short-time Fourier transformSpherical Fourier transform withmode strength compensationSubspace pseudointensity vectorsSmoothed histogramPeak picking and pruningMicrophone signalsEstimated DOAsFigure 1: System diagramand 2 of the LOCATA Challenge development dataset [13]. Finally,Section 5 concludes the paper.2. SYSTEM DESCRIPTIONFigure 1 shows an overview of the system used to perform DOAestimation for the LOCATA Challenge. The 32-channel Eigne-mike signals are first transformed to the short time Fourier trans-form (STFT) domain before further transformation to the SH do-main [14]. Mode strengh compensation is used to account for thescattering effect of the rigid spherical geometry of the mirophonearray. SSPIVs are calculated at each TF bin according to [11]. i.e.at each TF bin a Cartesian unit vector is obtained whose directionarXiv:1811.11663v1  [cs.SD]  28 Nov 2018LOCATA Challenge Workshop, a satellite event of IWAENC 2018 September 17-20, 2018, Tokyo, Japanpoints towards an estimate of the DOA for that TF bin.A 2-dimensional histogram of all the SSPIVs’ directions is ob-tained in terms of the azimuth and inclination (defined as per theLOCATA definition of elevation) components. The histogram gridis regularly spaced in azimuth and inclination which means that theequivalent surface area of each patch on the sphere is non-uniform.The raw histogram is smoothed with a Gaussian kernal, definedin terms of the solid angle between bins. In this way local peaksaround a true source direction are removed, which is especially im-portant near the poles where patches are more sparsely populated.The 10 largest peaks in the smoothed histogram are initiallypicked as candidate source directions. Only peaks whose height aregreater than β times the height of the lowest peak (which is assumedto be due to noise) are retained.3. IMPLEMENTATION DETAILSSpecific parameter values for the implementation are given in Ta-ble 1.Description [◦] Value UnitsSTFT frame duration 4 msSTFT overlap factor 75 %SH order of analsysis 3 —Covariance matrix time span 16 msCovariance matrix frequency span 350 HzMinimum frequency 800 HzMaximum frequency 3500 HzHistogram azimuth bin width 2 ◦Histogram inclination bin width 2 ◦Standard deviation of Gaussian smoothing kernel 4 ◦Peak height ratio threshold, β 2 —Table 1: Parameter values used in implementation.4. RESULTS4.1. Task 1Table 2 gives the accuracy of DOA estimation using the SSPIVmethod for Task 1, in which a single static source is present. Sinceit is known a priori that only one source is present, it is sufficientin the peak picking step to choose only the largest peak in the his-togram. The average error in azimuth is 8.6◦ while in elevation it is2.9◦ giving a combined solid angle error of 9.2◦.Rec # Azimuth [◦] Elevation [◦] Combined [◦]1 10.5 2.5 10.82 5.7 4.1 6.93 9.5 2.2 9.7Avg 8.6 2.9 9.2Table 2: Estimation error for source DOAs in Task 1.Smoothed histogram of SSPIVs with estimated DOAs0 50 100 150 200 250 300 350Azimuth [deg]020406080100120140160180Inclination [deg]EstimatedActual50100150200250300smoothed histogram countsFigure 2: Smoothed histogram of SSPIVs obtained for Task 2,recording 1 with ground truth and estimated DOAs.Smoothed histogram of SSPIVs with estimated DOAs0 50 100 150 200 250 300 350Azimuth [deg]020406080100120140160180Inclination [deg]EstimatedActual102030405060708090100110smoothed histogram countsFigure 3: Smoothed histogram of SSPIVs obtained for Task 2,recording 2 with ground truth and estimated DOAs.LOCATA Challenge Workshop, a satellite event of IWAENC 2018 September 17-20, 2018, Tokyo, Japan4.2. Task 2In Task 2 an unknown number of static sources are present. Thetask therefore includes both DOA estimation and source counting.Table 3 gives the accuracy of DOA estimation using the SSPIVmethod. It can be seen that for recording 1 only one of the twosources are detected. Figure 2 shows the smoothed histogram ofSSPIVs and there is clearly no second peak corresponding to thesecond source.In recordings 2 and 3, where more sources are active, all sourcesare identified. Figure 3 shows the smoothed histogram of SSPIVsfor recording 2. The source at azimuth 13◦ leads to a relativelysmall peak but is, nevertheless, detected.Neglecting the missed source, the average error in azimuth is8.9◦ while in elevation it is 2.7◦ giving a combined solid angle errorof 9.5◦. These values are remarkably close to those obtained for asingle source, suggesting that the SSPIV method is well suited tomultiple source DOA estimation in real-world environments.Rec # Src # Azimuth [◦] Elevation [◦] Combined [◦]1 1 7.1 3.5 8.52 — — —2 1 8.8 1.7 8.92 6.6 3.5 7.53 5.8 2.4 6.34 6.8 4.9 8.43 1 19.2 0.9 19.22 6 2.2 6.43 10.7 2.6 10.9Avg — 8.9 2.7 9.5Table 3: Estimation error for source DOAs in Task 2.5. CONCLUSIONSThe application of the SSPIV method to DOA estimation for singleand mulitple sources in the context of the LOCATA Challenge hasbeen described. Sources are estimated in both cases with a meanabsolute error of about 9◦.6. REFERENCES[1] B. Rafaely, “Plane-wave decomposition of the pressure on asphere by spherical convolution,” J. Acoust. Soc. Am., vol.116, no. 4, pp. 2149–2157, Oct. 2004.[2] H. Teutsch and W. Kellermann, “EB-esprit: 2D localizationof multiple wideband acoustic sources using eigen-beams,” inProc. IEEE Intl. Conf. on Acoustics, Speech and Signal Pro-cessing (ICASSP), vol. 3, Mar. 2005, pp. iii/89–iii/92.[3] D. Khaykin and B. Rafaely, “Coherent signals direction-of-arrival estimation using a spherical microphone array: Fre-quency smoothing approach,” in Proc. IEEE Workshop on Ap-plications of Signal Processing to Audio and Acoustics (WAS-PAA), New Paltz, NY, USA, Oct. 2009, pp. 221–224.[4] D. P. Jarrett, E. A. P. Habets, and P. A. Naylor, “3D source lo-calization in the spherical harmonic domain using a pseudoin-tensity vector,” in Proc. European Signal Processing Conf.(EUSIPCO), Aalborg, Denmark, Aug. 2010, pp. 442–446.[5] B. Rafaely, Y. Peled, M. Agmon, D. Khaykin, and E. Fisher,“Spherical microphone array beamforming,” in Speech Pro-cessing in Modern Communication: Challenges and Perspec-tives, I. Cohen, J. Benesty, and S. Gannot, Eds. PUB-SV,Jan. 2010.[6] H. Sun, E. Mabande, K. Kowalczyk, and W. Kellermann, “Lo-calization of distinct reflections in rooms using spherical mi-crophone array eigenbeam processing,” J. Acoust. Soc. Am.,vol. 131, pp. 2828–2840, 2012.[7] C. Evers, A. H. Moore, and P. A. Naylor, “Multiple sourcelocalisation in the spherical harmonic domain,” in Proc. Intl.Workshop on Acoustic Signal Enhancement (IWAENC), Nice,France, July 2014.[8] O. Nadiri and B. Rafaely, “Localization of multiple speakersunder high reverberation using a spherical microphone arrayand the direct-path dominance test,” IEEE/ACM Trans. Audio,Speech, Lang. Process., vol. 22, no. 10, pp. 1494–1505, Oct.2014.[9] A. H. Moore, C. Evers, P. A. Naylor, D. L. Alon, andB. Rafaely, “Direction of arrival estimation using pseudo-intensity vectors with direct-path dominance test,” in Proc.European Signal Processing Conf. (EUSIPCO), 2015.[10] D. Pavlidi, S. Delikaris-Manias, V. Pulkki, and A. Mouchtaris,“3D localization of multiple sound sources with intensity vec-tor estimates in single source zones,” in Proc. European SignalProcessing Conf. (EUSIPCO), 2015.[11] A. H. Moore, C. Evers, and P. A. Naylor, “Directionof arrival estimation in the spherical harmonic domainusing subspace psuedointensity vectors,” IEEE/ACM Trans.Audio, Speech, Lang. Process., 2016. [Online]. Available:http://dx.doi.org/10.1109/TASLP.2016.2613280[12] S. Rickard and Z. Yilmaz, “On the approximate W-disjoint or-thogonality of speech,” in Proc. IEEE Intl. Conf. on Acoustics,Speech and Signal Processing (ICASSP), vol. 1, Apr. 2002,pp. 529–532.[13] H. W. Löllmann, C. Evers, A. Schmidt, H. Mellmann, H. Bar-fuss, P. A. Naylor, and W. Kellermann, “The LOCATA chal-lenge data corpus for acoustic source localization and track-ing,” in IEEE Sensor Array and Multichannel Signal Process-ing Workshop (SAM), Sheffield, UK, July 2018.[14] B. Rafaely, Fundamentals of Spherical Array Processing, ser.Springer Topics in Signal Processing. Berlin Heidelberg:Springer-Verlag, 2015.

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