de Bree, Hans-Elias

Fricke, Julius T.

Siegel, André

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   Information Technology and Electrical  Engineering - Devices and Systems, Materials  and Technologies for the Future        Faculty of Electrical Engineering and Information Technology    Startseite / Index:  http://www.db-thueringen.de/servlets/DocumentServlet?id=14089 54. IWK Internationales Wissenschaftliches Kolloquium International Scientific Colloquium 07 - 10 September 2009 PROCEEDINGS Impressum  Herausgeber: Der Rektor der Technischen Universität llmenau  Univ.-Prof. Dr. rer. nat. habil. Dr. h. c. Prof. h. c. Peter Scharff  Redaktion: Referat Marketing   Andrea Schneider   Fakultät für Elektrotechnik und Informationstechnik  Univ.-Prof. Dr.-Ing. Frank Berger  Redaktionsschluss: 17. August 2009  Technische Realisierung (USB-Flash-Ausgabe):  Institut für Medientechnik an der TU Ilmenau  Dipl.-Ing. Christian Weigel  Dipl.-Ing. Helge Drumm  Technische Realisierung (Online-Ausgabe):  Universitätsbibliothek Ilmenau    Postfach 10 05 65  98684 Ilmenau  Verlag:   Verlag ISLE, Betriebsstätte des ISLE e.V.  Werner-von-Siemens-Str. 16  98693 llmenau   © Technische Universität llmenau (Thür.) 2009   Diese Publikationen und alle in ihr enthaltenen Beiträge und Abbildungen sind urheberrechtlich geschützt.   ISBN (USB-Flash-Ausgabe): 978-3-938843-45-1 ISBN (Druckausgabe der Kurzfassungen): 978-3-938843-44-4  Startseite / Index: http://www.db-thueringen.de/servlets/DocumentServlet?id=14089  SOURCE LOCALIZATION WITH ACOUSTIC VECTOR SENSORSJulius T. Fricke a), b), Hans-Elias de Bree b), André Siegel a)a) Ilmenau University of Technology, Subject Audiovisual Technology,P.O. Box 10 05 65, 98694, Ilmenau, Germanyb) Microflown Technologies, HAN Academy,Ruitenberglaan 26, 6826 CC Arnhem, The Netherlands{ fricke, debree}@microflown.com{ andre.siegel, schade}@tu-ilmenau.deABSTRACTIn this paper a localization method is analyzed, which uses Acoustic Vector Sensors (AVS). An AVS meas-ures the directed velocity and the pressure in an area approaching a single point. In order to localize sound sources, the Multiple Signal Classification (MUSIC) was  applied,  which  determines  the  signal  and  the noise components. MUSIC only uses the noise com-ponents (Noise Subspace) to estimate the direction of arrival. To estimate the quality of this method, the ac-curacy  and  the  resolution  of  the  localization  were compared with an established pressure-based method. The  accuracy  and  resolution  of  the  velocity-based method are  higher.  MUSIC was less  robust  against calibration errors of phase and frequency. Our meas-urements  showed  that  the  combination  of  acoustic vector sensors, appropriated calibration, and MUSIC provides an efficient localization system.Index Terms – source localization, beamforming, array,  direction  of  arrival  estimation,  MUSIC, subspace,  acoustic  vector  sensor,  particle  velocity, sound intensity1. INTRODUCTIONCommon localization  methods use the phase  differ-ence of pressure between spatially distributed points on an array to localize the sound sources. To estimate the phase difference, the measured oscillation has to be in the same period at all points of the array. This spatial sampling causes aliasing. To reduce this effect the distance between the points should be minimized. This, however, leads to a lower resolution, since the distance between the points is proportional to the res-olution of the localization. In this paper an alternative localization method is analyzed, which uses Acoustic Vector Sensors (AVS) (shown in figure (1)).2. ARRAYS OF ACOUSTIC VECTOR SENSORSAVS measure directed velocity and pressure in an area approaching a single point [2]. AVS are a combination of  three  orthogonal  velocity  sensors  and  an  omni-directional pressure sensor. In consequence, we do not need  a  spatial  distribution  of  the  AVS in  order  to measure phase differences. However, to determine the distance of the source two spatial distributed AVS are needed.Figure 2: To determine the  distance d of a source at  least two separated sensors are neededdFigure 1: Acoustic vector sensor (AVS)  consisting of three directed velocity  sensors and an omnidirectional pressure sensor© 2009 - 54th Internationales Wissenschaftliches KolloquiumTo  get  a  better  understanding  of  the  AVS  we executed  several  simulations.  For  example  we analyzed the relation of two AVS rotating around each other. In further simulations, we split an AVS in the three directed velocity sensors and analyzed them in a spatial distribution.During  all  simulations  the  effect  to  the  source localization was in the point of focus.3. CALIBRATION OF THE AVSThe acoustic vector sensors of Microflown Technolo-gies are ½" in diameter. Since the AVS measure the incident angles of sound a small error in the orienta-tion of the sensor elements can cause a significant er-ror in the measured direction of arrival.For this reason a calibration of direction was imple-mented, which consists of the translation, the rotation and the shearing of the sensor elements.These three possible movements are the integral part of a calibration matrix M:uc = M⋅um , (1)with um  as the measured direction of arrival and uc  as the calibrated direction of arrival. The calibration matrix  M can  be determined by measurements.  For this purpose a sound source is measured at different, exactly  defined  positions.  With  these  measurements we can build a system of linear equations. The system of  linear  equations  should  be  overdetermined  by  a high number of measurements. The best approxima-tion to the solution of the system of equations is the generalized inverse. If we multiply the generalized in-verse of all measured directions of arrival Vm with all correct directions of arrival  Vc we get the calibration matrix M:M = pinvV m⋅V c  (2)With  the  obtained  calibration  matrix  M and equation (2) we can calibrate every measured vector vm .4. MULTIPLE SIGNAL CLASSIFICATIONAs a localization algorithm, Multiple Signal Classific-ation (MUSIC) [5] was applied, which allows to in-clude directed velocity into computation [3]. MUSIC performs a principal components analysis in order to determine source and noise components.  These prin-cipal  components  can be  assigned to  all  theoretical possible directions of arrival. The possible directions of arrival are determined by using a physical model of the  acoustic  vector  sensors.  MUSIC  uses  only  the noise components ('Noise Subspace') to estimate the direction of arrival. The noise components are masked by the source signal in the direction of the source and therefore equal zero. As a consequence, the reciprocal value of the noise components creates sharp peaks in the directions of the sources [4]. 4.1. Principal Components Analysis PCAThe principal components analysis (PCA) determines the source and noise components of the measured sig-nals. The noise components of the measured signals are characterized by being uncorrelated at all sensors. Therefore it  makes sense  to  analyze  the correlation between the different sensors in order to separate the source and the noise components. For this reason we compute  the  cross  correlation  matrix  between  all sensor signals. Table (1) shows the cross correlation of a single AVS.p* ux* uy* uz*p pp* pux* puy* puz*ux uxp* uxux* uxuy* uxuz*uy uyp* uyux* uyuy* uyuz*uz uzp* uzux* uzuy* uzuz*Table 1: Cross correlation matrix of a single acoustic vector sensorFigure 3: Translation (left), rotation (middle) and shear mapping (right)black transformed, grey originThe higher the value in the calculated matrix, the higher the probability that a sound source is between the two sensor directions.In order to describe the obtained probabilities by independent  components  we  execute  an  eigenvalue decomposition  in  the  next  step.  These  components can  be  imagined  as  a  set  of  basis  vectors  of  a coordinate system. The set of basis vectors is chosen to  be  as  small  as  possible  but  still  big  enough  to describe  the  measured  probabilities.  In  other  words we  need  at  least  the  dimensions  of  this  coordinate system to represent the measured data. The obtained eigenvectors  of  the  cross  correlation  matrix correspond to the axis of the coordinate system. The eigenvalues  describe  the  influence  of  the corresponding  dimension  to  the  probability distribution.The  dominant  dimensions  of  the  probability distribution  can  be  referred  to  the  corresponding sources. The space, spanned by these dimensions is called  'Signal  Subspace'.  The  less  pronounced dimensions represent the 'Noise Subspace'.4.2. Direction of Arrival (DOA)MUSIC uses the Noise Subspace instead of the Signal Subspace  to  estimate  the  direction  of  arrival.  The noise is masked by the source signal in the direction of  the  source  and  therefore  equal  zero.  As  a  con-sequence, the reciprocal value of the noise compon-ents  creates  sharp  peaks  in  the  directions  of  the sources [4]. All theoretical existing directions of ar-rival are determined by using a physical model of the acoustic  vector  sensors.  A three-dimensional  array should have a specific response according to the dir-ection of arrival of a plane wave. This particular re-sponse can be characterized by specific amplitude and phase differences between the sensors. The physical model  determines  the  differences  of  amplitude  and phase for all possible directions of arrival.The  corresponding  equation  for  the  plane  wave model is:p = e j2 kx j2ky j2 kz  (3)Beside the plane wave model  the directivity  of  the sensors  have  influence  on  the  amplitude  and  phase differences. In figure (5) the directivity of an acoustic vector sensor is schematically shown.The directivity can be described through the following equations:sx  , = cos coss y  , = cos sinsz  , = sin (4) with   and   as spherical coordinates of the direc-tion and sx,y,z as the directivity of the three sensor ele-ments of the AVS. Combined with equation (3) we get the weights of the sensor elements:w p= exp  j2 sx kx j2 s y ky j2sz kzwx=s xexp  j2s x kx j2 sy ky j2 sz kz w y=s yexp  j2 sx kx j2 s y ky j2 sz kz wz=szexp  j2 sx kx j2 s y ky j2sz kz (5)The Noise Subspace is multiplied with these weights of all possible directions of arrival.Figure 4: The spherical array has a characteristic response to every  possible direction of arrivalFigure 5: Stretched figure of the directivity of an acoustic vector  sensor5. RESULTSIn order to evaluate the quality of the array of  AVS, we compared it in measurements with an array of mi-crophones. We were able do the measurements in the anechoic room of the Delft University of Technology. We used a spherical array of 50 points and the meas-urement setup shown in figure (6).5.1. ArrayAs a result of the simulations described in paragraph (2.), we used a spherical array for the measurements. A spherical array has a specific response according to the direction of arrival of a plane wave. The sensitiv-ity of a spherical array is the same for every direction.5.2. CalibrationThe calibration, described in paragraph (3.), reduces the error of direction from 5°-20° to 0.5°-4°. The im-provement of accuracy is shown in figure (7) and fig-ure (8).The most accurate results could be reached in a frequency range  from 0.7kHz to 1.3kHz . Since re-flections cause disturbance, the measurement were ex-ecuted in an anechoic room.Figure 7: Measured directions of arrival  (top)– black: real directions– grey: measured directionserror: 5° - 20°Figure 8: Calibrated directions of  arrival (top)– black: real directions– grey: calibrated directionserror: 0.5° - 4°Figure 6: Measurement setup of comparison  between pressure based and velocity based  localization1.2mArrayr=0.5m0.64mS2S11.2m5.3. LocalizationThe  comparison  between  pressure  based  array  and AVS based array brought an evident result. We used the same measurement setup for both arrays. Since the AVS include an omnidirectional pressure sensor, we could ensure exact the same array positions. At a fre-quency of 2 kHz the localization with a bartlett beam former causes aliasing (shown in figure(10) and fig-ure(12)). However MUSIC provides at 2 kHz a sharp peak in direction of arrival. The accuracy of the velo-city-based method was higher.6. CONCLUSIONWe can conclude that the number of necessary meas-uring points can be reduced with an AVS array. Of course, one could also increase the limit frequency.The influence of aliasing on MUSIC is much less strong. For the same reason, microphone arrays are much  more  sensitive  against  errors  in  phase  or position.  For  the  correct  estimation  of  direction  of arrival the calibration is essential. On one hand,  using MUSIC  with  correlated  sources  produces  a disappointing  result.  On  the  other  hand,  with  a moderate SNR, MUSIC provides an estimation which other beamformers would only achieve under optimal conditions.  The  combination  of  acoustic  vector sensors and MUSIC offers an appropriate localization method for uncorrelated sources in a broad frequency band.Now we develop  a  mobile  array  based  on  these conclusions.  Another  approach  will  use  the  Signal Subspace  to  weight  the  direction  estimated  by  the Noise  Subspace.  This  way  it  would  be  possible  to determine the strength of the source.Figure 10: Directions of arrival:estimation with a Bartlett beam former at 2 kHz (brightness is proportional to the probability)Figure 11: Result direction of arrival estimation with MUSIC  at 2 kHz (rolled up)0 0−ElevationAzimut−22MUSIC-SpectrumFigure 9: Directions of arrival: estimation with MUSIC at 2 kHz (brightness is  proportional to Spectrum)Figure 12: Result beamforming with a bartlett beam former at 2 kHz (rolled up)−2 Elevation−Azimut0 02Probability7. REFERENCES[1] van Veen, B.D.; Buckley, K.M.; Beamforming: A Versatile  Approach to Spatial  Filtering;  IEEE ASSP Magazine 1988.[2] de  Bree,  H.E.  et  al.;  The  Microflown:  A novel device  measuring  acoustical  flows;  PhD  thesis; University of Twente 1996.[3] Hawkes,  M.;  Nehorai,  A.;  Wideband  Source Localization  Using  a  Distributed  Acoustic  Vector-Sensor  Array;  IEEE  Transactions  on  Signal Processing 2003.[4] Wind,  J.;  Tijs,  E.;  de  Bree,  H.E.;  Source localization using acoustic vector sensors: A MUSIC approach; NOVEM Oxford 2009 [5] Schmidt, R.; Multiple emitter location and signal parameter estimation; IEEE Transactions on Antennas and Propagation, 34(3); 276–280, 1986.

Source localization with acoustic vector sensors

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Source localization with acoustic vector sensors

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