A Biomimetic Apparatus for Sound Source Localization

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A Biomimetic Apparatus for Sound Source
Localization (A System Identification
Problem from Lord Rayleigh)
Amir A. Handzel¹, Sean B. Andersson², Martha
Gebremichael³
and
P. S. Krishnaprasad
University of Maryland, College Park
Department of Electrical and Computer Engineering
Institute for Systems
Research
42nd IEEE Conference on Decision and Control, Dec
9-12, 2003
¹ Beyond Genomics Inc. ² Division of Engineering
and Applied Sciences, Harvard ³ Microsoft
Research
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Lord Rayleigh
Around 1876, Rayleigh was creating the theory of
sound. He was interested in the physics of sound
propagation and the perception of sound.
1842-1919
The problem of the whispering gallery, Philosoph
ical Magazine, pp 1001-1004, 1910
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Sound following
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Outline
Sound Source Localization
Model-free approaches A model and an
identification problem Ambiguity and determining
elevation References
Demonstration
Thanks to Shihab Shamma for inspiration. Vinay
Shah did recent measurements and demos.
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References

• A. A. Handzel and P. S. Krishnaprasad.
  Bio-mimetic sound source localization, IEEE
  Sensors Journal, 2(6), 607-617, 2002
• A. A. Handzel, S. B. Andersson, M. Gebremichael,
  and P. S. Krishnaprasad. A bio-mimetic apparatus
  for sound source localization, Proc. 42nd IEEE
  Conf. on Decision and Control, December, 2003.
• S. B. Andersson, A.A. Handzel, V. Shah and P. S.
  Krishnaprasad. Robot phonotaxis with dynamic
  sound source localization, submitted (November
  2003).

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Barn Owl and Robot
Can we capture the barn owls auditory acuity in
a binaural robot? 2
degrees microseconds resolution
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Sound Localization in Nature

• Localization spatial aspect of auditory sense
• Sensory organ arrangement
  
• Vision -- spatial topographic
  
• Audition -- tonotopic, transduction
  to sound
• pressure in
  frequency bands
• special computation
  required,
• performed in dedicated brainstem circuits
• and cortex

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Acoustic Cues for Localization

• Binaural/Inter-aural
• Level/Intensity Difference (ILD/IID)
• Time/Phase Difference (ITD/IPD)
• On-set difference/precedence effect
• Monaural spectral-directional filtering by
  Pinna, mostly for elevation

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Place Theory (L. Jeffress)J. Comp. Physiol.
Psychol., (1948) 4135-39
Jeffress model and schematic of brainstem
auditory circuits for detection of interaural
time (ITD) differences from Carr Amagai (1996)
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Stereausis (S. Shamma et. al.)J. Acoust. Soc.
Am. (1989) 86989-1006
AVCN
Ipsi- center contra- lateral lateral
Yj
Characteristic frequency
Ckk 1 Ckk Ckk -1
Xi
Cij
Characteristic frequency
Ipsi-lateral cochlea
AVCN
Sound
Contara- lateral cochlea
or
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Initial Motivation
The above approaches are static, and do not take
account of motion. But psychophysical
experiments inspired by early suggestions of Hans
Wallach (1940), show active horizontal head
rotations improve localization, break inter-aural
symmetry, and thus provide information on
elevation (Perret Noble 1997, Wightman
Kistler 1999). Formulating this as an
identification problem leads to insight and
algorithms. We will show how (head) movement can
be helpful is resolving ambiguities. Applications
arise in guiding a robot towards an acoustic
source. First, for a
model, we turn to Rayleigh.
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Lord Rayleigh and Binaural Perception

• ILD and ITD both needed for azimuth. (What
  about elevation?)

• Rayleigh set up the problem of sound
  propagation around
• an acoustically hard sphere. He introduced
  head-related
• transfer functions (HRTF).
• HRTF computed from sound pressure field
  generated at
• a point on the sphere by a point source
  located at (?, f).
• For a sphere, one has to solve the Helmholtz
  equation.

• See section 385 of
• The Theory of Sound
• Edition

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Coordinate Systems

• - Azimuthal q - Polar
  
• f - Elevation f -
  Azimuth

Microphones at poles on horizontal plane
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Static Solution

• Pressure field proportional to
• Does not depend on azimuthal angle (f)
• Head Related Transfer Function (HRTF)
• Numerical (e.g. FMP), and empirical methods for
  non-spherical heads

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A representation of HRTF information
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Some Related Work on HRTFs
Blauert, J. (1997). Spatial Hearing (Revised
Edition) (MIT Press, Cambridge, MA). C. P.
Brown and R. O. Duda (1998). A structural model
for binaural sound synthesis, IEEE Trans. Speech
and Audio Proc., 6(5)476-488. Duda, R. O.
(1995). Estimating azimuth and elevation from
the interaural head related transfer function,
in Binaural and Spatial Hearing, R. Gilkey and
T. Anderson, Eds. (Lawrence Erlbaum Associates,
Hillsdale, N.J.)
R. O. Duda
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Feature Plane (cylinder) and Signatures

• ILD IPD constitute an intermediate
  computational space for localization.
• At each frequency a source gives rise to a
  point in the ILD-IPD plane (cylinder).
• A (broadband) point source imprints a signature
  curve on this feature plane (cylinder) according
  to its location.

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Symmetry of Static Localization

• Sound pressure and resulting inter-aural
  functions depend only on polar angle
• azimuth invariant -- SO(2) symmetry
• Sources on same circle of directions have
  identical signatures. Hence the localization
  confusion.
• Introduce distance measures.

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Symmetry and Rotations

• - Azimuthal q - Polar
  
• f - Elevation f -
  Azimuth

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Breaking the Symmetry

• Azimuthal invariance, but polar rotations do
  change the localization functions.
• Key mathematical step infinitesimal rotations
  act as derivative operator -- generate vector
  fields on signatures.
• Derivatives modulated by Cos(f) -- thus
  elevation extracted from horizontal rotation!
• (Head movement helps)

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Experimental Results
Broad band source - sum of pure tones 43 Hz 11
KHz in steps of 43Hz. Passed through
anti-aliasing filter and sampled at 22KHz.
Knowles FG-3329 microphones used on head of 22.6
cm maximum diameter. To determine ILD and IPD,
each 512 point segment (23 ms) of data was
passed through an FFT. Measured IPD and ILD
were smoothed by a nine-point moving average.
This yields empirically determined (discrete)
signature curves on ILD-IPD space. Localization
computations based on minimizing distance
functions. Implementation of this step on
mobile robot achieved as a table lookup.
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Pumpkin head side-view (left) and top view
(right). Minimum diameter 19 cm and maximum
diameter 22.6 cm.
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Plot on left displays smoothed ILD against
theoretical ILD for source at 17.5 degrees in
horizontal plane. Plot on right shows smoothed
IPD against theoretical IPD for same source.
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Plot on left shows distance functions for source
at 15 deg and 17.5 deg. Plot on right shows
distance functions for source at 72.5 deg and 75
deg.
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Performance plots for IPD-ILD algorithm (left)
and traditional ITD algorithm (right)
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Implications and Applications

• Psychophysics auditory displays, auditory
  component of virtual environments and hearing
  aids.
• Bio-mimetic active robot head

References A. A. Handzel and
P. S. Krishnaprasad. Bio-mimetic sound source
localization, IEEE Sensors Journal, 2(6),
607-617, 2002 A. A. Handzel, S. B. Andersson, M.
Gebremichael, and P. S. Krishnaprasad. A
bio-mimetic apparatus for sound source
localization, Proc. 42nd IEEE Conf. on Decision
and Control, Dec. 2003. S. B. Andersson, A.A.
Handzel, V. Shah and P. S. Krishnaprasad. Robot
phonotaxis with dynamic sound source
localization, submitted (November 2003).
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Front Back Demo
Without front-back distinction
With front-back distinction