1. 42nd IEEE Conference on Decision and Control, Dec 9-12, 2003
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

2. 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.
“The problem of the whispering gallery”,
Philosophical Magazine, pp , 1910

3. Sound following

4. 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.

5. References
A. A. Handzel and P. S. Krishnaprasad. “Bio-mimetic sound source localization”, IEEE Sensors Journal, 2(6), , 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).

6. Barn Owl and Robot
Can we capture the barn owl’s auditory acuity in a binaural robot?
2 degrees ~ microseconds resolution

7. 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

8. 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

9. Place Theory (L. Jeffress) J. Comp. Physiol. & Psychol
Jeffress model and schematic of brainstem auditory circuits for detection of interaural time (ITD) differences; from Carr & Amagai (1996)

10. Stereausis (S. Shamma et. al.) J. Acoust. Soc. Am. (1989) 86:989-1006
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

11. 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.

12. 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 (θ, φ).
For a sphere, one has to solve the Helmholtz equation.
See section 385 of
The Theory of Sound
Edition

13. Coordinate Systems - Azimuthal q - Polar f - Elevation f - Azimuth
Microphones at poles on horizontal plane

14. Pressure field proportional to
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

15. A representation of HRTF information

16. 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):
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

17. 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.

19. 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.

22. Symmetry and Rotations
- Azimuthal q - Polar
f - Elevation f - Azimuth

23. 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)

27. 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.

28. Pumpkin head side-view (left) and top view (right). Minimum
diameter 19 cm and maximum diameter 22.6 cm.

29. 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.

30. 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.

31. Performance plots for IPD-ILD algorithm (left) and traditional ITD
algorithm (right)

32. 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), , 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
S. B. Andersson, A.A. Handzel, V. Shah and P. S. Krishnaprasad. “Robot phonotaxis with dynamic
sound source localization”, submitted (November 2003).

33. Front Back Demo Without front-back distinction
With front-back distinction