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### Acoustic Localization by Interaural Level Difference

Rajitha Gangishetty

q

sound source

f

compact

microphone

array

Acoustic LocalizationAcoustic Localization: Determining the location of a sound source by comparing the signals received by an array of microphones.

Issues: reverberation noise

Acoustic Localization by ILD

Overview

- What is Interaural Level Difference (ILD)?
- ILD Formulation
- ILD Localization
- Simulation Results
- Conclusion and Future Work

Acoustic Localization by ILD

Interaural time difference (ITD): relative time shift

sound source

microphones

ILD

ITD

Techniques- Interaural level difference (ILD): relative energy level

All previous methods (TDE, beamforming, etc.) use ITD alone.

Acoustic Localization by ILD

Previous Work

- Time Delay Estimation[M. S. Brandstein, H. F. Silverman, ICASSP 1997; P. Svaizer, M. Matassoni, M. Omologo, ICASSP 1997]
- BeamformingJ. L. Flanagan, J.D. Johnston, R. Zahn, JASA 1985;R. Duraiswami, D. Zotkin, L.Davis, ICASSP 2001]
- Accumulated Correlation[Stanley T. Birchfield, EUSIPCO 2004]
- Microphone arrays [Michael S. Brandstein, Harvey F. Silverman, ICASSP 1995; P. Svaizer, M. Matassoni, M. Omologo, ICASSP 1997]
- Hilbert Envelope Approach[David R. Fischell, Cecil H. Coker, ICASSP 1984]

Acoustic Localization by ILD

likelihood function computed by horizontal and vertical microphone pairs

contour plots of likelihood functions

(overlaid and combined)

microphones

true location

A sneak peek at the resultsLikelihood plots, Estimation error, Comparison of different approaches

Acoustic Localization by ILD

N microphones and a source signal s(t)

- Signal received by the i th microphone

di = distance from source to the ithmicrophone

= additive white Gaussian noise

- Energy received by i th microphone

Acoustic Localization by ILD

For 2 mics the relation between energies and distances is

- Given E1 and E2 the sound source lies on a locus of points (a circle or line) described by

where,

ILD FormulationAcoustic Localization by ILD

For E1 ≠ E2 the equation becomes

and radius

which is a circle with center

In 3D the circle becomes a sphere

- For E1= E2 the equation becomes

which becomes a plane in 3D

ILD FormulationAcoustic Localization by ILD

Isocontours for 10log(delta E)

Acoustic Localization by ILD

ILD Localization

Why multiple microphone pairs?

- With only two microphones source is constrained to lie on a curve
- The microphones cannot pinpoint the sound source location
- We use multiple microphone pairs
- The intersection of the curves yield the sound source location

Acoustic Localization by ILD

Combined Likelihood Approach

Localize sound source by computing likelihood at a number of candidate locations:

- Define the energy ratio as

- Then the estimate for the energy ratio at candidate locationis

where is the location of the

ith microphone

- is treated as a Gaussian
- random variable

- Joint probability from multiple microphone
- pairs is computed by combining the
- individual log likelihoods

Acoustic Localization by ILD

Hilbert Transform

- The Hilbert transform returns a complex sequence, from a real data sequence.
- The complex signal x = xr + i*xi has a real part, xr, which is the original data, and an imaginary part, xi, which contains the Hilbert transform.
- The imaginary part is a version of the original real sequence with a 90° phase shift.
- Sines are therefore transformed to cosines and vice versa.

Acoustic Localization by ILD

xr[n]

Complex Signal x[n]

Hilbert Transformer h[n]

xi[n]

-j , 0<w<pi

j , -pi<w<0

where ‘w’ is the angular frequency

H(ejw) =

Hilbert TransformerIn Frequency domain, Xi(ejw) = H(ejw)Xr(ejw)

The Hilbert transformed series has the same amplitude and frequency content as the original real data and includes phase information that depends on the phase of the original data.

Acoustic Localization by ILD

(90o)

(90o)2

Hilbert Envelope Approach- All-pass filter circuit produces two signals with equal amplitude but 90 degrees out of phase.
- Square root of the sum of squares is taken.

Acoustic Localization by ILD

Simulated Room

Acoustic Localization by ILD

Simulation Results

- The algorithm
- Accurately estimates the angle to the sound source in some scenarios
- Exhibits bias toward far locations (unable to reliably estimate the distance to the sound source)
- Is sensitive to noise and reverberation

Acoustic Localization by ILD

Results of delta E Estimation

- The estimation is highly dependent upon the
- sound source location
- amount of reverberation
- amount of noise
- size of the room
- relative positions of source and microphones

Acoustic Localization by ILD

5x5 m room, theta = 45 deg , no noise, no reverberation, d = 2m

Likelihood plotsAcoustic Localization by ILD

5x5 m room, theta = 90 deg , SNR = 0db, reflection coefficient = 9, d = 2m

Likelihood plotsAcoustic Localization by ILD

5x5 m room, theta = 0 deg , SNR = 0db, reflection coefficient = 9, d = 1m

Likelihood plotsAcoustic Localization by ILD

10x10 m room, theta = 0 deg , SNR = 0db, reflection coefficient = 9, d = 1m

angle error = 6.5 degrees

Likelihood plotsAcoustic Localization by ILD

5x5 m room, theta = 36 deg , SNR = 0db, reflection coefficient = 9, d = 2m

angle error = 9 degrees

Likelihood plotsAcoustic Localization by ILD

0.8 = dotted, red

0.9 = dashed, green

20 dB = solid line, blue

10 dB = dotted, red

0 dB = dashed, green

d = 1m, only reverberation

d = 2m, only reverberation

d = 1m, only noise

d = 2m, only noise

Angle Errors in a 5x5 m roomAcoustic Localization by ILD

Angle error in degrees for the 5x5 m room when the source is at a distance of 1m

Angle error in degrees for the 10x10 m room when the source is at a distance of 1m

Acoustic Localization by ILD

Angle error in degrees for the 5x5 m room when the source is at a distance of 2m

Angle error in degrees for the 10x10 m room when the source is at a distance of 2m

Acoustic Localization by ILD

10 dB

0 dB

Without Hilbert = solid line, blue

Matlab Hilbert = dotted line, red

Kaiser Hilbert = dashed line, green

0.7

Reflection coefficient

0.8

0.9

Comparison of errors with the Hilbert Envelope Approach in a 5x5 m roomAcoustic Localization by ILD

Comparison of errors with the Hilbert Envelope Approach in a 10x10 m room

20 dB

10 dB

0 dB

Without Hilbert = solid line, blue

Matlab Hilbert = dotted line, red

Kaiser Hilbert = dashed line, green

0.7

Reflection coefficient

0.8

0.9

Acoustic Localization by ILD

5x5 m room, theta = 18 deg , SNR = 0db, reflection coefficient = 9, d = 2m

angle error = 27 degrees

Likelihood plots without Hilbert EnvelopeAcoustic Localization by ILD

Frames approach

5x5 m room, theta = 18 deg , SNR = 0db, reflection coefficient = 9, d = 2m (left), d = 1m (right)

- Signal divided into 50 frames
- Frame size = 92.8ms
- 50% overlap in each frame

Mean error = 15 deg

Std Dev = 11 deg

Mean error = 7 deg

Std Dev = 6 deg

Acoustic Localization by ILD

Conclusion and Future Work

- ILD is an important cue for acoustic localization
- Preliminary results indicate potential for ILD (Algorithm yields accurate results for several configurations, even with noise and reverberation)
- Future work:
- Investigate issues (e.g., bias toward distant locations, sensitivity to reverberation)
- Experiment in real environments
- Investigate ILDs in the case of occlusion
- Combine with ITD to yield more robust results

Acoustic Localization by ILD

Acoustic Localization by ILD

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