Acoustic Localization by Interaural Level Difference

Rajitha Gangishetty

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Acoustic Localization

compactmicrophone

array

sound source

d

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

Issues: reverberation noise

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Overview

• What is Interaural Level Difference (ILD)?

• ILD Formulation• ILD Localization• Simulation Results• Conclusion and Future Work

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Techniques

• Interaural time difference (ITD): relative time shift

ITD

ILD

sound source

microphones

• Interaural level difference (ILD): relative energy level

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

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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]

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

approacheslikelihood function computed by

horizontal and vertical microphone pairs

contour plots of likelihood functions (overlaid and combined)

microphones true location

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ILD Formulation• N microphones and a source signal s(t)

• Signal received by the i th microphone

di = distance from source to the ith microphone = additive white Gaussian noise

• Energy received by i th microphone

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ILD Formulation• 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,

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ILD Formulation• For E1 ≠ E2 the equation becomes

which is a circle with center and radius

In 3D the circle becomes a sphere

• For E1= E2 the equation becomes

which becomes a plane in 3D

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Isocontours for 10log(delta E)

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ILD Localization

• 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

Why multiple microphone pairs?

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Combined Likelihood Approach

• Then the estimate for the energy ratio Then the estimate for the energy ratio at at candidate location candidate location isis

• Define the energy ratio asDefine the energy ratio as

where is the location of the where is the location of the ith microphoneith microphone

• is treated as a Gaussian is treated as a Gaussian random variablerandom variable

• Joint probability from multiple microphoneJoint probability from multiple microphone pairs is computed by combining the pairs is computed by combining the individual log likelihoodsindividual log likelihoods

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

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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.

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Hilbert Transformer

xr[n]Complex Signal x[n]

Hilbert Transformer

h[n]

xr[n]

xi[n]

-j , 0<w<pi

j , -pi<w<0

H(ejw) =

where ‘w’ is the angular frequency

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

In Frequency domain, Xi(ejw) = H(ejw)Xr(ejw)

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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.

Input Square

Square

SumSquare

R oot

H ilbert Speech Envelope

phase splitter

(0 o )

(90o)

(90o)2

(0o)2

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Simulated Room

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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

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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

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Likelihood plots5x5 m room, theta = 45 deg , no noise, no reverberation, d = 2m

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Likelihood plots5x5 m room, theta = 90 deg , SNR = 0db, reflection coefficient = 9, d

= 2m

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Likelihood plots5x5 m room, theta = 0 deg , SNR = 0db, reflection coefficient = 9, d =

1m

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Likelihood plots10x10 m room, theta = 0 deg , SNR = 0db, reflection coefficient = 9, d

= 1m

angle error = 6.5 degrees

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Likelihood plots5x5 m room, theta = 36 deg , SNR = 0db, reflection coefficient = 9, d =

2m

angle error = 9 degrees

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Angle Errors in a 5x5 m room

d = 1m, only noise d = 2m, only noise

d = 1m, only reverberation

d = 2m, only reverberation

0.7 = solid line, blue

0.8 = dotted, red

0.9 = dashed, green

20 dB = solid line, blue

10 dB = dotted, red

0 dB = dashed, green

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

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

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

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

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Comparison of errors with the Hilbert Envelope Approach in a 5x5 m room

0.7

0.8

0.9

20 dB 10 dB 0 dBWithout Hilbert = solid line, blue

Matlab Hilbert = dotted line, red

Kaiser Hilbert = dashed line, green

Reflection coefficient

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

0.7

0.8

0.9

20 dB 10 dB 0 dBWithout Hilbert = solid line, blue

Matlab Hilbert = dotted line, red

Kaiser Hilbert = dashed line, green

Reflection coefficient

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Likelihood plots without Hilbert Envelope

angle error = 27 degrees

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

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Frames approach

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

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

Mean error = 15 deg

Std Dev = 11 deg

Mean error = 7 deg

Std Dev = 6 deg

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Conclusion and Future Work•ILD is an important cue for acoustic localization ILD is an important cue for acoustic localization

• Preliminary results indicate potential for ILD Preliminary results indicate potential for ILD (Algorithm yields accurate results for several (Algorithm yields accurate results for several configurations, even with noise and reverberation) configurations, even with noise and reverberation)

• Future work:Future work:• Investigate issues (e.g., bias toward distantInvestigate issues (e.g., bias toward distant locations, sensitivity to reverberation) locations, sensitivity to reverberation)• Experiment in real environmentsExperiment in real environments• Investigate ILDs in the case of occlusionInvestigate ILDs in the case of occlusion• Combine with ITD to yield more robust resultsCombine with ITD to yield more robust results

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