Fast Bayesian Acoustic Localization

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Fast Bayesian Acoustic Localization

• Stan Birchfield
• Daniel Gillmor
• Quindi Corporation
• Palo Alto, California

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Principle of Least Commitment
Delay decisions as long as possible
Marr 1982 Russell Norvig 1995 etc.
Example
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Localization by Beamforming
mic 1 signal
delay
prefilter
mic 2 signal
delay
prefilter
q,f
find peak
sum
energy
mic 3 signal
delay
prefilter
mic 4 signal
delay
prefilter
Duraiswami et al. 2001
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Localization by Pair-wise TDE
mic 1 signal
decision is made early
prefilter
find peak
correlate
mic 2 signal
prefilter
q,f
intersect
(may be no intersection)
mic 3 signal
prefilter
find peak
correlate
mic 4 signal
prefilter
Brandstein et al. 1995 Brandstein Silverman
1997 Wang Chu 1997
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Localization by Accumulated Correlation
map to common coordinate system
mic 1 signal
prefilter
correlate
sampled locus
mic 2 signal
prefilter
correlate
final sampled locus

correlate
q,f
sum
find peak
correlate
correlate
temporal smoothing
map to common coordinate system
mic 3 signal
prefilter
correlate
mic 4 signal
prefilter
decision is made after combining all the
available evidence
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Bayesian Localization A Unifying View
Bayesian
Beamform
Correlation
(similarity)
(energy)
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Comparison of V_C and V_C
(sound generated at t )
(sound heard at t )
0
0
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Our Microphone Array Geometry
microphone
sampled hemisphere
d15cm
(Can handle arbitrary geometries)
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Results Comparison of Algorithms
f
q
SNR
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Results Comparison of Algorithms
Beamform
Correlation
Farfield
Birchfield Gillmor 2001
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Speed
Algorithm Running time (ms)per 55 ms window
Farfield 5.5
Correlation 6.2
Beamform 4160.1
Bayesian 3968.5
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Multiple Uncorrelated Sound Sources


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Noise Localization Model
background noise source
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Noise Localization Model -- Videos
standard
with noise localization model subtracted
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Conclusion

• Bayesian localization
• follows principle of least commitment
• similar to beamforming (weights energy
  differently)
• Accumulated correlation
• close approximation to Bayesian and beamforming
  similar to TDE
• just as accurate, but 1000 times faster (for
  compact arrays)
• handles multiple sound sources, including
  subtracting constant background noise source