1. Fast Bayesian Acoustic Localization
Stan Birchfield
Daniel Gillmor
Quindi Corporation
Palo Alto, California

2. Principle of Least Commitment
“Delay decisions as long as possible”
[Marr 1982;
Russell & Norvig 1995; etc.]
Example:

3. Localization by Beamforming
mic 1 signal
prefilter
delay
mic 2 signal
prefilter
delay
find peak
q,f
sum
energy
mic 3 signal
prefilter
delay
mic 4 signal
prefilter
delay
[Duraiswami et al. 2001]

4. 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]

5. Localization by Accumulated Correlation
map to common coordinate system
mic 1 signal
prefilter
correlate
mic 2 signal
prefilter
sampled locus
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

6. Bayesian Localization: A Unifying View
Beamform ’
Correlation
(similarity)
(energy)

7. Comparison of V_C and V’_C
(sound generated at t )
(sound heard at t’ )

8. Our Microphone Array Geometry
sampled hemisphere
d=15cm
(Can handle arbitrary geometries)

9. Results: Comparison of Algorithmsq
SNR

10. Results: Comparison of Algorithms
Correlation
Beamform
Farfield
[Birchfield &
Gillmor 2001]

11. Speed Algorithm Running time (ms) per 55 ms window Farfield 5.5
Correlation
6.2
Beamform
4160.1
Bayesian
3968.5

12. Multiple Uncorrelated Sound Sources+ =

13. Noise Localization Model
background noise source

14. Noise Localization Model -- Videos
standard
with noise localization
model subtracted

15. Conclusion Bayesian localization Accumulated correlation
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