Signal Processing - July 2016 - 26

Table 2. An overview of the methods used in the evaluation.
Array Shape
(S1)

Microphone Configuration
(S2)

Array Configuration
(S3)

DNC + MDS
[24]

ToA rank [11]

DoA + TDoA scaling
[19], [39]

mTDoA + MDS
[28]

mTDoA + MDS [28]

DoA-TDoA [31]

ASfS [43]

DoA + Video [30]

Evaluation setups and metrics
The location was a highly reverberant 3.7 m # 6.8 m # 2.6 m
conference room of a smart house installation at TU Dortmund University. Signals from three circular microphone
arrays that were arranged in an irregular triangle of an
approximate edge size of 1 m were recorded at 48 kHz
(Figure 7). Each array was embedded in the table and consisted of five microphones arranged equidistantly on a circle of radius 5 cm. The signals were captured synchronized.
A reverberation time (T60) of 0.67 seconds was calculated
using a blind estimation algorithm [21]. Five cameras mounted at the ceiling captured the scene at 10 frames/second and
384 × 288 pixel resolution. They have a field of view of
48° × 36°. Acoustic events were produced from ten locations around the table. For the first recording, a smartphone

was held at the same height as the microphones, and a white
noise signal was played back. In the second case, a speaker
was either sitting (four positions) or standing (six positions)
at the table. Consequently, his mouth was approximately 0.4 m
or 0.7 m above the microphones, respectively.
t
As mentioned previously, the estimated geometry M
exhibits an arbitrary translation and rotation with respect
to the true geometry that needs to be removed before an
error can be measured. To this end, a translation vector
t and a rotation matrix R are determined by SVD, such
that the mean location error between the estimated microphone positions after correction and the true microphone
positions is minimized. Therefore the estimated positions
t li = Rm
t i + t, where m
t i repafter correction are given by m
resents the original estimates. The performance measure
for the positions is the root-mean-square (RMS) error
M

ep =

1 / m - ml
i
M i=1 i

(24)

In the case of array configuration calibration, the orientation of the arrays is also an important parameter to estimate.
The estimate has an arbitrary rotation relative to the ground
truth. To compensate for this, an angle d c is determined such
that the deviation of the ground truth from the estimated angles
ct j after rotation by d c is minimal. Then the average orientation error is computed as
M

ec =

1 / c - d - ct .
c
m
M m=1 m

(25)

Since several algorithms solve nonlinear problems and use
random initializations, each experiment is repeated ten times.
The average and standard deviation computed over these runs
is reported.

Microphone array shape calibration (S1)
Microphone
Arrays

FIGURE 7. The recording setup. The conference table is embedded with
three circular microphone arrays.
26

We compare the DNC approach [24] and the mTDoA [28]
algorithm, which both estimate PDs, from which the overall
geometry is inferred by MDS. The comparison includes the
ASfS approach [43], which originally was developed for microphone configuration calibration but can also be employed for
microphone array shape calibration.
The methods achieved a positioning accuracy of 0.3-
1.5 cm for the microphones of the circular array described
above. The overall results for the DNC and mTDoA method were rather similar, while ASfS, which was developed
for microphone configuration calibration problems, performed slightly worse (Figure 8). We observed, though,
that the mTDoA + MDS method does not degrade as
quickly as the DNC approach when the interelement
distance is increased. The DNC approach relies on the
presence of ambient diffuse noise, while the mTDoA
algorithm relies in the presence of sound sources being in
the endfire position of microphone pairs. Either requirement may not always be fulfilled.

IEEE Signal Processing Magazine

July 2016

Table of Contents for the Digital Edition of Signal Processing - July 2016