Signal Processing - July 2016 - 27

Microphone configuration calibration (S2)
(cm)

DNC [24]

mTDoA [28]

0.5

ASfS [43]

FIGURE 8. Array shape calibration. The mean position error for tabletop
microphones in a reverberant smart room.

mTDoA [28]

(cm)

∋

Array configuration calibration (S3)

1.5

∋

The microphone configuration calibration performance was
evaluated on all 15 microphones of the three circular arrays.
The mTDoA approach combined with MDS [28] worked for
pairs of microphones from different arrays with a distance of
up to about 1 m. We therefore included it in our evaluation
and compared it to the ASfS approach [43] and the ToA rank
approximation scheme [11].
Figure 9 compares the calibration error of the methods
using either white noise or speech as calibration signals.
The best localization is achieved with mTDoA, resulting in
an RMS error of 4.5 cm ! 1.8 cm using a speech signal,
while 1.3 cm ! 0.7 cm was achieved with noise excitation.
The ASfS approach performed slightly worse with 6.0 cm
! 2.7 cm and 1.8 cm ! 0.8 cm, respectively. Our implementation of the ToA rank scheme did not perform well. This
might be a consequence of the arrangement, since experiments with uniformly distributed microphones performed
significantly better.

ToA Rank [11]

ASfS [43]

0
Noise

Speech

FIGURE 9. Microphone configuration calibration. The mean position error
using either noise or speech as input signals.

For the array configuration calibration, the DoA-TDoA method [31], the DoA + Video method [30], and the DoA + TDoA
scaling approach [19], [39] were used.
The required DoAs were estimated by a neurobiologically inspired method [29], since it is robust to noise and
excludes nonspeech sounds. The event locations were automatically identified as segments with a small angular variance. The error in the DoA angle estimation was around 3°.
The TDoA information was extracted by computation of the
GCC-PHAT.
The TDoAs over all microphone pairs had an error of
around 6 cm. For the multimodal method, visual localization by background subtraction and an upper-body detector
was used [30]. Seven localizations with an accuracy of 20 cm
were derived for the ten detected speech segments. For the
noise sequence, the ground truth positions marked on the floor
where the sounds were produced were used.
The calibration results are shown in Figure 10. All methods achieved an average position error e p of less than 7 cm.
The maximum position error for the DoA-TDoA method was
0.6 cm for noise and 6.0 cm for speech. For the DoA + Video
approach, it was 5 cm for noise and 7 cm for speech. For the
DoA + TDoA scaling method, it was 4 cm for noise and 2.5 cm
for speech. The angular error is close to 1° for all methods,
except for the DoA-TDoA method using speech, where only
3° was achieved.

respectively. This can also be achieved using the ASfS method
[43], with a slightly higher error. We were able to show that
state-of-the-art methods [19], [31] are capable of calibrating
array configurations with an orientation error of well below 5°
and a position error well below 10 cm. This provides sufficient
accuracy for triangulation-based processing algorithms.

Summary

Conclusions and outlook

In our experiments, array calibration could be performed
quite accurately using diffuse noise or mTDoA from multiple
distributed speech events. Below 1-cm precision is close to
the requirements for beamforming. While the diffuse noise
approach is limited to small array sizes, the latter method
also allowed the calibration of distributed microphones on a
table using speech or noise with 10-cm and 3-cm precision,

This article provided a survey of acoustic geometry calibration algorithms, which attempt to reveal the position of microphones solely from the acoustic signals received by them. The
algorithms can be categorized on the basis of such things as
the kind of acoustic signals used, the kind of position-related
measurements employed, the kind of objective function used,
and the necessity of synchronization.

γ (°)

∋

m (cm)

2
1

0
Noise Speech

Noise Speech

DoA + TDoA Scaling [19]
DoA - TDoA [31]
DoA + Video [30]

FIGURE 10. Array configuration calibration. The mean position and orientation error for three DOA-based algorithms.

IEEE Signal Processing Magazine

July 2016

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