Signal Processing - July 2016 - 25

Table 1. An overview of the calibration methods discussed, ordered by scenario and measurement.
Array Shape (S1)

Microphone Configuration (S2)

PD (M1)

*  MDS
- Manual measurements [3]
- Diffuse noise [24], [46]
*  Rank approximation
- Diffuse noise + far-field
microphones [41]

*  NMF
  -  Incomplete + Noisy distance [1]

ToA (M2)

*  BMDS
- Known distances [4]
*  Direct minimization
- Known loudspeaker
configuration [6], [38]

*  Direct minimization
- Known loudspeaker configuration [38]
*  Rank approximation via SVD
- Known emission time [7], [8]
- Impulse train [12]
- Manually labeled handclaps [11]
*  Active devices
- One microphone and event are colocated [35]
- Unsynchronized + MDS [13], [36]

TDoA (M3)

Array Configuration (S3)

*  Direct minimization
  -  No initialization [34]
- Auxiliary function [25]
*  Rank approximation via SVD
- Far-field sources [43]
- Unsynchronized [47]
*  mTDoA
- MDS + speech [26]-[28]

*  Coordinate mapping
- Direct minimization [45]
- Random sampling [14]
- Acoustic camera [37]

DoA (M4)

*  RANSAC
- Random walk + speech [16], [19]
*  Intra-array TDoA
- Fixed speaker positions [32]
- Random walk [39]

Visual support (M5)

*  Audiovisual
- Trajectory mapping [17]
  -  Visual speaker localization [30]
- Joint calibration [18]

methods tends to be lower, but fortunately high enough for
practical applications.

Synchronization
If the clocks of transmitter and receiver are synchronized, PDs can be obtained from ToA measurements.
TDoA measurements require only a synchronization
among the microphones. A further relaxation is possible if only DoA measurements are incorporated. Some
algorithms couple the estimation of the sampling deviation and the calibration process itself [11], [25], [47],
while the mTDoA method elegantly removes a potential
unknown delay [26], [27] (cf. the treatment of timing
difference by the mTDOA approach in the "Unsynchronized Microphones" section).

Experimental evaluation of selected methods
The section "Approaches to Geometry Calibration"
provided an overview about a broad range of geometry

calibration algorithms. The authors of the corresponding
publications evaluate their algorithms usually on their
proprietary data sets, which makes a comparison among
different approaches difficult. This section tries to fill
this gap and provides a comparison under a common
evaluation framework. We conducted experiments for
all three application scenarios, and for each scenario we
evaluated a selection of algorithms in a two-dimensional
calibration experiment in a reverberant laboratory environment. We also did our best to correctly implement
and optimize those algorithms that we have not proposed. We do not claim, however, that we achieved their
best possible performance. Table 2 provides an overview
of the algorithms selected and the scenarios where they
have been applied. In the following, we first describe the
test environment and the performance evaluation metrics used. Afterward, we present the results for each of
the three scenarios. The evaluation is concluded by a
short summary.

IEEE Signal Processing Magazine

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July 2016

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

Signal Processing - July 2016 - Cover1
Signal Processing - July 2016 - Cover2
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