# The LOCATA Challenge:
Acoustic Source Localization and Tracking

Christine Evers, Heinrich W. Löllmann,
Heinrich Mellmann, Alexander Schmidt, Hendrik Barfuss,
Patrick A. Naylor, and Walter Kellermann C. Evers is with the School of
Electronics and Computer Science, University of Southampton, SO17 1BJ, UK
(e-mail: c.evers@soton.ac.uk).H. W. Löllmann, A. Schmidt, H. Barfuss, and W.
Kellermann are with the Chair of Multimedia Communications and Signal
Processing, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen 91058,
Germany (e-mail<EMAIL_ADDRESS>walter.kellermann@fau.de).H.
Mellmann is with the Institut für Informatik, Humboldt-Universität zu Berlin,
Berlin 10099, Germany (e-mail: mellmann@informatik.hu-berlin.de).P. A. Naylor
is with the Dept. Electrical and Electronic Engineering, Imperial College
London, Exhibition Road, SW7 2AZ, UK (e-mail: p.naylor@imperial.ac.uk).The
research leading to these results has received funding from the UK EPSRC
Fellowship grant no. EP/P001017/1 while C. Evers was with the Dept. Electrical
and Electronic Engineering, Imperial College London, UK.

###### Abstract

The ability to localize and track acoustic events is a fundamental
prerequisite for equipping machines with the ability to be aware of and engage
with humans in their surrounding environment. However, in realistic scenarios,
audio signals are adversely affected by reverberation, noise, interference,
and periods of speech inactivity. In dynamic scenarios, where the sources and
microphone platforms may be moving, the signals are additionally affected by
variations in the source-sensor geometries. In practice, approaches to sound
source localization and tracking are often impeded by missing estimates of
active sources, estimation errors, as well as false estimates. The aim of the
LOCAlization and TrAcking (LOCATA) Challenge is an open-access framework for
the objective evaluation and benchmarking of broad classes of algorithms for
sound source localization and tracking. This paper provides a review of
relevant localization and tracking algorithms and, within the context of the
existing literature, a detailed evaluation and dissemination of the LOCATA
submissions. The evaluation highlights achievements in the field, open
challenges, and identifies potential future directions.

###### Index Terms:

Acoustic signal processing, Source localization, Source tracking,
Reverberation.

##  I Introduction

The ability to localize and track acoustic events is a fundamental
prerequisite for equipping machines with awareness of their surrounding
environment. Source localization provides estimates of positional information,
e.g., Directions-of-Arrival or source-sensor distance, of acoustic sources in
scenarios that are either permanently static, or static over finite time
intervals. Source tracking extends source localization to dynamic scenarios by
exploiting ‘memory’ from information acquired in the past in order to infer
the present and predict the future source locations. It is commonly assumed
that the sources can be modelled as point sources.

Situational awareness acquired through source localization and tracking
benefits applications such as beamforming [1, 2, 3], signal extraction based
on Blind Source Separation (BSS) [4, 5, 6, 7], automatic speech recognition
[8], acoustic Simultaneous Localization and Mapping (SLAM) [9, 10], and motion
planning [11], with wide impact on applications in acoustic scene analysis,
including robotics and autonomous systems, smart environments, and hearing
aids.

In realistic acoustic environments, reverberation, background noise,
interference and source inactivity lead to decreased localization accuracy, as
well as missed and false detections of acoustic sources. Furthermore, acoustic
scenes are often dynamic, involving moving sources, e.g., human talkers, and
moving sensors, such as microphone arrays integrated into mobile platforms,
such as drones or humanoid robots. Time-varying source-sensor geometries lead
to continuous changes in the direct-path contributions of sources, requiring
fast updates of localization estimates.

The performance of localization and tracking algorithms is typically evaluated
using simulated data generated by means of the image method [12, 13] or its
variants [14]. Evaluation by real-world data is a crucial requirement to
assess the relevant performance of localization and tracking algorithms.
However, open-access datasets recorded in realistic scenarios and suitable for
objective benchmarking are available only for scenarios involving static
sources, such as loudspeakers, and static microphone array platforms. To
provide such data also for a wide range of dynamic scenarios, and thus foster
reproducible and comparable research in this area, the LOCalization And
TrAcking (LOCATA) challenge provides a novel framework for evaluation and
benchmarking of sound source localization and tracking algorithms, entailing:

  1. 1.

An open-access dataset [15] of recordings from four microphone arrays in
static and dynamic scenarios, completely annotated with the ground-truth
positions and orientations for all sources and sensors, hand-labelled voice
activity information, and close-talking microphone signals as reference.

  2. 2.

An open-source software framework [16] of comprehensive evaluation measures
for performance evaluation.

  3. 3.

Results for all algorithms submitted to the LOCATA challenge for benchmarking
of future contributions.

The LOCATA challenge corpus aims at providing a wide range of scenarios
encountered in acoustic signal processing, with an emphasis on speech sources
in dynamic scenarios. The scenarios represent applications in which machines
should be equipped with the awareness of the surrounding acoustic environment
and the ability to engage with humans, such that the recordings are focused on
human speech sources in the acoustic far-field. All recordings contained in
the corpus were made in a realistic, reverberant acoustic environment in the
presence of ambient noise from a road in front of the building. The recording
equipment was chosen to provide a variety of sensor configurations. The LOCATA
corpus therefore provides recordings from arrays with diverse apertures. All
arrays integrate omnidirectional microphones in a rigid baffle. The majority
of arrays use consumer-type low-cost microphones.

The LOCATA corpus was previously described in [17, 18], and the evaluation
measures were detailed in [19]. This paper provides the following additional
and substantial contributions:

  * •

A concise, yet comprehensive literature review, providing the background and
framing the context of the approaches submitted to the LOCATA challenge.

  * •

A detailed discussion of the benchmark results submitted to the LOCATA
challenge, highlighting achievements, open challenges, and potential future
directions.

This paper is organized as follows: Section II summarizes the scope of the
LOCATA challenge. Section III and Section IV summarize the LOCATA corpus and
challenge tasks. Section V reviews the literature on acoustic source
localization and tracking in the context of the approaches submitted to the
LOCATA challenge. Section VI details and discusses the evaluation measures.
The benchmarked results are presented in Section VII. Conclusions are drawn
and future directions discussed in Section VIII.

##  II Scope of the LOCATA Challenge and Corpus

Evaluation of localization and tracking approaches is often performed in a
two-stage process. In the first stage, microphone signals are generated using
simulated room impulse responses in order to control parameters, such as the
reverberation time, signal-to-noise ratio, or source-sensor geometries. The
second stage validates the findings based on measured impulse responses using
a typically small number of recordings in real acoustic environments.

Since the recording and annotation of data is expensive and time-consuming,
available open-access recordings are typically targeted at specific scenarios,
e.g., for static sources and arrays [20], or for moving sources [21]. For
comparisons of different algorithms across a variety of scenarios, measurement
equipment (notably microphone arrays) should be identical, or at least
equivalent in all scenarios. In addition, annotation with ground-truth should
be based on the same method, especially for assessing tracking performance.

###  II-A Related Challenges & Corpora

Previous challenges related to LOCATA include, e.g., the CHiME challenges [22]
for speech recognition, the ACE challenge [23] for acoustic parameter
estimation, and the REVERB challenge [24] for reverberant speech enhancement.
These challenges provide datasets of the clean speech signals and microphone
recordings across a variety of scenarios, sound sources, and recording
devices. In addition to the audio recordings, accurate ground-truth positional
information of the sound sources and microphone arrays are required for source
localization and tracking in LOCATA.

Available datasets of audio recordings for source localization and tracking
are either limited to a single scenario, or are targeted at audio-visual
tracking. For example, the SMARD dataset [20] provides audio recordings and
the corresponding ground-truth positional information obtained from multiple
microphone arrays and loudspeakers in a low-reverberant room $(T_{60}\approx
0.15$ s). Only a static single-source scenario is considered, involving
microphone arrays and loudspeakers at fixed positions in an acoustically dry
enclosure. The DIRHA corpus [25] provides multichannel recordings for various
static source-sensor scenarios in three realistic, acoustic enclosures.

For dynamic scenarios, corpora targeted at audio-visual tracking, such as the
AV16.3 dataset [21], typically involve multiple moving human talkers. The
RAVEL and CAMIL datasets [26, 27] provide camera and microphone recordings
from a rotating robot head. Annotation of the ground-truth source positions is
typically performed in a semi-automatic manner, where humans label bounding
boxes on small video segments. Therefore, ground-truth source positions are
available only as 2D pixel positions, specified relative to the local frame of
reference of the camera. For evaluation of acoustic source localization and
tracking algorithms, the mapping from the pixel positions to DoA or Cartesian
positions is required. In practice, this mapping is typically unknown and
depends on the specific camera used for the recordings.

For the CLEAR challenge [28], pixel positions were interpolated between
multiple cameras in the environment in order to estimate the Cartesian
positions of the sound sources. The CLEAR challenge provided audio-visual
recordings from seminars and meetings involving moving talkers. In contrast to
LOCATA, which also involves moving microphone arrays, the CLEAR corpus is
based on static arrays only.

Infrared tracking systems are used for accurate ground-truth acquisition in
[29] and by the DREGON dataset [30]. However, the dataset in [29] provides
recordings from only a static, linear microphone array. DREGON is limited to
signals emitted by static loudspeakers. Moreover, the microphone array is
integrated in a drone, whose self-positions are only known from the motor data
and may be affected by drift due to wear of the mechanical parts [31].

##  III LOCATA Challenge Tasks

The scenarios contained in the LOCATA challenge corpus are represented by
multichannel audio recordings and corresponding positional data. The scenarios
were designed to be representative of practical challenges encountered in
human-machine interaction, including variation in orientation, position, and
speed of the microphone arrays as well as the talkers. Audio signals emitted
in enclosed environments are subject to reverberation. Hence, dominant early
reflections often cause false detections of source directions, whilst late
reverberation, as well as ambient noise, can lead to decreased localization
accuracy. Furthermore, temporally sparse or intermittently active sources,
e.g., human speakers, result in missing detections during pauses. Meanwhile,
interference from competing, concurrent sources requires multi-source
localization approaches to ensure that situational awareness can be
maintained. In practice, human talkers are directional and highly spatially
dynamic, since head and body rotations and translations can lead to
significant changes in the talkers’ positions and orientations within short
periods of time. The challenge of localization in dynamic scenarios, involving
both source and sensor motion, is to provide accurate estimates for source-
sensor geometries that vary significantly over short time frames.

TABLE I: LOCATA Challenge Tasks. Array | Static Loudspeakers | Moving Human Talkers
---|---|---
Single | Multiple | Single | Multiple
Fixed | Task 1 | Task 2 | Task 3 | Task 4
Moving | - | - | Task 5 | Task 6

(a) Robot head

(b) DICIT array

(c) Hearing aids on head-torso simulator

Figure 1: Schematics of microphone array geometries of (a) the robot head, (b)
the DICIT array, (c) the hearing aids used for the LOCATA corpus recordings.
Schematics of the Eigenmike can be found in [32].

Therefore, machines must be equipped with sound source localization algorithms
that prove to be robust against reverberation, noise, interference, and
temporal sparsity of sound sources for static as well as time-varying source-
sensor geometries. The scenarios covered by the LOCATA corpus are therefore
aligned with six increasingly challenging tasks, listed in Table I.

The controlled scenarios of Task 1, involving a single, static sound source,
facilitate detailed investigations of the adverse affects of reverberation and
noise on source localization. Crucial insights about the robustness against
interference and overlapping speech from multiple, simultaneously active
sources can be investigated using the static, multi-source scenarios in Task
2. Using the data for Task 3, the impact of source directivity, as well as
head and body rotations for human talkers, can be studied. Task 4 provides the
recordings necessary to address the ambiguities arising in scenarios involving
multiple moving human talkers, such as occlusion and shadowing of crossing
talkers, the resolution of individual speakers, and the identification and
initialization of new speaker tracks, subject to periods of speech inactivity.
The fully dynamic scenarios in Task 5 and Task 6 are designed to bridge the
gap between traditional signal processing applications that typically rely on
static array platforms, and future directions in signal processing,
progressing towards mobile, autonomous systems. Specifically, the data
provides the framework required to identify and tackle challenges such as the
self-localization of arrays [9, 10] and the integration of acoustic data for
motion planning [33].

##  IV LOCATA Data Corpus

###  IV-A Recording Setup

The recordings for the LOCATA data corpus were conducted in the computing
laboratory at the Department of Computer Science at the Humboldt Universität
zu Berlin, which is equipped with the optical tracking system OptiTrack [34].
The room size is $7.1\times 9.8\times 3$ m3 with a reverberation time of about
0.55 s.

####  IV-A1 Microphone Arrays

The following four microphone arrays were used for the recordings (see [18]):

Robot head:

A pseudo-spherical array with 12 microphones integrated into a prototype head
for the humanoid robot NAO (see Fig. 1a), developed as part of the EU-funded
project ‘Embodied Audition for Robots (EARS)’, [35, 36].

Eigenmike:

The Eigenmike by mh acoustics, which is a spherical microphone array equipped
with 32 microphones integrated in a rigid baffle of $84$ mm diameter [32].

Distant talking Interfaces for Control of Interactive TV (DICIT) array:

A planar array providing a horizontal aperture of width 2.24 m, and sampled by
15 microphones, realizing four nested linear uniform sub-arrays (see Fig. 1b)
with inter-microphone distances of 4, 8, 16 and 32 cm respectively (see also
[37]).

Hearing aids:

A pair of non-commercial hearing aids (Siemens Signia, type Pure 7mi) mounted
on a head-torso simulator (HMS II of HeadAcoustics). Each hearing aid (see
Fig. 1c) is equipped with two microphones (Sonion, type 50GC30-MP2) with an
inter-microphone distance of $9$ mm. The Euclidean distance between the
hearing aids at the left and right ear of the head-torso simulator is $157$
mm.

The array geometries were selected to sample the diversity of commonly used
arrays in a meaningful and representative way. The multichannel audio
recordings were performed with a sampling rate of $48$ kHz and synchronized
with the ground-truth positional data acquired by the OptiTrack system (see
Section IV-C). A detailed description of the array geometries and recording
conditions is provided by [18].

###  IV-B Speech Material

For Tasks 1 and 2, involving static sound sources, anechoic utterances from
the Centre for Speech Technology Research (CSTR) Voice Cloning ToolKit (VCTK)
dataset [38] were played back at $48$ kHz sampling rate using Genelec 1029A &
8020C loudspeakers. For Tasks 3 to 6, involving moving sound sources, 5 non-
native human talkers read randomly selected sentences from the CSTR VCTK
dataset. The talkers were equipped with a DPA d:screet SC4060 microphone near
their mouth, such that the close-talking speech signals were recorded. The
anechoic and close-talking speech signals were provided to participants as
part of the development dataset, but were excluded from the evaluation
dataset.

###  IV-C Ground-Truth Positional Data

For the recordings, a $4\times 6$ m2 area was chosen within the $7.1\times
9.8\times 3$ m3 room. Along the perimeter of the recording area, $10$
synchronized and calibrated Infra-Red (IR) OptiTrack Flex 13 cameras were
installed. Groups of reflective markers, detectable by the IR sensors, were
attached to each source (i.e., loudspeaker or human talker) and microphone
array. Each group of markers was arranged with a unique, asymmetric geometry,
allowing the OptiTrack system to identify, disambiguate, and determine the
orientation of all sources and arrays.

The OptiTrack system provided estimates of each marker position with
approximately $1$ mm accuracy [34] and at a frame rate of $120$ Hz by
multilateration using the IR cameras. Isolated outliers of the marker position
estimates, caused by visual occlusions and reflections of the IR signals off
surfaces, were handled in a post-processing stage that reconstructed missing
estimates and interpolated false estimates. Details about the experimental
setup are provided in [18].

Audio data was recorded in a block-wise manner and each data block was labeled
with a time stamp generated by the global system time of the recording
computer. On the the same computer, positional data provided by the OptiTrack
system was recorded in parallel. Every position sample was labeled with a time
stamp. After each recording was finished, the audio and positional data were
synchronized using the time stamps.

For DoA estimation, local reference frames were specified relative to each
array centre as detailed in [18]. For convenient transformations of the source
coordinates between the global and local reference frames, the corpus provides
the translation vectors and rotation matrices for all arrays for each time
stamp. Source DoA are defined within each array’s local reference frame.

###  IV-D Voice Activity Labels

The Voice-Active Periods for the recordings of the LOCATA datasets were
determined manually using the source signals, i.e., the signals emitted by the
loudspeakers (Task 1 and 2) and the close-talking microphone signals (Tasks 3
to 6). The VAP labels for the signals recorded at the distant microphone
arrays were obtained from the VAP labels for the source signals by accounting
for the sound propagation delay between each source and the microphone array
as well as the processing delay required to perform the recordings. The
propagation delay was determined using the ground-truth positional data. The
processing delay was estimated based on the cross-correlation between the
source and recorded signals.

The ground-truth VAP labels were provided to the participants of the challenge
as part of the development dataset but were excluded from the evaluation
dataset.

##  V Localization Scenarios, Methods and Submissions

TABLE II: Summary of localization and tracking frameworks submitted to the LOCATA challenge. ID | Details | Tasks | VAD | Localization | Tracking | Arrays
---|---|---|---|---|---|---
Algorithm | Section | Algorithm | Section
1 | [39] | 1 | - | LDA classification | V-B2 | - | - | Hearing Aids
2 | [40] | 4 | - | MUSIC | V-B1 |  |  | Robot Head
Particle PHD filter | V-C2 | DICIT
\+ Particle Flow |  | Hearing Aids
|  | Eigenmike
3 | [41] | 1,3,5 | - | GCC-PHAT | V-A1 | Particle filter | V-C1 | DICIT
4 | [42] | 1-6 | Variational EM | Direct-path RTF + | V-A1 | Variational EM | V-C2 | Robot Head
GMM |  |
6 | [43] | 1,3,5 | - | SRP-PHAT | V-A3 | - | - | Eigenmike
| Robot Head
7 | [44] | 1,3,5 | CPSD trace | SRP Beamformer | V-A3 | Kalman filter | V-C1 | DICIT
8 | [45] | 1,3,5 | - | TDE using IPDs |  V-A1, V-A2 | Wrapped Kalman filter | V-C1 | Hearing Aids
9 | [46] | 1 | - | DNN | V-B2 | - | - | DICIT
10 | [47] | 1-4 | Noise PSD | PIVs from | V-A4 | Particle filter | V-C1 | Eigenmike
first-order ambisonics
11 | [48] | 1,2 | - | DPD-Test + MUSIC | V-B1 | - | - | Robot Head
12 | [48] | 1,2 | - | DPD-Test + |  V-B1, | - | - | Eigenmike
MUSIC in SH-domain | V-A4
13 | [49] | 1,3 | Zero-crossing rate | MUSIC (SVD) | V-B1 | Kalman filter | V-C1 | DICIT
14 | [49] | 1,3 | Zero-crossing rate | MUSIC (GEVD) | V-B1 | Kalman filter | V-C1 | DICIT
15 | [50] | 1 | Baseline [51] | Subspace PIV |  V-A4, V-B1 | - | - | Eigenmike
16 | [50] | 2 | Baseline [51] | Subspace PIV + | V-A4, V-B1 | - | - | Eigenmike
Peak Picking

Localization systems process the microphone signals either as one batch for
offline applications and static source-sensor geometries, or using a sliding
window of samples for dynamic scenes. For each window, the instantaneous
estimates of the source positions are estimated either directly from the
signals, or using spatial cues inferred from the data, such as Time Delay of
Arrivals. To avoid spatial aliasing, nearby microphone pairs or compact arrays
are typically used for localization. A few approaches are available to range
estimation for acoustic sources, e.g., by exploiting the spatio-temporal
diversity of a moving microphone array [10, 52], or by exploiting
characteristics of the room acoustics [53, 54]. Nevertheless, in general, it
is typically difficult to obtain reliable range estimates using static arrays.
As such, the majority of source localization approaches focus on the
estimation of the source DoA, rather than the three-dimensional positions. In
the following, the term ‘source localization’ will be used synonymously with
DoA estimation unless otherwise stated.

Due to reverberation, noise, and non-stationarity of the source signals, the
position estimates at the output of the localization system are affected by
false, missing and spurious estimates, as well as localization errors. Source
tracking approaches incorporate spatial information inferred from past
observations by applying spatio-temporal models of the source dynamics to
obtain smoothed estimates of the source _trajectories_ from the instantaneous
DoA estimates presented by the localization system.111We note that, within the
context of the LOCATA challenge, the following discussion focuses on speech,
i.e., non-stationary wideband signals corresponding to energy that is
concentrated in the lower acoustic frequency bands.

This section provides the background and context for the approaches submitted
to the LOCATA challenge so that the submissions can be related to each other
and the existing literature in the broad area of acoustic source localization
(see Table II and Fig. 2). As such, it does not claim the technical depth of
surveys like those specifically targeted at sound source localization for
robotics, or acoustic sensor networks, e.g., [55, 56, 57]. The structure of
the review is aligned with the LOCATA challenge tasks as detailed in Section
III. Details of each submitted approach are provided in the corresponding
LOCATA proceedings paper, provided in the references below. Among the 16
submissions to LOCATA, 15 were sufficiently well documented to allow
consideration in this paper. 11 were submitted from academic research
institutions, 2 from industry, and 2 were collaborations between academia and
industry. The global scope of the challenge is reflected by the geographic
diversity of the submissions originating from the Asia (3 submissions), Middle
East (2 submissions) and Europe (10 submissions).

Figure 2: Submissions to the LOCATA Challenge, ordered by Challenge Task (see
Table I). Numbers indicate the submission ID. White shade: approaches
incorporating source localization only. Grey shade: Approaches incorporating
source localization and tracking.

###  V-A Single-Source Localization

The following provides a review of approaches for localization of a single,
static source, such as a loudspeaker.

####  V-A1 Time Delay Estimation

If sufficient characteristics of a source signal are known _a priori_ , the
time delay between the received signals obtained at spatially diverse
microphone positions can be estimated and exploited to triangulate the
position of the emitting sound source. Time Delay Estimation (TDE) effectively
maximizes the ‘synchrony’ [58] between time-shifted microphone outputs in
order to identify the source position. A brief summary of TDE techniques is
provided in the following. Details and references can be found in, e.g., [3,
Chap. 9].

The TDoA, $\tau_{m,\ell}({\mathbf{x}}_{s})$, of a signal emitted from source
position, ${\mathbf{x}}_{s}$, between two microphones, $m$ and $\ell$, at
positions ${\mathbf{x}}_{m}$ and ${\mathbf{x}}_{\ell}$, respectively, is given
by:

$\displaystyle\tau_{m,\ell}({\mathbf{x}}_{s})\triangleq\frac{f_{s}}{c}\left(\|{\mathbf{x}}_{s}-{\mathbf{x}}_{m}\|-\|{\mathbf{x}}_{s}-{\mathbf{x}}_{\ell}\|\right),$
(1)

where $f_{s}$ is the sampling frequency, $c$ is the speed of sound, and
$\|\cdot\|$ denotes the Euclidean norm. If the source signal corresponds to
white Gaussian noise and is emitted in an anechoic environment, the TDoA
between two microphones can be obtained by identifying the peaks in the cross-
correlation between microphone pairs. Since speech signals are often nearly
periodic for short intervals, the cross-correlation may exhibit spurious peaks
that do not correspond to spatial correlations. The cross-correlation is
therefore typically generalized to include a weighting function in the
Discrete-Time Fourier Transform (DTFT) domain that causes a phase transform to
pre-whiten the correlated speech signals, an approach referred to as
Generalized Cross-Correlation (GCC)- PHAse Transform (PHAT). The GCC,
$R_{m,\ell}(\tau)$, is defined as:

$\displaystyle
R_{m,\ell}(\tau)\triangleq\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}\phi_{m,\ell}(e^{\jmath\,\omega})\,S_{m}(e^{\jmath\,\omega})\,S_{\ell}^{\ast}(e^{\jmath\,\omega})\,e^{\jmath\,\omega\,\tau}d\omega,$
(2)

where $S_{m}(e^{\jmath\,\omega})$ denotes the DTFT of the received signal,
$s_{m}$, at microphone $m$, and $\ast$ denotes the complex conjugate. The PHAT
corresponds to a weighting function, $\phi_{m,\ell}(e^{\jmath\,\omega})$, of
the GCC, where

$\displaystyle\phi_{m,\ell}(e^{\jmath\,\omega})\triangleq|S_{m}(e^{\jmath\,\omega})\,S_{\ell}^{\ast}(e^{\jmath\,\omega})|^{-1}.$
(3)

The signal models underpinning the GCC as well as its alternatives rely on a
free-field propagation model of the sound waves. Therefore, in reverberant
environments, spectral distortions and temporal correlations due to sound
reflections often lead to spurious peaks in the GCC function. The presence of
multiple, simultaneously active sources can cause severe ambiguities in the
distinction of peaks due to the direct path of sources from peaks arising due
to reflections.

To explicitly model the reverberant channel, the fact that the Time-of-Arrival
(ToA) of the direct-path signal from a source impinging on a microphone
corresponds to a dominant peak in the Acoustic Impulse Response (AIR) can be
exploited. The EVD [59], realized by, e.g., the gradient-descent constrained
Least-Mean-Square (LMS) algorithm, can be applied for estimation of the early
part of the relative impulse response. The work in [60] extracts the TDoA as
the main peak in the relative impulse response corresponding to the Relative
Transfer Function (RTF) [61] for improved robustness against reverberation and
stationary noise. The concept of RTFs was also used in [62] for a supervised
learning approach for TDoA estimation.

For localization, it is often desirable to estimate the source directions from
TDoA estimates, e.g., using multi-dimensional lookup tables [63], by
triangulation using Least Squares (LS) optimization if the array geometry is
known _a priori_ [64, 65], or by triangulation based on the intersection of
interhyperboloidal spatial regions formed by the TDoA estimates, e.g., [66,
67].

The following single-source tracking approaches were submitted to the LOCATA
challenge:

ID 3 [41]

combines TDE for localization with a particle filter (see Section V-C1) for
tracking using the DICIT array for the single-source Tasks 1, 3 and 5.

ID 4 [42]

combines DoA estimation using the direct-path RTF approach in [62] with a
variational Expectation-Maximization (EM) algorithm [68] (see Section V-C2)
for multi-source tracking using the robot head for all Tasks.

ID 8 [45]

combines TDE (see Section V-A1) with binaural features (see Section V-A2) for
localization and applies a wrapped Kalman filter [69] for source tracking
using the hearing aids in the single-source Tasks 1, 3 and 5.

####  V-A2 Binaural Localization

The Head-Related Transfer Functions [70] at a listener’s ears encapsulate
spatial cues about the relative source position including Interaural Level
Differences, Interaural Phase Differences, and Interaural Time Differences
[71, 72, 73], equivalent to TDoAs, and are used for source localization in,
e.g., [74, 75, 76, 77, 78].

Sources positioned on the ‘cone of confusion’ lead to ambiguous binaural cues
that cannot distinguish between sources in the frontal and rear hemisphere of
the head [79, 80]. Human subjects resolve front-back ambiguities by movements
of either their head [81, 82, 83] or the source controlled by the subject [84,
85]. Changes in ITDs due to head movements are more significant for accurate
localization than changes in ILDs [86]. In [87], the head motion is therefore
exploited to resolve front-back ambiguity for localization algorithms. In
[88], the attenuation effect of an artificial pinna attached to a spherical
robot head is exploited in order to identify level differences between signals
arriving from the frontal and rear hemisphere of the robot.

The following binaural localization approaches were submitted to the LOCATA
challenge:

ID 8 [45]

combines TDE (see Section V-A1) with IPDs for localization and apply a wrapped
Kalman filter [69] (see Section V-C1) for source tracking using the hearing
aids in the single-source Tasks 1, 3 and 5.

####  V-A3 Beamforming and Spotforming

Beamforming and spotforming techniques can be applied directly to the raw
sensor signals in order to ‘scan’ the acoustic environment for positions
corresponding to significant sound intensity [89, 90, 91, 92]. In [93], a beam
is steered in each direction corresponding to a grid, $\mathcal{X}$, of
discrete candidate directions. Hence, the Steered Response Power (SRP),
$P_{\text{SRP}}({\mathbf{x}}_{s})$, is:

$\displaystyle P_{\text{SRP}}({\mathbf{x}})$
$\displaystyle=\sum\limits_{m=1}^{M}\sum\limits_{\ell=1}^{M}R_{m,\ell}(\tau_{m,\ell}({\mathbf{x}}_{s})),$
(4a)

where $M$ is the number of microphones. An estimate, $\hat{{\mathbf{x}}}_{s}$,
of the source positions is obtained as:

$\displaystyle\hat{{\mathbf{x}}}_{s}$
$\displaystyle=\operatornamewithlimits{arg\,max}_{{\mathbf{x}}\in\mathcal{X}}P_{\text{SRP}}({\mathbf{x}}).$
(5)

Similar to GCC, SRP relies on uncorrelated source signals and, hence, may
exhibit spurious peaks when evaluated for speech signals. Therefore, SRP-PHAT
[94] applies PHAT for pre-whitening of SRP.

The following beamforming approaches were submitted to the LOCATA challenge:

ID 6 [43]

applies SRP-PHAT for the single-source Tasks 1, 3, and 5 using the robot head
and the Eigenmike.

ID 7 [44]

combines diagonal unloading beamforming [95] for localization with a Kalman
filter (see Section V-C1) for source tracking using a 7-microphone linear
subarray of the DICIT array for the single-source Tasks 1, 3 and 5.

####  V-A4 Spherical Microphone Arrays

Spherical microphone arrays [96] sample the soundfield in three dimensions
using microphones that are distributed on the surface of a spherical and
typically rigid baffle. The spherical geometry of the array elements
facilitates efficient computation based on an orthonormal wavefield
decomposition. The response of a spherical microphone array can be described
using spherical harmonics [97]. Equivalent to the Fourier series for circular
functions, the spherical harmonics form a set of orthonormal basis functions
that can be used to represent functions on the surface of a sphere. The sound
pressure impinging from the direction,
$\boldsymbol{{\mathrm{\Omega}}}=\begin{bmatrix}\theta,\phi\end{bmatrix}^{T}$,
on the surface a spherical baffle with radius, $r$, from plane wave with unit
amplitude and emitted from the source DoA,
$\boldsymbol{{\mathrm{\Phi}}}_{s}=\begin{bmatrix}\theta_{s},\phi_{s}\end{bmatrix}^{T}$,
with elevation, $\theta_{s}$, and azimuth, $\phi_{s}$, is given by [98]:

$\displaystyle f_{nm}(k,r,\boldsymbol{\Omega})$
$\displaystyle=\sum\limits_{n=0}^{\infty}\sum\limits_{m=-n}^{n}b_{n}(kr)\,\left(Y_{n}^{m}(\boldsymbol{\Phi})\right)^{\ast}\,Y_{n}^{m}(\boldsymbol{\Omega}),$
(6)

where $k$ is the wavenumber, the weights, $b_{n}(\cdot)$, are available for
many array configurations, and $Y_{n}^{m}(\cdot)$ denotes the spherical
harmonic of order $n$ and degree $m$.

Therefore, existing approaches to source localization can be extended to the
signals in the domain of spherical harmonics. A Minimum Variance
Distortionless Response (MVDR) beamformer [2] is applied for near-field
localization in the domain of spherical harmonics in [99]. The work in [14,
100] proposes a ‘pseudo-intensity vector‘ approach that steers a dipole
beamformer along the three principal axes of the coordinate system in order to
approximate the sound intensity using the spherical harmonics coefficients
obtained from the signals acquired from a spherical microphone array.

The following approaches, targeted at spherical microphone arrays, were
submitted to the LOCATA challenge:

ID 10 [47]

combines localization using the first-order ambisonics configuration of the
Eigenmike with a particle filter (see Section V-C1) for Tasks 1-4.

ID 12 [48]

extends MUltiple SIgnal Classification (MUSIC) (see Section V-B) to processing
in the domain of spherical harmonics of the Eigenmike signals for Tasks 1 and
2.

ID 15 [50]

applies the subspace pseudo-intensity approach in [101] to the Eigenmike
signals in the static-source Task 1.

ID 16 [50]

extends the approach of ID 15 for the static multi-source Task 2 by
incorporating source counting.

###  V-B Multi-Source Localization

This subsection reviews multi-source localization approaches. Beyond the
algorithms submitted to the LOCATA challenge, approaches based on, e.g., blind
source separation [102, 103, 104, 105] can be used for multi-source
localization.

####  V-B1 Subspace Techniques

Since spatial cues inferred from the received signals may not be sufficient to
resolve between multiple, simultaneously active sources, subspace-based
localization techniques rely on diversity between the different sources.
Specifically, assuming that the sources are uncorrelated, subspace-based
techniques, such as MUSIC [106] or Estimation of Signal Parameters via
Rotational Invariance Techniques (ESPRIT) [107, 108, 109] resolve between
temporally overlapping signals by mapping the received signal mixture to a
space where the source signals lie on orthogonal manifolds.

MUSIC [106] exploits the subspace linked to the largest eigenvalues of the
correlation matrix to estimate the locations of $N$ sources. The fundamental
assumption is that the correlation matrix, $\boldsymbol{{\mathrm{R}}}$, of the
received signals can be decomposed, e.g., using Singular Value Decomposition
(SVD) [110], into a signal subspace,
$\boldsymbol{{\mathrm{U}}}_{s}=\begin{bmatrix}\boldsymbol{{\mathrm{U}}}_{s}^{1}\,\dots,\boldsymbol{{\mathrm{U}}}_{s}^{N}\end{bmatrix}$,
consisting of $N$ uncorrelated plane-wave signals,
$\boldsymbol{{\mathrm{U}}}_{s}^{n}$ for $n\in\\{1,\dots,N\\}$, and an
orthogonal noise subspace. The spatial spectrum from direction,
$\boldsymbol{{\mathrm{\Omega}}}$, for plane wave, $n\in\\{1,\dots,N\\}$, is:

$\displaystyle P_{\text{MUSIC}}(\boldsymbol{{\mathrm{\Omega}}})$
$\displaystyle=\left({\mathbf{v}}^{T}(\boldsymbol{{\mathrm{\Omega}}})\left(\boldsymbol{{\mathrm{I}}}-\boldsymbol{{\mathrm{U}}}_{s}^{n}\,(\boldsymbol{{\mathrm{U}}}_{s}^{n})^{H}\right){\mathbf{v}}^{\ast}(\boldsymbol{{\mathrm{\Omega}}})\right)^{-1},$
(7)

where $H$ denotes the Hermitian transpose, $\boldsymbol{{\mathrm{I}}}$ denotes
the identity matrix, and ${\mathbf{v}}$ corresponds to the steering vector.
MUSIC extensions to broadband signals, such as speech, can be found in, e.g.,
[111, 63]. However, the processing of correlated sources remains challenging
since highly correlated sources correspond to a rank-deficient correlation
matrix, such that the signal and noise space cannot be separated effectively.
This is particularly problematic in realistic acoustic environments, since
reverberation corresponds to a convolutive process, in contrast to the
additive noise model underpinning MUSIC.

For improved robustness in reverberant conditions, [112] introduce a ‘direct-
path dominance’ test. The test retains only the time-frequency bins that
exhibit contributions of a single source, i.e., whose spatial correlation
matrix corresponds to a rank-1 matrix, hence reducing the effects of temporal
smearing and spectral correlation induced by reverberation. For improved
computational efficiency, [101] replaces MUSIC with the pseudo-intensity
approach in [100].

The following subspace-based localization approaches were submitted to the
LOCATA challenge:

ID 2 [40]

utilizes DoA estimates from MUSIC as inputs to a Probability Hypothesis
Density (PHD) filter [113, 114] (see Section V-C2) for Task 4, evaluated for
all four arrays.

ID 11 [48]

utilizes the direct-path dominance test [112] and MUSIC in the Short-Time
Fourier Transform (STFT) domain for the robot head signals for static-source
Tasks 1 and 2.

ID 12 [48]

extends the approach of ID 11 to processing in the domain of spherical
harmonics (see Section V-A4) of the Eigenmike signals for Tasks 1 and 2.

ID 13 [49]

applies MUSIC for localization and a Kalman filter (see Section V-C1) for
tracking to single-source Tasks 1 and 3 using the robot head and the
Eigenmike.

ID 14 [49]

extends the approach of ID 13 to apply the Generalized  (GEVD) to MUSIC.

ID 15 and 16 [50]

apply the subspace pseudo-intensity approach in [101] (see Section V-A4) to
the Eigenmike signals in Tasks 1 and 2, respectively.

####  V-B2 Supervised Learning and Neural Networks

Data-driven approaches can be used to exploit prior information available from
large-scale datasets. The work in [115] assumes that frequency-dependent ILD
and IPD values are located on a locally linear manifold. In a supervised
learning approach, the mapping between the binaural cues and the source
locations is learnt from annotated data using a probabilistic piecewise affine
regression model. A semi-supervised approach is proposed in [116] that uses
RTF values input features in order to learn the source locations based on
manifold regularization.

To avoid the efforts for hand-crafted signal models, neural network-based
(’deep’) learning approaches can also be applied to sound source localization.
Previous approaches use hand-crafted input vectors including established
localization parameters such as GCC [117, 118], eigenvectors of the spatial
coherence matrix [119, 120] or ILDs and cross-correlation function in [121].
TDoAs were used in, e.g., [122, 123], to reduce the adverse affects of
reverberation. End-to-end learning for given acoustic environments uses either
the time-domain signals or the STFT-domain signals only as the input for the
network. In [124], the DoA of a single desired source from a mixture of the
desired source and an interferer is estimated by a Deep Neural Network (DNN)
with separate models for the desired source and the interferer. In [125], DoA
estimation is considered as a multi-label classification problem, where the
range of candidate DoA values is divided into small sectors, each sector
representing one class.

The following approaches were submitted to LOCATA:

ID 1 [39]

proposes a classifier based on linear discriminant analysis and trained using
features based on the amplitude modulation spectrum of the hearing aid signals
for Task 1.

ID 9 [46]

uses a DNN regression model for localization of the source DoA for Task 1
using four microphone signals of the DICIT array.

###  V-C Tracking of Moving Sources

Source localization approaches provide instantaneous estimates of the source
DoA, independent of information acquired from past observations. The DoA
estimates are typically unlabelled and cannot be easily associated with
estimates from the past. In order to obtain smoothed source trajectories from
the noisy DoA estimates, tracking algorithms apply a two-stage process that
a) predicts potential future source locations based on past information, and
b) corrects the localized estimates by trading off the uncertainty in the
prediction against the estimation error of the localization system.

####  V-C1 Single-Source Tracking

Tracking algorithms based on Bayesian inference aim to estimate the marginal
posterior Probability Density Function (pdf) of the current state of the
source, conditional on the full history of observations. In the context of
acoustic tracking, the source state often corresponds to either the Cartesian
source position, ${\mathbf{x}}(t)$, or the DoA,
$\boldsymbol{{\mathrm{\Phi}}}(t)$, at time stamp, $t$. The state may also
contain the source velocity and acceleration. The observations correspond to
estimates of either the source position, ${\mathbf{y}}(t)$, TDoAs,
$\tau_{m,\ell}({\mathbf{x}}(t))$, or DoA, $\boldsymbol{\omega}(t)$ provided by
the localization system. Assuming a first-order Markov chain and observations
in the form of DoA, the posterior pdf can be expressed as:

$\displaystyle\begin{split}&p\left(\left.\boldsymbol{{\mathrm{\Phi}}}(0:t^{\prime})\,\right|\,\boldsymbol{\omega}(1:t^{\prime})\right)\\\
&=p\left(\boldsymbol{{\mathrm{\Phi}}}(0)\right)\,\prod\limits_{t=1}^{t^{\prime}}p\left(\left.\boldsymbol{{\mathrm{\Phi}}}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(0:t-1),\boldsymbol{\omega}(1:t)\right),\end{split}$
(8)

where
$\boldsymbol{{\mathrm{\Phi}}}(0:t^{\prime})\triangleq\begin{bmatrix}\boldsymbol{{\mathrm{\Phi}}}^{T}(0),\dots,\boldsymbol{{\mathrm{\Phi}}}^{T}(t^{\prime})\end{bmatrix}^{T}$.
Using Bayes’s theorem:

$\displaystyle\begin{split}&p\left(\left.\boldsymbol{{\mathrm{\Phi}}}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(0:t-1),\boldsymbol{\omega}(1:t)\right)\\\
&=\frac{p\left(\left.\boldsymbol{\omega}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(t)\right)\,p\left(\left.\boldsymbol{{\mathrm{\Phi}}}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(t-1)\right)}{\int\limits_{{\mathcal{P}}}p\left(\left.\boldsymbol{\omega}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(t)\right)\,p\left(\left.\boldsymbol{{\mathrm{\Phi}}}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(t-1)\right)d\boldsymbol{{\mathrm{\Phi}}}(t)},\end{split}$
(9)

where
$p\left(\left.\boldsymbol{\omega}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(t)\right)$
is the likelihood function,
$p\left(\left.\boldsymbol{{\mathrm{\Phi}}}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(t-1)\right)$
is the prior pdf, determined using a dynamical model, and ${\mathcal{P}}$ is
the support of $\boldsymbol{{\mathrm{\Phi}}}(t)$. For online processing, it is
often desirable to estimate sequentially the filtering density,
$p\left(\left.\boldsymbol{{\mathrm{\Phi}}}(t)\,\right|\,\boldsymbol{\omega}(1:t)\right)$,
instead of (9). For linear Gaussian state spaces [126], where the dynamical
model and the likelihood function correspond to normal distributions, the
filtering density reduces to a Kalman filter [127, 128].

However, the state space models used for acoustic tracking are typically non-
linear and/or non-Gaussian [10, 53]. For example, in [129, 130], the
trajectory of Cartesian source positions is estimated from the TDoA estimates.
Since the relationship between a source position and the corresponding TDoAs
is non-linear, the integral in (9) is analytically intractable. The particle
filter is a widely used sequential Monte Carlo method [131] that approximates
the intractable posterior pdf by importance sampling of a large number of
random variates, $\\{\boldsymbol{\hat{\phi}}^{(i)}(t)\\}_{i=1}^{I}$, - or
‘particles’ -, from a proposal distribution,
$g\left(\left.\boldsymbol{{\mathrm{\Phi}}}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(0:t-1),\boldsymbol{\omega}(1:t)\right)$,
i.e.,

$\displaystyle
p\left(\left.\boldsymbol{{\mathrm{\Phi}}}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(0:t-1),\boldsymbol{\omega}(1:t)\right)\approx\sum\limits_{i=1}^{I}w^{(i)}(t)\,\delta_{\hat{\boldsymbol{{\mathrm{\Phi}}}}^{(i)}(t)}(\boldsymbol{{\mathrm{\Phi}}}(t)),$
(10)

where $\delta$ denotes the Dirac measure, and the importance weights,
$w^{(i)}(t)$, are given by:

$\displaystyle\begin{split}&w^{(i)}(t)=w^{(i)}(t-1)\,\frac{p\left(\left.\boldsymbol{\omega}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(t)\right)\,p\left(\left.\boldsymbol{{\mathrm{\Phi}}}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(t-1)\right)}{g\left(\left.\boldsymbol{{\mathrm{\Phi}}}(t)\,\right|\,\boldsymbol{{\mathrm{\Phi}}}(0:t-1),\boldsymbol{\omega}(1:t)\right)}.\end{split}$
(11)

The authors of [129, 130] rely on prior importance sampling [132] from the
prior pdf. Each resulting particle is assigned a probabilistic weight,
evaluated using the likelihood function of the TDoAs estimates. The work in
[133] uses the SRP function instead of TDoA estimates as observations. Rao-
Blackwellized particle filters [134] are applied in [135, 136] instead of
prior importance sampling. Resampling algorithms [137, 138, 139, 140, 141]
ensure that only stochastically relevant particles are retained and propagated
in time.

The tracking accuracy is highly dependent on the specific algorithm used for
localization. Moreover, tracking approaches that rely on TDoA estimates are
crucially dependent on accurate calibration [142] and synchronization [143].
To relax the dependency on calibration and synchronization, DoA estimates can
be used as observations instead of TDoA estimates. To appropriately address
the resulting non-Gaussian state-space model, a wrapped Kalman filter is
proposed in [69] that approximates the posterior pdf of the source directions
by a Gaussian mixture model, where the mixture components account for the
various hypotheses that the state at the previous time step, the predicted
state at the current time step, or the localized DoA estimate may be wrapped
around $\pi$. To avoid an exponential explosion of the number of mixture
components, mixture reduction techniques [144] are required.

Rather than approximating the angular distribution by a Gaussian mixture, a
von Mises filter, based on directional statistics [145, 146], is proposed in
[53]. The Coherent-to-Diffuse Ratio (CDR) [147, 148] is used as a measure of
reliability of the DoA estimates in order to infer the unmeasured source-to-
sensor range.

The following single-source tracking approaches were submitted to the LOCATA
challenge:

ID 3 [41]

combines TDE (see Section V-A1) for localization with a particle filter for
tracking using the DICIT array for the single-source Tasks 1, 3 and 5.

ID 7 [44]

combines diagonal unloading beamforming [95] (see Section V-A3) for
localization with a Kalman filter for source tracking using a 7-microphone
linear subarray of the DICIT array for Tasks 1, 3 and 5.

ID 8 [45]

combines TDE (see Section V-A1) with IPDs (see Section V-A2) for localization
and apply a wrapped Kalman filter [69] for source tracking using the hearing
aids for Tasks 1, 3 and 5.

ID 10 [47]

combines localization using the first-order ambisonics configuration (see
Section V-A4) of the Eigenmike with a particle filter for Tasks 1-4.

ID 13 and ID 14 [49]

apply variants of MUSIC (see Section V-B1) for localization and a Kalman
filter for tracking the source DoA for Tasks 1 and 3 using the robot head and
the Eigenmike.

####  V-C2 Multi-Source Tracking

For multiple sources, not only the source position, but also the number of
sources is subject to uncertainty. However, this uncertainty cannot be
accounted for within the classical Bayesian framework.

Heuristic data association techniques are often used to associate existing
tracks and observations, as well as to initialize new tracks. Data association
partitions the observations into track ‘gates’ [149], or collars, around each
predicted track in order to eliminate unlikely observation-to-track pairs.
Only observations within the collar are considered when evaluating the track-
to-observation correlations. Nearest-neighbour approaches determine a unique
assignment between each observation and at most one track by minimizing an
overall distance metric. However, in dense, acoustic environments, such as the
cocktail party scenario [150, 151], many pairs between tracks and observations
may result in similar distance values, and hence a high probability of
association errors. For improved robustness, probabilistic data association
can be used instead of heuristic gating procedures, e.g., the Probabilistic
Data Association Filter (PDAF) [152, 153], or Joint Probabilistic Data
Association (JPDA) [154, 155].

To avoid explicit data association, the work in [68] models the observation-
to-track associations as discrete latent variables within a variational EM
approach for multi-source tracking. Estimates of the latent variables provide
the track-to-observation associations. The work in [156] extends the
variational EM in [68] to a incorporate a von Mises distribution [53] for
robust estimation of the DoA trajectories.

To incorporate track initiation and termination in the presence of false and
missing observations, the states of multiple sources can be formulated as
realizations of a Random Finite Set (RFS) [114, 157]. In contrast to random
vectors, RFSs capture not only the time-varying source states, but also the
unknown and time-varying number of sources. Finite set statistics [158, 159]
provide the mathematical mechanisms to treat RFSs within the Bayesian
paradigm. Since the pdf of RFS realizations is combinatorially intractable,
its first-order approximation, the PHD filter [114] provides estimates of the
intensity function – as opposed to the pdf – of the number of sources and
their states.

The PHD filter was applied in [160, 161] for the tracking of the positions of
multiple sources from the TDoA estimates. Due to the non-linear relationship
between the Cartesian source positions and TDoAs estimates, the prediction and
update for each hypothesis within the PHD filter is realized using a particle
filter as previously detailed in Section V-C1. A PHD filter for bearing-only
tracking from the localized DoA estimates was proposed in [162], incorporating
a von Mises mixture filter for the update of the source directions. The work
in [10, 9] applies a PHD filter in order to track the source positions from
DoA estimates for SLAM.

The following multi-source tracking approaches were submitted to the LOCATA
challenge:

ID 2 [40]

utilizes DoA estimates from MUSIC (see Section V-B1) as inputs to a PHD filter
[113, 114] with intensity particle flow [163] for Task 4, using all four
arrays.

ID 4 [42]

combines DoA estimation using the direct-path RTF approach in [62] (see
Section V-A1) with the variational EM algorithm in [68] for all Tasks using
the robot head.

##  VI Evaluation Measures

This section provides a discussion of the performance measures used for
evaluation of the LOCATA challenge.

Figure 3: Tracking ambiguities. Colors indicate unique track IDs.

###  VI-A Source Localization & Tracking Challenges

In realistic acoustic scenarios, source localization algorithms are affected
by a variety of challenges (see Fig. 3). Fast localization estimates using a
small number of time frames often result in estimation errors for signals that
are affected by late reverberation and noise. Sources are often missed, e.g.,
due to periods of voice inactivity, for distant sources corresponding to low
signals levels, or for sources oriented away from the sensors. False estimates
arise due to, e.g., strong early reflections mistaken as the direct path of a
source signal, or reverberation causing temporal smearing of speech energy
beyond the endpoint of a talker’s utterance, and due to overlapping speech
energy in the same spectral bins for multiple, simultaneously active talkers.

Source tracking algorithms typically use localization estimates as
observations. To distinguish inconsistent false estimates from consistent
observations, tracking approaches often require multiple, consecutive
observations of the same source direction or position before a track is
initialized. Furthermore, track termination rules are necessary to distinguish
between speech endpoints and missing estimates. To avoid premature track
deletions due to short-term missing estimates, track termination rules are
often based on the lapsed time since the last track update. Uncertainty due to
the onsets and endpoints of speech activity may therefore lead to a latency
between the onsets and endpoints of speech and the initialization and
termination, respectively, of the corresponding source track.

In practice, uncertainty in the source dynamical model and in the observations
may lead to divergence of the track from the ground-truth trajectory of an
inactive source. In multi-source scenarios, track divergence may also occur by
mistakenly updating a source’s track with estimates of a different, nearby
source. As a consequence, track swaps may occur due to the divergence of a
track to the trajectory of a different source. Furthermore, a track may be
broken if the track is not assigned to any source for one or more time steps,
i.e., the assignment between a source and its estimates is temporarily
‘interrupted’.

Measures selected for the objective evaluation are:

Estimation accuracy: The distance between a source position and the
corresponding localized or tracked estimate.

Estimation ambiguity: The rate of false estimates directed away from sound
sources.

Track completeness: The robustness against missing detections in a track or a
sequence of localization estimates.

Track continuity: The robustness against fragmentations due to track
divergence or swaps affecting a track or a sequence of localization estimates.

Track timeliness: The delay between the speech onset and either the first
estimate in a sequence of localization estimates, or at track initialization.

The evaluation measures detailed in the following subsections are defined
based on the following nomenclature. A single recording of duration
${\mathcal{T}}_{\text{rec}}$, including a maximum number of $N_{\text{max}}$
sources, is considered. Each source $n\in\\{1,\dots,N_{\text{max}}\\}$ is
associated with $A(n)$ periods of activity of duration
${\mathcal{T}}(a,n)=T_{\text{end}}(a,n)-T_{\text{srt}}(a,n)$ for
$a\in\\{1,\dots,A(n)\\}$, where $T_{\text{srt}}(a,n)$ and
$T_{\text{end}}(a,n)$, respectively, mark the start and end time of the VAP.
The corresponding time step indices are $t_{\text{srt}}(a,n)\geq 0$ and
$t_{\text{end}}(a,n)\geq t_{\text{srt}}(a,n)$. Each VAP corresponds to an
utterance of speech, which is assumed to include both voiced and unvoiced
segments. $\Delta_{\text{valid}}(a,n)$ and $L_{\text{valid}}(a,n)$,
respectively, denote the duration and the number of time steps in which source
$n$ is assigned to a valid track during VAP $a$. Participants were required to
submit azimuth estimates of each source for a sequence of pre-specified time
stamps, $t$, corresponding to the rate of the optical tracking system used for
the recordings. Each azimuth estimate had to be labelled by an integer-valued
Identity (ID), $k=1,\dots,K_{\text{max}}$, where $K_{max}$ is the maximum
number of source IDs in the corresponding recording. Therefore, each source ID
establishes an assignment from each azimuth estimate to one of the active
sources.

###  VI-B Individual Evaluation Measures

To highlight the various scenarios that need to be accounted for during
evaluation, consider, for simplicity and without loss of generality, the case
of a single-source scenario, i.e., $N_{\text{max}}=1$, where $N(t)=1$ during
speech activity and $N(t)=0$ if the source is inactive. A submission either
results in $K(t)=0$, $K(t)=N(t)=1$ or $K(t)>N(t)$, where $N(t)$ and $K(t)$,
respectively, denote the true and estimated number of sources active at $t$.
If $K(t)=0$, the source is either inactive, i.e., $N(t)=0$, or the estimate of
an active source is missing, if $N(t)=1$. For $K(t)=1$, the following
scenarios are possible.  a) The source is active, i.e., $N(t)=1$, and the
estimate corresponds to a typically imperfect estimate of the ground-truth
source direction.  b) The source is active, $N(t)=1$, but its estimate is
missing, whereas a false estimate, e.g., pointing towards the direction of an
early reflection, is provided.  c) The source is inactive, i.e., $N(t)=0$, and
a false estimate is provided . Evaluation measures are therefore required that
quantify, per recording, any missing and false estimates as well as the
estimation accuracy of estimates in the direction of the source. Prior to
performance evaluation, an assignment of each source to a detection must be
established by gating and source-to-estimate association, as detailed in
Section VI-B1 and Section VI-B2. The resulting assignment is for evaluation of
the estimation accuracy, completeness, continuity, and timeliness (see Section
VI-B3 and Section VI-B4).

####  VI-B1 Gating between Sources and Estimates

Gating [164] provides a mechanism to distinguish between estimation errors,
missing, and false estimates. Gating removes improbable assignments of a
source with estimates corresponding to errors exceeding a preset threshold.
Any estimate removed by gating is counted as a false estimate. If no detection
lies within the gate of a source, the source is counted as missed. The gating
threshold needs to be selected carefully: If set too low, estimation errors
may lead to unassociated sources where a distorted estimate along an existing
track is classified as a false estimate and the source estimate is considered
as missing. In contrast, if the gating threshold is set too high, a source may
be incorrectly assigned to a false track.

For evaluation of the LOCATA challenge, the gating threshold is selected such
that the majority of submissions within the single-source Tasks 1 and 3 is not
affected. As will be shown in the evaluation in Section VII, a threshold of
$30^{\circ}$ applied to the azimuth error allows to identify systematic false
estimates.

####  VI-B2 Source-to-Estimate Association

For $K(t)>1$, source localisation may be affected by false estimates both
inside and outside the gate. Data association techniques are used to assign
the source to the nearest estimate within the gate. Spurious estimates within
the gate are included in the set of false estimates. At every time step, a
pair-wise distance matrix corresponding to the angular error between each
track and each source is evaluated. The optimum source-to-estimate assignment
is established using the Munkres algorithm [165] that identifies the source-
to-estimate pairs corresponding to the minimum overall distance. Therefore,
each source is assigned to at most one track and _vice versa_.

Source-to-estimate association therefore allows to distinguish estimates
corresponding to the highest estimation accuracy from spurious estimates.
Similar to data association discussed in Section V, and by extension of the
single-source case, gating and association establish a one-to-one mapping of
each active source with an estimate within the source gate. Any unassociated
estimates are considered false estimates, whereas any unassociated sources
correspond to missing estimates.

Based on the assignments between sources and estimates, established by gating
and association, the evaluation measures are defined to quantify the
estimation errors and ambiguities as a single value per measure, per
recording. For each assignment between a source and an estimate, the measures
detailed in the following are applied to quantify, as a single measure per
recording, the estimation accuracy, ambiguity, track completeness, continuity,
and timeliness (see Section VI-A).

For brevity, a ‘track’ is synonymously used in the following to describe both,
the trajectory of estimates obtained from a tracker, as well as a sequence of
estimates labelled with the same ID by a localization algorithm. The sequence
of ground-truth source azimuth values of a source is referred to as the
source’s ground-truth azimuth trajectory.

####  VI-B3 Estimation Accuracy

The angular errors are evaluated separately in azimuth and elevation for each
assigned source-to-track pair for each time stamp during VAPs. The azimuth and
elevation error, $d_{\phi}\left(\phi(t),\hat{\phi}(t)\right)$ and
$d_{\theta}\left(\theta(t),\hat{\theta}(t)\right)$, respectively, are defined
as:

$\displaystyle d_{\phi}\left(\phi(t),\hat{\phi}(t)\right)$
$\displaystyle=\text{mod}\left(\phi(t)-\hat{\phi}(t)+\pi,2\pi\right)-\pi,$
(12a) $\displaystyle d_{\theta}\left(\theta(t),\hat{\theta}(t)\right)$
$\displaystyle=\theta(t)-\hat{\theta}(t),$ (12b)

where $\text{mod}(q,r)$ denotes the modulo operator for the dividend, $q$, and
the divisor, $r$; $\phi(t)\in[-\pi,\pi)$ and $\theta(t)\in[0,\pi]$ are the
ground-truth azimuth and elevation, respectively; and $\hat{\phi}(t)$ and
$\hat{\theta}(t)$ are the azimuth and elevation estimates, respectively.

####  VI-B4 Ambiguity, Track Completeness, Continuity, and Timeliness

In addition to the angular errors, multiple, complementary performance
measures are used to quantify estimation ambiguity, completeness, continuity,
and timeliness.

At each time step, the number of valid, false, missing, broken, and swapped
tracks are counted. Valid tracks are identified as the tracks assigned to a
source, whereas false tracks correspond to the unassociated tracks. The number
of missing tracks is established as the number of unassociated sources. Broken
tracks are obtained by identifying each source that was assigned to a track at
$t-1$, but are unassociated at $t$, where $t$ and $t-1$ must correspond to
time steps within the same voice-activity period. Similar to broken tracks,
swapped tracks are counted by identifying each source that was associated to
track ID $j\in\\{1,\dots,K_{\text{max}}\\}$, and is associated to track ID,
$\ell\in\\{1,\dots,K_{\text{max}}\\}$, where $j\neq\ell$.

Subsequently, the following measures of estimation ambiguity, completeness,
continuity, and timeliness are evaluated:

Probability of detection ($p_{d}$) [164]: A measure of completeness,
evaluating for each source and voice-activity period the percentage of time
stamps during which the source is associated with a valid track.

False Alarm Rate (FAR) [166]: A measure of ambiguity, evaluating the number of
false estimates per second. The FAR can be evaluated over the duration of each
recording [53], in order to provide a gauge of the effectiveness of any Voice
Activity Detector (VAD) algorithms that may have been incorporated in a given
submitted localization or tracking framework. In addition, the FAR is
evaluated in this paper over the duration of each VAP in order to provide a
measure of source counting accuracy of each submission.

Track Latency (TL) [166]: A measure of timeliness, evaluating the delay
between the onset and the first detection of source $n$ in VAP $a$.

Track Fragmentation Rate (TFR) [167]: A measure of continuity, indicating the
number of track fragmentations per second. The number of fragmentations
corresponds to the number of track swaps plus the number of broken tracks.

The evaluation measures defined above therefore quantify errors and
ambiguities by single numerical values per measure, per recording. These
individual measures can also be used to quantify, across all recordings in
each task, the mean of and standard deviation in the estimation accuracy and
ambiguity as well as the track completeness, continuity and timeliness.

TABLE III: Average azimuth errors during VAP. Submissions corresponding to minimum average errors are highlighted in bold font. Column colour indicates type of algorithm, where white indicates frameworks involving only DoA estimation (Submission IDs 1, 6, 9, 11, 12, 15, 16 and the baseline (BL)), and grey indicates frameworks that combine DoA estimation with source tracking (Submission IDs 2, 3, 4, 7, 8, 10). Task | Array | Submission ID
---|---|---
1 | 2 | 3 | 4 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 15 | 16 | BL
Single Source | 1 | Robot Head | - | - | - | 2.1 | 1.5 | 1.8 | - | - | - | 0.7 | - | - | - | 4.2
DICIT | - | - | 1.0 | - | - | 2.2 | - | 9.1 | - | - | - | - | - | 12.3
Hearing Aids | 8.5 | - | - | - | - | - | 8.7 | - | - | - | - | - | - | 15.9
Eigenmike | - | - | - | - | 6.4 | 7.0 | - | - | 8.9 | - | 1.1 | 8.1 | - | 10.2
3 | Robot Head | - | - | - | 4.6 | 3.2 | 3.1 | - | - | - | - | - | - | - | 9.4
DICIT | - | - | 1.8 | - | - | 4.5 | - | - | - | - | - | - | - | 13.9
Hearing Aids | - | - | - | - | - | - | 7.2 | - | - | - | - | - | - | 16.0
Eigenmike | - | - | - | - | 8.1 | 9.3 | - | - | 11.5 | - | - | - | - | 17.6
5 | Robot Head | - | - | - | 4.9 | 2.2 | 3.7 | - | - | - | - | - | - | - | 5.4
DICIT | - | - | 2.7 | - | - | 3.4 | - | - | - | - | - | - | - | 13.4
Hearing Aids | - | - | - | - | - | - | 11.8 | - | - | - | - | - | - | 14.6
Eigenmike | - | - | - | - | 6.3 | 7.5 | - | - | - | - | - | - | - | 12.9
Multiple Sources | 2 | Robot Head | - | - | - | 3.8 | - | - | - | - | - | 2.0 | - | - | - | 9.0
DICIT | - | - | - | - | - | - | - | - | - | - | - | - | - | 11.0
Hearing Aids | - | - | - | - | - | - | - | - | - | - | - | - | - | 15.6
Eigenmike | - | - | - | - | - | - | - | - | 7.3 | - | 1.4 | - | 7.1 | 10.2
4 | Robot Head | - | 9.4 | - | 6.0 | - | - | - | - | - | - | - | - | - | 9.2
DICIT | - | 13.5 | - | - | - | - | - | - | - | - | - | - | - | 12.9
Hearing Aids | - | 13.8 | - | - | - | - | - | - | - | - | - | - | - | 13.7
Eigenmike | - | 12.8 | - | - | - | - | - | - | 9.0 | - | - | - | - | 11.8
6 | Robot Head | - | - | - | 8.1 | - | - | - | - | - | - | - | - | - | 8.5
DICIT | - | - | - | - | - | - | - | - | - | - | - | - | - | 13.9
Hearing Aids | - | - | - | - | - | - | - | - | - | - | - | - | - | 13.9
Eigenmike | - | - | - | - | - | - | - | - | - | - | - | - | - | 12.9
TABLE IV: Difference in average azimuth errors with and without gating, evaluated for single-source tasks 1, 3, 5 for all submissions and the baseline (BL). Submissions unaffected by gating, and hence outliers, are highlighted in bold font. Task | Array | Submission ID
---|---|---
1 | 2 | 3 | 4 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 15 | 16 | BL
Single Source | 1 | Robot Head | - | - | - | 0.0 | 0.0 | 0.0 | - | - | - | 0.0 | - | - | - | 0.2
DICIT | - | - | 0.0 | - | - | 0.0 | - | 0.5 | - | - | - | - | - | 49.6
Hearing Aids | 42.3 | - | - | - | - | - | 4.0 | - | - | - | - | - | - | 49.2
Eigenmike | - | - | - | - | 0.1 | 0.1 | - | - | 0.0 | - | 0.0 | 0.0 | - | 0.4
3 | Robot Head | - | - | - | 0.0 | 1.2 | 0.0 | - | - | - | - | - | - | - | 3.4
DICIT | - | - | 0.0 | - | - | 0.0 | - | - | - | - | - | - | - | 63.2
Hearing Aids | - | - | - | - | - | - | 0.4 | - | - | - | - | - | - | 46.8
Eigenmike | - | - | - | - | 0.6 | 0.2 | - | - | 1.6 | - | - | - | - | 8.3
5 | Robot Head | - | - | - | 0.1 | 0.8 | 1.2 | - | - | - | - | - | - | - | 1.8
DICIT | - | - | 0.6 | - | - | 16.7 | - | - | - | - | - | - | - | 53.8
Hearing Aids | - | - | - | - | - | - | 12.7 | - | - | - | - | - | - | 43.7
Eigenmike | - | - | - | - | 1.1 | 1.9 | - | - | - | - | - | - | - | 14.9

###  VI-C Combined Evaluation Measure

The Optimal SubPattern Assignment (OSPA) metric [168] and its variants, e.g.,
[169], correspond to a comprehensive measure that consolidates the cardinality
error in the estimated number of sources and the estimation accuracy across
all sources into a single distance metric at each time stamp of a recording.
The OSPA therefore provides a measure that combines the estimation accuracy,
track completeness and timeliness. The OSPA selects, at each time stamp, the
optimal assignment of the subpatterns between sources and combines the sum of
the corresponding cost matrix with the cardinality error in the estimated
number of sources. Since the OSPA is evaluated independently of the IDs
assigned to the localization and tracking estimates, the measure is agnostic
to uncertainties in the identification of track labels.

The OSPA [113, 170] is defined as:

$\displaystyle\begin{split}&\text{OSPA}(\hat{\boldsymbol{{\mathrm{\Phi}}}}(t),\boldsymbol{{\mathrm{\Phi}}}(t))\triangleq\\\
&\biggl{[}\frac{1}{K(t)}\min_{\pi\in\boldsymbol{{\mathrm{\Pi}}}_{K(t)}}\sum\limits_{n=1}^{N(t)}d_{c}(\phi_{n}(t),\hat{\phi}_{\pi(n)}(t))^{p}+(K(t)-N(t))c^{p}\biggr{]}^{\frac{1}{p}},\end{split}$
(13)

for $N(t)\leq K(t)$, where
$\hat{\boldsymbol{{\mathrm{\Phi}}}}(t)\triangleq\\{\hat{\phi}_{1}(t),\dots,\hat{\phi}_{K(t)}(t)\\}$
denotes the set of $K(t)$ track estimates;
$\boldsymbol{{\mathrm{\Phi}}}(t)\triangleq\\{\phi_{1}(t),\dots,\phi_{N(t)}(t)\\}$
denotes the set of $N(t)$ ground-truth sources active at $t$; $1\leq p<\infty$
is the order parameter; $c$ is the cutoff parameter;
$\boldsymbol{{\mathrm{\Pi}}}_{K(t)}$ denotes the set of permutations of length
$N(t)$ with elements $\\{1,\dots,K(t)\\}$ [170];
$d_{c}(\phi_{n}(t),\hat{\phi}_{\pi(n)}(t))\triangleq\min{\left(c,\text{abs}\left(d_{\phi}(\phi_{n}(t),\hat{\phi}_{\pi(n)}(t))\right)\right)}$,
where $\text{abs}(\cdot)$ denotes the absolute value; $d_{\phi}(\cdot)$ is the
angular error (see (12)); and $\pi(n)$ denotes the $n^{th}$ element of each
subset $\pi\in\boldsymbol{{\mathrm{\Pi}}}$. For $N(t)>K(t)$, the OSPA distance
is evaluated as
$\text{OSPA}(\boldsymbol{{\mathrm{\Phi}}}(t),\hat{\boldsymbol{{\mathrm{\Phi}}}}(t))$
[170]. The impact of the choice of $p$ and $c$ is discussed in [168]. In this
paper, $c=30^{\circ}$.

To provide further insight into the OSPA measure, we note that the term
$\frac{1}{K(t)}\min_{\pi\in\boldsymbol{{\mathrm{\Pi}}}_{K(t)}}\sum_{n=1}^{N(t)}d_{c}(\phi_{n}(t),\hat{\phi}_{\pi(n)}(t))^{p}$
evaluates the average angular error by comparing each angle estimate against
every ground-truth source angle. The OSPA is therefore agnostic of the
estimate-to-source association. The cardinality error is evaluated as
$K(t)-N(t)$. The order parameter, $p$, determines the weighting of the angular
error relative to the cardinality error.

Due to the dataset size of the LOCATA corpus, a comprehensive analysis of the
OSPA at each time stamp for each submission, task, array, and recording is
impractical. Therefore, the analysis of the LOCATA challenge results is
predominantly based on the mean and variance of the OSPA across all time
stamps and recordings for each task.

##  VII Evaluation Results

The following section presents the performance evaluation for the LOCATA
challenge submissions using the measures detailed in Section VI. The
evaluation in Section VII-A focuses on the single-source tasks 1, 3 and 5.
Section VII-B presents the results for the multi-source tasks 2, 4 and 6.

The evaluation framework establishes an assignment between each ground-truth
source location and a source estimate for every time stamp during voice-active
periods in each recording, submission, task, and array (see Section VI). The
azimuth error in (12a) between associated source-to-track pairs is averaged
over all time stamps and all recordings. The resulting average azimuth errors
for each task, submission, and array are provided in Table III. The baseline
(BL) corresponds to the MUSIC implementation as detailed in [19]. One
submission (ID 5) is not included in the discussion as details of the method
are not available at the time of writing. Two further submissions (ID 13 and
ID 14) are also not included due to inconclusive results.

###  VII-A Single-Source Tasks 1, 3, 5

####  VII-A1 Task 1 - Azimuth Accuracy

For Task 1, involving a single, static source and a static microphone array,
average azimuth accuracies of around $1^{\circ}$ can be achieved (see Table
III). Notably, Submission 3 results in $1.0^{\circ}$ using the DICIT array by
combining TDE with a particle filter for tracking; Submission 11 results in an
average azimuth accuracy of $0.7^{\circ}$ using the robot head; and Submission
12 achieves an accuracy of $1.1^{\circ}$ using the Eigenmike. Submissions 11
and 12 are MUSIC implementations, applied to the microphone signals in the
STFT domain and domain of spherical harmonics, respectively.

A possible reason for the performance of Submissions 11 and 12 is that MUSIC
does not suffer from spatial aliasing if applied to arrays that incorporate a
large number of microphones. As such, the overall array aperture can be small
for low noise levels. Therefore, the performance of the two MUSIC-based
Submissions 11 (robot head) and 12 (Eigenmike) is comparable. Moreover, for
the Eigenmike, Submission 12 ($1.1^{\circ}$) leads to improvements of the SRP-
based Submissions 6 ($6.4^{\circ}$) and 7 ($7.0^{\circ}$).

For the pseudo-intensity-based approaches that were applied to the Eigenmike,
Submission 10 achieves an azimuth accuracy of $8.9^{\circ}$ by extracting
pseudo-intensity vectors from the first-order ambisonics and applying a
particle filter for tracking. Submission 15, which extracts the pseudo-
intensity from the signals in the domain of spherical harmonics and applies
subspace-based processing, results in $8.1^{\circ}$. The pseudo-intensity-
based Submissions 10 and 15 lead to a performance degradation of approximately
$7^{\circ}$, compared to the MUSIC-based Submission 12, also applied in the
domain of spherical harmonics. The reduced accuracy may be related to the
resolution of the spatial spectra provided by the pseudo-intensity-based
approaches compared to MUSIC. The spatial spectrum is computed using MUSIC by
scanning each direction in a discrete grid, specified by the steering vector.
In contrast, pseudo-intensity-based approaches approximate the spatial
spectrum by effectively combining the output of three dipole beamformers,
steered along the $x$-, $y$-, and $z$-axis relative to the array. Therefore,
compared to MUSIC, pseudo-intensity approaches evaluate a coarse approximation
of the spatial spectrum, but require reduced computational load.

A performance degradation from the 12-channel robot head to the 32-channel
Eigenmike is observed for the submissions that involved both arrays. For
ground-truth acquisition using the OptiTrack system, the reflective markers
were attached to the shockmount of the Eigenmike, rather than the baffle of
the array, to minimize shadowing and scattering effects, see [17, 18].
Therefore, a small bias in the DoA estimation errors is possible due to
rotations of the array within the shockmount. Nevertheless, this bias is
expected to be significantly smaller than some of the errors observed for the
Eigenmike in Table III. Possible reasons are that  1. the irregular array
topology of the robot head may lead to improved performance for some of the
algorithms, or that  2. the performance improvements in localization accuracy
may be related to the larger array aperture of the robot head, compared to the
Eigenmike . However, with the remaining uncertainty regarding the actual
implementation of the algorithms, conclusions remain somewhat speculative at
this point.

Submission 6, applying SRP-PHAT to a selection of microphone pairs, results in
average azimuth errors of $1.5^{\circ}$ using the robot head and $6.4^{\circ}$
using the Eigenmike. Similar results of $1.8^{\circ}$ and $7.0^{\circ}$ for
the robot head and Eigenmike, respectively, are obtained using Submission 7,
which combine an SRP beamformer for localization with a Kalman filter for
tracking. Therefore, the SRP-based approaches in Submissions 6 and 7, applied
without and with tracking, respectively, lead to comparably accurate results.

(a) Azimuth ground-truth and estimates

(b) Ground-truth range between source and robot head

Figure 4: Azimuth estimates for Task 3, recording 4 for (a) azimuth estimates
for Submissions 3, 6, 7. As a reference, the ground-truth range between the
robot head and the source is shown in (b).

Table III also highlights a significant difference in the performance results
between the approaches submitted to Task 1 using the DICIT array. Submission 3
achieves an average azimuth accuracy of $1.0^{\circ}$ by combining GCC-PHAT
with a particle filter. Submission 7, combining SRP beamforming and a Kalman
filter, results in a small degradation to $2.2^{\circ}$ in average azimuth
accuracy. Submission 9 leads to a decreased accuracy of $9.1^{\circ}$.
Submission 3 uses the subarray of microphone pairs corresponding to $32$ cm
spacings to exploit spatial diversity between the microphones; Submission 7
uses the 7-microphone linear subarray at the array centre; Submission 9 uses
three microphones at the centre of the array, with a spacing of $4$ cm, to
form two microphone pairs. A reduction of the localization accuracy can
therefore be intuitively expected for Submission 9, compared to Submissions 3
and 7, due to  a) the reduced number of microphones, and  b) the reduced
inter-microphone spacing, and hence reduced spatial diversity of the sensors .

For the hearing aids in Task 1, both Submissions 1 and 8 result in comparable
azimuth errors of $8.5^{\circ}$ and $8.7^{\circ}$ respectively. The recordings
for the hearing aids were performed separately from the remaining arrays, and
are therefore not directly comparable to the results for other arrays.
Nevertheless, a reduction in azimuth accuracy for the hearing aids is
intuitively expected due to the small number of microphones integrated in each
of the arrays.

To conclude, we note that the results for the static single-source Task 1
indicate a comparable performance between the submissions that incorporate
localization and those submissions that combine localization with source
tracking. Since the source is static, long blocks of data can be used for
localization. Furthermore, temporal averaging can be applied across data
blocks. Therefore, since a dynamical model is not required for the static
single-source scenario, localization algorithms can apply smoothing directly
to the DoA estimate, without the need for explicit source tracking.

(a) Task 1

(b) Task 3

(c) Task 5

Figure 5: Probability of detection (bars) and standard deviation over
recordings (whiskers) for Tasks 1, 3, 5, for each submission and array.
Legends indicate the submission IDs available for each of the tasks.

(a) Task 1, for entire recording duration

(b) Task 1, during voice activity only

Figure 6: FAR for Task 1 involving single static loudspeakers (a) for entire
recording duration, and (b) during voice-activity periods only.

####  VII-A2 Task 3 - Azimuth Accuracy

In the following, ${\mathcal{S}}_{135}=\\{3,4,6,7,8\\}$ denotes the set of
submissions that were evaluated for Tasks 1, 3 and 5. For Task 3, involving a
single, moving source, a small degradation is observed in the azimuth error
over ${\mathcal{S}}_{135}$ from $4.3^{\circ}$ for Task 1 to $5.5^{\circ}$ for
Task 3. For example, Submission 7 leads to the lowest average absolute error
in azimuth with only $3.1^{\circ}$ for Task 3 using the robot head,
corresponding to a degradation of $1.3^{\circ}$ compared to Task 1. The
accuracy of Submission 3 reduces from $1.0^{\circ}$ for Task 1 to
$1.8^{\circ}$ for Task 3.

The reduction in azimuth accuracy from static single-source Task 1 to moving
single-source Task 3 is similar for all submissions. Trends in performance
between approaches for each array are identical to those discussed for Task 1.
The overall degradation in performance is therefore related to differences in
the scenarios between Task 1 and Task 3. Recordings from human talkers are
subject to variations in the source orientation and source-sensor distance.
The orientation of sources directed away from the microphone array leads to a
decreased direct-path contribution to the received signal. Furthermore, with
increasing source-sensor distance, the noise field becomes increasingly
diffuse. Hence, reductions in the Direct-to-Reverberant Ratio (DRR) [23] due
to the source orientation, as well as the CDR due to the source-sensor
distance, result in increased azimuth estimation errors.

To provide further insight into the results for Task 3, Fig. 4 provides a
comparison for recording 4 of the approaches leading to the highest accuracy
for each array, i.e., Submission 7 using the robot head, Submission 3 using
the DICIT array, and Submission 6 using the Eigenmike. For Submission 7,
accurate and smooth tracks of the azimuth trajectories are obtained during
VAPs. Therefore, diagonal unloading SRP beamforming clearly provides power
maps of sufficiently high resolution to provide accurate azimuth estimates
whilst avoiding systematic false detections in the directions of early
reflections. Moreover, application of the Kalman filter provides smooth
azimuth trajectories.

Similar results in terms of the azimuth accuracy are obtained for Submission
3, combining GCC-PHAT with a particle filter for the DICIT array. However, due
to the lack of a VAD, temporary periods of track divergence can be observed
for Submission 3 around periods of voice inactivity, i.e., between [3.9,4.4] s
and [8.5,9.2] s.

For the voice-active period between [16.9,19.6] s, the results of Submission 7
are affected by a significant number of missing detections, whilst the results
for Submission 3 exhibits diverging track estimates. Fig. 4b provides a plot
of the range between the source and robot head, highlighting that the human
talker is moving away from the arrays between [15.1,20] s. Therefore, the
Cross-Power Spectral Density (CPSD)-based VAD algorithm of Submission 7
results in missing detections of voice activity with decreasing CDR. For
Submission 3 and 6, that do not involve a VAD, the negative DRR leads to
missing and false DoA estimates in the direction of early reflections.
Therefore, increasing DoA estimation errors are observed in voice-active
periods during which the source-sensor distance increases beyond 2 m.

####  VII-A3 Task 5 - Azimuth Accuracy

The mean azimuth accuracy over ${\mathcal{S}}_{135}$, averaged over the
corresponding submissions and arrays, decreases from $5.5^{\circ}$ for Task 3,
using static arrays, to $9.7^{\circ}$ for Task 5, using moving arrays. Despite
the reduced number of submissions for Task 5, the overall performance trends
are similar to those in Task 1 and Task 3 (see Table III).

The trend of an overall performance degradation is related to the increasingly
challenging conditions. Similar to Task 3, the motion of the source and arrays
lead to time-varying source-sensor distances and source orientations relative
to the array. Furthermore, due to the motion of the array, it is crucial that
the microphone signals in Task 5 are processed over analysis windows of
sufficiently short duration.

(a) Azimuth ground-truth for Source 1 and estimates

(b) Ground-truth source-sensor range

Figure 7: Comparison of (a) azimuth estimates for Task 3, recording 2 using
the Eigenmike for Submissions 6, 7, and (b) ground-truth range between the
source and the Eigenmike array origin. Results indicate outliers during voice
inactivity for Submission 6 and temporary track divergence during voice
activity between [15.1,17] s for Submissions 6 and 7.

(a) Task 1

(b) Task 3

(c) Task 5

Figure 8: Track latency (bars) and standard deviation over recordings
(whiskers) for Tasks 1, 3 and 5, for each submission and array. Legends
indicate the submission IDs available for each of the tasks.

(a) Task 2, Track Fragmentation Rate

(b) Task 4, Track Fragmentation Rate

(c) Task 6, Track Fragmentation Rate

Figure 9: Track fragmentation rate (bars) and standard deviation over
recordings (whiskers) for Tasks 2, 4, 6, for each submission and array.

####  VII-A4 Tasks 1, 3, 5: Impact of Gating on Azimuth Accuracy

To illustrate the effect of gating on the evaluation results, the evaluation
was repeated without gating by assigning each source to its closest
estimate.222Even though Tasks 1, 3 and 5 correspond to single-source
scenarios, gating and association is required for evaluation, since azimuth
estimates corresponding to multiple source IDs were provided for some
submissions. Table IV provides the difference in the average azimuth errors
with and without gating. In Table IV, entries with value $0.0$ indicate that
evaluation with and without gating lead to the same result. Entries with
values greater than $0.0$ highlight that the azimuth error increases without
gating, i.e., the submitted results are affected by outliers outside of the
gating collar.

For the majority of submissions, a gating threshold of $30^{\circ}$ results in
improved azimuth accuracies in the range of $0.1^{\circ}$ to $4^{\circ}$
across Tasks 1, 3 5. A significant number of outliers are observed for
Submissions 1, 7 and 8. To reflect outliers in the analysis of the results,
evaluation measures, such as the FAR and probability of detection, are
required in addition to the average azimuth error.

####  VII-A5 Completeness & Ambiguity

As detailed in Section VI, the track cardinality and probability of detection
are used as evaluation measures of the track completeness. For single-source
scenarios, the track completeness quantifies the robustness of localization
and tracking algorithms against changes in the source orientation and source-
sensor distance. Furthermore, the FAR is used as an evaluation measure of the
track ambiguity, quantifying the robustness against early reflections and
noise in the case of the single-source scenarios.

The probability of detection and FAR, averaged over all recordings in each
task, are shown in Fig. 5 and Fig. 6, respectively. The results indicate that
the probability of detection between Tasks 1, 3 and 5 remains approximately
constant, with a trend towards a small reduction in $p_{d}$, when changing
from static to dynamic sources.

The results also highlight that Submissions 11 and 12, corresponding to the
highest average azimuth accuracy for Task 1 using the robot head and Eigenmike
(see Section VII-A1), exhibit $100$% probability of detection. The same
submissions also correspond to a comparatively high FAR of 50 false estimates
per second, averaged across all recordings for Task 1 and evaluated for the
full duration of each recording (see Fig. 6a). These results are indicative of
the fact that Submissions 11 and 12 do not incorporate VAD algorithms. For
comparison, Fig. 6b depicts the average FARs for Task 1 evaluated during
voice-activity only. The results in Fig. 6b clearly highlight a significant
reduction in the FAR for Submissions 3, 6, 11, which do not incorporate VAD.

Fig. 7a, selected from Submission 6 for Task 3 and recording 2, shows that
estimates during periods of voice inactivity are affected by outliers, which
are removed from the measure for azimuth accuracy due to the gating process,
and are accounted for in the FAR. The majority of DoA estimates provided
during voice-activity correspond to smooth tracks near the ground-truth source
azimuth. In the time interval [15.1,17] s, the estimates exhibit a temporary
period of track divergence. The results for Submission 7 in Fig. 7a highlight
that outliers during voice inactivity are avoided since the submission
incorporates VAD. The results also indicate diverging track estimates in the
interval [15.1,17] s. The track divergence affecting both submissions is
likely caused by the time-varying source-sensor geometry due to the motion of
the source. Fig. 7b highlights that the source is moving away from the array
after 13 s. As the source orientation is directed away from the array, the
contribution of the direct-path signal decreases, resulting in reduced
estimation accuracy in the source azimuth. The reduction in azimuth accuracy
eventually results in false estimates outside of the gating threshold.

####  VII-A6 Timeliness

The track latency is used as an evaluation measure of the timeliness of
localization and tracking algorithms. Therefore, the track latency quantifies
the sensitivity of algorithms to speech onsets, and the robustness against
temporal smearing at speech endpoints.

Fig. 8 shows the track latency, averaged across all recordings for Tasks 1, 3
and 5. Submissions 1, 3, 6, 8, 9, 11 and 12 do not incorporate VAD. Hence,
estimates are provided at every time stamp for all recordings. Submissions 3
and 8 incorporate tracking algorithms, where the source estimates are
propagated through voice-inactive periods by track prediction. Submissions 1,
11 and 12, submitted for only the static tasks, estimate the average azimuth
throughout the full recording duration and extrapolate the estimates across
all time steps.

Therefore, for Task 1, Submissions 1, 3, 11 and 12 correspond to $0$ s track
latency throughout. However, these algorithms also correspond to high FARs,
when the FAR is evaluated across voice-active and inactive periods (see Fig.
6a). Submissions 3 and 8, which do not involve a VAD and were submitted to the
tasks involving moving sources, result in track latencies of below $0.2$ s for
Tasks 3 and 5, where the extrapolation of tracks outside of VAPs is non-
trivial.

Submission 4 incorporates a VAD that estimates voice activity as a side-
product of the variational EM algorithm for tracking. The results show that
Submission 4 effectively detects speech onsets, leading to negligible track
latencies across Tasks 1, 3 and 5. Submission 10, incorporating the noise
Power Spectral Density (PSD)-based VAD of [171], detects speech onsets
accurately in the static source scenario in Task 1. However, the track latency
for Task 3, involving a moving source, increases to $0.35$ s. It is important
to note that Submissions 7 and 10 incorporate Kalman or particle filters with
heuristic approaches to track initialization. Therefore, it is likely that
track initialization rules - rather than the VAD algorithms - lead to delays
in the confirmation of newly active sources.

(a) Azimuth estimates: Task 2, Recording 5

(b) VAD: Task 2, Recording 5

(c) Azimuth estimates: Task 4, Recording 4

(d) VAD: Task 4, Recording 4

(e) Azimuth estimates: Task 6, Recording 2

(f) VAD: Task 6, Recording 2

Figure 10: Azimuth estimates and VAD for Submission 4 using the robot head for
(a)-(b) Task 2, (c)-(d) Task 4, and (e)-(f) Task 6.

(a) Submission 2, Eigenmike

(b) Submission 2, Eigenmike

(c) Submission 10, Eigenmike

(d) Submission 10, Eigenmike

(e) VAD, Eigenmike

Figure 11: Azimuth trajectories and corresponding OSPA metric for recording 1
of Task 4 for (a)-(b) Submission 2 using the Eigenmike, (c)-(d) Submission 10
using the Eigenmike. The VAD periods are shown in (e).

###  VII-B Multi-Source Tasks 2, 4, 6

####  VII-B1 Accuracy

For the multi-source Tasks 2, 4 and 6, the results in Table III indicate
similar trends as discussed for the single-source Tasks 1, 3 and 5. However,
the overall performance of all submissions for Tasks 2, 4 and 6 is decreased
compared to Tasks 1, 3 and 5.

The reduction in azimuth accuracy is due to the adverse effects of
interference from multiple simultaneously active sound sources. Due to the
broadband nature of speech, the speech signals of multiple talkers often
correspond to energy in the overlapping time-frequency bins, especially for
talkers with similar voice pitch. Therefore, localization approaches that rely
on the $W$-disjoint orthogonality of speech may result in biased estimates of
the DoA (see, e.g., Submission 4).

Robustness against interference can be achieved by incorporating time-
frequency bins containing the contribution of a single source only, e.g., at
the onset of speech. For example, Submission 11 and 12 incorporate the Direct
Path Dominance (DPD)-test in [112], and result in azimuth accuracies of
$2.0^{\circ}$ and $1.4^{\circ}$, respectively, for the robot head and
Eigenmike in Task 2, compared to $0.7^{\circ}$ and $1.1^{\circ}$ in Task 1.

An increasing number of sources also results in an increasingly diffuse sound
field in reverberant environments. For data-dependent beamforming techniques
[1], the directivity pattern of the array is typically evaluated based on the
signal and noise levels. For increasing diffuse noise, it is therefore
expected that the performance of beamforming techniques decreases in multi-
source scenarios.

In addition to a reduction in the angular accuracy, ambiguities arising in
scenarios involving multiple, simultaneously active sound sources result in
missing and false DoA estimates, affecting the completeness, continuity, and
ambiguity of localization and tracking approaches.

####  VII-B2 Continuity

The TFR is used as an evaluation measure for track continuity (see Section
VII). Fig. 9 provides the TFRs for Tasks 2, 4 and 6 for each array and
submission and averaged over the recordings.

The results indicate that the subspace-based Submissions 11, 12 and 16 are
robust to track fragmentation. Although the submissions rely on the assumption
of $W$-disjoint orthogonal sources, localization is performed only on a subset
of frequency bins that correspond to the contribution of a single source. In
contrast, BSS-based approaches assume that the $W$-disjoint orthogonality
applies to all frequency bands required for the reconstruction of the source
signals.

The advantage of subspace-based processing for robustness against track
fragmentation is reinforced when comparing the results for Submission 10,
based on pseudo-intensity vectors for ambisonics, against Submission 16, using
subspace pseudo-intensity vectors in the domain of spherical harmonics. The
azimuth accuracies of both submissions are comparable, where Submission 10
results in an average azimuth error of $7.3^{\circ}$ and Submission 16 leads
to $7.1^{\circ}$ in Task 2. In contrast, Submission 10 leads to $0.3$
fragmentations per second, whereas Submission 16 exhibits only $0.07$
fragmentations per second.

Comparing the results for static Task 2 against the moving-source Task 4 and
the fully dynamic Task 6, the results in Fig. 9 highlight increasing TFRs
across submissions. For example, Submission 4, the only approach that was
submitted for all three multi-source tasks, corresponds to 0.53 fragmentations
per second for Task 2, involving multiple static loudspeakers, to 0.64
fragmentations per second for Task 4, involving multiple moving human talkers,
and to 0.71 fragmentations per second for Task 6 involving multiple moving
human talkers and moving arrays. The increasing TFR is due to the increasing
spatio-temporal variation of the source azimuth between the three tasks. Task
2 corresponds to constant azimuth trajectories of the multiple static
loudspeakers, observed from static arrays (see Fig. 10a, showing the azimuth
estimates for Task 2, recording 5). The motion of the human talkers that are
observed from static arrays in Task 4 correspond to time-varying azimuth
trajectories within limited intervals of azimuth values. For example, for Task
4, recording 4 shown in Fig. 10c, source 1 is limited to azimuth values in the
interval between $[6,24]^{\circ}$, whilst source 2 is limited between
$[-66,50]^{\circ}$. The motion of the moving sources and moving arrays in Task
6 result in azimuth trajectories that vary significantly between
$[-180,180]^{\circ}$ (see Fig. 10e for the azimuth estimates provided for Task
6, recording 2). Furthermore, the durations of recordings for Task 4 and Task
6 are substantially longer than those for Task 2. As to be expected, periods
of speech inactivity and the increasing time-variation of the source azimuth
relative to the arrays result in increasing TFRs when comparing Task 2, Task
4, and Task 6.

TABLE V: Average OSPA results. Column colour indicates type of algorithm, where white indicates frameworks involving only DoA estimation (Submission IDs 11, 12, 16 and the baseline (BL)), and grey indicates frameworks that combine DoA estimation with source tracking (Submission IDs 2, 4, 10). Task | Array | Submission ID
---|---|---
2 | 4 | 10 | 11 | 12 | 16 | BL
$p$ | $p$ | $p$ | $p$ | $p$ | $p$ | $p$
$1$ | $5$ | $1$ | $5$ | $1$ | $5$ | $1$ | $5$ | $1$ | $5$ | $1$ | $5$ | $1$ | $5$
2 | Robot Head | - | - | 17.5 | 22.4 | - | - | 12.4 | 17.6 | - | - | - | - | 19.5 | 23.8
DICIT | - | - | - | - | - | - | - | - | - | - | - | - | 26.6 | 28.0
Hearing Aids | - | - | - | - | - | - | - | - | - | - | - | - | 26.1 | 27.7
Eigenmike | - | - | - | - | 17.5 | 22.3 | - | - | 12.2 | 17.3 | 12.4 | 18.2 | 21.5 | 25.0
4 | Robot Head | 13.8 | 18.9 | 13.5 | 16.4 | - | - | - | - | - | - | - | - | 16.3 | 18.9
DICIT | 15.6 | 20.0 | - | - | - | - | - | - | - | - | - | - | 25.8 | 26.6
Hearing Aids | 15.2 | 19.6 | - | - | - | - | - | - | - | - | - | - | 27.7 | 28.1
Eigenmike | 14.6 | 19.3 | - | - | 13.1 | 16.4 | - | - | - | - | - | - | 18.4 | 20.8
6 | Robot Head | - | - | 13.8 | 15.0 | - | - | - | - | - | - | - | - | 14.8 | 15.8
DICIT | - | - | - | - | - | - | - | - | - | - | - | - | 24.8 | 25.2
Hearing Aids | - | - | - | - | - | - | - | - | - | - | - | - | 25.2 | 25.8
Eigenmike | - | - | - | - | - | - | - | - | - | - | - | - | 21.1 | 21.7

####  VII-B3 OSPA \- Accuracy vs. Ambiguity, Completeness and Continuity

The results for the OSPA measure, averaged over all recordings for the multi-
source Tasks 2, 4 and 6, is summarized for order parameters $p=\\{1,5\\}$ (see
(13)) in Table V. In contrast to the averaged azimuth errors in Table III, the
OSPA results trade off the azimuth accuracy against cardinality errors, and
hence false and missing track estimates. For example, the results for Task 2
in Table III indicate a significant difference in the results for Submission
12 ($1.4^{\circ}$) and Submission 16 ($7.1^{\circ}$). In contrast, due to
false track estimates during periods of voice inactivity, Table V highlights
only a small difference between the OSPA for Submissions 12 and 16.

To provide intuitive insight into the OSPA results and the effect of the order
parameter, $p$, Fig. 11 compares the azimuth estimates obtained using
Submissions 2 and 10 for the Eigenmike, Task 4, Recording 1.

The results highlight distinct jumps of the OSPA between periods during which
a single source is active and the onsets of periods of two simultaneously
active sources. During periods of voice inactivity, detection errors in the
onsets of speech lead to errors corresponding to the cutoff threshold of
$c=30^{\circ}$. Therefore, the cardinality error dominates the OSPA when
$N(t)=0$ and $K(t)>0$. During VAPs where $N(t)=K(t)$, the OSPA is dominated by
the angular error between each estimate and the ground-truth direction of each
source, resulting in values in the range of $[0,20]^{\circ}$. For $N(t)=K(t)$,
the order parameter, $p$, does not affect the results since the cardinality
error is $K(t)-N(t)=0$. During periods where $K(t)<N(t)$, the cardinality
error causes the OSPA to increase to between $[15,30]^{\circ}$. The OSPA
increases with the order parameter $p$.

The results highlight that both approaches are affected by cardinality errors,
indicated by jumps in the OSPA. For Submission 10, which incorporates VAD, the
cardinality errors arise predominantly due to missing detections and broken
tracks (see Fig. 11d). In contrast, Submission 2 is mainly affected by false
estimates during voice inactivity. Since Submission 2 does not involve a VAD,
tracks are propagated through periods of voice inactivity using the prediction
step of the tracking filter. Temporary periods of track divergence therefore
lead to estimates that are classified as false estimates by gating and data
association.

##  VIII Discussion and Conclusions

The open-access LOCATA challenge data corpus of real-world, multichannel audio
recordings and open-source evaluation software provides a framework to
objectively benchmark state-of-the-art localization and tracking approaches.
The challenge consists of six tasks, ranging from the localization and
tracking of a single static loudspeaker using static microphone arrays to
fully dynamic scenes involving multiple moving sources and microphone arrays
on moving platforms. Sixteen state-of-the-art approaches were submitted for
participation in the LOCATA challenge, one of which needed to be discarded for
evaluation due to the lack of documentation. Seven submissions corresponded to
sound source localization algorithms, obtaining instantaneous estimates at
each time stamp of a recording. The remaining submissions combined
localization algorithms with source tracking, where spatio-temporal models of
the source motion are applied in order to exploit constructively knowledge of
the history of the source trajectories. The submissions incorporated
localization algorithms based on time-delay estimation, subspace processing,
beamforming, classification, and deep learning. Source tracking submissions
incorporated the Kalman filter and its variants, particle filters, variational
Bayesian approaches and PHD filters.

The controlled scenarios of static single-source in Task 1 are used to
evaluate the robustness of the submissions against reverberation and noise.
The results highlighted azimuth estimation accuracies of up to approximately
$1.0^{\circ}$ using the pseudo-spherical robot head, spherical Eigenmike and
planar DICIT array. For the hearing aids, recorded separately but in the same
environment, the average azimuth error was $8.5^{\circ}$. Interference from
multiple static loudspeakers in Task 2 leads to only small performance
degradations of up to $3^{\circ}$ compared to Task 1. Variations in the
source-sensor geometries due to the motion of the human talkers (Tasks 3 and
4), or the motion of the arrays and talkers (Tasks 5 and 6) affect
predominantly the track continuity, completeness and timeliness.

The evaluation also provides evidence for the intrinsic suitability of a given
approach for particular arrays or scenarios. For static scenarios (i.e., Tasks
1 and 2), subspace approaches demonstrated particularly accurate localization
using the Eigenmike and the robot head incorporating a large number of
microphones. Time delay estimation combined with a particle filter resulted in
the highest azimuth estimation accuracy for the planar DICIT array. Tracking
filters were shown to reduce FARs and missing detections by exploiting models
of the source dynamics. Specifically, the localization for moving human
talkers in Tasks 3-6 benefits from the incorporation of tracking in dynamic
scenarios, resulting in azimuth accuracies of up to $1.8^{\circ}$ using the
DICIT array, $3.1^{\circ}$ using the robot head, and $7.2^{\circ}$ using the
hearing aids.

Results for the Eigenmike highlighted that localization using spherical arrays
benefits from signal processing in the domain of spherical harmonics. The
results also indicated that the number of microphones in an array, to some
extent, can be traded off against the array aperture. This conclusion is
underpinned by the localization results for the 12-microphone robot head that
consistently outperformed the 32-microphone Eigenmike for approaches evaluated
for both arrays. Nevertheless, increasing microphone spacings also lead to
increasingly severe effects of spatial aliasing. As a consequence, all
submissions for the 2.24 m-wide DICIT array used subarrays of at most 32 cm
inter-microphone spacings.

Several issues remain open challenges for localization and tracking
approaches. Intuitively, localization approaches benefit from accurate
knowledge of the onsets and endpoints of speech to avoid false estimates
during periods of speech inactivity. Several approaches therefore incorporated
voice activity detection based on power spectral density estimates, zero-
crossing rates, or by implicit estimation of the onsets and endpoints of
speech from the latent variables estimated within a variational Bayesian
tracking approach. For the single-source scenarios, particularly low track
latency was achieved by the submission based on implicit estimation of the
voice activity periods. However, for the multi-source scenarios, approaches
incorporating voice activity detection led to increased track fragmentation
rates.

Morover, whereas sufficiently long frames are required to address the non-
stationarity of speech, dynamic scenes involving moving sources and/or sensors
require sufficiently short frames to accurately capture the spatio-temporal
variation of the source positions. Therefore, in dynamic scenes, estimation
errors due to the non-stationarity of speech must be traded off against biased
DoA estimates due to spatio-temporal variation in the source-sensor geometries
when selecting the duration of the microphone signals used for localization.
In combination with the adverse effects of reverberation and noise, non-
stationary signals in dynamic scenes therefore often lead to erroneous, false,
missing, spurious DoA estimates in practice.

To conclude, current research is predominantly focused on static scenarios.
Only a small subset of the approaches submitted to the LOCATA challenge
address the difficult real-world tasks involving multiple moving sources. The
challenge evaluation highlighted that there is significant room for
improvement, and hence substantial potential for future research. Except for
localizing a single static source in not too hostile scenarios none of the
problems is robustly solved to the extent desirable for, e.g., informed
spatial filtering with high spatial resolution. Therefore, research on
appropriate localization and tracking techniques remains an open challenge and
the authors hope that the LOCATA dataset and evaluation tools will be found
useful to also evaluate future progress.

Inevitably, there are substantial practical limitations in setting up data
challenges. In the case of LOCATA, it has resulted in the use of only one
acoustic environment because of the need for spatial localization of the
ground-truth. Future challenges may beneficially explore variation in
performance across different environments.

## Acknowledgement

The authors would like to thank all participants of the LOCATA challenge for
their submissions and feedback; Claas-Norman Ritter for his contributions to
the recordings of the LOCATA corpus; Prof. Verena Hafner for providing access
to the facilities at Humboldt-Universität zu Berlin; the anonymous reviewers
for their positive and helpfully detailed comments that led to significant
improvements of this manuscript; and the IEEE SPS Technical Committee on Audio
and Acoustic Signal Processing and the IEEE SPS Challenges and Data
Collections subcommittee for the support of the LOCATA challenge.

## References

  * [1] B. D. V. Veen and K. M. Buckley, “Beamforming: A Versatile Approach to Spatial Filtering,” _IEEE ASSP Magazine_ , vol. 5, no. 2, pp. 4–24, Apr. 1988.
  * [2] H. L. V. Trees, _Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory_. New York: Wiley, 2004.
  * [3] J. Benesty, J. Chen, and Y. Huang, _Microphone Array Signal Processing_. Berlin, Germany: Springer, 2008.
  * [4] L. C. Parra and C. V. Alvino, “Geometric Source Separation: Merging Convolutive Source Separation with Geometric Beamforming,” _IEEE Trans. on Speech and Audio Processing_ , vol. 10, no. 6, pp. 352–362, Sep. 2002\.
  * [5] Y. Zheng, K. Reindl, and W. Kellermann, “BSS for Improved Interference Estimation for Blind Speech Signal Extraction with two Microphones,” in _IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)_ , Dec. 2009, pp. 253–256.
  * [6] K. Reindl, S. Meier, H. Barfuß, and W. Kellermann, “Minimum Mutual Information-based Linearly Constrained Broadband Signal Extraction,” _IEEE Trans. on Audio, Speech, and Language Processing_, vol. 22, pp. 1096–1108, 2014.
  * [7] S. Markovich-Golan, S. Gannot, and W. Kellermann, “Combined LCMV-TRINICON Beamforming for Separating Multiple Speech Sources in Noisy and Reverberant Environments,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 25, no. 2, pp. 320–332, Feb. 2017.
  * [8] S. Harding, J. Barker, and G. J. Brown, “Mask Estimation for Missing Data Speech Recognition based on Statistics of Binaural Interaction,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 14, no. 1, pp. 58–67, Jan. 2006.
  * [9] C. Evers and P. A. Naylor, “Optimized Self-Localization for SLAM in Dynamic Scenes Using Probability Hypothesis Density Filters,” _IEEE Trans. on Signal Processing_, vol. 66, no. 4, pp. 863–878, Feb. 2018.
  * [10] ——, “Acoustic SLAM,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 26, no. 9, pp. 1484–1498, Sep. 2018.
  * [11] K. Harada, E. Yoshida, and K. Yokoi, _Motion Planning for Humanoid Robots_. Springer, 2014.
  * [12] J. B. Allen and D. A. Berkley, “Image Method for Efficiently Simulating Small-Room Acoustics,” _Journal of the Acoustical Society of America_ , vol. 64, no. 4, pp. 943–950, Apr. 1979.
  * [13] E. A. P. Habets, I. Cohen, and S. Gannot, “Generating Nonstationary Multisensor Signals under a Spatial Coherence Constraint,” _Journal of the Acoustical Society of America_ , vol. 124, no. 5, pp. 2911–2917, Nov. 2008\.
  * [14] D. P. Jarrett, E. A. P. Habets, M. R. P. Thomas, and P. A. Naylor, “Simulating Room Impulse Responses for Spherical Microphone Arrays,” in _Proc. of IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP)_, Prague, Czech Republic, May 2011, pp. 129–132.
  * [15] H. W. Löllmann, C. Evers, A. Schmidt, H. Mellmann, H. Barfuss, P. A. Naylor, and W. Kellermann, _IEEE-AASP Challenge on Source Localization and Tracking: Data Corpus_ , [Online] https://doi.org/10.5281/zenodo.3630470, Jan. 2020.
  * [16] C. Evers, H. W. Löllmann, A. Schmidt, H. Mellmann, H. Barfuss, P. A. Naylor, and W. Kellermann, _IEEE-AASP Challenge on Source Localization and Tracking: MATLAB Evaluation Framework_ , [Online] https://github.com/cevers/sap_locata_eval, Jan. 2020.
  * [17] H. W. Löllmann, C. Evers, A. Schmidt, H. Mellmann, H. Barfuss, P. A. Naylor, and W. Kellermann, “The LOCATA Challenge Data Corpus for Acoustic Source Localization and Tracking,” in _Proc. of IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)_ , Sheffield, UK, Jul. 2018.
  * [18] ——, _IEEE-AASP Challenge on Source Localization and Tracking: Documentation for Participants_ , [Online] www.locata-challenge.org, Apr. 2018.
  * [19] C. Evers, H. W. Löllmann, H. Mellmann, A. Schmidt, H. Barfuss, P. A. Naylor, and W. Kellermann, “LOCATA challenge - Evaluation tasks and measures,” in _Proc. of Intl. Workshop on Acoustic Signal Enhancement(IWAENC)_, Tokyo, Japan, Sep. 2018.
  * [20] J. K. Nielsen, J. R. Jensen, S. H. Jensen, and M. G. Christensen, “The Single- and Multichannel Audio Recordings Database (SMARD),” in _Proc. of Intl. Workshop on Acoustic Signal Enhancement(IWAENC)_, Antibes, France, Sep. 2014. [Online]. Available: http://www.smard.es.aau.dk/
  * [21] G. Lathoud, J.-M. Odobez, and D. Gatica-Perez, “AV16.3: An Audio-Visual Corpus for Speaker Localization and Tracking,” in _Machine Learning for Multimodal Interaction_ , S. Bengio and H. Bourlard, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005, pp. 182–195.
  * [22] J. Barker, R. Marxer, E. Vincent, and S. Watanabe, “The Third ‘CHiME’ Speech Separation and Recognition Challenge: Dataset, Task and Baselines,” in _Proc. of IEEE Workshop on Automatic Speech Recognition and Understanding (ASRU)_ , Scottsdale (Arizona), USA, Dec. 2015, pp. 504–511.
  * [23] J. Eaton, N. D. Gaubitch, A. H. Moore, and P. A. Naylor, “Estimation of Room Acoustic Parameters: The ACE Challenge,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 24, no. 10, pp. 1681–1693, Oct. 2016.
  * [24] K. Kinoshita, M. Delcroix, S. Gannot, E. Habets, R. Haeb-Umbach, W. Kellermann, V. Leutnant, R. Maas, T. Nakatani, B. Raj, A. Sehr, and T. Yoshioka, “A summary of the REVERB challenge: state-of-the-art and remaining challenges in reverberant speech processing research,” _EURASIP Journal on Advances in Signal Processing_ , no. 7, Jan. 2016.
  * [25] M. Ravanelli, L. Cristoforetti, R. Gretter, M. Pellin, A. Sosi, and M. Omologo, “The DIRHA-English Corpus and Related Tasks for Distant-Speech Recognition in Domestic Environments,” in _Proc. IEEE Work. Auto. Speech Recog. & Under. (ASRU)_, Dec. 2015, pp. 275–282.
  * [26] X. Alameda-Pineda, J. Sanchez-Riera, J. Wienke, V. Franc, J. Cech, K. Kulkarni, A. Deleforge, and R. P. Horaud, “RAVEL: An Annotated Corpus for Training Robots with Audiovisual Abilities,” _Journal on Multimodal User Interfaces_ , vol. 7, no. 1-2, pp. 79–91, 2013.
  * [27] A. Deleforge and R. Horaud, “Learning the Direction of a Sound Source Using Head Motions and Spectral Features,” INRIA, Research Report RR-7529, Feb. 2011\. [Online]. Available: https://hal.inria.fr/inria-00564708
  * [28] R. Stiefelhagen, K. Bernardin, R. Bowers, J. Garofolo, D. Mostefa, and P. Soundararajan, “The CLEAR 2006 Evaluation,” in _Multimodal Technologies for Perception of Humans_ , R. Stiefelhagen and J. Garofolo, Eds. Berlin, Heidelberg: Springer, 2007, pp. 1–44.
  * [29] M. Krindis, G. Stamou, H. Teutsch, S. Spors, N. Nikolaidis, R. Rabenstein, and I. Pitas, “An Audio-Visual Database for Evaluating Person Tracking Algorithms,” in _Proc. of IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP)_, Philadelphia, PA, 2005.
  * [30] M. Strauss, P. Mordel, V. Miguet, and A. Deleforge, “DREGON: Dataset and Methods for UAV-Embedded Sound Source Localization,” in _IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2018)_. Madrid, Spain: IEEE, Oct. 2018, pp. 5735–5742.
  * [31] R. N. Jazar, _Theory of Applied Robotics: Kinematics, Dynamics, and Control_ , 2nd ed. Springer, 2010.
  * [32] mh acoustics, _EM32 Eigenmike microphone array release notes (v17.0)_ , [Online] www.mhacoustics.com/sites/default/files/ReleaseNotes.pdf, Oct. 2013.
  * [33] Q. V. Nguyen, F. Colas, E. Vincent, and F. Charpillet, “Motion planning for robot audition,” _Autonomous Robots_ , vol. 43, no. 8, pp. 2293–2317, Dec. 2019. [Online]. Available: https://hal.inria.fr/hal-02188342
  * [34] OptiTrack, _Product Information about OptiTrack Flex13_ , [Online] http://optitrack.com/products/flex-13/, http://optitrack.com/products/flex-13/, [Feb. 24, 2018].
  * [35] V. Tourbabin and B. Rafaely, “Theoretical Framework for the Optimization of Microphone Array Configuration for Humanoid Robot Audition,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 22, no. 12, Dec. 2014.
  * [36] ——, “Optimal Design of Microphone Array for Humanoid-Robot Audition,” in _Proc. of Israeli Conf. on Robotics (ICR)_ , Herzliya, Israel, Mar. 2016, (abstract).
  * [37] A. Brutti, L. Cristoforetti, W. Kellermann, L. Marquardt, and M. Omologo, “WOZ Acoustic Data Collection for Interactive TV,” _Language Resources and Evaluation_ , vol. 44, no. 3, pp. 205–219, Sep. 2010.
  * [38] C. Veaux, J. Yamagishi, and K. MacDonald, “English Multi-speaker Corpus for CSTR Voice Cloning Toolkit,” [Online] http://homepages.inf.ed.ac.uk/jyamagis/page3/page58/page58.html, [Jan. 9, 2017].
  * [39] S. Aǧcaer and R. Martin, “Binaural Source Localization based on Modulation-Domain Features and Decision Pooling,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018.
  * [40] Y. Liu, W. Wang, and V. Kilic, “Intensity Particle Flow SMC-PHD Filter for Audio Speaker Tracking,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018.
  * [41] X. Qian, A. Cavallaro, A. Brutti, and M. Omologo, “LOCATA Challenge: Speaker Localization with a Planar Array,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018\.
  * [42] X. Li, Y. Ban, L. Girin, X. Alameda-Pineda, and R. Horaud, “A Cascaded Multiple-Speaker Localization and Tracking System,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018.
  * [43] R. Lebarbenchon, E. Camberlein, D. di Carlo, C. Gaultier, A. Deleforge, and N. Bertin, “Evaluation of an Open-Source Implementation of the SRP-PHAT Algorithm within the 2018 LOCATA Challenge,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018.
  * [44] D. Salvati, C. Drioli, and G. L. Foresti, “Localization and Tracking of an Acoustic Source using a Diagonal Unloading Beamforming and a Kalman Filter,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018.
  * [45] L. D. Mosgaard, D. Pelegrin-Garcia, T. B. Elmedyb, M. J. Pihl, and P. Mowlaee, “Circular Statistics-based Low Complexity DOA Estimation for Hearing Aid Application,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018.
  * [46] J. Pak and J. W. Shin, “LOCATA Challenge: A Deep Neural Networks-Based Regression Approach for Direction-Of-Arrival Estimation,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018.
  * [47] S. Kitić and A. Guérin, “TRAMP: Tracking by a Realtime Ambisonic-Based Particle Filter,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018\.
  * [48] L. Madmoni, H. Beit-On, H. Morgenstern, and B. Rafaely, “Description of Algorithms for Ben-Gurion University Submission to the LOCATA Challenge,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018.
  * [49] K. Nakadai, K. Itoyama, K. Hoshiba, and H. G. Okuno, “MUSIC-Based Sound Source Localization and Tracking for Tasks 1 and 3,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018.
  * [50] A. H. Moore, “Multiple Source Direction of Arrival Estimation using Subspace Pseudointensity Vectors,” in _Proc. of LOCATA Challenge Workshop - a satellite event of IWAENC 2018_, Tokyo, Japan, Sep. 2018.
  * [51] J. Sohn, N. S. Kim, and W. Sung, “A Statistical Model-Based Voice Activity Detection,” _IEEE Signal Processing Letters_, vol. 6, no. 1, pp. 1–3, Jan. 1999.
  * [52] C. Evers, Y. Dorfan, S. Gannot, and P. A. Naylor, “Source Tracking Using Moving Microphone Arrays for Robot Audition,” in _Proc. of IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP)_, New Orleans (Louisiana), USA, Mar. 2017.
  * [53] C. Evers, E. A. P. Habets, S. Gannot, and P. A. Naylor, “DoA Reliability for Distributed Acoustic Tracking,” _IEEE Signal Processing Letters_, vol. 25, no. 9, pp. 1320–1324, Sep. 2018.
  * [54] A. Brendel and W. Kellermann, “Learning-based Acoustic Source-Microphone Distance Estimation using the Coherent-to-Diffuse Power Ratio,” in _Proc. of IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP)_, Apr. 2018, pp. 61–65.
  * [55] S. Argentieri, P. Danès, and P. Souères, “A Survey on Sound Source Localization in Robotics: From Binaural to Array Processing Methods,” _Computer Speech & Language_, vol. 34, no. 1, pp. 87 – 112, 2015.
  * [56] C. Rascon and I. Meza, “Localization of Sound Sources in Robotics: A Review,” _Robotics and Autonomous Systems_ , vol. 96, pp. 184 – 210, 2017\.
  * [57] M. Cobos, F. Antonacci, A. Alexandridis, A. Mouchtaris, and B. Lee, “A Survey of Sound Source Localization Methods in Wireless Acoustic Sensor Networks,” _Wireless Acoustic Sensor Networks and Applications_ , May 2017.
  * [58] M. Souden, J. Benesty, and S. Affes, “Broadband Source Localization From an Eigenanalysis Perspective,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 18, no. 6, pp. 1575–1587, Aug. 2010.
  * [59] J. Benesty, “Adaptive Eigenvalue Decomposition Algorithm for Passive Acoustic Source Localization,” _The Journal of the Acoustical Society of America_ , vol. 107, no. 1, pp. 384–391, 2000.
  * [60] T. G. Dvorkind and S. Gannot, “Time Difference of Arrival Estimation of Speech Source in a Noisy and Reverberant Environment,” _Signal Processing_ , vol. 85, no. 1, pp. 177 – 204, 2005.
  * [61] S. Gannot, D. Burshtein, and E. Weinstein, “Signal Enhancement using Beamforming and Nonstationarity with Applications to Speech,” _IEEE Trans. on Signal Processing_, vol. 49, no. 8, pp. 1614–1626, Aug. 2001.
  * [62] X. Li, L. Girin, R. Horaud, and S. Gannot, “Estimation of the Direct-Path Relative Transfer Function for Supervised Sound-Source Localization,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 24, no. 11, pp. 2171–2186, Nov. 2016.
  * [63] J. P. Dmochowski, J. Benesty, and S. Affes, “Broadband MUSIC: Opportunities and Challenges for Multiple Source Localization,” in _Proc. of Workshop on Applications of Signal Processing to Audio and Acoustics(WASPAA)_, New Paltz (New York), USA, Oct. 2007, pp. 18–21.
  * [64] B. Berdugo, M. A. Doron, J. Rosenhouse, and H. Azhari, “On Direction Finding of an Emitting Source from Time Delays,” _Journal of the Acoustical Society of America_ , vol. 105, no. 6, pp. 3355–3363, 1999.
  * [65] Y. Huang, J. Benesty, G. W. Elko, and R. M. Mersereau, “Real-time Passive Source Localization: A Practical Linear-Correction Least-Squares Approach,” _IEEE Trans. on Speech and Audio Processing_ , vol. 9, no. 8, pp. 943–956, Nov. 2001.
  * [66] H. Cao, Y. T. Chan, and H. C. So, “Maximum Likelihood TDOA Estimation From Compressed Sensing Samples Without Reconstruction,” _IEEE Signal Processing Letters_, vol. 24, no. 5, pp. 564–568, May 2017.
  * [67] H. Sundar, T. V. Sreenivas, and C. S. Seelamantula, “TDOA-Based Multiple Acoustic Source Localization Without Association Ambiguity,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 26, no. 11, pp. 1976–1990, Nov. 2018.
  * [68] X. Li, Y. Ban, L. Girin, X. Alameda-Pineda, and R. Horaud, “Online Localization and Tracking of Multiple Moving Speakers in Reverberant Environments,” _IEEE Journal of Selected Topics in Signal Processing_ , vol. 13, no. 1, pp. 88–103, Mar. 2019.
  * [69] J. Traa and P. Smaragdis, “A Wrapped Kalman Filter for Azimuthal Speaker Tracking,” _IEEE Signal Processing Letters_, vol. 20, no. 12, Dec. 2013.
  * [70] J. Blauert, _Spatial Hearing: The Psychophysics of Human Sound Localization_. Cambridge, MA: MIT Press, 1983.
  * [71] G. F. Kuhn, “Model for the Interaural Time Differences in the Azimuthal Plane,” _Journal of the Acoustical Society of America_ , vol. 62, no. 1, pp. 157–167, 1977.
  * [72] F. L. Wightman and D. J. Kistler, “The Dominant Role of Low‐Frequency Interaural Time Differences in Sound Localization,” _Journal of the Acoustical Society of America_ , vol. 91, no. 3, pp. 1648–1661, 1992.
  * [73] D. Wang and G. J. Brown, _Computational Auditory Scene Analysis: Principles, Algorithms, and Applications_. Wiley, 2006.
  * [74] M. Raspaud, H. Viste, and G. Evangelista, “Binaural Source Localization by Joint Estimation of ILD and ITD,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 18, no. 1, pp. 68–77, Jan. 2010.
  * [75] M. Farmani, M. S. Pedersen, Z. Tan, and J. Jensen, “Informed Sound Source Localization Using Relative Transfer Functions for Hearing Aid Applications,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 25, no. 3, pp. 611–623, Mar. 2017.
  * [76] ——, “Bias-Compensated Informed Sound Source Localization Using Relative Transfer Functions,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 26, no. 7, pp. 1275–1289, Jul. 2018.
  * [77] E. L. Benaroya, N. Obin, M. Liuni, A. Roebel, W. Raumel, and S. Argentieri, “Binaural Localization of Multiple Sound Sources by Non-Negative Tensor Factorization,” _IEEE/ACM Trans. on Audio, Speech, and Language Processing_ , vol. 26, no. 6, pp. 1072–1082, Jun. 2018.
  * [78] A. Shashua and T. Hazan, “Non-negative Tensor Factorization with Applications to Statistics and Computer Vision,” in _Intl. Conf. Machine Learning_ , ser. ICML ’05. New York, NY, USA: ACM, 2005, pp. 792–799.
  * [79] E. H. A. Langendijk and A. W. Bronkhorst, “Contribution of Spectral Cues to Human Sound Localization,” _Journal of the Acoustical Society of America_ , vol. 112, no. 4, pp. 1583–1596, 2002.
  * [80] T. V. den Bogaert, E. Carette, and J. Wouters, “Sound Source Localization using Hearing Aids with Microphones placed Behind-the-Ear, In-the-Canal, and In-the-Pinna,” _International Journal of Audiology_ , vol. 50, no. 3, pp. 164–176, 2011.
  * [81] H. Wallach, “The Role of Head Movement and Vestibular and Visual Cues in Sound Localization,” _J. Exp. Psychol._ , vol. 27, p. 339–368, 1940.
  * [82] J. Burger, “Front-Back Discrimination of the Hearing Systems,” _Acta Acustica united with Acustica_ , vol. 8, no. 5, pp. 301–302, 1958.
  * [83] W. R. Thurlow, J. W. Mangels, and P. S. Runge, “Head Movements During Sound Localization,” _Journal of the Acoustical Society of America_ , vol. 42, no. 2, pp. 489–493, 1967.
  * [84] F. L. Wightman and D. J. Kistler, “Resolution of Front–Back Ambiguity in Spatial Hearing by Listener and Source Movement,” _Journal of the Acoustical Society of America_ , vol. 105, no. 5, pp. 2841–2853, 1999.
  * [85] S. Perrett and W. Noble, “The Contribution of Head Motion Cues to Localization of Low-Pass Noise,” _Perception & Psychophysics_, vol. 59, no. 7, pp. 1018–1026, Jan 1997.
  * [86] D. M. Leakey, “Some Measurements on the Effects of Interchannel Intensity and Time Differences in Two Channel Sound Systems,” _Journal of the Acoustical Society of America_ , vol. 31, no. 7, pp. 977–986, 1959.