=Paper=
{{Paper
|id=Vol-3666/paper02
|storemode=property
|title=Edge computing applications: using a linear MEMS microphone array for UAV position detection through sound source localization
|pdfUrl=https://ceur-ws.org/Vol-3666/paper02.pdf
|volume=Vol-3666
|authors=Andrii V. Riabko,Tetiana A. Vakaliuk,Oksana V. Zaika,Roman P. Kukharchuk,Valerii V. Kontsedailo
|dblpUrl=https://dblp.org/rec/conf/doors/RiabkoVZKK24
}}
==Edge computing applications: using a linear MEMS microphone array for UAV position detection through sound source localization==
https://ceur-ws.org/Vol-3666/paper02.pdf
Edge computing applications: using a linear MEMS
microphone array for UAV position detection through
sound source localization
Andrii V. Riabko1 , Tetiana A. Vakaliuk2,3,4,5 , Oksana V. Zaika1 , Roman P. Kukharchuk1 and
Valerii V. Kontsedailo6
1
Oleksandr Dovzhenko Hlukhiv National Pedagogical University, 24 Kyivska Str., Hlukhiv, 41400, Ukraine
2
Zhytomyr Polytechnic State University, 103 Chudnivsyka Str., Zhytomyr, 10005, Ukraine
3
Institute for Digitalisation of Education of the NAES of Ukraine, 9 M. Berlynskoho Str., Kyiv, 04060, Ukraine
4
Kryvyi Rih State Pedagogical University, 54 Universytetskyi Ave., Kryvyi Rih, 50086, Ukraine
5
Academy of Cognitive and Natural Sciences, 54 Universytetskyi Ave., Kryvyi Rih, 50086, Ukraine
6
Inner Circle, Nieuwendijk 40, 1012 MB Amsterdam, Netherlands
Abstract
This study explores the use of a microphone array to determine the position of an unmanned aerial vehicle (UAV)
based solely on the sound of its engines. The accuracy of localization depends crucially on the arrangement of
the microphones. The study also considers a mathematical model of pulse density modulation for a digital MEMS
microphone. It demonstrates the frequency dependence of the efficiency of a differential array of first-order
microphones. Based on this frequency dependence of directivity and the instability model of the microphone
parameters, a rational operating frequency range for the normal functioning of the microphone array can
be established. The study proposes a model of a linear microphone array based on MEMS omnidirectional
microphones. With a specific geometrical arrangement, this array produces a bidirectional pattern, which can
be easily transformed into a unidirectional pattern using specialized algorithms or hardware (e.g., ADAU1761
codecs).
Keywords
edge computing, UAV, sound source localization, MEMS microphone, microphone array, frequency, directivity
1. Introduction
Determining the position of a UAV (Unmanned Aerial Vehicle) by the sound of its engines can be
important for several reasons. In military or security applications, being able to identify and locate UAVs
by their engine sounds can help in detecting potential threats, including hostile drones or unauthorized
surveillance. Sound-based localization can aid in the development of countermeasures to mitigate the
risks posed by UAVs in sensitive areas.
Sound-based UAV detection can complement existing air traffic management systems, providing
additional situational awareness for managing airspace and preventing collisions with manned aircraft.
In search and rescue operations or in case of lost or malfunctioning drones, sound-based tracking can
assist in locating and recovering UAVs.
In conservation efforts, it can help monitor UAVs used for illegal activities like poaching or wildlife
disturbance. In urban areas or regions with dense UAV traffic, sound-based tracking can be useful for
enforcing regulations related to UAV flight paths, altitudes, and no-fly zones. For protecting privacy,
doors-2024: 4th Edge Computing Workshop, April 5, 2024, Zhytomyr, Ukraine
" ryabko@meta.ua (A. V. Riabko); tetianavakaliuk@acnsci.org (T. A. Vakaliuk); ksuwazaika@gmail.com (O. V. Zaika);
kyxap4yk1@ukr.net (R. P. Kukharchuk); valerakontsedailo@gmail.com (V. V. Kontsedailo)
~ http://irbis-nbuv.gov.ua/ASUA/0051396 (A. V. Riabko); https://acnsci.org/vakaliuk/ (T. A. Vakaliuk);
http://pfm.gnpu.edu.ua/index.php/struktura1/2015-04-01-14-50-26 (O. V. Zaika); http://irbis-nbuv.gov.ua/ASUA/0076404
(R. P. Kukharchuk)
0000-0001-7728-6498 (A. V. Riabko); 0000-0001-6825-4697 (T. A. Vakaliuk); 0000-0002-8479-9408 (O. V. Zaika);
0000-0002-7588-7406 (R. P. Kukharchuk); 0000-0002-6463-370X (V. V. Kontsedailo)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
14
sound-based detection can help identify UAVs flying near private properties, providing a means to take
legal action against intrusive drones.
Studying the acoustic signatures of UAVs can aid in research and development efforts to design quieter
and more environmentally friendly drones. During natural disasters or emergencies, knowing the
positions of UAVs, such as those used for aerial surveys or damage assessment, can assist in coordinating
response efforts. Sound-based UAV detection can be employed in border control to monitor and respond
to unauthorized drone incursions.
As drone delivery and urban air mobility concepts develop, sound-based localization can contribute
to managing UAV traffic in urban environments. While sound-based UAV localization offers several
advantages, it also has limitations, such as accuracy challenges in noisy environments and the need
for specialized equipment. Therefore, it is often used in conjunction with other tracking and detection
methods, such as radar, visual recognition, and GPS, to provide comprehensive situational awareness
and enhance safety and security in various applications.
The goal of our work is to develop a software and hardware system for capturing hardware-
synchronized sound using digital MEMS microphones (Microelectromechanical Systems, MEMS) for
further use in sound source localization systems. This system is intended for further use in sound
source localization systems, marking a significant advancement in the field of edge computing.
2. Theoretical background
Over the past few decades, acoustic source localization has emerged as a focal point of interest within the
research community [1, 2]. Most studies of sound source identification are based on the analysis of the
physiological mechanism of human hearing [3, 4]. It is common practice to use arrays of microphones
[5]. An actual problem is acoustic beam formation for sound source localization and its application [6].
Microphone array processing represents a well-established methodology employed in the estimation
of sound source direction. In a groundbreaking contribution by Yamada et al. [7], they introduce an
innovative approach referred to as Multiple Triangulation and Gaussian Sum Filter Tracking (MT-GSFT).
This advanced technique adeptly derives the precise location of sound sources through triangulation,
utilizing microphone arrays seamlessly integrated into a fleet of multiple drones [7]. The domain of
speech signal processing encompasses several critical areas, and among them, multiple sound source
localization (SSL) stands out as a notable and relevant field. A notable contribution to this field comes
from Firoozabadi et al. [8], who introduced a two-step approach for the localization of multiple sound
sources in three dimensions (3D). This method relies on the precise estimation of time delays (TDE) and
strategically leverages distributed microphone arrays (DMA) to enhance the accuracy and effectiveness
of the localization process [8].
Sasaki et al. [9] present a method designed to map the 3D coordinates of a sound source by leveraging
data gathered from an array of microphones, with each microphone providing an autonomous directional
estimate. Additionally, LiDAR technology is employed to create a comprehensive 3D representation of
the surroundings and accurately determine the sensor’s position with six degrees of freedom (6-DoF).
Catalbas et al. [10] conduct a comparative analysis, assessing the effectiveness of generalized cross-
correlation techniques in contrast to noise reduction filters concerning the estimation of sound source
trajectory. Throughout the entire movement, they calculate the azimuth angle between the sound
source and the receiver. This calculation relies on the parameter of Interaural Time Difference (ITD) to
determine the azimuth angle. They then evaluate the accuracy of the estimated delay using various
types of Generalized Cross-Correlation (GCC) algorithms for comparison.
It is possible for unmanned aerial vehicles (UAVs) to use audio information to compensate for poor
visual information. Hoshiba et al. [11] developed a microphone array system built into the UAV to
localize the sound source in flight. They developed the Spherical Microphone Array System (SMAS),
consisting of a microphone array, a stable wireless network communication system, and intuitive
visualization tools.
Tachikawa et al. [12] introduced an innovative approach that involves estimating positions by utilizing
15
a modified variant of the convex clustering method in conjunction with sparse coefficients estimation.
Additionally, they put forth a technique for constructing a well-suited monopole dictionary, which is
based on coherence, ensuring that the convex clustering-based method can accurately estimate the
distances of sound sources. The study involved conducting a series of numerical and measurement
experiments aimed at assessing the effectiveness and performance of this novel methodology.
When dealing with multiple sound sources, establishing a reliable data association between local-
ization information and the corresponding sound sources becomes paramount for achieving optimal
performance. To address the challenges posed by data association uncertainty, Wakabayashi et al.
[13] extended the Global Nearest Neighbor (GNN) approach, introducing a modified version known
as GNN-c, specifically tailored to meet the real-time and low-latency requirements of drone audio
applications. The outcome of their efforts showcases a system capable of accurately estimating the
positions of multiple sound sources, achieving an impressive accuracy level of approximately 3 meters.
Many acoustic image-based sound source diagnosis systems suffer from spatial stationary limitations,
making it challenging to integrate information from various capture positions, thereby leading to unreli-
able and incomplete diagnostics. In their paper, Carneiro and Berry [14] introduce a novel measurement
methodology called Acoustic Imaging Structure From Motion (AISFM). This approach utilizes a mobile
spherical microphone array to create acoustic images through beamforming, seamlessly integrating data
from multiple capture positions. Their method is not only proposed but also meticulously developed
and rigorously validated, offering a promising solution to enhance the accuracy and comprehensiveness
of sound source diagnostics.
In a research conducted by Kita and Kajikawa [15] a sound source localization (SSL) technique is
introduced, specifically designed for the localization of sources situated within structures, including
mechanical equipment and buildings.
The registration of acoustic signals with cross-shaped antennas is widely discussed in the literature
[16].
Advanced signal processing methods involving multiple microphones can enhance noise resilience.
However, as the quantity of microphones employed escalates, the computational overhead rises con-
comitantly. This, in turn, curtails response time and hinders their extensive adoption across various
categories of mobile robotic platforms [17]. Within the realm of robot audition, sound source localization
(SSL) holds a pivotal role, serving as a fundamental component. SSL empowers a robotic platform to
pinpoint the origin of sound using auditory cues exclusively. Its significance extends beyond mere sound
localization, as it significantly influences other facets of robot audition, including source separation.
Moreover, SSL contributes to elevating the quality of human-robot interaction by augmenting the
robot’s perceptual prowess [18].
In general, machine learning is widely used in acoustics [19, 20]. In the realm of human-robot
interaction, He et al. [21] have introduced a pioneering approach. Their proposal involves harnessing
neural networks for the simultaneous detection and localization of multiple sound sources. This
innovative method represents a departure from conventional signal processing techniques by offering a
distinct advantage: it necessitates fewer stringent assumptions about the environmental conditions,
thereby enhancing its adaptability and effectiveness [21]. Ebrahimkhanlou and Salamone [22] have
put forth an advanced methodology for localizing acoustic emissions (AE) sources within metallic
plates, especially those with intricate geometric features like rivet-connected stiffeners. This innovative
approach leverages two deep learning techniques: a stack of autoencoders and a convolutional neural
network (CNN), strategically employed to enhance the accuracy and precision of the localization process
[22].
In their pioneering work, Adavanne et al. [23] have introduced an innovative solution – a convolu-
tional recurrent neural network (CRNN) – designed to address the intricate task of joint sound event
localization and detection (SELD) within three-dimensional (3-D) space. This method represents a
significant advancement in the field, enabling the simultaneous identification and spatial localization of
multiple overlapping sound events with remarkable precision.
Let’s summarize the theoretical review. Localizing a sound source means determining the direction
or location from which a sound is emanating. There are several algorithms and techniques used for
16
sound source localization, and the choice of method often depends on the specific application and
available hardware. Here are some commonly used algorithms. Time Difference of Arrival (TDOA) is
based on measuring the time it takes for a sound to reach multiple microphones. By comparing the
time differences, it’s possible to triangulate the source’s position. Cross-correlation or beamforming
techniques are often used to calculate the time differences accurately. Generalized Cross-Correlation
(GCC) is a technique used in conjunction with TDOA. It involves cross-correlating the signals from
two or more microphones to find the delay between them. GCC-PHAT (GCC with Phase Transform) is
a commonly used variant that works well in reverberant environments. Steering Vector Methods are
commonly used in microphone arrays or beamforming applications [24]. They estimate the direction of
arrival (DOA) by analyzing the phase differences between signals received by different microphones.
Popular algorithms include Multiple Signal Classification (MUSIC) and Estimation of Signal Parameters
via Rotational Invariance Techniques (ESPRIT). Acoustic Intensity Methods measure the sound intensity
at multiple microphone positions and use this information to estimate the source direction. The Steered
Response Power (SRP) algorithm is an example of this approach. Machine learning and deep learning
techniques, such as neural networks and support vector machines, can be used to train models for
sound source localization. These models can take input from multiple microphones and learn to predict
the source location based on training data. Particle filtering is a probabilistic method that estimates
the source location using a Bayesian filtering approach. It is useful when dealing with complex and
dynamic environments. Some methods use time-frequency analysis techniques like the Short-Time
Fourier Transform (STFT) or Wavelet Transform to analyze the spectral content of audio signals and
infer the source location. In mobile sound source localization, the Doppler effect can be used to estimate
the source’s speed and direction based on the frequency shift in the received signal. Many practical
systems use a combination of the above techniques to improve accuracy and robustness, especially in
real-world scenarios with noise and reverberation.
The choice of algorithm depends on factors like the number and arrangement of microphones, envi-
ronmental conditions, computational resources, and the desired level of accuracy. Different applications,
such as robotics, audio conferencing, surveillance, and hearing aids, may employ different algorithms
tailored to their specific requirements.
Determining the position of a UAV (Unmanned Aerial Vehicle) based solely on the sound of its
engines can be challenging but is feasible using a combination of sound source localization techniques
and signal processing. Here’s a high-level overview of the process:
1. Microphone Array Setup: Set up a microphone array on the ground. The microphones should
be strategically placed to capture the UAV’s sound from different angles. The arrangement of
microphones plays a crucial role in accurate localization. The response of microphone arrays
depends, first of all, on the number of microphones working on the array [25].
2. Sound Data Collection: Record the sound generated by the UAV’s engines as it flies overhead.
Ensure that the recording system has a high sampling rate to capture the sound accurately.
3. Time Delay of Arrival (TDOA): Analyze the recorded audio data to calculate the time delay of
arrival (TDOA) of the sound at each microphone. TDOA is the time difference between when the
sound reaches different microphones. This information is critical for triangulation.
4. Triangulation: Use the TDOA data from multiple microphones to triangulate the UAV’s posi-
tion. Several algorithms, such as multilateration or beamforming, can help estimate the UAV’s
coordinates based on the TDOA information.
5. UAV Sound Signature: To improve accuracy, consider using machine learning techniques to create
a database of UAV sound signatures. This involves training a model to recognize the unique
sound characteristics of different UAVs. When a new sound recording is obtained, the model can
help identify the specific UAV type.
6. Integration with Other Sensors: For real-time tracking, integrate sound-based localization with
other sensors like GPS, radar, or visual cameras. This fusion of data sources can provide more
accurate and robust positioning.
17
7. Calibration and Testing: Regularly calibrate and test the microphone array and signal processing
algorithms to ensure accurate and reliable results.
It’s important to note that the accuracy of sound-based UAV localization depends on various factors,
including the UAV’s altitude, speed, engine type, and background noise. Additionally, environmental
conditions, such as wind and temperature, can affect sound propagation and localization accuracy.
Therefore, this method may work best in controlled environments or in conjunction with other tracking
methods for enhanced precision and reliability.
3. Research methods
The goal of our work is to develop a software and hardware system for capturing hardware-synchronized
sound using digital MEMS microphones (Microelectromechanical Systems, MEMS) for further use in
sound source localization systems.
Despite the fact that the use of radar equipment has become part of everyday practice when monitoring
UAVs, there is some interest in assessing the possibility of using airborne acoustic signals for this purpose.
The above applies mainly to receiving hydroacoustic antennas, i.e. to conditions when the speed of
the source is much lower than the speed of sound 𝑀 = 𝑣/𝑐 ≪ 1. In the case of receiving air-acoustic
signals propagating at a speed of sound significantly lower than that of hydroacoustic signals in water
and created by fairly fast moving sources (passenger cars on autobahns, racing cars, the movement of
airliners along runways during takeoff and landing, UAVs), there is a different situation. Research into
the features of recording these signals with phased arrays remains relevant, since on their basis data
can be obtained on the current coordinates and speed of movement of a moving object. The purpose of
this work is to analyze the angular dependencies in the signal at the output of a receiving air-acoustic
antenna and those qualitative changes in their nature that are introduced due to a combination of
factors such as the Doppler effect and the sharp directivity of the antenna array.
A special case is considered, which is widespread in everyday practice, when the trajectory of an
object is rectilinear, lies in a horizontal plane, close and parallel to the Earth’s surface, and the speed of
its movement is constant.
As previously stated, the arrangement of microphones plays a crucial role in accurate localization.
The purpose of the study is to find the optimal configuration of a microphone array for localizing a
moving sound source (UAV).
Directivity is the sensitivity of a microphone to sound depending on the direction or angle from
which the sound is coming. Directionality or sound pickup angle is considered to be the area of possible
location of the sound signal source, within which there is no significant loss of microphone efficiency.
Microphones use different directivity characteristics. They are most often depicted as polar diagrams.
This is done to graphically display sensitivity variations around the microphone over a 360-degree
range, where the microphone is the center of the circle and the angular reference point is placed in
front of the microphone. The polar pattern shows how a microphone’s sensitivity to a sound signal
depends on the location of its source.
Microphone arrays are an array of several microphones combined by joint digital signal processing.
Microphone arrays provide the following advantages over single-channel systems: 1) directionality of
sound reception; 2) noise suppression of point sources; 3) suppression of non-stationary environmental
noise; 4) partial weakening of reverberation; 5) the possibility of spatial localization of the sound source;
6) the ability to accompany a moving point sound source.
A microphone array is one of the types of directional microphones, implemented as a set of sound
receivers operating in concert (in phase or with certain phase delays). Geometrically, gratings can
be implemented in different configurations – one-dimensional (linear, arc-shaped), two-dimensional
(flat, spherical), three-dimensional, spiral, with uniform or non-equidistant pitch. The array’s radiation
pattern is created by changing the ratio of phase delays for different channels (in the simplest case, an
in-phase array with a fixed position of the main lobe; in more complex and expensive implementations,
18
a scanning system). The implementation of phase delays can be hardware (for example, on analog delay
lines) or software (digital).
The basic microphone array structures are Broadside and Endfire (figure 1).
Figure 1: Basic array structures.
These structures use omnidirectional microphones (microphones that, regardless of their orientation,
receive signals from any direction). The figure 2 shows signal reception versus direction for various
frequencies with a single omnidirectional microphone. For one microphone, frequency invariance is
observed.
Figure 2: Dependence of signal reception on direction by one omnidirectional microphone for frequencies 500
Hz, 1 and 5 kHz.
The Broadside structure is an array of omnidirectional microphones positioned perpendicular to
the direction of the desired signal. Such arrays have an axis of symmetry, relative to which the sound
is released without attenuation both “in front” of the array and “behind”. Such structures are widely
used in applications where sound pressure waves enter the sensor array from one side. Consider a
Broadside structure consisting of two microphones spaced 7.5 cm apart. The minimum response is
19
observed when the signal is incident at an angle of 90∘ or 270∘ (in this case, the angle between the
direction of the useful signal and the normal to the line of elements is taken as 0∘ ). But this response
strongly depends on the frequency of the received signal. Theoretically, such a system has a perfect
zero at a frequency of 2.3 kHz. Above this frequency, depending on the direction of arrival, there are
zeros at other angles (figure 3). The microphone array shows a clear directional characteristic at 4 kHz,
and at 1 kHz its pattern is essentially omnidirectional. As a result, at lower frequencies the array cannot
achieve significant spatial filtering.
Figure 3: Dependence of signal reception on direction by a Broadside structure of two omnidirectional micro-
phones for frequencies of 1 kHz, 2 kHz, 3 kHz and 4 kHz.
The Endfire structure consists of several microphones located in the direction of the useful acoustic
signal. This design is called a differential array of microphones. The delayed signal from the first
microphone is summed with the signal from the next microphone. To create a cardioid polar pattern,
the signal from the rear microphones must be delayed by the same amount of time that the sound
waves travel between the two microphone elements. Such structures are used to produce cardioid,
hypercardioid or supercardioid directional response and theoretically completely eliminate sound
incident on the array at an angle of 180∘ . A unidirectional microphone is more sensitive to sound
coming from one direction and less sensitive to sounds from other directions. The most typical for such
microphones is the cardioid characteristic, representing a peculiar diagram in the shape of a heart. At
the same time, the peak of sensitivity is reached in the direction along the axis of the microphone, and
the decline is in the opposite direction (figure 4).
To generate a cardioid response in direction, the signal from the omnidirectional microphones must be
delayed for a time equal to the propagation of the acoustic wave between the two elements. Developers
of such systems have two degrees of freedom to change the output signal of the speaker system:
changing the distance between microphones and changing the delay time. Figure 5 shows the signal
reception versus direction for various frequencies by the Endfire structure with two elements and a
distance between them of 2.1 cm.
The distance between the microphones is crucial for the formation of a cardioid response. Figure 6
shows the same microphones, but placed at a distance of 15 cm.
The structures considered have the following advantages and disadvantages. Advantages of Broad-
side: flat geometry, simple processing implementation, ability to control the direction of the beam.
Disadvantages of the Broadside: less off-axis rejection, close microphone spacing, and a large number
of microphones needed to prevent spatial leakage.
20
Figure 4: Dependence of signal reception on a unidirectional microphone for frequencies of 500 Hz, 1 kHz and 2
kHz.
Figure 5: Dependence of signal reception on direction by an Endfire structure of two omnidirectional microphones
for frequencies from 1 to 10 kHz, which are located at a distance of 21 cm.
Advantages of Endfire: Better off-axis suppression, smaller overall size. Disadvantages of Endfire:
non-flat (volumetric) geometry, more complex processing, suppression of the useful signal in the low
frequency range, the direction of the source of the useful signal must coincide with the axis of the
microphone array; For two-dimensional gratings, beam formation is possible only in the horizontal
direction (the grating array).
To form a differential array of higher orders, you need to add additional microphones. Since the petals
will deviate more back and to the side in the directional diagram, the distance between the microphones
will have to be increased. The figure 7 shows an array of 4 microphones (third order), which forms
21
Figure 6: Dependence of signal reception on direction by an Endfire structure of two omnidirectional microphones
for frequencies from 1 to 10 kHz, which are located at a distance of 15 cm.
a supercardioid pattern. Consider how beam formation depends on the number of microphones and
the distance between them. It is worth noting that the sensitivity and frequency response of all array
microphones must be precisely matched.
Figure 7: Differential array of 4 microphones (third order).
Differential microphone arrays make it possible to obtain high directivity characteristics of the system
with its small size. But with such a construction, the problem arises of a significant change in the
characteristics of the entire system with a slight deviation of the parameters of an individual microphone
from its nominal values. If this approach is used for critical applications, measures must be taken
to reduce deviations of microphone parameters from nominal values. As stated earlier, a first-order
22
differential microphone array consists of two omnidirectional sensors separated by 𝑑 (figure 8).
Figure 8: Structure of a first order differential microphone array.
4. Results
When sound arrives from the main direction 𝜃 = 0, a delay appears between these sensors:
𝑑
𝜏𝐷 = , (1)
𝑐
where 𝑐 is the speed of sound.
→
−
A plane wave, which is characterized by wave number 𝑘 , arrives at the input of the differential
grating. Due to radial symmetry, the output signals of sensors 𝑋1 (𝜔) and 𝑋2 (𝜔) can be expressed
→
−
by a function depending on the angle 𝜃 and frequency 𝜔. There is a relationship | 𝑘 |𝑑 = 𝑘𝑑 = 𝜔𝜏𝐷
between the wave number and the frequency of the signal. At the central point of the array, you can
place a virtual microphone with an output signal 𝑋0 (𝜔). A plane wave incident at an angle 𝜃 with
wave number causes 𝑘 = 2𝜋/𝜆 the appearance of signals at the output of microphones 𝑋1 and 𝑋2 :
𝑘𝑑 𝑘𝑑
𝑋1 (𝜔) = 𝑋0 (𝜔)𝑒𝑗 2 cos 𝜃 , 𝑋2 (𝜔) = 𝑋0 (𝜔)𝑒−𝑗 2 cos 𝜃 . (2)
At the output of the differential lattice we get
1
𝑌𝐷 (𝜔) = (𝑋1 (𝜔) − 𝑋2 (𝜔)𝑒𝑗𝜔𝜏 . (3)
2
The directivity function of the differential array 𝐻𝐷 is the ratio of the signal at the output of the
array 𝑌𝐷 (𝜔) to the signal at the output of the virtual microphone 𝑋0 (𝜔):
(︂ (︂ )︂)︂
−𝑗 𝜔𝜏 𝑘𝑑 𝜏
𝐻𝐷 (𝜔, 𝜃) = 𝑗𝑒 2 sin + cos 𝜃 . (4)
2 𝜏𝐷
Usually very small values of 𝑘𝑑 ≪ 1 are considered, which makes it possible to use the approximation
sin 𝛼 ≈ 𝛼. In this case, the idealized directivity function 𝐻𝐷 has the form:
(︂ )︂
𝑘𝑑 𝜏
𝐻𝐷 (𝜔, 𝜃) ≈ 𝐻𝐷 (𝜃) = 𝑗
̃︀ + cos 𝜃 . (5)
2 𝜏𝐷
With this view, the main characteristics of differential microphone arrays are obvious: 1) the form of
𝐻̃︀ 𝐷 (𝜃) is determined by the expression 𝜏 /𝜏𝐷 + cos 𝜃, which does not depend on frequency; 2) due to
the subtraction of the signal a phase shift occurs by 𝜋/2; 3) the frequency response of the directivity
function 𝐻𝐷 (𝜔) has the form of a first-order high-pass filter.
At low frequencies, the output signal 𝑌𝐷 (𝜔) becomes highly susceptible to any changes in the shape
of the characteristic 𝐻𝐷 (𝜔). For this reason, the distance d should not be chosen too small, which may
lead to a conflict with the condition 𝑘𝑑 ≪ 1.
23
The exact expression for the directivity function (4) contains a sine function that scales the amplitude.
It is rational to limit the operating range of the differential grating in the low frequency range to the
first maximum of the sine. This first maximum fixes the cutoff frequency 𝜔𝑐:
𝜋
𝜔𝑐 = . (6)
𝜏𝐷 + 𝜏
For low frequencies, the directivity characteristics are practically independent of frequency. However,
as the frequency increases, the shape of the frequency response becomes more and more deformed. In
addition, at some frequencies the signal is completely suppressed.
In order to compensate for the high-frequency nature of the behavior 𝐻𝐷 (𝜔, 𝜃) it is necessary to
develop a filter 𝑊𝑒𝑞 (𝜔). For the main direction 𝜃 = 0, the adjusted frequency response𝐻𝐷 (𝜔, 𝜃 =
0)𝑊𝑒𝑞 (𝜔) must be constant and equal to 0 dB, and for frequencies below 𝜔𝑐 :
(︁1 )︁ , 0 < 𝜔 < 𝜔𝑐 ,
{︃
𝜋𝜔
𝑊𝑒𝑞 (𝜔) = sin 2𝜔𝑐 (7)
1, in other cases.
For low frequencies 𝜔 → 0, the filter gain 𝑊𝑒𝑞 has very large values. This means that any noise
present in the input signal will be greatly amplified. The level of this noise is determined by the specific
sensor. This circumstance limits the frequency range of the signal for processing using a differential
microphone array.
The directional properties of a microphone array are characterized by the directional coefficient (DI).
It can be expressed as the ratio of the squared modulus of the directivity function in the main direction
to the average value of the squared modulus in all directions:
|𝐻(𝜔, 𝜃 = 0)|2
𝐷𝐼(𝜔) = . (8)
1
∫︀2𝜋 ∫︀𝜋
4𝜋 |𝐻(𝜔, 𝜃)|2 sin 𝜃𝑑𝜃𝑑𝜙
0 0
Taking into account the exact expression for the directivity function (4), we can obtain a new
expression for the dependence of the directivity on frequency:
2𝑠𝑖𝑛2 𝜔2 (𝜏𝐷 + 𝜏 )
(︀ )︀
𝐷𝐼𝐷 (𝜔) = (9)
1 − 𝑠𝑖 (𝜔𝜏𝐷 ) cos (𝜔𝜏 )
where 𝑠𝑖(𝑥) = 𝑥1 sin(𝑥).
The efficiency factor for low frequencies is obtained similarly to the result of approximation 𝐻̃︀ 𝐷
according to expression (5):
2
lim 𝐷𝐼𝐷 (𝜔) = 𝐻 ̃︀ 𝐷 = 3(𝜏𝐷 + 𝜏 ) . (10)
𝜔→0 3𝜏𝐷2 + 3𝜏 2
Let us study the influence of microphone parameter mismatch for first-order differential arrays. We
use a model of instability of microphone parameters in the form of a transfer function 𝑀 = 𝑀𝑟𝑒𝑓 +Δ𝑀 .
The nominal transfer function of the sensor 𝑀𝑟𝑒𝑓 in this case is normalized to the value 1. It is assumed
that the deviation Δ𝑀 is an independent random variable with variance:
2
𝜎𝑀 = 𝐸{|Δ𝑀 |2 }, (11)
where 𝐸{|Δ𝑀 |2 } expectation operator. Signals from two sensors in figure 8 will then be written as
follows:
^ 1 (𝜔) = 𝑋0 (𝜔)(1 + Δ𝑀1 )𝑒𝑗 𝑘𝑑
𝑋 2
cos 𝜃 ^ 𝑘𝑑
, 𝑋 2 (𝜔) = 𝑋0 (𝜔)(1 + Δ𝑀2 )𝑒−𝑗 2 cos 𝜃 . (12)
The directivity function 𝐻
^ 𝐷 for a differential array, taking into account the instability of the micro-
phone parameters, can be obtained similarly to expression (4). But now there are additional conditions
24
that depend on Δ𝑀𝑖 (𝑖 = 1, 2). For random numbers, the quadratic terms remain, and the linear ones
are set to zero, so we get:
𝐸{|𝐻^ 𝐷 (𝜔, 𝜃)|2 } = |𝐻𝐷 (𝜔, 𝜃)|2 + 2𝜎𝑀
2
. (13)
As a result, we can obtain a modified expression for DI:
2 𝜔 2
(︀ )︀
2 sin (𝜏𝐷 + 𝜏 ) + 𝜎𝑀
^ 𝐷 (𝜔)|} =
𝐸{|𝐷𝐼 2
2 (14)
1 − 𝑠𝑖 (𝜔𝜏𝐷 ) cos (𝜔𝜏 ) 𝜎𝑀
It is important to understand that in expression (13) the efficiency factor 𝐻𝐷 (𝜔, 𝜃) characterizes the
behavior of the system at high frequencies. While the 𝑊𝑒𝑞 equalization filter takes into account the
effects of microphone instability and enhances them for low frequencies.
Thus, this work shows the dependence of the efficiency of a differential array of first-order micro-
phones on frequency. It can be supplemented using a model of instability of microphone parameters at
low frequencies.
Based on the presented dependence of the directivity on frequency and the instability model of
the microphone parameters, a rational operating frequency range for the normal functioning of the
microphone array can be determined. The lower limit of this range is limited by the instability of the
microphone parameters, and the upper cutoff frequency is determined by the geometry of the array 𝑑.
Currently, there are many applications in which acoustic signals are processed. Microelectromechan-
ical microphones (MEMS) are increasingly being used for these purposes. The use of such microphones
allows the construction of differential microphone arrays. Microelectromechanical systems (MEMS) are
a variety of microdevices of a wide variety of designs and purposes, in the production of which modified
microelectronics technological techniques are used. Typically, all elements of such systems are placed
on a common silicon base, the size of which is only a couple of millimeters. A MEMS microphone is an
electro-acoustic device for converting sound vibrations into electrical waves, which is small enough to
be installed in a tightly integrated product, for example: a smartphone, headset, speakerphone, laptop or
any other device. There are two fundamentally important elements in such microphones: an integrated
circuit (ASIC) and a MEMS sensor. It is the latter that ensures the capture and subsequent transmission
of sound. The MEMS sensor itself consists of a flexible membrane and a rigidly fixed cover. Under the
influence of air pressure, the membrane moves, changing the capacitance between the plates. This
data is recalculated and output as an electrical signal to an integrated circuit. It is this signal that is
converted into the sound that we hear.
Thanks to their design, MEMS microphones have the following advantages. Greater resistance to noise,
vibration and temperature changes due to the absence of unnecessary connecting elements. Multiple
MEMS microphones can be combined together to create a single array. Thanks to capacitive technology,
these microphone arrays can capture sound from a precisely defined direction, effectively canceling
echoes and background noise. Unlike other small microphones, such as electrets, MEMS microphones
include more additional elements, such as preamplifiers, various filters and analog-to-digital converters.
This means greater functionality while maintaining microscopic dimensions. Possibility of mounting
such devices on the board using soldering.
Despite their many advantages, MEMS microphones are also not without their disadvantages. As we
wrote above, MEMS microphones are often used as part of arrays, which increases the sound capture
area, but at the same time reduces the service life of the devices. To work correctly, all microphones
must work in unison, but the likelihood of one of them breaking is much higher than an individual
device. Worse protection from moisture and dust than other microphones.
Microphone arrays include two or more built-in microphones, to which is added a programmable
microprocessor designed to continuously determine the primary source of audio input and optimally
adjust the output to achieve the best sound quality.
Let us highlight the most significant quality indicators of sound capture systems:
• useful signal/noise ratio, where the useful signal is the sound of the drone engine, and the noise
is background noise, the microphone’s own noise, and sounds from non-target sources;
25
• the shape of the radiation pattern and the ability of the system to change it depending on the
environment;
• ability to localize the source of a useful signal and measurement accuracy parameters.
The most common way to build a signal capture unit is based on analog microphone arrays. A
description of the problems that arise when developing analog microphone arrays, as well as the
rationale for reducing the importance of the problem when using digital microphones in audio capture
systems, is given in table 1.
Table 1
Problems encountered in the development of analog microphone arrays and justification for the feasibility of
using digital microphones.
Problem when designing an analog ar- Rationale for using digital mirophones
ray microphones
Sharp increase in cost Lack of a large number of auxiliary analog components
Reduced yield of suitable products due Reducing the total number of microcircuits and topological com-
to the large number of components plexity leads to an increase in the percentage of usable products
due to the general laws of statistics
Increased development and debugging Implementation of algorithms in code and digital interface blocks,
costs which allows you to attract developers with less qualifications and
experience
High sensitivity to electromagnetic ra- The use of digital components is less sensitive to static failures and
diation and power quality degradation of power supply quality
Increased production cycle Less topological complexity guarantees the ability to produce a
product according to almost any modern technological standards,
making the launch process faster and cheaper
Increasing the testing cycle The digital implementation allows you to write synthetic tests and
generate input signals in the same way. Digital generators are more
flexible and low cost, and the testing and debugging process is
reduced to working with code
As an alternative to existing approaches that have the disadvantages outlined above, the authors
of this work proposed to use an architecture built using digital MEMS microphones, which have
become widespread recently. The meter for these microphones is located on-chip, so its digital output
is minimally affected by the components that surround it. The most simple, inexpensive and perfect
solution in terms of signal capture parameters was developed, which consists of using digital MEMS
microphones and an Arduino microcomputer.
When choosing a digital microphone for use in a linear differential microphone array, it is important
to consider the following factors:
• Sensitivity: The sensitivity of the microphone is a measure of how well it can convert sound
waves into electrical signals. A higher sensitivity microphone will be able to pick up quieter
sounds, but it may also be more susceptible to noise.
• Signal-to-Noise Ratio (SNR): The SNR of the microphone is a measure of the ratio of the desired
signal (sound) to the undesired signal (noise). A higher SNR microphone will have less noise,
resulting in cleaner recordings.
• Dynamic range: The dynamic range of the microphone is the range of sound pressure levels that
it can accurately measure. A wider dynamic range microphone will be able to capture both very
loud and very quiet sounds without distortion.
• Linearity: The linearity of the microphone is a measure of how accurately it can reproduce the
input signal. A more linear microphone will produce recordings that are more faithful to the
original sound. In addition to the above factors, it is also important to consider the cost and
availability of the microphone when making a selection.
26
Each digital MEMS microphone can be simplified into the model shown in figure 9. Input sound
vibrations are converted through a MEMS membrane into a weak electrical signal, which is then fed to
the input of amplifier A. The pre-amplified signal then passes through an analog low-pass filter (LPF),
which is necessary to protect against aliasing. The final element of signal processing in the microphone
is a 4th order Σ − Δ modulator, which converts the input analog signal into a one-bit digital stream.
The frequency of data bits from the output of the Σ − Δ modulator is equal to the frequency of the
input timing signal CLK and, as a rule, lies in the range from 1 to 4 MHz.
Figure 9: A simple model of a digital MEMS microphone.
In the time domain, the output of a Σ − Δ modulator is a jumbled collection of ones and zeros.
However, if we assign a value of 1.0 to each high logical level of the microphone output, and a value of
–1.0 to each low level and then perform a Fourier transform, we will obtain a spectrogram of the output
data from the microphone.
Let’s look at the pins of a digital microphone. VDD – microphone power supply, GND – Ground,
CLK – input clock signal, synchronously with which the DATA line switches its DATA states. During
one half of the CLK cycle this pin is in a high impedance state, and during the second half it serves
as a pin for reading data from the Σ − Δ output of the microphone modulator. 𝐿/𝑅𝑆𝑒𝑙 – this pin is
used to control switching of the DATA line. If 𝐿/𝑅𝑆𝑒𝑙 is connected to VDD, then after some time after
detecting the rising edge of the CLK signal, the DATA pin goes into a high impedance state, and after
the arrival of the falling edge of the CLK signal, the DATA pin is connected to the Σ − Δ output of the
microphone modulator. If 𝐿/𝑅𝑆𝑒𝑙 is connected to GND, the edges of the CLK signal, along which the
DATA line switches, are reversed (figure 10).
Figure 10: The pins of a digital microphone.
To isolate the audio frequency band signal, the data from the microphone must be filtered and
resampled at a lower frequency (usually 50–128 times lower than the sampling frequency of the Σ − Δ
modulator). A digital low-pass filter filters out external noise and the microphone’s own noise outside
the operating band (𝑓 > 𝐹𝐶𝐿𝐾 /2𝑀 ) to protect against aliasing, and also makes it possible to reduce
the data repetition rate. In figure 11 presents one of the possible options for processing a one-bit data
stream from a microphone, implemented in software on a DSP or in hardware in audio codecs. Shown
in figure 11, the sampling frequency compression circuit (compressor) lowers the sampling frequency
due to the fact that from every 𝑀 samples of the filtered signal 𝑤(𝑚𝑀 ), 𝑀 ˘1 sample is discarded. The
27
input and output of the converter shown in figure 8 are related by the following expression:
∞
∑︁
𝑦(𝑚) = 𝑤(𝑚𝑀 ) = ℎ(𝑘)𝑥(𝑚𝑀 − 𝑘). (15)
𝑘=−∞
Figure 11: Signal conversion by Σ − Δ modulator.
MEMS microphones have PDM (Pulse-Density Modulation, PDM) outputs. Pulse density modulation
is a method of transmitting the relative change in signal per sample, which can be mathematically
described by the formula
𝑥[𝑛] = −𝐴(−1𝑎[𝑛] ), (16)
where 𝑥[𝑛] contains in each term the relative change in the signal in the form of 1 bit with a sign, which
is specified by the transition. A negative increment is a transition from 1 to 0, a positive increment is
from 0 to 1. Repeating ones increases the overall amplitude of the signal, and repeating zeros decreases
(figure 12).
Figure 12: Period of a sine wave per 100 samples.
A mathematical model for pulse density modulation can be obtained using a delta-sigma modulator
model. In the discrete frequency domain, the operation of a delta-sigma modulator can be described by
the formula
𝑂(𝑧) = 𝐼(𝑧) + 𝐸(𝑧)(1 − 𝑧 −1 ), (17)
where 𝑂(𝑧), 𝐼(𝑧) are the signal spectra at the input and output of the modulator; 𝐸(𝑧) is the sampling
error of the delta-sigma modulator; 1 − 𝑧 −1 is high-pass filter. As a result of transforming the formula,
we get
1
𝑂(𝑧) = 𝐸(𝑧)[𝐼(𝑧) − 𝑂(𝑧)𝑧 −1 )] . (18)
1 − 𝑧 −1
According to this formula, the error 𝐸(𝑧) reduces the value of the signal at the output 𝑂(𝑧) in the
low-frequency region and increases it in the high-frequency region, as a result of which the quantization
noise spectrum shifts predominantly to the high-frequency region.
28
Table 2
Array characteristics (ULA with 2 microphones).
Array characteristic Value
Array directivity 2.97 dBi at 0 Az; 0 El
Array span x=0 m y=17 mm z=0 m
Number of elements 2
HPBW 60.50∘ Az / 360.00∘ El
FNBW 180.00∘ Az / -∘ El
SLL - dB Az / - dB El
Element polarization None
Let 𝑖[𝑛] be a sample of the signal at the input of the modulator in the time domain, and 𝑜[𝑛] be a
sample of the output signal, then, using the inverse 𝑧-transform, we can proceed to the expression
𝑜[𝑛] = 𝑖[𝑛] + 𝑒[𝑛] − 𝑒[𝑛 − 1], (19)
where
if𝑥[𝑛] ≥ 𝑒[𝑛 − 1];
{︂
1
𝑜[𝑛] = (20)
−1 if𝑥[𝑛] < 𝑒[𝑛 − 1];
𝑒[𝑛] = 𝑜[𝑛] − 𝑖[𝑛] + 𝑒[𝑛 − 1]. (21)
The signal from the output signal sample 𝑜[𝑛] is represented as 1 bit and takes values ±1, and is
implemented so that the value of the current quantization error 𝑒[𝑛] is minimal. In this case, the
quantization error 𝑒[𝑛] of each sample appears at the device input during the subsequent sample.
When implementing frequency converters in software, a finite impulse response (FIR) filter or an
Infinite impulse response (IIR) filter can be used as a digital LPF. Developers should be very careful
when choosing the type of filter, its length and bit depth, since the performance of the entire system as a
whole directly depends on this. A correctly calculated and implemented decimator (frequency converter)
in some cases will significantly reduce the cost of products and increase its technical characteristics.
As a second option, audio codecs adapted for this can be used to convert data from the output of a
digital microphone, which will significantly reduce product development time. For example, Analog
Devices offers the ADAU1361 and ADAU1761 codecs, which are suitable for the ADMP521 microphones.
In our work we used a microphone ADMP521. However, the process of creating digital audio devices
becomes simple in terms of hardware implementation and complex in terms of writing programs for
the microcontrollers used.
Next, we conducted a simulation and computational experiment of a uniform linear array of 2
omnidirectional microphones using Matlab Sensor Array Analyzer.
The following model parameters were used. The distance between the microphones is 20 mm. The
board has two MEMS microphones spaced 20 mm apart. This spacing is ideal for detecting acoustic
events. Additionally, the 20 mm spacing is equivalent to 8 · 2.54 mm, which makes it suitable for
DIP (Dual In-line Package) – a type of housing for microcircuits, electronic modules and some other
electronic components. Experimentally, a distance of 0.017 m was determined for the formation of a
bi-directional pattern.
Next, we conducted a simulation and computational experiment of a uniform linear array of 2
omnidirectional microphones using Matlab Sensor Array Analyzer. The following model parameters
were used. The distance between the microphones is 17 mm. The speed of sound is 343 m/s, the signal
frequency is 10 kHz. As a result, we obtained the parameters listed in table 2.
The Matlab script is listed below:
% Create a Uniform Linear Array Object
Array = phased.ULA(’NumElements’,2, ’ArrayAxis’,’y’);
Array.ElementSpacing = 0.017;
29
Array.Taper = ones(1,2).’;
% Create an omnidirectional microphone element
Elem = phased.OmnidirectionalMicrophoneElement;
Elem.FrequencyRange = [0 10000];
Array.Element = Elem;
% Assign Frequencies and Propagation Speed
Frequency = 10000;
PropagationSpeed = 343;
% Create Figure
% Plot Array Geometry figure;
viewArray(Array,’ShowNormal’,true,
’ShowTaper’,true,’ShowIndex’,’All’,
’ShowLocalCoordinates’,true,’ShowAnnotation’,true,
’Orientation’,[0;0;0]);
% Find the weights
w = ones(getNumElements(Array), length(Frequency));
% Plot 2d azimuth graph
format = ’polar’;
cutAngle = 0;
plotType = ’Directivity’;
plotStyle = ’Overlay’;
figure;
pattern(Array, Frequency, -180:180, cutAngle, ’PropagationSpeed’,
PropagationSpeed, ’CoordinateSystem’, format ,’weights’, w,
’Type’, plotType, ’PlotStyle’, plotStyle);
% Find the weights
w = ones(getNumElements(Array), length(Frequency));
% Plot 2d elevation graph
format = ’polar’;
cutAngle = 0;
plotType = ’Directivity’;
plotStyle = ’Overlay’;
figure;
pattern(Array, Frequency, cutAngle, -90:90, ’PropagationSpeed’,
PropagationSpeed, ’CoordinateSystem’, format ,’weights’, w,
’Type’, plotType, ’PlotStyle’, plotStyle);
% Find the weights
w = ones(getNumElements(Array), length(Frequency));
% Plot U Pattern
format = ’uv’;
plotType = ’Directivity’;
plotStyle = ’Overlay’;
figure;
pattern(Array, Frequency, -1:0.01:1, 0, ’PropagationSpeed’,
PropagationSpeed, ’CoordinateSystem’, format,’weights’, w,
’Type’, plotType, ’PlotStyle’, plotStyle);
The resulting pattern has the shape of a bi-directional (figure 13). As you can see, the design of
the grille allows you to create a grille with the main lobes directed at -90 and 90 degrees. To form a
cardiode radiation pattern, as mentioned above, it is necessary to use delay-and-sum and filter-and-sum
algorithms. The meaning of these algorithms is that microphone signals are added with different
delays (different phase shifts), aligning the phases of signals coming from the selected direction (source
30
localization) for each frequency. In this case, the beamforming algorithm makes it possible to amplify
the signals generated by sound coming from the selected direction, i.e. performs a kind of focusing of
sounds.
Figure 13: The geometry of the array and the directional diagram (linear array of 2 microphones).
ADMP521 microphones were connected to the ADAU1761 codec in accordance with the technical
specifications of both products (figure 14).
A model was also created based on an array of four omnidirectional microphones located at a distance
of 20 mm (figure 15). The following model parameters were used. The distance between the microphones
is 17 mm. The speed of sound is 343 m/s, the signal frequency is 10 kHz. As a result, we obtained the
parameters listed in table 3.
Table 3
Array characteristics (ULA with 4 microphones).
Array characteristic Value
Array directivity 5.98 dBi at 0 Az; 0 El
Array span x=0 m y=51 mm z=0 m
Number of elements 4
HPBW 26.52∘ Az / 360.00∘ El
FNBW 60.58∘ Az / -∘ El
SLL 11.30 dB Az / - dB El
Element Polarization None
The Matlab script has the following form:
% Create a Uniform Linear Array Object
Array = phased.ULA(’NumElements’,4, ’ArrayAxis’,’y’);
Array.ElementSpacing = 0.017;
Array.Taper = ones(1,4).’;
% Create an omnidirectional microphone element
Elem = phased.OmnidirectionalMicrophoneElement;
Elem.FrequencyRange = [0 10000];
Array.Element = Elem;
31
Figure 14: Connection diagram of ADMP521 microphones to ADAU1761 codec.
% Assign Frequencies and Propagation Speed
Frequency = 10000;
PropagationSpeed = 343;
% Create Figure
% Plot Array Geometry
figure;
viewArray(Array,’ShowNormal’,true,’ShowTaper’,true,’ShowIndex’,’All’,
’ShowLocalCoordinates’,true,’ShowAnnotation’,true,’Orientation’,[0;0;0]);
% Calculate Steering Weights
Freq3D = 10000;
% Find the weights
w = ones(getNumElements(Array), length(Frequency));
% Plot 3d graph
format = ’polar’;
plotType = ’Directivity’;
figure;
pattern(Array, Freq3D , ’PropagationSpeed’, PropagationSpeed,
’CoordinateSystem’, format,’weights’, w(:,1),
’ShowArray’,false,’ShowLocalCoordinates’,true,
’ShowColorbar’,true,’Orientation’,[0;0;0],’Type’, plotType);
% Find the weights
w = ones(getNumElements(Array), length(Frequency));
32
Figure 15: The geometry of the array and the directional diagram (linear array of 4 microphones).
% Plot 2d azimuth graph
format = ’polar’;
cutAngle = 0;
plotType = ’Directivity’;
plotStyle = ’Overlay’;
figure;
pattern(Array, Frequency, -180:180, cutAngle, ’PropagationSpeed’,
PropagationSpeed,’CoordinateSystem’, format ,’weights’, w,
’Type’, plotType, ’PlotStyle’, plotStyle);
% Find the weights
w = ones(getNumElements(Array), length(Frequency));
% Plot 2d elevation graph
format = ’polar’;
cutAngle = 0;
plotType = ’Directivity’;
plotStyle = ’Overlay’;
figure;
pattern(Array, Frequency, cutAngle, -90:90, ’PropagationSpeed’,
PropagationSpeed,’CoordinateSystem’, format ,’weights’, w,
’Type’, plotType, ’PlotStyle’, plotStyle);
So, during the computational experiment, we built 2 linear microphone arrays with bi-directionality.
The directionality of these arrays can be easily converted to unidirectional (cardioid) using known
algorithms or hardware (codecs). The tuning of the circuit to create cardioid directivity will be considered
in further studies.
33
5. Discussion
The following questions require additional discussion and clarification: the dependence of the azimuthal
pattern of the proposed linear microphone arrays on the source frequency; the choice of analog or
digital MEMS microphones and labor-intensiveness in the development of a microphone array; the use
of directional microphones instead of omnidirectional; peculiarities of localization of a moving sound
source (Doppler effect, reflection from obstacles, etc.); higher-order differential beam array formers;
signal processing algorithms of microphone arrays.
6. Conclusions
The study looks at setting up a microphone array to determine the position of a UAV (unmanned aerial
vehicle) based solely on the sound of its engines. The location of the microphones plays a crucial role for
accurate localization. A mathematical model of pulse density modulation of a digital MEMS microphone
is also considered. This work shows the dependence of the efficiency of a differential array of first-order
microphones on frequency. Based on the presented dependence of the directivity on frequency and the
instability model of the microphone parameters, a rational operating frequency range for the normal
functioning of the microphone array can be determined.
A model of a linear microphone array based on MEMS omnidirectional microphones is proposed,
which with a certain geometrical arrangement give a bi-directional pattern, which, in principle, can
be easily transformed into a unidirectional one with the use of special algorithms or hardware (for
example, ADAU1761 codecs). Refinement of the circuit to achieve cardioid directivity will be addressed
in forthcoming research.
7. Author contributions
Conceptualization, methodology – Andrii V. Riabko, Oksana V. Zaika; setting tasks, conceptual analysis
– Tetiana A. Vakaliuk, Oksana V. Zaika; development of the model – Andrii V. Riabko, Valerii V.
Kontsedailo; software development, verification – Andrii V. Riabko, Roman P. Kukharchuk; analysis of
results, visualization – Roman P. Kukharchuk, Tetiana A. Vakaliuk; drafting of the manuscript – Valerii
V. Kontsedailo, reviewing and editing – Tetiana A. Vakaliuk.
All authors have read and approved the published version of this manuscript.
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