259
1 INTRODUCTION
Sound localisation has been present since the dawn of
time and is a fundamental aspect of spatial orientation
for humans. Alongside visual localisation based on the
sense of sight, it is a key skill for humans to determine
the direction from which a sound originates.
Sound localisation has contributed to the
development of humanity by facilitating
communication and spatial orientation. By recognising
the direction of sound, humans can avoid dangers or
efficiently carry out their activities. Survival in a
hazardous environment would be limited without this
ability.
Modern technological solutions draw inspiration
from natural echolocation, which animals utilise.
Examples include radars and sonars used in maritime
and aviation industries. These systems are based on
principles similar to those employed by bats and
dolphins, enabling the determination of the position of
objects in space even if they are beyond visual range.
Currently, the most commonly used navigation tool
for unmanned aerial vehicles (UAVs) is the GPS, which
functions well when available. The challenge arises
when this system becomes unavailable for various
reasons (e.g., in urban areas with dense buildings, in
tunnels or when the signal is being jammed) or when
multiple UAVs operate in the same area. In such cases,
an alternative could be visual navigation, sup-ported
by acoustic navigation. This work lays the foundation
for building a hybrid navigation system based on
images and acoustic signals for UAV swarms.
However, both GPS and vision-based systems face
limitations in environments with high occlusion,
Echolocation as Acoustic Form of Relative Positioning
P. Targowski & J. Furtak
Military University of Technology, Warsaw, Poland
ABSTRACT: To introduce order in the movement of many objects, they need to avoid collisions with their
neighbours by knowing their position and reacting to it. This paper proposes using sound localisation, which can
be used for short distances because of its limitations. The study is focused on implementing small distance
echolocation for the relative positioning of objects by comparing the time difference of arrival to microphones
used by the same object. Unlike previous works that rely on communication or external infrastructure this method
allows each autonomous system to localise neighbour using only passive sound signals and on-board microphone
array. The research aims to develop a navigation system for mobile objects moving in a swarm without
communication between the objects. The study develops an alternative for GPS and visual navigation with
limitations in specific environments. The software created showed the effectiveness and weakness of echolocation
as the choice for different environments, increasing the need to use more types of navigation for drone swarms.
This work contributes and early-stage lightweight approach to relative positioning in UAV swarms and provides
insight into integrating acoustic sensing into hybrid navigation systems.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 19
Number 1
March 2025
DOI: 10.12716/1001.19.01.30
260
limited lighting, or intentional interference. This raises
the need for robust, low-resource navigation
alternatives. Echolocation-based positioning, inspired
by biological systems, offers such potential, especially
for swarming UAVs operating without central
coordination or communication.
This study introduces a lightweight echolocation-
based approach for relative positioning by
implementing and evaluating a passive acoustic
method using Time Difference of Arrival and signal
strength, demonstrating the potential of echolocation
as a complementary technique in hybrid navigation
systems for GPS-denied environments.
The remainder of the article is structured as follows.
Section 2 discusses the literature on acoustic
navigation. Section 3 presents the physical phenomena
that can be used to develop a system for the acoustic
localisation of mobile objects. Section 4 presents the
concept of the laboratory setup and the results of
studies on the suitability of acoustic signals for
determining object positions. Section 5 provides
concluding remarks.
2 RELATED WORKS
An example of sound localisation is the Simultaneous
Localisation and Mapping (SLAM) algorithm [1]. This
solution is designed to localise a drone indoors and
calculate its position based on direct and reflected
signals. The drone is equipped with four microphones
and a siren. The siren emits sound at a specific
frequency received by the microphones at two
moments: right after emission and after reflecting off
the walls. By analysing the variability of the sound's
amplitude and phase and filtering the results, the
positions of obstacles and the objects relative to them
are calculated. This approach enabled the drone to
move within a room without colliding with obstacles.
A similar solution to the audio localisation problem
is using a phone to map a room [2]. Using the built-in
devices in the phone, a microphone and speakers emit
inaudible sounds. The microphone registers the echoes
reflected from objects. The difference between these
solutions lies in mapping: in the first example, it was
performed in real-time from the drone's perspective,
while in the second case, locations were assigned
features during mapping. Such an approach allowed
for error correction during localisation by comparing
features. Research into localisation methods used by
bats is a base for both solutions.
The described solutions were applied indoors,
where the objects in the environment were fixed. The
situation changes when multiple objects, such as
drones, move in open spaces. Besides accounting for
static obstacles, the relative positioning of mobile
objects in open space must be introduced. In both cases,
mobile objects must be equipped with microphones
and speakers that transmit and receive sound signals.
These signals allow objects to locate each other using
differences in signal delay times and signal strength.
Solution presented in this article replaces echo as
the main localisation method with direct signal
transmission and reception between different
components of the navigation system. As a result, it
enables smooth transitions from indoor to outdoor
environments and significantly shortens localisation
time by avoiding the need to wait for reflected sound
signals. The developers focused on relative
positioning, intentionally leaving out absolute
localisation due to the system's specific application.
Although echolocation is not most commonly used
as method for swarm localisation, recent surveys[3]
highlight need for diverse navigation solutions.
Making it more reliable in different environments and
resistant for various external factors. Current methods
rely on vision, LiDAR and wireless communication,
each with own specific limitations. In this context
acoustic localisation could emerge as complementary
or alternative approach. This study explores potential
of echolocation to fill gaps in scenarios where
traditional sensors may fail.
3 SOUND AND ECHOLOCATION
Animals use sound far better than humans to
determine their position relative to other elements in
their surroundings. Echolocation, also known as
biosonar, allows them to navigate, search for food and
hunt. To locate objects in space, they use sound
reflected off the surfaces of objects or other animals.
Among the animals that utilise this navigation method
are well-known bats, dolphins, whales, some bird
species and hedgehogs. Interestingly, some blind
individuals have developed the ability to echo-locate.
The reasons why this skill has evolved include:
− navigating in environments with limited visibility,
such as darkness, murky water or fog;
− detecting prey;
− identifying obstacles along a path.
All these reasons connect to localisation and
navigation. Therefore, it can be concluded that
echolocation is a practical navigation method. Despite
many years of evolution and change, many organisms
still use it as a fundamental method.
Marine animals such as dolphins and whales [4] use
high-frequency sounds produced by forcing air
through their nasal passages. These sound waves
travel to the forehead and are focused into a beam.
When the signal reflects off an object, it is received by
the animal's jaw and transmitted to its ears. This
process allows the animal to determine the object's size,
direction, speed and distance.
Echolocation in the air works somewhat differently.
Bats produce sound in their larynx and emit it through
their mouths. These sounds can reach up to 140
decibels, but their frequency is too high (ranging from
20–80 kHz [5]) for humans to hear. Bats use reflected
sound to identify the size and hardness of objects, and
they can detect small insects at distances of up to about
5 meters. To avoid deafening themselves by producing
such loud sounds, they deactivate their middle ear just
before emitting the sound and restore their hearing just
before the echo returns.
Sound is a physical phenomenon involving the
creation of a longitudinal acoustic wave that represents
a disturbance in the density of a medium. These waves
propagate through gases, liquids and solids. Based on
261
frequency, acoustic waves are divided into four types,
as described in Table 1.
Table 1. Types of acoustic waves
Type of wave
Infrasound
Sound
Ultrasound
Hypersound
Humans can hear acoustic waves, referred to as
sounds, while others are inaudible. The speed of such
a wave is a key factor in determining the distance from
the sound source and its position relative to the
receiver.
For gases like air, the speed of sound at a
temperature of 15ºC (288 K) can be calculated using the
formula:
1,4 8,314 288
339,99
0,029
y R T m
v
Ms
= =
(1)
where:
γ - adiabatic coefficient (for air ~ 1.4)
R - universal gas constant (8.314 J/(mol*K))
T - temperature in Kelvin
M - molar mass of the gas (for air ~ 0.029 kg/mol)
Sound frequency offers opportunities to improve
research and utilise filtering to detect only sounds of
interest. Various filters exist, and the band-pass filter is
the most relevant for limiting frequency ranges. This
filter allows frequencies within a defined range
between two boundary values to pass through.
Basic navigation for humans is visual navigation.
However, sound navigation has supported survival for
thousands of years by helping detect danger. It allowed
for the detection of threatening objects before they
became visible. Therefore, it can be stated that it is
essential to support the primary form of navigation.
M. Gröhn, T. Lokki, and T. Takala conducted a
study comparing sound, visual, and combined audio-
visual navigation [6]. Participants in the study had the
task of moving from point to point along a specific path
in a virtual environment while controlling the direction
and speed of movement. They were equipped with a
controller that set a motion vector when pressed and
moved, whose length and direction corresponded to
the speed and direction of movement in the virtual
space. Three experiments were conducted: the first
involved navigating using sound alone, the second
using only vision and the third using both sound and
vision.
The study showed that visual navigation
outperformed sound navigation, but the combination
provided high precision and speed in task completion.
The researchers noted that when participants used
both the eyes and ears, sound was initially employed
to determine the path, while vision was used for
greater precision in the final phase. These observations
suggest that audio navigation is faster but less precise.
The comparison of visual and sound navigation can
also be considered in the context of their use by
humans and animals and their influence on
environmental adaptation. Both senses play key roles
but differ in their mechanisms, advantages and
limitations. Table 2 presents the properties of visual
and sound navigation.
Table 2. Comparison of visual and sound localisation.
Sound navigation
Operating principle
It relies on the interpretation of
sound waves reflected from
objects or emitted by the
surroundings
Uses sound signals, which are
then interpreted by the brain to
create a "sound image" of the
environment
In real-time, it allows for the
determination of the direction of
a signal with the ability to
approximate the distance from its
source
Range and accuracy
The ability to determine direction
and range significantly surpasses
visual navigation but is more
susceptible to interference, such
as noise or other nearby sounds.
Approximate distance estimation
without detailed information
about the surroundings
Adaptation to environment
Despite its limitations in
accuracy, it is much better suited
for nighttime, underwater or
enclosed spaces where obstacles
obstruct vision.
Approximate distance estimation
without detailed information
about the surroundings
Related Technology
Sonars, radars, ultrasonography
4 LABORATORY SETUP AND RESEARCH
DESCRIPTION
Ultimately, each UAV in the drone swarm will have
acoustic sensors and cameras. This study will examine
the potential of using acoustic signals to approximate
the mutual positions of UAVs during flight. The
objective will be to determine the distance to the sound
source and the direction from which the sound
originates in the local coordinates of the UAV station.
For this purpose, each drone should have an acoustic
signal source and microphones arranged in an array.
This approach allows the TDOA (Time Difference of
Arrival) algorithm to determine the direction of the
sound and the received signal strength to calculate the
distance from the source. Based on the data from the
microphones, the drone can estimate the position of a
neighbour with decent precision over short distances.
Each UAV has its reference frame and changes its
position without requiring direct communication or
GPS navigation. Figure 1 and Figure 2 shows an
example of installing microphones and a sound source
on a drone.
262
Figure 1. Example of the construction of a drone for acoustic
navigation (microphones are marked in yellow, and the
sound source is marked in red)
Figure 2. Coordinate systems for a drone and microphone
array
Figure 3 illustrates a situation where one drone
transmits a sound signal while another receives it using
microphones. Assuming that the acoustic signal
sources emit signals with the same power, the strength
of the microphone's signal allows the distance
determination. In such a situation, the position is
relative to the coordinate system of the drone receiving
the signal. The position of the signal-transmitting
drone is determined based on the distance and the
direction from which the signal arrives. Figure 4
illustrates the method for determining the position of
the sound source on a surface.
Figure 3. Relative position of drones in their coordination
systems
Figure 4. Determining the position of the sound source on a
surface
Sound propagates evenly in space. Individual
microphones in the microphone array receive the
signal at different times. Based on the measured time
difference of signal reception by individual
microphones ∆t_n and the speed of sound, as well as
the azimuth from which the sound arrived, can be
determined. Firstly, the distance is calculated as it is
used to calculate azimuth based on the time difference
of arrival.
ndn
d v t=
(2)
where:
dn - distance of the n-th microphone,
vd - speed of sound,
∆t
n
- time difference for the microphone.
Assuming that in the coordinate system of the
microphone array, the microphones have coordinates
(x1,y1), (x4,y4), and the sound source has coordinates
(x,y), the actual distances of individual microphones
from the sound source is calculated using the following
formula.
( ) ( )
22
dn n n
d x x y y= − + −
(3)
where:
ddn - distance of the sound source from the n-th
microphone,
x, y - coordinates of the sound source,
xn, yn - coordinates of the n-th microphone.
For each microphone, a distance difference
equation can be written relative to the sound source:
0dn n
d d d−=
(4)
where:
ddn - distance of the sound source from the n-th
microphone,
d0 - distance of the sound source from the beginning of
the system of coordination
22
0
d x y=+
(5)
dn - distance difference for the microphone.
Taking into consideration formulas (2), (3), (4) and
(5), the following system of equations is determined.
263
( ) ( )
( ) ( )
( ) ( )
( ) ( )
22
22
1 1 1
22
22
2 2 2
22
22
3 3 3
22
22
4 4 4
d
d
d
d
x x y y x y v t
x x y y x y v t
x x y y x y v t
x x y y x y v t
− + − − + =
− + − − + =
− + − − + =
− + − − + =
(6)
In order to determine the position of the sound
source (x, y), it is necessary to find the solution of the
system of equations (6) using, for example, the least
squares method. The direction of sound ∅ can be
determined using the following formula.
arctan 0
arctan 0 0
arctan 0 0
00
2
00
2
y
if x
x
y
if x and y
x
y
if x and y
x
if x and y
if x and y




+



=
−


=
− =
(7)
where:
∅ - azimuth of the sound source relative to the centre of
the coordinate system given in degrees,
The ReSpeaker USB Mic Array microphone is the
core element to conduct the experiments. Figure 5
shows the arrangement of the device's microphones
after removing the cover. This device contains four
microphones. To operate the ReSpeaker, the ODAS
(Open Embedded Audition System) library software
can be used to detect the direction and distance of the
sound source relative to the device.
The ODAS library software provides the ability to
determine the following parameters [7]:
Determining the time difference of arrival of signals
– analyses the time differences at which sound signals
reach individual microphones. These differences allow
for estimating the direction from which the sound is
coming.
Selecting the direction of the signal – enables
focusing on the sound source and ignoring noise or
other sounds from other directions.
Determining the angle of the sound source – the
ReSpeaker Mic Array, thanks to its microphone
configuration, can determine this angle in the
horizontal plane and within a limited range in the
vertical plane.
Figure 5. The ReSpeaker USB Mic Array device with the four
microphones labelled
The approximate distance to the sound source can
also be estimated using an algorithm based on signal
strength. This distance is calculated based on the
decrease in signal amplitude and the time difference of
signal arrival.
The experiment involved the microphone array
acting as a receiver of acoustic signals with a frequency
of 1500 Hz generated from a mobile phone(The phone
played the role of the sound source and corresponded
to the drone's distance and azimuth). The experiment
was conducted in two environments: indoors and in an
open space.
In each experiment, the direction of the signal origin
and the distance to the signal source were determined.
The direction of the signal origin was determined using
the ODAS library software, while the author prepared
a custom program to calculate the distance. Figure 6
illustrates the laboratory setup used for the
experiments. The studies were conducted in
environments where various natural sources of sound
interference and phenomena that complicated
calculations were present. This approach aimed to
simulate real-world conditions that might occur when
determining the relative positions of flying drones. In
the open space, sound disturbances were generated by
wind, rustling trees and a barking dog. While indoors,
the primary factors affecting results were echoes of the
reflected signal and noise from a running laptop.
Figure 6. Laboratory setup view (laptop, microphone array,
and phone as the acoustic signal generator).
The microphone array and the acoustic signal
source were located on the same surface in each
experiment. When determining the distance to the
signal source, the source's distance was changed every
0.5 meters, ranging from 0.5 m to 3.0 m (see Figure 7)
the signal source was located at an azimuth of 220
degrees. Each measurement was repeated ten times.
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Figure 7. Illustration of distance measurement.
Obtained results of the sound source distance test
are shown in Table 3. The columns containing the
distance values present the arithmetic mean of the
results obtained in each of the ten measurements.
Table 3. Summary of calculated distances for 10
measurements.
Actual
Distance [m]
Calculated
Distance
Indoors [m]
Error
Indoors [m]
Calculated
Distance in
Open Space
[m]
Error in
Open Space
[m]
0,5
0,995
0,495
0,58
0,08
1
2,623
1,623
0,84
0,16
1,5
2,581
1,081
1,827
0,327
2
1,864
0,136
1,619
0,381
2,5
2,611
0,111
2,248
0,252
3
2,75
0,25
2,87
0,13
After analysing the obtained results, it can be
concluded that determining the distance to the acoustic
signal source using the described indoor method does
not yield satisfactory results. The likely cause is the
insufficient selectivity of the microphones used in the
experiment, which prevents the original signal from
being distinguished from its echo reflected off objects
in the room. The distance measurement results
obtained in open space are much better and promising
for the approximate determination of distances
between drones flying in a swarm.
During the second experiment, the acoustic signal
source was placed 1 m from the centre of the
microphone array to determine the direction. The
source's angle relative to the array was changed in
increments of 90 degrees (Figure 8), starting from an
arbitrarily chosen angle of 70 degrees. Also, for each
angle performed 10 measurements.
Figure 8. Illustration of azimuth measurement.
The results of the azimuth measurements of the
sound source are presented in Table 4. The columns
containing azimuth values show the arithmetic mean
of the results obtained in each of the ten measurements.
Table 4. Summary of calculated angles.
Real angle [°]
Calculated angle
indoors [°]
Calculated angle
outdoors [°]
70
221
70
160
220
140
250
144
236
340
244
325
Similar to determining the distance to the source,
the results of determining the azimuth of the sound
source obtained indoors are significantly worse than
those obtained in open spaces. The reason is similar
and lies in the inability to separate the original signal
from its echo.
5 CONCLUSIONS AND FUTURE WORK
The presented results are one of the first steps in
developing a hybrid dead reckoning navigation system
based on images and acoustic signals without relying
on GPS. The primary goal of this approach is to ensure
awareness of the position of a drone moving within a
swarm relative to other members of the swarm. Since
drone systems usually have limited energy and
computational resources, solutions with low resource
requirements are needed.
The results obtained for acoustic signals are not
entirely satisfactory but are promising. Upcoming
research will focus on reducing the impact of signal
echo on the results. This research will include the
application of better sound filtering, more precise
analysis of received signals and work on frequency
ranges and microphone sensitivity.
In the next stage, efforts will concentrate on
developing an AI-based system to determine the
direction and distance of the sound source using
acoustic signals. We anticipate the system's design will
operate within the limited energy and computational
resources available onboard the drone.
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