Detecting Indoor Tiny Autonomous Malicious Drones within Critical
Infrastructures: An Innovative Algorithm based on Harmonic Radar-
Equipped Mini-Drones
ATHANASIOS N. SKRAPARLIS1, KLIMIS S. NTALIANIS1, MARIA S. NTALIANI2,
FILOTHEOS S. NTALIANIS3, NIKOS E. MASTORAKIS4
1University of West Attica,
28, Agiou Spyridonos Str., 122-44, Egaleo,
GREECE
2Agricultural University of Athens,
75, Iera Odos Str., 118-55, Athens,
GREECE
3University of Piraeus,
80, A. Dimitriou & M. Karaoli Str., 185-34, Piraeus,
GREECE
4Industrial Engineering Department,
Technical University of Sofia,
Sofia,
BULGARIA
Abstract: - Critical infrastructures play a central role in the welfare of contemporary societies and they should
properly function 24/7. Since their role is so important, they regularly become targets of malicious parties,
terrorists, industrial spies, and even hostile governments. In this paper, the scenario of cyber or physical attacks
to CIs from tiny autonomous malicious drones is analyzed. In particular, this work focuses on indoor spaces,
protected by mini-drones. The mini-drones are equipped with harmonic radar and run a novel algorithm, which
guides them to scan the whole area. Assuming that the malicious drones behave as non-linear systems, the
mini-drones transmit signals and analyze the received signals, creating a non-linear system 3D location map for
the whole space. In the consecutive scans, any changes on the 3D location map indicate that the malicious
drone has changed location. Simulated results and comparisons to state-of-the-art approaches exhibit the cost-
effectiveness and time efficiency of the proposed scheme as well as its limitations.
Key-Words: - Malicious drone, Autonomous, Critical Infrastructure, Mini-drone, Harmonic Radar, Indoor.
Received: December 15, 2023. Revised: August 14, 2024. Accepted: September 17, 2024. Published: October 14, 2024.
1 Introduction
Critical infrastructures (CIs) are the backbone of
modern societies, encompassing vital sectors such
as energy, transportation, communication, and water
supply. Their proper functioning is crucial for
economic stability, public safety, and national
security. Any disruption or compromise of these
infrastructures could have far-reaching and severe
consequences, impacting not only the economy but
also the well-being of citizens. Recognizing and
safeguarding CIs is essential to ensure resilience
against potential threats, both natural and man-made
and to maintain the overall stability and
functionality of a nation.
On the other hand, CIs can be subjected to cyber
or physical attacks by tiny malicious drones. In the
scenario of this paper, a malicious staff member of
the CI brings the tiny autonomous malicious drone
within the premises (indoors) of the CI and places it
at an unattended location. During the night (or other
circumstances), when the CI operates in low
capacity with a minimum number of personnel, the
tiny malicious drone may move to specific offices
and record (for a specific timeframe) sensitive
conversations (industrial espionage), interfere with
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Athanasios N. Skraparlis, Klimis S. Ntalianis,
Maria S. Ntaliani, Filotheos S. Ntalianis,
Nikos E. Mastorakis
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various critical systems and devices of the CI and/or
install malicious software (electronic war), destroy
parts of the CI by e.g. setting fire (physical damage),
etc. In other words, it is like a virus inside a human
body. After completing its mission, the tiny
malicious drone may autonomously leave the CI and
return to its base, or it may be picked up by the
malicious staff member.
As it can be understood, such threats are very
serious and should be efficiently tackled. Our
previous research has focused on the physical
security of CIs. In particular, in [1] a real-time threat
assessment framework has been proposed to protect
CIs from trucks carrying explosive substances. In
[2] an innovative screening architecture has been
introduced to protect CIs from various threats, such
as guns, explosives, and radioactive substances. The
current work extends our previous research by
detecting tiny autonomous malicious drones. The
proposed scheme focuses on indoor spaces of CIs.
More specifically, it is assumed that the CI is
protected by a mini-drone. The mini-drone is
equipped with a harmonic radar and runs the
proposed algorithm, which guides the mini-drone to
scan the whole indoor space by moving on a 3D
grid. It is also assumed that the tiny malicious drone
behaves as a non-linear system. Each time the mini-
drone visits a new node of the grid, it transmits a
signal and analyses the received signal. After
visiting all nodes, the mini-drone creates a non-
linear system location map for the whole indoor
space. The 3D location map contains all non-linear
devices, including the malicious drone. In the next
scans, any changes on the 3D location map indicate
that the malicious drone has moved to a new
location. Experimental results and comparisons to
state-of-the-art approaches exhibit the advantages of
the proposed scheme.
To summarize, this paper offers the following
major contributions:
It examines the case of tiny autonomous
malicious drones, which may not send or
receive signals. This case has not been
thoroughly studied in the literature.
It proposes a novel algorithm, which guides the
mini-drone to scan the whole indoor space and
create a 3D location map.
Through extensive simulations, the study not
only validates the effectiveness of the proposed
algorithm but also compares it with state-of-the-
art approaches, highlighting its advantages and
limitations, thereby contributing valuable
insights for future research in drone detection
technology.
The rest of the paper is organized as follows:
Section 2 provides related work and Section 3
describes the proposed scheme. Simulated results
and extensive comparison to state-of-the-art
methods are presented in Section 4. Finally, Section
5 concludes this paper.
2 Related Work
In the literature, there are some works related to
malicious drones. In particular, [3] introduces an
approach for identifying critical drones by
leveraging distributed features, communication
intensity, and communication scale. Initially, a
dynamic communication prediction network is
constructed for drone swarms. Then, a dynamic
giant connected component-based scale-intensity
centrality method is proposed. In [4] an anti-RF
solution that possesses the capability to identify,
detect, and disrupt the communication link between
a miniature drone and its remote controller is
presented. This countermeasure has been seamlessly
integrated into a Software Defined Radio platform
to secure No Fly Zones (airports, public events,
etc.). In [5] various cybercrime usages of drones are
examined and the requirements of future security
systems are discussed. In [6] a computer vision-
powered monitoring system employs a supervised
machine intelligence model and SqueezeNet, a deep
neural network-based image embedder, to identify a
malevolent UAV carrying an extraneous payload. In
[7] detection of malicious UAVs is achieved by a
machine-learning algorithm. Initially, sensor nodes
deployed in a Wireless Sensor Network gather
environmental data and send them to the UAV. To
ensure data security, a proxy re-encryption scheme
encrypts the feedback packet containing the sensed
input data. Finally, the feedback packet undergoes
decryption at the base station, revealing the actual
input information. In [8] the viability of employing
wireless localization methods for identifying drones
engaged in location spoofing attacks is explored.
GhostBuster, a modular solution designed to detect
rogue RID-enabled drones is introduced and a
comprehensive experimental campaign, utilizing
open-source data derived from real drone flights is
carried out. In [9] a dataset encompassing five
classes, including images of airplanes, birds, drones,
helicopters, and malicious UAVs is utilized.
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It investigates the protection of indoor CI
spaces by mini-drones equipped with harmonic
radar, an approach that is much more efficient
and flexible compared to the state-of-the-art.
Fig. 1: Overview of the proposed scheme
Three distinct CNN models are employed to
extract features from the images and the extracted
features are classified using various machine
learning methods. In [10] a protective framework
designed to mitigate threats posed by malicious
actors and to recover control of rogue UAVs is
proposed. The framework implements a dynamic
conceptual grid system overlaid on real-world
geographical deployment, where the grid undergoes
periodic shuffling or configurations based on
abnormal behavior. In [11] unauthorized drones in
an urban setting are detected through RF-based
sensing, employing evenly distributed sensors. The
study evaluates detection performance using the
Neyman-Pearson criterion combined with Bayesian
inference. In [12] a drone detection system designed
for minimal prior configuration is introduced,
utilizing affordable off-the-shelf hardware to
identify privacy invasion attacks. By employing a
model of the attack structure, statistical metrics for
movement and proximity are derived and applied to
the communication signals exchanged between a
drone and its controller.
Additionally, there are several other works
focusing on the detection of drones, [13], [14], [15],
[16], [17], [18], [19], [20], [21], [22], [23], [24].
Most of them use computer vision techniques and
may incorporate 3D depth maps, multi-spectral
imaging, electro-optical sensors, multi-camera
fields, and other approaches. Even though
interesting, most of the aforementioned methods do
not consider indoor spaces. Furthermore, they do
not propose specific area scanning methods.
Moreover, they cannot solve the problem of “silent”
drones, which do not move (or move under cover)
and do not receive or transmit signals. This paper
confronts the aforementioned issues, by proposing a
novel algorithm to scan indoor CIs and detect tiny
malicious drones. The method is based on harmonic
radar-equipped mini-drones and incorporates the
concept of a 3D non-linear device location map.
3 The Proposed Scheme
3.1 Problem Formulation
Harmonic radar technology is a specialized radar
system that functions through the transmission of a
specific radio frequency signal and the detection of
its harmonics, which are multiples of the original
frequency that bounce back from a tagged object.
Tags embedded with non-linear elements such as
diodes produce these harmonic frequencies upon
being struck by the radar's signal. This approach is
distinguished by its ability to decrease
environmental noise and clutter, given that natural
reflections seldom imitate these exact frequency
multiples. Therefore, harmonic radar proves to be
highly efficient in monitoring small, tagged objects
with precision and minimal disruption, rendering it
well-suited for wildlife observation and other
delicate tracking tasks. An overview of the proposed
scheme is provided in Figure 1.
According to [25] and [26] many non-linear
systems can be modeled by a power series. Let us
assume that the malicious drone behaves as a non-
linear system. Then the output of the system can be
modeled by a power series:
(1)
If the input contains only one frequency, then
the power series indicates that harmonics of that
frequency will be generated by the non-linear
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system. If:
(2)
then the response of the non-linear system can be
written as:
+
… (3)
where:
(4)
(5)
Let us assume that ci = 0, i ≥ 4 and E0 is small.
Then the output Er can be written as:
+
(6)
Fig. 2: The mini-drone’s harmonic radar transmits a
signal and receives its response from the malicious
drone
Let us now examine Figure 2. In this figure the
signal is transmitted from point 1, and it arrives at
point 2 (target at a distance equal to r from the mini-
drone’s harmonic radar). The malicious drone
behaves as a non-linear system and transmits back a
signal from point 3. Finally, the mini-drone’s
harmonic radar receives the signal that returns back
at point 4. The power at point “1” is:
(7)
where Ptr is the power of the transmitted signal,
while gtr is the gain of the mini-drones harmonic
radar transmitter. Assuming that the signal spreads
homogeneously (spherically) the power at point “2”
is:
(8)
By modeling the relationship between the input
and output signals that the non-linear malicious
drone receives and transmits, according to Eq. (1)
we have:
(9)
where
is the input power received by the
non-linear malicious drone (point “2”) and P3 is the
output power of the non-linear malicious drone
(point “3”). Furthermore, fai is a factor, scaling i-th
harmonic.
is related to the effective aperture
() of the malicious drone (how much power the
malicious drone can capture) and is calculated by:
(10)
where is for the lowest frequency
(fundamental - frlow=θ0/2π) of the transmitted signal
(e.g. of Eq. (2)). More specifically, the effective
aperture is related to the malicious drone’s gain
(antenna that receives the signal):
(11)
where
is the malicious drone’s gain for the
lowest frequency of the transmitted signal and is
the wavelength of the lowest frequency. By
combining Eq. 9 and 10 for each harmonic i:
(12)
Then the power of the i-th harmonic, leaving the
non-linear malicious drone (point “3”) can be
expressed as:
(13)
where
is the gain of the malicious drone’s
transmission antenna at the i-th harmonic.
Considering a spherical spread back to the harmonic
radar-equipped mini-drone, the power at point “4”
can be expressed as:
(14)
Then, the power that the mini-drone’s harmonic
radar receives is estimated by incorporating the
radar’s effective aperture:
(15)
where
is the effective aperture at the i-th
harmonic and can be expressed as:
(16)
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where
is the gain of the mini-drone’s
harmonic radar receiver at the i-th harmonic and λi
is the respective wavelength.
By grouping all parameters of the non-linear
malicious drone, we have:
(17)
Then Eq. (15) becomes:
(18)
According to Eq. (18), the mini-drone’s
harmonic radar receives a power which is analogous
to
for the ith harmonic frequency. Thus, as the
mini-drone approaches the malicious drone, the
power that the mini-drone’s harmonic radar receives
increases very fast. Additionally, the power that the
mini-drone’s harmonic radar receives is
proportional to the power of the signal it transmits
and the gain of its antenna. The gain is raised to i
(for the ith harmonic). Thus, if the mini-drone
receives enough power, the existence of a malicious
drone can be confirmed. However, in order to also
estimate the distance between the mini-drone and
the malicious drone, the phase of the received signal
should also be analyzed.
Towards this direction, let us recall Eq. (2) for
the transmitted signal at point “1”. Then the analytic
representation of Eq. (2), for θ0 >0 is:
(19)
where θ0 is the lowest frequency (fundamental), φ is
the initial phase of θ0, and is the wavelength of
θ0. E0 is the amplitude of the transmitted signal,
related to the signal’s power, which has already
been discussed. The following analysis focuses on
the phase of the signal (θ0t + φ). In particular, the
signal propagates from point “1” to point “2”
traveling a distance r, which results in a change of
its phase by Δθ1,2. More particularly:
(20)
As a result, the signal at point “2” will be:
(21)
Again, by modelling the relationship between
the input and output signals that the non-linear
malicious drone receives and transmits, according to
Eq. (1) we have:
(22)
where hai corresponds to the amplitude of the
ith harmonic of the signal transmitted back from the
malicious drone.
For notation simplicity and by dropping hai and
E0 (since they are not related to the signal’s phase)
we get:
(23)
Finally, the signal propagates back from point
“3” to point “4” traveling a distance r, which results
in a change of its phase by
:
(24)
or
(25)
is different for each harmonic frequency i.
More specifically and based on Eq. (20):
(26)
where λi is the wavelength of the ith harmonic
frequency. Considering that:
(27)
we have that:
(28)
Then Eq. (25) becomes:
(29)
Fig. 3: Mini-drone scanning indoor space to create
3D non-linear device location map and detect tiny
malicious drones
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3.2 The Innovative Indoor Spy-Drone
Detection Algorithm
According to Eq. (29) and assuming the existence of
a malicious drone, the mini-drone will receive: (a) a
signal with power calculated using Eq.(18) for i=1,
frequency frlow (wavelength ) and phase (
), (b) a signal (first harmonic) with
power calculated using Eq.(18) for i=2, frequency
2frlow (wavelength ) and phase 2(
), which is double compared to the phase of
frlow etc. Without loss of generality, if φ=0, then we
have for frlow:
(30)
and since is measured by the mini-drone
(since the mini-drone knows the transmitted and
estimates the received signal), the distance of the
malicious drone can be calculated by:
(31)
Thus, if the indoor space is empty, it is
straightforward to detect the malicious drone.
However, in most cases the indoor space of a CI is
not empty but it contains several electronic devices,
which behave in a non-linear way, just as the
malicious drone does. In order to detect the
malicious drone in such an environment, the mini-
drone runs the proposed innovative algorithm. In
particular, the mini-drone, scans the whole indoor
space by moving on a 3D grid. An example is
provided in Figure 3. More specifically, the mini-
drone can start from a node (where two red lines
cross) and each time move by a distance equal to Td,
which defines the size of the scan-cube (represented
in black color, within Figure 3). Each time it visits a
new node ndi, i=1, …,n, the mini-drone transmits a
signal at frlow and analyses the received signal. After
visiting all nodes, the mini-drone creates a non-
linear system location map for the whole indoor
space by using Eq. (31). The 3D location map
contains all non-linear devices, including the
malicious drone.
If the mini-drone could have been provided in
advance with a legitimate location map, then it
would be an easy task to detect the malicious drone.
However, the creation of a legitimate map needs
accurate and time-consuming preliminary work. The
proposed algorithm does not need a legitimate map.
To do so, the mini-drone periodically re-scans the
indoor space. As long as the 3D location map
remains the same, either there is not any malicious
drone or the malicious drone does not move. If the
malicious drone moves, then the 3D location map
will change, leading to the detection of the
malicious drone (new location within the 3D
location map).
There is only one case, where the malicious
drone may remain undetectable by the 3D location
map method. In this case, it is assumed that the
malicious drone is able to stick to the legitimate
devices (approach as close as possible) that exist
within the indoor space. Thus, when the mini-drone
is far away during the scanning process, the
malicious drone can move to the next legitimate
device. However, in order to locate indoor
legitimate devices, the malicious drone has to
transmit a signal, operating in a similar - to the
mini-drone- way. But, if a signal is transmitted, then
the malicious drone reveals its existence. The same
happens if the malicious drone is remotely operated.
The aforementioned analysis results in Algorithm 1.
Algorithm 1: Indoor Space Scanning and Malicious
Drones Detection
// ######## INITIALIZATION ########
mini_drone.move.to -> (x0, y0) // mini drone can start from any node,
but for simplicity, it is assumed that it moves to initial node of the 3D
grid e.g. bottom right
if (3D_map.available == “true”) // 3D map of the indoor infrastructure
is available at the system’s server
then {
mini_drone.receive -> 3D_map
go.to(MALICIOUS DRONE LOCATION)
}
// ######## CREATE 3D MAP ########
else {
SCAN(j):
for (i=1:n)
{
mini_drone.move.to -> ndi //mini-drone moves to all nodes of
the 3D grid
mini_drone.transmit_signal = true // mini-drone transmits
signal to detect non-linear device (NLD)
mini_drone.receive_signal ->
//Eq. (18)
mini_drone.select -> max(
) // mini-drone keeps only the
NLD providing the maximum value of
mini_drone.estimate.distance.max_NLD -> ri //Eq. (31)
R_all-> (r1, r2, …, rn) //all measured distances are stored in
R_all
}
mini_drone.create(R_all)-> 3D_map(j) //R_all is used to create
3D_map
system_server.receive-> 3D_map(j) // 3D_map is received by the
system’s server
}
// ######## MALICIOUS DRONE LOCATION########
while (mini_drone.on_duty == “true”) // a specific mini-drone is on
duty, scanning the indoor area. If it needs re-charging, then another
mini-drone takes its place
do {
3D_map(j) <- SCAN(j).return.3D_map //the mini-drone scans the
whole 3D grid to provide the jth instance of the3D_map
if (3D_map(j) 3D_map(i), for ) //if the jth instance of the
3D_map is different from the ith instance of the3D_map
{
spy_drone.detection = true // spy-drone is detected, occupying a
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new position within the 3D_map
spy_drone.location.(x,y,z)->(3D_map(j).(x,y,z)-
-3D_map(i).(x,y,z)).nonzero // the location (x,y,z coordinates)
of the malicious_drone is calculated
}
}
4 Experimental Results
A PC with Intel(R) Core i7-12700 CPU @ 3.60GHz
plus 16 GB DDR4 RAM was used for running the
experiments. Results and comparisons were
simulated using R 4.3.2. For the following
calculations Ptr is assumed to be 0.1 Watt (30 dBm),
since: (a) the antenna of a small drone does not have
to transmit high-power signals and (b) in this way
less energy is used for malicious drone detection.
On the other hand, gtr for frlow is assumed to be 5
dBi,
is assumed to be 5 dBi and
is assumed
to be 3 dBi. Additionally,
, since it is considered that the gain
of the malicious drone does not resemble the gain of
real antennas, but it is significantly less.
Furthermore, frlow is set to 900 MHz (
) with its first harmonic at 1,800 MHz (
). Finally, fa1=1, fa2= 0.5, and
. Here it should be
mentioned that the most common parameters have
been selected for the problem under consideration,
but even if other parameters are selected, they will
lead to similar results.
Fig. 4: Power received by the antenna of the mini-
drone for the lowest frequency and its first harmonic
Based on the aforementioned parameters,
and
(Eq. 18) are calculated and visualized in
Figure 4. As it can be observed, the received power
at a distance of 0.1m is 19.77 dBm and 2.76 dBm
for the lowest frequency and the first harmonic,
while, in the case of 2m it falls to -32.27 dBm and -
75.3 dBm respectively. Here it should be mentioned
that each receiver has a sensitivity. If the strength of
the received signal is less than the sensitivity
threshold, then the receiver will not be able to
receive the signal. According to [27], the common
802.11g products have a sensitivity of -85 dBm,
many wireless market products offer a sensitivity of
-105 dBm, while professional devices provide a
receiver sensitivity of almost -120 dBm. Thus, the
proposed scheme with its specific parameters
enables the mini-drone to detect the malicious
drone, even if its antenna is a common market
product and not a highly specialized and specifically
designed antenna. Reliable detection of the
malicious drone can be achieved even at a distance
of 2 meters.
(a)
(b)
Fig. 5: (a) Hand-held scanning device (b) Passive
infrared sensor
Fig. 6: Foldable grid of sensors
4.1 Comparison to State-of-the-Art
Approaches
Sensors emitting laser beams could somehow
confront the problem of tiny malicious drones, but
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such a solution would need a huge number of laser
sensors to cover the whole space and possibly
produce many false alarms (due to bugs, insects,
etc.). For this reason, in this paper, two common
approaches are considered and compared to the
proposed scheme. The first, traditional approach is
based on a human guard who holds a scanning
device (Figure 5(a)) and inspects the whole CI. The
second approach is based on passive infrared
sensors (Figure 5(b)), e.g. and without loss of
generality, Panasonic’s PaPIRs passive infrared
sensors [28], [29]. Additionally, let us assume that
the CI resembles a rectangular tank with a length
equal to 100 m, a width equal to 4 m, and a height
equal to 4 m. In this case, the volume of the CI is
estimated to be 1,600 m3. According to [28], [29]
PaPIRs can detect an area of 70×25 cm (1,750 cm2)
at a distance of 12 m. Assuming that the tiny spy-
drone has a size of 7.5×7.5 cm (56.25 cm2) and
considering that PaPIRs exhibit a linear behavior
regarding the distance – detectable area relation,
then PaPIRs sensors should be placed about every
0.8m in order to be able to detect the tiny malicious
drone, in a foldable grid (Figure 6). The grid of
sensors could be unfolded on non-working hours
and folded on working hours.
On the other hand, it is assumed that the human
guard can raise the hand-held scanning device to a
height of 2 – 2.2 meters. In this case, the malicious
drone’s maximum distance could be 1.8 – 2 meters.
Considering similar to the mini-drone’s receiver
sensitivity, the human guard can effectively scan the
whole CI, using the hand-held scanning device.
Next, the three approaches are compared
quantitatively and qualitatively. In particular, the
quantitative comparisons include the time to scan
the CI and the cost of scanning, while the qualitative
comparisons include false alarms and parameters
such as sensitivity, human mistakes, preparation
time, and ease of installing/uninstalling.
Regarding the time to scan the CI, let us
consider that the CI is cut into slices and the
distance between slices is 1 m. Let us also consider
that the human guard moves at a speed of 1.4 m/sec
and spends 5 seconds to scan each slice. Let us also
consider that the mini drone passes through the
center of the slices (following the axis of the grid),
transmits a signal every 0.01 seconds, and moves at
a speed of 1 m/sec. In order to scan the CI under
consideration, the human guard needs 571.4 sec, the
passive infrared sensors approach needs 0 sec and
the proposed approach needs 100 sec. Figure 7
provides the scan time per CI’s cubic meter for the
three approaches. Volume is provided in the log10
scale. As it can be observed, the passive infrared
sensors approach needs zero time, since the grid of
sensors covers the whole volume of the CI.
Additionally, the human scanning approach
provides the worst performance (in case of 50,000
m3, scanning takes 17,856.25 sec), while the
proposed approach provides a time reduction of
82.5% compared to the human scanning approach
(e.g. in the case of 50,000 m3, scanning takes 3,125
sec).
Fig. 7: Time to scan CI versus CI’s volume (in cubic
meters – log10 scale)
Now, regarding the cost of scanning, let us
assume that a human guard has a total cost (daily
rate, insurance, etc.) of 80 Euros per 8 hours and the
hand-held scanning device costs 300 Euros. Let us
also assume that each passive infrared sensor costs
on average 10 Euros [30] (depending on the number
of purchased sensors). In order to cover the whole
CI, each slice (foldable grid of passive infrared
sensors) should contain 36 sensors (one every 0.8
meters), while the total number of slices is 125
(each slice every 0.8 meters). As a result, the whole
CI is covered by 4,500 sensors. On the other hand,
the cost of buying an autonomous mini drone like
e.g. Pegasus mini [31] and making all necessary
adaptations (e.g. addition of transmitter, receiver,
signal analyzer, etc.) may reach 2,000 Euros. It is
also assumed that in one day, the CI should be
scanned 10 times. This is reasonable, since the
malicious drone may move at any time from its
position. Then the overall cost for one day and for
one year are visualized in Figures 8(a) and 8(b)
respectively.
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Table 1. Qualitative comparison of the three approaches
False Alarms
Sensitivity
Human
Mistakes
Preparation
Time
Ease of
Installing /
Uninstalling
Human
Scanning
Very Low
Very Low
Yes
No
Easy
Passive Infrared
Sensors
Moderate
Moderate
No
Moderate
Difficult
Proposed
Very Low
Very Low
No
No
Easy
(a)
(b)
Fig. 8: (a) Cost in Euro (log10 scale) of One-Day
Scanning versus CI’s volume (in cubic meters –
log10 scale) (b) Cost in Euro (log10 scale) of One-
Year Scanning versus CI’s volume (in cubic meters
– log10 scale)
As it can be observed, the minimum cost for one
day is provided by the human scanning approach
(304.96 Euro for a CI of 500 m3 and 796 Euro for a
CI of 50,000 m3). This is expected in the short term
since the cost of the hand-held device is much lower
(300 Euro) than the cost of the modified mini-drone
(2,000 Euro). However, in the long term, the
proposed approach provides much lower operational
costs compared to the other two approaches. In
particular (Figure 8(b)), the minimum cost for one
year is provided by the proposed scanning approach
(2,000 Euro for a CI of any volume), while the
human scanning approach requires 2,110.43 Euro
for a CI of 500 m3 and 181,342.54 Euro for a CI of
50,000 m3 and the passive infrared sensors approach
requires 14,062.5 Euro for a CI of 500 m3 and
1,406,250 Euro for a CI of 50,000 m3.
Thus, (a) compared to the human scanning
approach, the proposed approach reduces the
scanning cost from 5.23% to 98.9% (b) compared to
the passive infrared sensors approach, the proposed
approach reduces the scanning cost from 85.78% to
99.86 %. Here it should be mentioned that the cost
of recharging the mini-drone’s batteries is neglected
since it is low. Even if it is considered, the costs of
the other two approaches (especially for large CIs)
are still orders of magnitude greater.
Finally, a qualitative comparison of the three
approaches is provided in Table 1. In particular,
regarding false alarms, the passive infrared sensors
approach may be vulnerable to insects, swarms of
bugs, etc. Regarding sensitivity, the passive infrared
sensors approach may be more sensitive to
temperature and for this reason, it is recommended
that sensors are 3 to 5 meters away from heat
sources. Additionally, the passive infrared sensors
approach cannot detect malicious drones if they are
not moving. The proposed approach and the human
scanning approach can detect malicious drones if a
ground truth 3D location map is available. If there is
not a ground truth 3D location map and the
malicious drone does not move it cannot be located.
In this case, a malicious worker (maybe a staff
member of the CI) could pick up the malicious
drone and leave the CI.
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Furthermore, the human scanning approach may
be vulnerable to human mistakes (e.g. if the human
guard does not properly scan the CI). On the other
hand, the passive infrared sensors approach may
need some time for preparation, especially in order
to unfold (and fold) the grid of sensors. Finally, the
passive infrared sensors approach takes much time
to install/uninstall and it is a solution of low
portability, compared to the other two approaches.
For reproducing the simulated results, datasets are
provided in Table 2, Table 3, Table 4 and Table 5 of
the appendix.
5 Conclusion
Critical infrastructures face a significant risk of
rapid destruction or becoming targets of various
cyber-attacks at minimal cost, if not adequately
defended against tiny malicious drones. This study
concentrated on countering autonomous tiny
malicious drones, by incorporating mini-drones
equipped with harmonic radar and a novel algorithm
that creates 3D non-linear device location maps of
indoor areas. Extensive comparisons to state-of-the-
art methods revealed both the advantages and
limitations of the proposed approach.
Future research can address various unresolved
issues. For instance, the scenario where the
malicious drone does not move, the case of very
large CIs or the case of CIs that combine indoor and
outdoor sensitive areas. Further research initiatives
might also involve creating a more extensive
simulation framework that incorporates practical
challenges such as dynamic obstacles and various
drone speeds, thus enhancing the evaluation of the
algorithm's efficacy in complex scenarios. Lastly,
there is potential for implementing security plans
optimized for specific critical infrastructures, taking
into account their unique characteristics.
Acknowledgement:
The authors would like to thank Dr. Dimitrios
Kouremenos, Mr. Vasilios Yfantis, Mr. Andreas
Kener† and Mr. Konstantinos Psaraftis for their
support, ideas, comments and remarks regarding the
experimentation phase.
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Maria S. Ntaliani, Filotheos S. Ntalianis,
Nikos E. Mastorakis
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Volume 21, 2024
APPENDIX
Table 2. Power received by the antenna of the mini-
drone for the lowest frequency and its first harmonic
(Figure 4)
Distance in
meters
(dBm)
(dBm)
0.1
19.7708684
2.760176
0.2
7.7296686
-15.301624
0.3
0.6860182
-25.867100
0.4
-4.3115312
-33.363424
0.5
-8.1879318
-39.178025
0.6
-11.3551816
-43.928899
0.7
-14.0330532
-47.945707
0.8
-16.3527311
-51.425223
0.9
-18.3988320
-54.494375
1
-20.2291316
-57.239824
1.1
-21.8848390
-59.723385
1.2
-23.3963814
-61.990699
1.3
-24.7868657
-64.076425
1.4
-26.0742530
-66.007506
1.5
-27.2727819
-67.805300
1.6
-28.3939309
-69.487023
1.7
-29.4470884
-71.066760
1.8
-30.4400318
-72.556175
1.9
-31.3792756
-73.965040
2
-32.2703314
-75.301624
Table 3. Time to scan CI versus CI’s volume (in
cubic meters – log10 scale) (Figure 7)
Volume in
m3 (log10)
Human
Scanning
(sec)
Passive
Infrared
Sensors
(sec)
Propose
d
(sec)
2.698970
178.5625
0
31.25
3.000000
357.1250
0
62.50
3.176091
535.6875
0
93.75
3.301030
714.2500
0
125.00
3.397940
892.8125
0
156.25
3.477121
1071.3750
0
187.50
3.544068
1249.9375
0
218.75
3.602060
1428.5000
0
250.00
3.653213
1607.0625
0
281.25
3.698970
1785.6250
0
312.50
3.875061
2678.4375
0
468.75
4.000000
3571.2500
0
625.00
4.096910
4464.0625
0
781.25
4.176091
5356.8750
0
937.50
4.243038
6249.6875
0
1093.75
4.301030
7142.5000
0
1250.00
4.397940
8928.1250
0
1562.50
4.477121
10713.7500
0
1875.00
4.544068
12499.3750
0
2187.50
4.698970
17856.2500
0
3125.00
Table 4. Cost in Euro (log10 scale) of One-Day
Scanning versus CI’s volume (in cubic meters –
log10 scale) (Figure 8(a))
Volume
in m3
(log10)
Human
Scanning in
Euro (log10)
Passive
Infrared
Sensors in
Euro
(log10)
Proposed
in Euro
(log10)
2.698970
2.484243
4.148063
3.30103
3.000000
2.491250
4.449093
3.30103
3.176091
2.498145
4.625184
3.30103
3.301030
2.504933
4.750123
3.30103
3.397940
2.511616
4.847033
3.30103
3.477121
2.518199
4.926214
3.30103
3.544068
2.524682
4.993161
3.30103
3.602060
2.531071
5.051153
3.30103
3.653213
2.537366
5.102305
3.30103
3.698970
2.543572
5.148063
3.30103
3.875061
2.573337
5.324154
3.30103
4.000000
2.601192
5.449093
3.30103
4.096910
2.627368
5.546003
3.30103
4.176091
2.652055
5.625184
3.30103
4.243038
2.675414
5.692131
3.30103
4.301030
2.697580
5.750123
3.30103
4.397940
2.738783
5.847033
3.30103
4.477121
2.776414
5.926214
3.30103
4.544068
2.811042
5.993161
3.30103
4.698970
2.900917
6.148063
3.30103
Table 5. Cost in Euro (log10 scale) of One-Year
Scanning versus CI’s volume (in cubic meters –
log10 scale) (Figure 8(b))
Volume
in m3
(log10)
Human
Scanning in
Euro (log10)
Passive
Infrared
Sensors in
Euro (log10)
Proposed
in Euro
(log10)
2.698970
3.324370
4.148063
3.30103
3.000000
3.593380
4.449093
3.30103
3.176091
3.758251
4.625184
3.30103
3.301030
3.877469
4.750123
3.30103
3.397940
3.970910
4.847033
3.30103
3.477121
4.047763
4.926214
3.30103
3.544068
4.113040
4.993161
3.30103
3.602060
4.169774
5.051153
3.30103
3.653213
4.219947
5.102305
3.30103
3.698970
4.264918
5.148063
3.30103
3.875061
4.438643
5.324154
3.30103
4.000000
4.562394
5.449093
3.30103
4.096910
4.658590
5.546003
3.30103
4.176091
4.737294
5.625184
3.30103
4.243038
4.803900
5.692131
3.30103
4.301030
4.861636
5.750123
3.30103
4.397940
4.958188
5.847033
3.30103
4.477121
5.037130
5.926214
3.30103
4.544068
5.103906
5.993161
3.30103
4.698970
5.258500
6.148063
3.30103
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Maria S. Ntaliani, Filotheos S. Ntalianis,
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
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