Method of Binary Detection of Small Unmanned Aerial
Vehicles
Denys Bakhtiiarov1, 2, Bohdan Chumachenko2, Oleksandr Lavrynenko2,
Serhii Chumachenko2, and Vitalii Kurushkin2
1 State Scientific and Research Institute of Cybersecurity Technologies and Information Protection, 3 Maksym
Zaliznyak, Kyiv, 03142, Ukraine
2 National Aviation University, 1 Kosmonavta Komarova ave., Kyiv, 03058, Ukraine
Abstract
This research offers a method for detecting Small Unmanned Aerial Vehicles (sUAVs) in
binary using state-of-the-art technology and signal processing techniques. The proposed
method combines machine learning and signal analysis techniques to reliably determine
the presence of sUAVs in a particular airspace. Pattern recognition, real-time data
processing, and spectral analysis are the three primary phases of the approach.
Qualitative characteristics of sUAV signals can be identified by spectral analysis. The
system can learn and identify these properties and make judgments regarding the
presence or absence of sUAVs thanks to the application of machine learning methods.
Furthermore, the system’s ability to recognize common patterns of sUAV activity is
improved by the integration of pattern recognition. Processing data in real-time
guarantees system responsiveness and lowers the number of false signals. The efficiency
of the suggested sUAV detection system is strongly demonstrated by experimental results
acquired in a variety of environmental circumstances. This highlights how the system can
improve airspace monitoring measures’ effectiveness and safety.
Keywords 1
Binary detection, signal processing, spectral analysis, detection accuracy, airspace
monitoring.
1. Introduction by processing a set of n amplitude beat signals in
an FMCW radar, determined for each probing
Let’s consider the task of binary detection of FMCW radio signal over a specific observation
small-sized targets against the background noise interval t = [0; T].
of the receiving channel of an active radar system The amplitude of the ith beat signal
from the perspective of the statistical hypothesis corresponds to the ith probing FMCW radio
testing theory in the presence of interference. pulse in the series [5].
Initially, let’s assume that the movement
parameters of the UAV are known [1–3], hence 2. Problem Statement
the form of the useful signal is known. Similar
tasks were addressed by many authors when The formulation of this task is determined by the
developing algorithms to detect signals of a specific nature and technical implementation of
known form, which comprise a bunch of received receiving channels in typical ground-based short-
radio pulses, against the backdrop of additive range active radars with probing FMCW radio
Gaussian noise [4]. In this section, we examine signals. In such contemporary digital radars, for
the task of detecting a small-sized moving target each probing FMCW radio signal, signal beat
CPITS-2024: Cybersecurity Providing in Information and Telecommunication Systems, February 28, 2024, Kyiv, Ukraine
EMAIL: bakhtiiaroff@tks.nau.edu.ua (D. Bakhtiiarov); bohdan.chumachenko@npp.nau.edu.ua (B. Chumachenko);
oleksandrlavrynenko@tks.nau.edu.ua (O. Lavrynenko); serhii.chumachenko@npp.nau.edu.ua (S. Chumachenko);
vitaliy.kurushkin@npp.nau.edu.ua (V. Kurushkin)
ORCID: 0000-0003-3298-4641 (D. Bakhtiiarov); 0000-0002-0354-2206 (B. Chumachenko); 0000-0002-3285-7565 (O. Lavrynenko); 0009-
0003-8755-5286 (S. Chumachenko); 0009-0000-4411-0509 (V. Kurushkin)
©️ 2024 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
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Workshop ISSN 1613-0073
Proceedings
312
samples from the output of the analog-digital approximation, we’ll describe the correlation
converter are processed [6]. This processing function of the Gaussian random process using
involves calculating the Fast Fourier Transform, a delta function. As can be inferred from
followed by delineating the amplitude spectrum expression (1), random variations in the
to determine the distance to relevant objects [7, background’s RCS lead to a multiplicative
8]. Such objects could be a background surface of transformation of the useful signal A (t ) ,
a particular type. Hence, a distinctive feature of meaning they act as multiplicative interference.
the method discussed in this subsection is the The background’s RCS, f (b 2 b 2 ) , is
processing of a set of amplitude samples of
signals reflected from background surfaces or nonlinearly incorporated into the amplitude
objects included in a burst of radio pulses. expression of the reflected signal, as described
First, let’s determine the probability density of by expression (1) (through the square root).
instantaneous signal values at the detector’s Let’s determine the density distribution of
input both in the presence and absence of UAVs the square root of the RCS and subsequently
[9]. the density distribution of the amplitude of the
During the observation time t = 0; T , such reflected signal.
It’s well-known that a nonlinear
amplitude variation of the radio signal is transformation of a random variable results in
represented by the time function A (t ) . This time the alteration of its distribution law in the
function A (t ) contains information about the following way [11]:
presence of UAVs. Therefore, we’ll consider d ( B) ,
W ( B) = W [ X = ( B)] (2)
A (t ) it as the useful signal at the detector’s dB
input. Let’s first address the task of detecting where W ( X ) is the normal probability density
UAVs for a specific set of model parameters, distribution of the random variable X.
described by expression (1). W ( B ) is the sought-after probability density
Let’s assume that the detector’s input receives distribution of the random variable A.
an additive mixture of the useful signal A (t ) and ( B ) is the function inverse to the function
the noise of the receiving path, which we will B = ( X ) .
consider as Gaussian and delta-correlated. As In this context, X = f (b 2 b 2 ) represents a
inferred from the materials presented earlier, the
power of the useful signal exceeds the power of stationary random process, B = f (b 2 b 2 ) ,
the additive noise of the receiving path by 25–30 and the density distribution of instantaneous
dB [6]. Under these conditions, the density RCS values at a certain point in time is
distribution of the envelope of the observed radio described by a Gaussian law:
signal follows a normal law with an average value 2
1 f − m f
equal to the instantaneous value of the useful 1
−
2 f
signal envelope. Let’s represent the observed W ( f ) = e , (3)
2 f
signal Y(t) as the sum of the useful signal A (t )
and the receiving path noise n(t): where m f is the average RCS of the
Y (t ) = A (t ) + n(t ) . (1) background ( m = f 0 ), in square meters; σ
f
In [10], it is demonstrated that the effective represents the root mean square deviation of
scattering surface of the background during the instantaneous RCS values of the background
observation of the useful signal acts as a over the observation time of the useful signal,
stationary Gaussian random process. The in square meters [12].
temporal correlation interval of this process is In this expression, to simplify the notation,
considerably shorter than the duration of the bi-static angle designations b 2 and b 2 have
observed useful signal. As a first
313
been omitted. In general, they are functions of 2
1 B − m f
2
−
time during the observation of the useful signal 2 B 2 f
. (7)
W ( B) = e
A (t ) . However, in the context discussed, 2 f
variations of the mentioned bi-static angles do
The useful signal A (t ) is the product of the
not result in changes to the background RCS as
described by expression (2). deterministic function f (t ) and the square root
The random variations in the background of the random variable f :
RCS f over the observation time of the useful 1 + k A (t ) + 2 k A (t ) cos (t )
A (t ) = f f (t ) = f AOTR (8)
signal can be represented as the sum of the
It’s known that multiplying a stationary
average value f 0 and the fluctuation
random process f by a non-random time
component f : function f (t ) results in a non-stationary
random process with the same distribution law
f = f 0 +f . (4)
W ( f ) over the observation [14] interval of
The multiplicative nature of interference the useful signal. Note that the multiplier AOTR
about the useful signal arises from fluctuations also varies over time as the UAV moves due to
in the RCS (Radar Cross-Section) of the changes in distances RAB , RBC , RAC , and the
background. However, the average value of the antenna gain factor. We consider these changes
background’s RCS doesn’t distort the shape of to be insignificant compared to the influence of
the useful signal. the oscillating multiplier f (t ) . In this case, the
The probability density distribution of the
fluctuating component of the background RCS non-stationary process is the result of the
can be written as [13]: product of the useful signal A (t ) and the
2 multiplicative interference f . The non-
1 f
−
2 stationarity of the random process A (t ) is due
W ( f ) =
1
e
f
. (5)
2 to the variability of the variance D( f ) by
f
f 2 (t ) times, leading to a change in the scale of
Expressing the random variable X through B the probability density distribution W ( f ) .
and calculating the derivative, we obtain: The change in dispersion over time,
d ( B) described by expression (8), according to the
X = ( B) = B 2 , = 2 B . (6)
dB law of the useful signal can be written as
follows:
From this, we derive the sought distribution
law of the square root from RCS:
2
1 f − m f
−
f 2 f
DA (t ) = AOTR
/
1 + k A (t ) + 2 k A (t ) cos (t ) e
d f (9)
− 2 f
The probability distribution density of Regrettably, the integrals in formulas (7)–
instantaneous values of the useful signal over (9) cannot be expressed in terms of elementary
the observation period can be written as functions and can only be determined by
follows [15]: numerical integration.
314
2
A 2 − m f
− /
1
2 A
2 AOTR 1+ k A ( t ) + 2k A ( t )cos
W ( A , t ) e f
(10)
/
A
OTR 1 + k A (t ) + 2 k A (t ) cos (t ) 2 f
3. Method of Binary Detection of Where σn is the root mean square deviation of
the noise measurements in the receiving system.
SUAV
The random process A (t ) is independent of
The useful signal A (t ) , modulated by the receiving system noise. The probability
density function of the instantaneous values of
multiplicative interference, is observed against
the process Y (t ) from formula (1), represented as
the backdrop of additive Gaussian noise in the
reception path. The noise correlation interval the sum of two independent random processes, is
of the reception path does not exceed one determined by the convolution of the probability
microsecond. The duration of the useful signal density of the receiving system noise, described
is in the order of seconds [16]. Hence, by expression (11), and the probability density of
disregarding the correlated noise samples n(t), the useful signal, described by expression (10), as
we regard it as white Gaussian noise with a follows:
zero mean value and a probability distribution
density of instantaneous values: W (Y , t ) = WA (Y − n, t ) Wn (n)dn . (12)
−
2
1 n
1 −
Or, taking into account (10) and (11), we
e n . (11)
2
Wn (n) =
2 n obtain:
2
2
2
2
1 (Y − n ) − m f n 1 (Y − n ) − m f n
2 2
− + − +
2 f ( t ) f n 2 f ( t ) f n
Y e
dn − n e
dn (13)
W (Y , t ) = − −
f (t ) f n
The density function described by formula signal Y (t ) at the detector’s input characterizes a
(13) of the instantaneous values of the observed non-stationary random process with time-
signal Y (t ) at the input of the detector varying variance due to the target’s movement
characterizes a non-stationary random process relative to the background surface.
with time-varying variance due to the motion of It is known that the detection of small targets
the target relative to the background surface [16]. is based on the processing of the observed signal.
It is known that the detection of small targets In this case, the samples of such a signal are the
is based on the processing of the observed signal. amplitudes of the LFMC radio pulse batch
In this case, the samples of such a signal are the observed over the time interval t 0, T . The
amplitudes of LFM radio pulses observed over a optimal algorithm for detecting the useful signal
time interval t 0, T . The optimal signal will be sought based on the minimization of the
detection algorithm will be sought based on the average risk, the consideration of which leads to
minimum average risk criterion, taking into the determination of a specific expression for the
account which leads to the determination of a likelihood ratio [17].
specific expression of the likelihood ratio. W (Y / H1 ) .
L(Y ) = (14)
The density distribution described by formula W (Y / H 0 )
(13) of the instantaneous values of the observed
315
Hypothesis H₁ corresponds to the case of the signal observed at the detector’s input under
UAV’s movement in front of the background the assumption of the validity of the hypothesis
surface, where the radio signal reflected from H1 is described by the following expression:
the background is modulated by the reflected
radio signal from the UAV. The model of the
Y (t ) = AOTR
/
f (b 2 b 2 ) 1 + k A (t ) + 2 k A (t ) cos (t ) = AOTR
/
f (b 2 b 2 ) f (t ) (15)
The randomness of the process Y (t ) is caused condition of UAV movement. Assuming that the
by fluctuations in the Radar Cross-Section (RCS) correlation interval of RCS fluctuations is much
f (b 2 b 2 ) of the background. The modulation smaller than the duration of the useful signal, we
can express the density distribution of sample
law Y (t ) is determined by the function f(t), which
values Y under the presence of a moving UAV as
accounts for the non-stationary nature of the follows:
sample distribution density Y under the
2
n Y 2 −m
f
1 i
−
2 f i =1 f ( ti )
n
2 Yi 2 AOTR
/2
W (Y / H1 , t ) = e (16)
/
AOTR 2 f i =1 f (ti )
Hypothesis H₀ corresponds to the case of the validity of the hypothesis H1 is described
receiving a radio signal reflected from the
by the following expression:
background. The model of the signal observed
at the detector’s input under the assumption of
Y (t ) = AOTR
/
f (b 2 b 2 ) = AOTR
/
f (b 2 b 2 ) (17)
The density distribution of the sample Y pattern to expressions (10) and (11), it is
under the assumption of hypothesis H₀, in this expressed as follows:
case, is stationary, and, following a similar
n
(Yi2 −m f )2
1
n −
2
Yi e
2 AOTR
/2
2 f i=1
W (Y / H 0 ) = / (18)
AOTR 2 f i =1
Substituting the conditional probability
density functions (16) and (17) into (18), we
obtain:
2
n n Y 2 −m
f
n Y f (ti )
1 i
−
2 2 A/2 2
/ i e OTR f i=1
AOTR 2 i =1 f (ti )
L(Y ) = (19)
f
n n
n (Yi2 − m f )2
1
−
2
AOTR 2
2 AOTR
/2
2 f i=1
/ Yi e
f
i =1
The obtained expression describes the
desired likelihood ratio for the problem of
316
detecting UAVs in the case of multiplicative certain threshold 0 . We simplify the optimal
interaction between a known useful signal and
detection algorithm described by formula (19)
amplitude fluctuations of the background.
through logarithmization.
The algorithm for detecting UAVs involves
comparing the expression (19), L (Y ) , with a
2
n m
2
Yi 2
n
n n
1
i =1
+ f − (Yi 2 ) 2 + n m2 f + 2 m f Yi 2 1 −
i =1 ti ) (20)
f (ti
) i =1 f (t )
i f (
n
ln L(Y ) = ln f (ti ) −
−1 i =1
i =1
2 AOTR
/2
2 f
Therefore, the optimal algorithm for UAV between a known useful signal and amplitude
detection based on the Bayesian criterion, fluctuations of the background, takes the
considering the multiplicative interaction following form [17]:
n n
Yi 4 n
1
Y − f (t ) − 2 m Y 1 − f (t )
i
4
2 f i
2
z 1 (ti )
H
z=
i =1 i =1 i i =1 i where
z (ti )
H0
2 AOTR
/2
2 f
A1 − B1 n
− ln f (ti ) + ln 0 —the modified threshold of the detector,
−1
z (ti ) =
2 AOTR f i =1
/2 2
2
n m
A1 = f
i =1
. (21)
f (ti )
B1 = n m2 f
In the case of discrete sampling of The structure of the optimal detector for
observations Y (t ) at the detector’s input, it detecting a moving UAV under the considered
follows from expression (21) that to decide the conditions is depicted in Fig. 1.
presence of a signal caused by UAV at the
detector’s input, a series of operations
involving the summation of nonlinearly
transformed samples from the observed
realization Y (t ) and the multiplication of the
square of the realization Y (t ) with a copy of the
expected useful signal, followed by summation
of the obtained results and comparison with a
threshold, should be performed [16].
A distinctive feature of the modified
detector threshold z (ti ) is its time Figure 1: Structural diagram of the optimal
detector for UAV with known motion parameters
dependency proportional to the expected
signal due to the non-stationary nature of the The structural diagram of the optimal detector
random process. When the threshold level is does not show the synchronization device
exceeded, the presence of the moving UAV is responsible for clocking the detector blocks.
confirmed; otherwise, a decision is made about Since the additional phase shift during the
its absence [17]. reflection of the radio signal by the target and the
background surface is random, it is necessary to
add a second quadrature channel to the
317
structural diagram presented in Fig. 2.16, where background” line of sight is unknown. In the
the function f (t ) is defined with a phase shift of conditions of a priori uncertainty about these
π/2 relative to the initial phase of the f (t ) parameters, the application of known
approaches to eliminate this uncertainty
function.
significantly complicates the above algorithm
The detection algorithm for UAV (21) is
and the structural diagram of the optimal
expedient to implement in the digital processing
detector [18]. To obtain a practically
block of the amplitude signals received in the
implementable UAV detection algorithm, we will
pulse sequence. However, for the
make a series of simplifications relative to the
implementation of this algorithm, including
observation model Y (t ) . These simplifications
setting the threshold, precise knowledge of
parameters such as the coordinates (angular will lead to the implementation of a quasi-
position) of the phase center (point) of the optimal detection algorithm.
background surface reflection, the values of We will consider the model of the observed
current bistatic angles, the three-dimensional input signal of the detector on the interval [0, T]
shape of the bistatic RCS of the target and as an additive sum of a non-random useful signal
background, is required. Furthermore, the start and Gaussian noise limited to f b in bandwidth:
time of the UAV flight relative to the “radar-
Y (t ) = AOTR 1 + k A (t ) + 2 k A (t ) cos (t ) + n(t ) (22)
For such an observation model, the detector For the likelihood ratio (22), the probability
design has been explored by numerous authors density in the presence of a signal H1 is
[19, 20]. Let’s briefly outline the results of
expressed as follows:
solving this problem. We will assume that the
data observation sampling interval is t = 1 .
2 fb
n
(Yi2 −m f )2
1
n −
2
Yi e
2 AOTR
/2
2 f i=1
W (Y / H1 ) = (23)
/
A
OTR 2 f i =1
1 n
2 Instead of comparing it to the threshold of
−
1 2 the likelihood ratio or function, we can
Wn (n) = e n . (24)
compare the logarithms of expressions (25) or
2 n
(26). Thus, we obtain the following decision
Where σn is the root mean square deviation rule for the considered detection problem [21]:
of the noise samples in the receiving path. T zH1 (t )
Under these conditions, the expression for 2
N 0 0
z= Y (t ) A(t )dt H0 . (26)
the likelihood ratio will be written in a known z (t )
manner [19]:
t
n
2 t
n The formula z (t ) = ln 0 + E y represents the
− Ai2 Yi Ai
(25) N0
L(Y ) = e e
N0 i=1 N0 i=1
.
modified threshold. Therefore, the detection
The formula can be alternatively expressed device for a moving small-sized target under
as a likelihood ratio functional, which these conditions corresponds to the well-
N 0 = 2n f b represents the spectral power known correlation receiver scheme depicted in
density of the noise in the receiving system. Fig. 2.
318
The synchronization device ensures coordinated In this case, the reference signal of the
operation between the reference generator and the correlation detector should be time-shifted
integrator, facilitating the comparison of its output relative to the observed signal, and a procedure
signal z (t ) with the threshold. To ensure the for searching and capturing the useful signal
functionality of the correlation detector, it is should be performed. To simplify this
necessary to multiply the reference and observed procedure, instead of a correlation detector for
signals at coincident time points. However, the the useful signal, its version with matched
arrival time of the observed signal is unknown. filters should be used. When the useful signal’s
time coincides with the impulse response of the
matched filter, the value of the correlation
integral will match the amplitude of the output
signal of the matched filter. The impulse
response of the matched filter h() for the
useful signal A(t ) is its mirrored copy, shifted
in time by t₀. The structural diagram of the UAV
Figure 2: Structural diagram of the correlation
detector with known parameters of its motion
detector for UAV with known parameters of its
using matched filters is shown in Fig. 3.
motion and initial phase
Figure 3: Structural diagram of the UAV detector using a matched filter with known parameters
of its motion and initial phase
The reference signal A(t ) has a random initial contains two quadrature generators of
reference signals, A0 (t ) and A0s (t ) :
c
phase due to the reflection of radio waves from
the target, underlying surfaces, and
background. When radio waves are reflected A0 (t ) = ( A0c ) 2 + ( A0s ) 2 = const. (27)
from these objects, an additional phase shift Similarly to how the envelope of a harmonic
becomes random. signal expressed through quadrature
To eliminate the dependence of the components does not depend on time:
reference signal on the influence of random
phase shifts during the reflection of radio E0 (t ) = E 2 cos() 2 + E 2 sin() 2 = E . (28)
waves, we use a structural scheme of a detector In this case, processing the observed signal
for a signal of known shape with a random in the small-sized target detection task will
initial phase. In this scheme, the detector involve comparing it to a threshold using the
following decision statistic:
2 2
z (t ) = Y (t ) A0c (t − )d + Y (t ) A0s (t − )d , (29)
− −
where Y (t ) is the observed realization of the A0s (t ) is the sine component of the reference
signal at the input of the detector. signal for the matched filter hs (t ) .
A0c (t ) is the cosine component of the
The structural diagram of the quadrature
reference signal for the matched filter hc (t ) . detector for the UAV with known parameters
of its motion using matched filters is shown in
Fig. 4 [5].
319
Figure 4: Structural diagram of the quadrature detector for UAV with known parameters of its
motion
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