Doppler-based navigation for mobile protection system of strategic maritime facilities in GNSS jamming and spoofing conditions

Abstract

The use of unmanned surface vehicles (USVs) to protect strategic maritime facilities is one of the directions of development of state security systems. The reliable operation of these devices depends on the immunity of their navigation system to targeted interference. This study presents the concept of an autonomous navigation system for the USV. The Doppler effect, which occurs in signals received from radio beacons with known coordinates of position, is the basis for its operation. Analytic expressions that describe the relationship between the coordinates of the current USV position and the frequency Doppler shift of the received signals are presented in this study. The evaluation of the effectiveness of this system is based on simulation tests for the selected research scenario. The navigation error along the entire trajectory of the USV motion is adopted as a measure for this assessment. Obtained results show the possibility of the practical application of the developed navigation procedure.

Full text

IET Radar, Sonar & Navigation
Research Article
Doppler-based navigation for mobile
protection system of strategic maritime
facilities in GNSS jamming and spoofing
conditions
ISSN 1751-8784
Received on 20th August 2019
Revised 12th November 2019
Accepted on 16th December 2019
E-First on 19th February 2020
doi: 10.1049/iet-rsn.2019.0413
www.ietdl.org
Cezary Ziółkowski1, Jan M. Kelner1
1Institute of Communication Systems, Faculty of Electronics, Military University of Technology, Gen. Sylwester Kaliski St. No. 2, 00-908 Warsaw,
Poland
E-mail: jan.kelner@wat.edu.pl
Abstract: The use of unmanned surface vehicles (USVs) to protect strategic maritime facilities is one of the directions of
development of state security systems. The reliable operation of these devices depends on the immunity of their navigation
system to targeted interference. This study presents the concept of an autonomous navigation system for the USV. The Doppler
effect, which occurs in signals received from radio beacons with known coordinates of position, is the basis for its operation.
Analytic expressions that describe the relationship between the coordinates of the current USV position and the frequency
Doppler shift of the received signals are presented in this study. The evaluation of the effectiveness of this system is based on
simulation tests for the selected research scenario. The navigation error along the entire trajectory of the USV motion is adopted
as a measure for this assessment. Obtained results show the possibility of the practical application of the developed navigation
procedure.
1 Introduction
In recent years, we have been observing the intensive development
of the communication and transport systems. This results in an
increase in population migration. The large economic, ideological,
and cultural diversities that are related to this phenomenon is the
basic premise for the increase in the number of negative social
phenomena, such as terrorist activities and attacks. Hence, one of
the main problems faced by governments is to ensure the safe
functioning of all state institutions. In practice, this problem boils
down to the protection of all strategic objects that create the
material structure of the entire state. The important strategic
objects that determine the security and undisturbed functioning of
the economy are sea objects, and especially ports. Monitoring and
protection of these facilities require large human and equipment
outlays due to the size of the area occupied. Therefore, the need to
apply security systems, the elements of which will ensure
autonomous, remote, and unmanned implementation of security
procedures, is one of the main objectives of the internal and
external state security agencies. In the case of marine objects, these
tasks may be performed by unmanned surface vehicles (USVs) [1–
4]. The importance of this problem is contributed by the
development of research works on the construction of the USV,
which are implemented in all economically developed countries. A
comparison of exemplary and practically already worked out
constructions such as Sea Fox MkI/MkII (USA), Interceptor (USA/
Israel), SARPAL (Canada), Barracuda (Canada), Sentinel (USA),
is presented in [5, 6] and a detailed description of the Polish
solution called EDREDON is contained in [7].
The basic elements of USV equipment are as follows:
navigation system, communication system, vision observation
systems, sensors for detecting contaminations, and weapon system,
optional [3, 7]. The correct performance of USV tasks in
accordance with destiny is conditioned by the resistance of its
elements to interference, and especially intentional. The navigation
system is one of the most vulnerable elements, as a global
navigation satellite system (GNSS) [8–10] is the basis of its
operation.
The widespread use of this system, generally available
knowledge in the range of information coding methods and signal
structures in the time and frequency domains gives the possibility
of its easy jamming [11–26] and spoofing [12, 13, 18, 20, 26–35],
i.e. the intentional interferences. These techniques are a serious risk
for transport security, especially air and maritime [17, 18, 20, 26],
and military operations. Utilising these techniques in national
security or military context is referred to as an electronic or
navigation warfare [21].
Jamming techniques prevent the determination of position,
velocity, and time (PVT) using the GNSS [11–21]. Generally, they
are used in twofold aims. Firstly, to protect some areas or strategic
infrastructure, e.g. before attack or movement of autonomous
unmanned vehicles (drones) in these areas, because the GNSS is
the navigation basis of most drones. Secondly, as an attack by
terrorists or enemy forces to prevent authorised use of GNSS
receivers. The most popular jamming technique is a chirp signal
emitted in the GNSS band [14–17]. Recently, low-power jammers,
called personal or privacy protection devices (PPDs), are also
becoming more and more popular [15–19]. The PPDs are illegally
used to turning off car anti-theft-systems, bypassing pay-as-you-
drive insurance, withdrawing fleet management system, or
protecting the privacy of parcel delivery agents from their
employers [18]. However, it should be highlighted that utilising the
PDP by somebody causes the loss of the GNSS signal by other
users located around [12, 16–19].
To countermeasure of the jamming, new devices, e.g. an anti-
jamming antenna GAJT-710ML [21, 22] dedicated for military
vehicles, or new navigation methods in GNSS denied environment
are developed [14, 15, 23–25]. In [23], a novel anti-jamming
GNSS receiver structure, which preserves the GNSS signal phase
continuity, is presented. A novel scheme of the GNSS receiver that
based on an antenna array and vector delay lock loop is a proposal
of Li et al. [24] to ensure the reliability in the interference
presence. Another approach to a robust scheme of the GNSS
receiver is shown in [25]. In this case, it is a hybrid receiver, i.e.
based on the GNSS and an inertial navigation system (INS). The
key idea of this solution is a multiple constrained minimum
variance-spatial temporal adaptive processing beamforming
algorithm is proposed for enhancing satellite signals and
suppressing interferences. Surveys of different anti-jamming
techniques are presented in [14, 15]. Generally, we may distinguish
four groups of these techniques, i.e. utilising the INS as a
IET Radar Sonar Navig., 2020, Vol. 14 Iss. 4, pp. 643-651
© The Institution of Engineering and Technology 2020
643

supportive positioning system, spatial filtering, time-frequency
filtering, and vector tracking.
Spoofing is a transmission of fake GNSS signals with the
intention of fooling the GNSS receiver into providing false PVT
[12, 13, 18, 20, 26–35]. A receiver autonomous integrity
monitoring at the pseudo-range level is the basis of rudimentary
defence against spoofing used in the GNSS receiver. However, the
currently used spoofing techniques know how to see around this
functionality. In the first stage, code-phases of true and false
signals are aligned. Next, the false signal increases in power and
takes control over code tracking loops by its gain. In the final
stage, moving the correlation peak away from the true position is
made [18, 27–30]. In [28–30], surveys of popular spoofing attacks
and the methods of their detection are presented. Attack techniques
include, i.a., nulling, meaconing with a single or multiple antennas,
security code estimation and replay, open-loop signal simulator.
For detection and prevention, many anti-spoofing methods are
developed [28–31], i.a., analysis of sample values at correlator
output [32], monitoring power- or time-related parameters of the
GNSS signals [33, 34], spatial processing based on a mobile
single-antenna multiple-antennas of the GNSS receiver [27, 31,
35], cryptographic protection, using the INS as a support of the
GNSS (hybrid navigation). The use of the Doppler effect resulting
from the deterministic movement of the receiving antenna and the
GNSS signals is one of the current trends in spoofing detection
[35].
This is particularly significant because recently, an increase in
the GNSS interference incidents has been reported, especially with
the effective spoofing in marine and coastal zones [17, 18, 20, 26].
Other solutions for GNSS-denied environments are also being
developed [36–38]. In these cases, terrestrial positioning systems
dedicated to specific applications may be used. An example of such
a system is presented in the paper.
In this paper, we present a proposal of a completely
autonomous navigation system in which any choice and the
possibility of changing the frequencies used significantly hampers
its recognition and disturbance. The essence of the presented
solution consists of using the Doppler effect of signals emitted by
radio beacons (RBs) and received by a USV navigation receiver.
The use of this effect for simultaneous localisation of several
emission sources is presented in [39] and a solution example for a
navigation system is contained in [40, 41]. In comparison to the
concept of navigational procedure presented in this paper, the
approach shown in [40, 41] is significantly simplified due to a
straight-line movement trajectory of the object in coastal areas.
The proposed solution has higher accuracy in comparing to
historical maritime navigation systems like the Decca [42], Loran-
C, and its Polish equivalent – the Jemioluszka [43, 44], which were
based on signal phase measurements. In the spoofing or jamming
conditions, using a differential GNSS [45] does not allow the
autonomous USV control. Whereas, a new Polish system concept
called the AEGIR [44, 46], which is based on a time difference of
arrival (TDOA) method, requires a significantly wider bandwidth
than the proposed method. Average positioning errors are about
180, 200, and 46 m for the Loran (Jemioluszka), Decca, and
AEGIR systems, respectively. In the positioning systems, different
location methods are used.
Due to the used signal parameter, we can distinguish, i.a. [47],
time- (e.g. TDOA, time of arrival), angular- [i.e. angle of arrival
(AOA)], amplitude- [e.g. received signal strength (RSS)], phase-,
frequency-based, and hybrid methods. The accuracy of the AOA-
based method is usually determined in relation to an angle-
measurement error for a single network element (e.g. direction
finder). With a high accuracy in the range of 1–5°, linear errors are
equal about to 18–87 m at 1 km distance between the receiver and
transmitter. The accuracy for the time-based methods may estimate
on the basis of the product of the electromagnetic wave speed, c,
and a time-measurement accuracy, δt. For example, for a signal
bandwidth equal B = 10 MHz, δt ≃ 1/B = 0.1 µs and the time-based
method accuracy is about Δr = c·δt = 30 m. In the RSS-based
method, a path loss model must be known for analysed terrains. In
a mobile harbour scenario, this is difficult due to a big change of
soil parameters (concrete, salt or sweet waters) and irregularity of
buildings. It should be emphasised that the use of the above
methods to the object localisation on an XY-plane requires the use
of at least two reference stations, i.e. RBs.
The formal allocation of radio resources dedicated to a new
local terrestrial navigation system, e.g. 10 MHz bandwidth for the
TDOA-based AEGIR system, is a serious problem in most
countries. The developed frequency-based approach requires the
narrow-band radio channel. Practically, its bandwidth may reach
only a few-hundred hertz or several kilohertz. Our solution may
operate based on multiple separate harmonic signals with
additively using a frequency hopping (FH) technique. This signal
type introduces low intersystem interference so it may operate at
licensed-bands' boundaries. The low demand for radio resources
over other positioning methods is the biggest advantage of the
proposed navigation system. In addition, the possibility of using
typical radio receivers to receive the navigation signals determines
the simplicity of the technical implementation of the proposed
system in practice. On the other hand, our frequency-based
method, as the only one, gives the ability of the object localisation
on the basis of the signal received from a single RB, which is
shown in this paper.
The remainder of this paper is organised as follows. In Section
2, an analytical description of the formulas that are the basis for the
implementation of the navigation procedure is shown. The
assessment of the practical use of the Doppler effect and its
measure are introduced in Section 3. Section 4 provides a
description of a spatial scenario and assumptions of simulation
tests. The methodology of processing measurement data from
several RBs used in the developed navigation system finds its
justification in the form of simulation results presented in Section
5. The summary with a way indication to increase the safety of
functioning the presented system is included in Section 6.
2 Fundamentals of Doppler navigation
The practical relationship, which describes the value of the
Doppler frequency shift, fD(t), along with the change of the moving
receiver position, is the basis for the developed navigation
procedure [48]
fDt≅kx−vt
x−vt 2+ 1 − k2y2+z2f0
(1)
where x, y, z are the location coordinates of the signal source, k =
v/c, v is the receiver speed, and f0 represents the carrier frequency
of the emitted signal.
To simplify the presented analysis, the origin of the coordinate
system is placed at a reference point with known geographic
coordinates. This approach has also a practical justification,
because the position error, which is associated with numerical
processing of measurement data, is minimised in the navigation
system. For maritime scenario, the navigation issue may consider
in a two-dimensional space (z = const.). Therefore, in the remainder
of the paper, the analysis of the proposed procedure is reduced to
surface navigation. In this case, the coordinates of the nth RB are
marked in the form (xn, yn).
Note that in (1), vt is the current coordinate of the moving
object. In this paper, we mark this coordinate as x(t). Thus, the
relationship that describes x(t) as a function of the Doppler
frequency shift is
xt=x−y⋅fDt1 − k2
k2f0
2−fD
2t
(2)
Equation (2) is true only for segments of the receiver movement
trajectory where fD(t) < fDmax, because fDmax = kf0. In the case of
the solution (1), which was obtained for the scenario described in
[48], the coordinates of the current position of the moving object
have the form (x(t), 0). Therefore, to use (2) in the navigation
procedure, corresponding coordinate system changes are required
for each straight segment of the trajectory. The idea of
transforming the coordinate system is shown in Fig. 1.
644 IET Radar Sonar Navig., 2020, Vol. 14 Iss. 4, pp. 643-651
© The Institution of Engineering and Technology 2020

Let the endpoint of the trajectory segment has coordinates
(x(tm), y(tm)). Moving the origin of the coordinate system to this
point (displacement by the vector a = [x(tm), y(tm)] and rotation by
the angle α) causes the corresponding change of the nth RB
coordinates
x
~n=xn−x tmcos α+yn−y tmsin α
(3)
y
~n= − xn−x tmsin α+yn−y tmcos α
(4)
Based on (2)–(4), the coordinates of the current USV position in
the changed coordinate system take the form
xt=xn−x tmcos α+yn−y tmsin α
+xn−x tmsin α−yn−y tmcos α
×fDt1−k2
k2f0
2−fD
2tfor t≥tm
(5)
y t = 0 for t≥tm
(6)
As a result, moving the origin of the coordinate system from (x(tm),
y(tm)) to the reference point (displacement by the vector –a = [–
x(tm), –y(tm)] and rotation by the angle –α), we obtain the current
position (x0(t), y0(t)) of the USV
x0t=x t +x tmcos α−y tmsin α
(7)
y0t=x t +x tmsin α−y tmcos α
(8)
where x(t) is defined by (5).
Equations (5), (7), and (8) describe the relationship between the
coordinates of the current position of the moving object and the
Doppler frequency shift. They are the basis for the USV navigation
procedure. Thus, the problem of the practical use of this procedure
boils down to the measurement of the Doppler shift.
In this paper, the assessment of navigation accuracy is carried
out for the line-of-sight (LOS) propagation conditions. This
approach results from the application dedicated to harbours and
related assumptions for the simulation scenario described in
Section 4. For LOS or obscured LOS (OLOS) conditions, we use a
typical spectrum analysis of the received signal, i.e. based on the
Fourier transform, to obtain the instantaneous Doppler frequency
shifts [39, 49]. To this aim, more complex and accurate spectral
methods may be used, e.g. the multiple signal classification [50–
52], estimation of subspace rotational invariance technology [52,
53], space-alternating generalised expectation-maximisation [54,
55], sparse power angle spectrum estimation [56], CLEAN [57], or
algorithm based on the exponential frequency correlation function
[58].
For non-LOS conditions, a dispersion Doppler spectrum is
obtained instead of the single Doppler frequency shifts for direct
and reflected components of the received signal. In this case, the
Doppler spectrum analysis is needed. The empirical measurements,
e.g. [59], show that a local maximum of the Doppler spectrum is
often strictly related to the transmitter–receiver direction, i.e. a
hypothetical direct path [60, 61]. This fact is used to determine the
appropriate value of the Doppler shift [62]. In the harbour scenario,
such an approach would be necessary to consider the impact of a
port infrastructure located in the RBs–USV directions. To provide
the LOS/OLOS propagation conditions, we assume that the
transmitting antennas of the RBs are located at high masts.
3 Evaluation of navigation error
The accuracy of determining the current position of the moving
object is one of the basic parameters that determine the possibilities
of practical use of the developed navigation procedure. As a
measure of a navigation error, we assumed
Δr t =x0t−xr0t2+y0t−yr0t2
(9)
where (xr0(t), yr0(t)) represent the actual location coordinates of the
USV for the time moment t.
In this paper, Δr(t) obtained through simulation tests is the basis
for the assessment of the navigation procedure presented in Section
2.
In addition, we consider a mean error (ME) and root mean
squared error (RMSE) to assess the navigation accuracy on the
selected segment or whole trajectory of the USV movement. These
accuracy measures are defined as follows:
ME = 1
T∫0
T
Δr t dt
(10)
RMSE = 1
T∫0
T
Δr2tdt
(11)
where T is the time of the USV moving over the analysed segment
or whole trajectory (see Table 1).
4 Spatial scenario and assumptions for
simulation studies
We assume that the USV is equipped with the following devices:
• magnetic compass – for determining the north direction,
• speedometer,
• navigational receiver dedicated to the Doppler-based system,
which is responsible for determining the current position of the
USV based on the RB signals.
Fig. 1 Coordinate system transformation
Table 1 Comparison of movement time and ME obtained
for individual trajectory segments
Trajectory
segment
T, s ME, m
Weighted
averaging
estimator
Maximum weight
estimator
A→B 63 14.3 11.3
B→C 98 10.6 12.3
C→D 174 13.8 2.9
D→C 174 14.7 2.7
C→E 75 4.3 3.9
E→C 75 4.3 4.0
C→F 75 4.7 4.8
F→G 149 15.7 10.4
G→H 39 30.5 16.9
H→A 211 17.5 13.5
MEa, m 1133 13.4 7.8
RMSEa, m 1133 18.0 11.4
aME and RMSE obtained for whole trajectory.
IET Radar Sonar Navig., 2020, Vol. 14 Iss. 4, pp. 643-651
© The Institution of Engineering and Technology 2020
645

The navigation error assessment for the proposed system is based
on simulation tests. To this aim, we adopted the spatial scenario
shown in Fig. 2 (based on Google Earth [63]). In this case, the
USV patrols the Gdynia harbour area, where three reference RBs
(RB-1, RB-2, and RB-3) are located.
The USV trajectory segments are marked with yellow arrows
between points A→B→C→D→C→E→C→F→G→H→A, where
it is a change direction of the USV movement. Three RBs of the
navigation system are located in the Gdynia harbour, which is
secured by the patrolling USV. The Universal Transverse Mercator
(UMT) coordinates of A–H points, RB-1, RB-2, and RB-3 are
included in Table 2 (based on Google Earth [63]). The heights of
the RB transmitting antennas are determined relative to the height
of the USV receiving antenna. Therefore, the z-coordinates are
assumed as 0 for A–H.
In addition, in simulation tests, we adopted the following
assumptions:
• carrier frequencies of the signals transmitted by the RB-1, RB-2,
and RB-3 are f01 = f0 − F, f02 = f0, and f03 = f0 + F, respectively,
where f0 = 2.4 GHz and F = 400 Hz;
• operating frequency and bandwidth of the USV navigation
receiver are equal to fR = f0 and BR = 1.5 kHz, respectively;
• time and frequency resolutions of the Doppler frequency shift
estimation are Δt = 1 s and Δf = 0.1 Hz, respectively;
• current USV position is determined based on ten instantaneous
fD values, i.e. the signal acquisition time in the positioning
process is equal to TA = 10 s;
• constant speed of the USV is v = 15 m/s ≃ 29.16 knots, i.e. the
maximum speed for the USV EDREDON [6, 7] (the maximum
speed for most USVs is in the range 20–48 knots [7]);
• transmitting antennas of the RBs are located at high masts that
provide LOS/OLOS propagation conditions between the RBs
and USV receiver and an additive white Gaussian noise channel
with a signal-to-noise ratio (SNR) SNR > −5 dB for the whole
trajectory of the USV motion.
Considering the fact that the frequency stability of the signal
source generator significantly influences on the positioning
accuracy in the frequency-based location methods [64], we provide
high stability of the used RB generators using a rubidium or cesium
frequency standard [41]. Additionally, one of the RBs might
measure instantaneous fluctuations of the carrier frequencies of the
individual RB signals and transmit this data to the USV in a
dedicated channel. This approach is proposed in [65].
In the further part of simulation research, we also show the
impact of the USV speed, v, and basic frequency of the spectral
analysis (i.e. frequency resolutions of the Doppler frequency shift
estimation), Δf, on the USV navigation error. In these cases, we
consider Δf from the set {0.1, 0.2, 1.0} Hz and v equal to 5, 10, or
15 m/s, i.e. about 10, 20, or 30 knots, respectively.
5 Results of simulation tests
The scenario of simulation studies described in Section 4 is the
basis for the assessment of the practical use of the developed
navigation procedure. In this paper, we analyse the effectivity of
the Doppler frequency shift use for four different methods of USV
coordinate estimation presented below, i.e. positioning based on
single RB, positioning based on an arithmetic, weighted, and
maximum-weight estimators. Additionally, we show the impact of
the USV speed and basic frequency of spectrum analysis on the
accuracy of the developed method. We also compare the proposed
navigation system with the TDOA-based AEGIR system.
Fig. 2 Spatial scenario for protected area of Gdynia harbour, locations of RBs, and USV movement trajectory
Table 2 UMT coordinates of USV movement trajectory
points and RBs
Point Coordinates (m to East, m to North, m)
A (342,700; 6,046,737; 0)
B (342,457; 6,045,836; 0)
C (341,000; 6,045,836; 0)
D (338,640; 6,046,936; 0)
E (340,087; 6,045,188; 0)
F (342,124; 6,045,800; 0)
G (342,124; 6,043,580; 0)
H (342,700; 6,043,580; 0)
RB-1 (341,220; 6,046,252; 30)
RB-2 (340,615; 6,044,991; 30)
RB-3 (339,340; 6,045,978; 30)
646 IET Radar Sonar Navig., 2020, Vol. 14 Iss. 4, pp. 643-651
© The Institution of Engineering and Technology 2020

5.1 USV positioning based on single RB
The developed method gives the possibility of positioning the USV
based on a single RB. The accuracy evaluation based on the
individual RBs is the goal of the first stage of the research. The
simulation results, i.e. fD(t) and Δr(t) along the analysed trajectory
of the USV movement are illustrated in Fig. 3 for the RB-1, RB-2,
and RB-3, respectively. In this case, fD(t) represents the Doppler
frequency shifts estimated based on the spectrum analysis of the
received signal. Analysing the obtained results, we see that the
USV positioning is the most accurate based on the RB-2. This
choice confirms empirical cumulative distribution functions
(CDFs) of the navigation errors, F(Δr), for three analysed RBs that
are illustrated in Fig. 4. However, a user of the proposed system
does not have a priori knowledge, which RB signal should use in
the receiver to accurate navigation.
In the Doppler-based localisation, the significant impact on
positioning accuracy has the relative changes of the frequency
Fig. 3 CDFs of navigation error for individual RB
Fig. 4 Doppler frequency shift and navigation accuracy for different RB positions in relation to USV movement trajectory
IET Radar Sonar Navig., 2020, Vol. 14 Iss. 4, pp. 643-651
© The Institution of Engineering and Technology 2020
647

shift. If the USV moves towards or from certain RB, the
instantaneous changes of fD are minor because the Doppler
frequency tends to extreme values, i.e. ± fDmax. In Fig. 2, we can
see that these USV motion directions are near the D, E, and G
points for the RB-1, and near the D point for the RB-2. For the
RB-3, the USV movement at the B→C and C→F trajectory
sections takes place exactly in the USV-RB direction. In Fig. 4, we
point this by brown arrows in graphs showing the estimated
frequency shifts, which is associated with the increase in the
navigation error. On the other hand, the proposed method is very
accurate when the instantaneous changes of fD are major. This is
typical, if the Doppler frequencies are small, i.e. near the inflection
point of the Doppler curve also called the point of the closest-
approach [66, 67].
The results depicted in Figs. 3 and 4 show that navigation errors
can reach even very low values in case using a single RB.
However, throughout the entire route, we see trajectory segments
where these errors may reach values above 250 m. It follows that
the values of navigation errors are dependent on the RB positions
in relation to the USV movement trajectory. We would like to
highlight that the selection of the RB positions has not been
optimised in relation to the analysed trajectory!
5.2 USV positioning based on arithmetic averaging
To assure a relatively uniform spread of navigation errors along the
entire route, we use arithmetic averaging of data from three RBs
x
~0t=1
3x01 t+x02 t+x03 t
(12)
y
~0t=1
3y01 t+y02 t+y03 t
(13)
where (x0n(t), y0n(t)) are the coordinates of the USV current
position determined based on nth RB, n = 1, 2, 3.
This is the second stage of the research. The obtained results are
shown in Fig. 5.
As shown in Fig. 5, the use of arithmetic averaging of data from
all RBs slightly minimises the spread of navigation error along the
whole route. Based on the results of the theoretical analysis, we can
describe the changes in the received signal frequency relative to the
position of the moving object. These changes depend on the object
movement trajectory relative to the signal source locations.
The use of the arithmetic averaging estimator is not a good
solution. Admittedly, large navigation errors for individual RBs are
generally reduced over the averaging process. However, these large
errors are transferred also into a large error of the average USV
position with equal weights (i.e. 1/3). It is especially visible at the
B→C and C→F sections of the USV movement trajectory and near
the D point.
5.3 USV positioning based on weighted averaging and
maximum weight estimator
The impact of the RB position relative to the USV motion
trajectory on the Doppler curve changes is shown in Fig. 3. A
comparison of these graphs with graphs of Δr(t) shows the
relationship between analysed parameters. We can see that the
highest navigation accuracy is provided by the RB, for which the
Doppler curve of the signal received by the USV has the greatest
change-dynamics. On the other hand, the small changes of the
Doppler shift for the B→C and C→F segments relative to RB-3 are
the cause of a significant increase of the navigation error. We use
this fact in the navigation procedure to minimise the error. The
slopes of the Doppler curves for each RB are the basis for
determining the weight coefficients wn [41]
wnt=1
W t 1 − fDn t
fDnmax
(14)
and
W t =∑
n= 1
N
1 − fDn t
fDnmax
(15)
where N = 3 is the number of the RBs, fDn(t) and fDnmax are the
current and maximum Doppler frequency shifts of the signal
received from the nth RB, respectively.
In the procedure of determining the resultant coordinates of the
current USV position, these coefficients ensure adequate gradation
of coordinates obtained based on the individual RBs
x
~0t=w1t x01 t+w2t x02 t+w3t x03 t
(16)
y
~0t=w1t y01 t+w2t y02 t+w3t y03 t
(17)
where w1(t) + w2(t) + w3(t) = 1.
The use of the weighted averaging estimator is the third stage of
the research.
The weight coefficients, wn, may also be used to determine the
RB whose coordinates provide the smallest navigation error. In this
case, the decision rule has the form
x
~0t,y
~0t=
x01 t,y01 tfor w1= max w1,w2,w3
x02 t,y02 tfor w2= max w1,w2,w3
x03 t,y03 tfor w3= max w1,w2,w3
(18)
where wn = wn(t).
The use of the maximum weight estimator is the fourth stage of
the research.
The results of simulation tests using the procedure for
determining weighted coordinates are presented in Fig. 6. Table 1
provides a comparison of the ME obtained for each trajectory
segment for these two coordinate estimators. Additionally, the ME
and RMSE on the whole trajectory are determined.
Fig. 6 and Table 1 show that the weighted coordinate
determination procedure used in the navigation process reduces the
positioning error. For the analysed scenario, a comparison of
simulation test results shows that choosing the RB that provides the
highest weight coefficient reduces the maximum error from 78.4 to
45.4 m and the ME for the entire route from 13.4 m to 7.8 m.
Fig. 5 Navigation accuracy using arithmetic averaging of data from all
RBs
Fig. 6 Navigation accuracy using weighted averaging and maximum
weight estimators
648 IET Radar Sonar Navig., 2020, Vol. 14 Iss. 4, pp. 643-651
© The Institution of Engineering and Technology 2020

Therefore, the practical use of this procedure requires continuous
analysis of the Doppler curves to evaluate the weight coefficients
of coordinates from the individual RBs.
The close relationship between the mutual location of the USV
movement trajectory and RBs is also confirmed by the MEs
obtained on symmetrical segments (C→D, D→C) and (C→E,
E→C). In these cases, the USV motion directions are opposite (see
Fig. 2), while the dynamic ranges of the Doppler frequency shift
are similar (see Fig. 3). The MEs for corresponding symmetrical
segments are similar (see Table 1).
For the two analysed estimators, the large errors at the B→C
and C→F sections of the USV trajectory deriving from the RB-3
(see Fig. 3) are significantly reduced. The weighted averaging
estimator copes better with this issue than the arithmetic averaging
estimator. However, using the weighted averaging estimator, we
have still quite big error near the D point. In this case, in
determining the USV position, we consider all RB signals with
different weights, but not equal weights as in the arithmetic
averaging estimator. For the maximum weight estimator, this issue
is resolved. Then, we do not consider the RB signals which
characterise the small changes of the Doppler frequencies, i.e. large
navigation errors. Effectivity comparison of three analysed
estimators illustrates also Fig. 7 that presents the empirical CDFs
of the navigation error, F(Δr). In the remainder of simulation
research, we use the most accurate estimator, i.e. the maximum
weight estimator.
5.4 Impact of basic frequency of spectrum analysis on
positioning accuracy
The basic frequency of spectrum analysis, Δf, is a parameter, which
vitally influences on the estimation accuracy of the Doppler
frequency shift. In the conducted analysis, we consider the spatial
scenario and simulation assumptions described in Section 4,
whereas Δf is changed from 0.1 to 1.0 Hz. Fig. 8 shows the average
and extreme estimation-errors of the Doppler shift, ΔfD, versus the
basic frequency of spectrum analysis. The empirical CDFs of the
navigation error, F(Δr), for the selected Δf are depicted in Fig. 9.
We may see that as Δf increases, the accuracy of fD
determination decreases. However, it should be remembered that
decreasing Δf requires an increase in computing power necessary
to determine the Fourier transform for the signal spectrum.
5.5 Impact of USV speed on positioning accuracy
Analysing the impact of the USV speed, v, on the accuracy of its
positioning, we consider three following values: 5, 10, and 15 m/s.
Other simulation parameters and the USV trajectory are consistent
with the assumptions made in Section 4. In this case, the empirical
CDFs of the navigation error are presented in Fig. 10.
As shown in Fig. 10, reducing the USV speed decreases the
instantaneous changes and extreme values of the Doppler
frequencies. Thus, it brings for increasing the USV positioning
error. This negative effect can be minimised by increasing the
acquisition time, TA. To maintain relative changes of fD in the time
window equal to TA, this parameter should be changed according to
the principle TA′ = TA·v/v′, where TA = 10 s, v = 15 m/s are
reference values, while TA′ is the value corresponding to the new
analysed speed v′. Using this principle, the appropriate empirical
CDFs are depicted in Fig. 11.
We might see that navigation accuracy is increased. To achieve
even greater accuracy of the USV positioning, a reduction of Δf
would be required. This is due to the fact that fDmax decreases with
Fig. 7 CDFs of navigation error for analysed estimators
Fig. 8 Estimation error of fD versus Δf
Fig. 9 CDFs of navigation error for selected Δf
Fig. 10 CDFs of navigation error for selected USV speed and constant
time acquisition
Fig. 11 CDFs of navigation error for selected USV speed and variable
time acquisition
IET Radar Sonar Navig., 2020, Vol. 14 Iss. 4, pp. 643-651
© The Institution of Engineering and Technology 2020
649

the reduction of v. Therefore, the relative accuracy of the Doppler
frequency estimation based on the spectrum is smaller at a constant
Δf.
5.6 Comparison of the proposed navigation system with
TDOA-based AEGIR system
Finally, we compare the developed navigation system with the
hyperbolic asynchronous AEGIR system [44, 46]. This simplified
comparison is based on a scenario and empirical measurement
results presented in [46]. As a comparative measure, we use the
CDFs of the navigation error, which is shown in Fig. 12.
For the AEGIR system, the presented empirical CDF is based
on [46, Fig. 11]. For extracting numerical data from graphs, the
WebPlotDigitizer software [68] is used. We also utilise this
program and Google Earth [63] to extract a vessel trajectory from
[46, Fig. 9]. Next, we implement this spatial scenario to simulation
studies for the developed navigation system and make the other
assumptions as in Section 4. This scenario is different from shown
in Fig. 2 and similar to presented in [41], i.e. for navigation needs
in a coastal zone. The distances between the RBs and the section
lengths of the ship movement trajectory are much larger than in the
previously considered scenario (Fig. 2). Therefore, we assume that
the acquisition time, TA, is larger, i.e. 60 or 120 s, because the
Doppler frequencies change slower and the trajectory sections are
longer. We would like to highlight that regardless of TA, the current
USV position is determined every Δt = 1 s.
For the scenario analysed in [46, Fig. 9], the systems have
similar positioning accuracy when we use TA = 60 s. However, it
should be noted that the AEGIR used wide bandwidth, i.e. BR = 1
MHz, while the proposed system is based on BR = 1.5 kHz. In
addition, the mutual location of the RBs and the movement
trajectory in the scenario [46, Fig. 9] is characterised by a better
geometric dilution of precision than in the one considered in Fig. 2.
The TDOA-based systems cannot determine the USV position
based on only a single RB.
6 Conclusions
The presented concept of the navigation procedure and obtained
simulation results show the possibility of increasing the reliability
of the autonomous and remote monitoring system and the
protection of maritime facilities using the USVs. Increasing the
number of the RBs and especially their appropriate location in
relation to the anticipated trajectories of the USV movements
provides a significant improvement in the accuracy of the USV
navigation. Particularly noteworthy is the fact that the spectral
resources required for operating the proposed navigation system
are minimised. In this case, harmonic signals are used. To increase
the system resistance to detection and interference, slow FH
modulation may also be used. The possibility of using the typical
radio receivers to receive navigation signals determines the
simplicity of the technical implementation of this system. In the
future, the authors plan to conduct empirical tests of the developed
system in an actual harbour scenario.
7 Acknowledgments
This work was developed within a framework of the Research
Grant ‘Basic research in sensor technology field using innovative
data processing methods’ no. GBMON/13-996/2018/WAT
sponsored by the Polish Ministry of Defense.
8 References
[1] Caccia, M., Bibuli, M., Bono, R., et al.: ‘Unmanned surface vehicle for
coastal and protected waters applications: the Charlie project’, Mar. Technol.
Soc. J., 2007, 41, (2), pp. 62–71
[2] Caccia, M., Bibuli, M., Bruzzone, G., et al.: ‘Modular USV and payload
design for advanced capabilities in marine security applications’. Proc. 2011
19th Mediterranean Conf. on Control Automation (MED), Corfu, Greece,
June 2011, pp. 430–435
[3] Kitowski, Z., Garus, J., Szymak, P.: ‘Architecture of the control system of an
unmanned surface vehicle in the process of harbour protection’, Solid State
Phenom., 2012, 180, pp. 20–26
[4] Miętkiewicz, R.: ‘Unmanned surface vehicles in maritime critical
infrastructure protection applications — LNG terminal in Świnoujście’, Sci. J.
Pol. Nav. Acad., 2018, 213, (2), pp. 43–51
[5] Liu, Z., Zhang, Y., Yu, X., et al.: ‘Unmanned surface vehicles: an overview of
developments and challenges’, Annu. Rev. Control, 2016, 41, pp. 71–93
[6] Kalinowski, A., Małecki, J.: ‘Polish USV ‘EDREDON’ and non-European
USV: a comparative sketch’, J. Mar. Eng. Technol., 2017, 16, (4), pp. 416–
419
[7] Kitowski, Z.: ‘Autonomous unmanned surface vehicle ‘Ededron’, Pol.
Hyperb. Res., 2012, 2012, (3), pp. 7–22
[8] Groves, P.D.: ‘Principles of GNSS, inertial, and multisensor integrated
navigation systems’ (Artech House, Norwood, MA, USA, 2013, 2nd edn.)
[9] Kaplan, E.D., Hegarty, C. (Eds.): ‘Understanding GPS: principles and
applications’ (Artech House, Norwood, MA, USA, 2005, 2nd edn.)
[10] Diggelen, F. van: ‘A-GPS: assisted GPS, GNSS, and SBAS’ (Artech House,
Norwood, MA, USA, 2009, 1st edn.)
[11] Iyidir, B., Ozkazanc, Y.: ‘Jamming of GPS receivers’. Proc. 2004 IEEE 12th
Signal Processing and Communications Applications Conf. (SIU), Kusadasi,
Turkey, April 2004, pp. 747–750
[12] Bonebrake, C., O'Neil, L.R.: ‘Attacks on GPS time reliability’, IEEE Secur.
Priv., 2014, 12, (3), pp. 82–84
[13] Cuntz, M., Konovaltsev, A., Dreher, A., et al.: ‘Jamming and spoofing in
GPS/GNSS based applications and services – threats and countermeasures’, in
Aschenbruck, N., Martini, P., Meier, M., Tölle, J. (Eds.): ‘Future security’
(Springer, 2012), pp. 196–199
[14] Felski, A.: ‘Methods of improving the jamming resistance of GNSS receiver’,
Annu. Navig., 2016, 23, (1), pp. 185–198
[15] Gao, G.X., Sgammini, M., Lu, M., et al.: ‘Protecting GNSS receivers from
jamming and interference’, Proc. IEEE, 2016, 104, (6), pp. 1327–1338
[16] ‘The chirp jammer: A GPS hit and run’, Septentrio, Available at https://
www.septentrio.com/en/insights/chirp-jammer-gps-hit-and-run, accessed
October 2019
[17] ‘Set adrift by GPS jamming’, Septentrio, Available at https://
www.septentrio.com/en/insights/set-adrift-gps-jamming, accessed October
2019
[18] Rügamer, A., Kowalewski, D., GmbH, N.: ‘Jamming and spoofing of GNSS
signals – an underestimated risk?!’, Proc. 2015 FIG Working Week, Sofia,
Bulgaria, May 2015, pp. 1–21
[19] Arthur, C.: ‘Thousands using GPS jammers on UK roads pose risks, say
experts’. The Guardian, 2013, https://www.theguardian.com/technology/
2013/feb/13/gps-jammers-uk-roads-risks
[20] Hammernes, A.: ‘GNSS jamming and spoofing, risks and mitigation for
maritime users’. Kongsberg, 2018, https://www.ths.org.uk/documents/
ths.org.uk/downloads/thsis_-
_gnss_jamming_and_spoofing,_risks_and_mitigation.pdf
[21] Gerein, N., Soar, P.: ‘Navigation warfare: GNSS denied – threat and
mitigation’. Military Embedded Systems, Available at http://mil-
embedded.com/articles/navigation-denied-241-threat-mitigation/, accessed
October 2019
[22] ‘Defense GAJT-710MLTM. Single-enclosure GPS anti-jam technology
(GAJT®)’. NovAtel, 2014, https://www.novatel.com/assets/Documents/
Papers/GAJT-710ML-PS.pdf, accessed October 2019
[23] Zhang, Y.D., Amin, M.G.: ‘Anti-jamming GPS receiver with reduced phase
distortions’, IEEE Signal Process. Lett., 2012, 19, (10), pp. 635–638
[24] Li, Q., Xu, D., Wang, W., et al.: ‘Anti-jamming scheme for GPS receiver with
vector tracking loop and blind beamformer’, Electron. Lett., 2014, 50, (19),
pp. 1386–1388
[25] Li, Q., Wang, W., Xu, D., et al.: ‘A robust anti-jamming navigation receiver
with antenna array and GPS/SINS’, IEEE Commun. Lett., 2014, 18, (3), pp.
467–470
[26] Felski, A.: ‘Let us prepare the officer of the watch on jamming and spoofing’,
TransNav. Int. J. Mar. Navig. Saf. Sea Transp., 2019, 13, (4), pp. 847–851
[27] Magiera, J.: ‘A multi-antenna scheme for early detection and mitigation of
intermediate GNSS spoofing’, Sensors, 2019, 19, (10), pp. 1–17, Article ID
2411
[28] Psiaki, M.L., Humphreys, T.E.: ‘GNSS spoofing and detection’, Proc. IEEE,
2016, 104, (6), pp. 1258–1270
[29] Xiao, L., Ma, P.-C., Tang, X.-M., et al.: ‘GNSS receiver anti-spoofing
techniques: a review and future prospects’. Proc. of the 2015 5th Int. Conf. on
Electronics, Communications and Networks (CECNet), Shanghai, China,
December 2015, pp. 59–68
Fig. 12 CDFs of navigation error for AEGIR and developed system
650 IET Radar Sonar Navig., 2020, Vol. 14 Iss. 4, pp. 643-651
© The Institution of Engineering and Technology 2020

[30] Jafarnia-Jahromi, A., Broumandan, A., Nielsen, J., et al.: ‘GPS vulnerability
to spoofing threats and a review of antispoofing techniques’, Int. J. Navig.
Obs., 2012, 2012, pp. 1–16, Article ID 127072
[31] Magiera, J., Katulski, R.J.: ‘Detection and mitigation of GPS spoofing based
on antenna array processing’, J. Appl. Res. Technol., 2015, 13, (1), pp. 45–57
[32] Piaki, M.L., O'Hanlon, B.W., Bhatti, J.A., et al.: ‘GPS spoofing detection via
dual-receiver correlation of military signals’, IEEE Trans. Aerosp. Electron.
Syst., 2013, 49, (4), pp. 2250–2267
[33] Risbud, P., Gatsis, N., Taha, A.: ‘Vulnerability analysis of smart grids to GPS
spoofing’, IEEE Trans. Smart Grid, 2019, 10, (4), pp. 3535–3548
[34] Jansen, K., Schäfer, M., Moser, D., et al.: ‘Crowd-GPS-sec: leveraging
crowdsourcing to detect and localize GPS spoofing attacks’. Proc. 2018 IEEE
Symp. on Security and Privacy (SP), San Francisco, CA, USA, May 2018, pp.
1018–1031
[35] Li, H., Hong, L., Mingquan, L., et al.: ‘Global navigation satellite system
spoofing-detection technique based on the Doppler ripple caused by vertical
reciprocating motion’, IET Radar Sonar Navig., 2019, 13, (10), pp. 1655–
1664
[36] Duckworth, G.L., Baranoski, E.J.: ‘Navigation in GNSS-denied
environments: signals of opportunity and beacons’. Proc. Military Capabilities
Enabled by Advances in Navigation Sensors Meeting, RTO-MP-SET-104
(NATO STO), Antalya, Turkey, October 2007, pp. 3-1–3-14
[37] Zahran, S., Moussa, A., El-Sheimy, N.: ‘Enhanced UAV navigation in GNSS
denied environment using repeated dynamics pattern recognition’. Proc. 2018
IEEE/ION Position, Location and Navigation Symp. (PLANS), Monterey,
CA, USA, April 2018, pp. 1135–1142
[38] Panigrahi, N., Doddamani, S.R., Singh, M., et al.: ‘A method to compute
location in GNSS denied area’. Proc. 2015 IEEE Int. Conf. on Electronics,
Computing and Communication Technologies (CONECCT), Bangalore,
India, July 2015, pp. 1–5
[39] Gajewski, P., Ziółkowski, C., Kelner, J.M.: ‘Using SDF method for
simultaneous location of multiple radio transmitters’. Proc. 2012 19th Int.
Conf. on Microwave Radar and Wireless Communications (MIKON),
Warsaw, Poland, May 2012, vol. 2, pp. 634–637
[40] Kelner, J.M., Ziółkowski, C.: ‘Mobile radio beacons in coastal reserved
navigation system for ships’, TransNav. Int. J. Mar. Navig. Saf. Sea Transp.,
2019, 14, (20), pp. 1–9
[41] Kelner, J.M., Ziółkowski, C., Nowosielski, L., et al.: ‘Reserve navigation
system for ships based on coastal radio beacons’. Proc. 2016 IEEE/ION
Position, Location and Navigation Symp. (PLANS), Savannah, GA, USA,
April 2016, pp. 393–402
[42] Blanchard, W.: ‘The genesis of the Decca navigator system’, J. Navig., 2015,
68, (2), pp. 219–237
[43] Specht, C., Weintrit, A., Specht, M.: ‘A history of maritime radio-navigation
positioning systems used in Poland’, J. Navig., 2016, 69, (3), pp. 468–480
[44] Ambroziak, S.J., Katulski, R.J., Sadowski, J., et al.: ‘Comparative analysis of
the two polish hyperbolic systems AEGIR and Jemioluszka’. Proc. 2013 10th
Int. Conf. on Marine Navigation and Safety of Sea Transportation (TransNav),
Gdynia, Poland, June 2013, pp. 237–240
[45] Specht, C., Specht, M., Dąbrowski, P.: ‘Polish DGPS system: 1995–2018 –
studies of reference station operating zones’, TransNav. Int. J. Mar. Navig.
Saf. Sea Transp., 2019, 13, (3)
[46] Ambroziak, S.J., Katulski, R.J., Sadowski, J., et al.: ‘Asynchronous and self-
organizing radiolocation system – AEGIR’. Proc. 2011 IEEE Int. Conf. on
Technologies for Homeland Security (HST), Waltham, MA, USA, November
2011, pp. 419–425
[47] Kelner, J.M., Ziółkowski, C.: ‘SDF technology in location and navigation
procedures: A survey of applications’. Conf. on Reconnaissance and
Electronic Warfare Systems, Oltarzew, Poland, November 2016 (SPIE
Proceedings Volume 10418, XI Conference on Reconnaissance and Electronic
Warfare Systems), pp. 1–13
[48] Rafa, J., Ziółkowski, C.: ‘Influence of transmitter motion on received signal
parameters – analysis of the Doppler effect’, Wave Motion, 2008, 45, (3), pp.
178–190
[49] Kelner, J.M., Ziółkowski, C.: ‘The use of SDF technology to BPSK and
QPSK emission sources’ location’ (in polish)’, Prz. Elektrotech., 2015, 91,
(3), pp. 61–65
[50] Schmidt, R.O.: ‘Multiple emitter location and signal parameter estimation’,
IEEE Trans. Antennas Propag., 1986, 34, (3), pp. 276–280
[51] Friedlander, B.: ‘A sensitivity analysis of the MUSIC algorithm’, IEEE Trans.
Acoust. Speech Signal Process., 1990, 38, (10), pp. 1740–1751
[52] Jäntti, T.P.: ‘The influence of extended sources on the theoretical performance
of the MUSIC and ESPRIT methods: narrow-band sources’. Proc. 1992 IEEE
Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), San
Francisco, CA, USA, March 1992, vol. 2, pp. 429–432
[53] Roy, R., Kailath, T.: ‘ESPRIT—estimation of signal parameters via rotational
invariance techniques’, IEEE Trans. Acoust. Speech Signal Process., 1989,
37, (7), pp. 984–995
[54] Fleury, B.H., Tschudin, M., Heddergott, R., et al.: ‘Channel parameter
estimation in mobile radio environments using the SAGE algorithm’, IEEE J.
Sel. Areas Commun., 1999, 17, (3), pp. 434–450
[55] Taparugssanagorn, A., Alatossava, M., Holappa, V.M., et al.: ‘Impact of
channel sounder phase noise on directional channel estimation by space-
alternating generalised expectation maximisation’, IET Microw. Antennas
Propag., 2007, 1, (3), pp. 803–808
[56] Wallace, J.W., Jensen, M.A.: ‘Sparse power angle spectrum estimation’, IEEE
Trans. Antennas Propag., 2009, 57, (8), pp. 2452–2460
[57] Tsao, J., Steinberg, B.D.: ‘Reduction of sidelobe and speckle artifacts in
microwave imaging: the CLEAN technique’, IEEE Trans. Antennas Propag.,
1988, 36, (4), pp. 543–556
[58] Liu, L., Zhang, L., Yu, T., et al.: ‘Exponential frequency correlation function
and its application in Doppler shift estimation’, IET Radar Sonar Navig.,
2019, 13, (10), pp. 1628–1635
[59] Felhauer, T., Baier, P.W., König, W., et al.: ‘Wideband characterisation of
fading outdoor radio channels at 1800 MHz to support mobile radio system
design’, Wirel. Pers. Commun., 1994, 1, (2), pp. 137–149
[60] Ziółkowski, C., Kelner, J.M.: ‘Influence of receiver/transmitter motion
direction on the correlational and spectral signal properties’. Proc. 2016 10th
European Conf. on Antennas and Propagation (EuCAP), Davos, Switzerland,
March 2016, pp. 1–4
[61] Kelner, J.M., Ziółkowski, C.: ‘Numerical transformation of power azimuth
spectrum into normalized Doppler spectrum’. Proc. 2019 13th European
Conf. on Antennas and Propagation (EuCAP), Krakow, Poland, March 2019,
pp. 1–5
[62] Kelner, J.M., Ziółkowski, C., Nowosielski, L., et al.: ‘Localization of
emission source in urban environment based on the Doppler effect’. Proc.
2016 Spring IEEE 83rd Vehicular Technology Conf. (VTC Spring), Nanjing,
China, May 2016, pp. 1–5
[63] Google Inc.: ‘Google earth’, Available at https://www.google.com/earth/,
accessed 15 August 2019
[64] Kelner, J.M., Ziółkowski, C., Marszałek, P.: ‘Influence of the frequency
stability on the emitter position in SDF method’. Proc. 2016 17th Int. Conf.
on Military Communications and Information Systems (ICMCIS), Brussels,
Belgium, May 2016, pp. 1–6
[65] Kelner, J.M., Ziółkowski, C.: ‘Doppler effect-based automatic landing
procedure for UAV in difficult access environments’, J. Adv. Transp., 2017,
2017, pp. 1–9, e8092718
[66] Levanon, N.: ‘Interferometry against differential Doppler: performance
comparison of two emitter location airborne systems’, IEE Proc. F, Radar
Signal Process., 1989, 136, (2), pp. 70–74
[67] Levanon, N., Ben-Zaken, M.: ‘Random error in ARGOS and SARSAT
satellite positioning systems’, IEEE Trans. Aerosp. Electron. Syst., 1985,
AES-21, (6), pp. 783–790
[68] Rohatgi, A.: ‘Webplotdigitizer 4.2’, Available at https://automeris.io/
WebPlotDigitizer/, accessed October 2019
IET Radar Sonar Navig., 2020, Vol. 14 Iss. 4, pp. 643-651
© The Institution of Engineering and Technology 2020
651