Effectiveness of Mobile Emitter Location by Cooperative Swarm of Unmanned Aerial Vehicles in Various Environmental Conditions

Abstract

This paper focused on assessing the effectiveness of the signal Doppler frequency (SDF) method to locate a mobile emitter using a swarm of unmanned aerial vehicles (UAVs). Based on simulation results, we showed the impact of various factors such as the number of UAVs, the movement parameters of the emitter and the sensors on location effectiveness. The study results also showed the dependence of the accuracy and continuity of the emitter coordinate estimation on the type of propagation environment, which was determined by line-of-sight (LOS) or non-LOS (NLOS) conditions. The applied research methodology allowed the selection of parameters of the analyzed location system that would minimize the error and maximize the monitoring time of the emitter position.

Full text

sensors
Article
Effectiveness of Mobile Emitter Location by
Cooperative Swarm of Unmanned Aerial Vehicles in
Various Environmental Conditions
Jan M. Kelner * and Cezary Ziółkowski
Institute of Communications Systems, Faculty of Electronics, Military University of Technology, Gen. Sylwester
Kaliski Str. No. 2, 00-908 Warsaw, Poland; cezary.ziolkowski@wat.edu.pl
*Correspondence: jan.kelner@wat.edu.pl; Tel.: +48-261-837-733
Received: 1 April 2020; Accepted: 29 April 2020; Published: 1 May 2020


Abstract:
This paper focused on assessing the effectiveness of the signal Doppler frequency
(SDF) method to locate a mobile emitter using a swarm of unmanned aerial vehicles (UAVs).
Based on simulation results, we showed the impact of various factors such as the number of UAVs,
the movement parameters of the emitter and the sensors on location effectiveness. The study results
also showed the dependence of the accuracy and continuity of the emitter coordinate estimation
on the type of propagation environment, which was determined by line-of-sight (LOS) or non-LOS
(NLOS) conditions. The applied research methodology allowed the selection of parameters of the
analyzed location system that would minimize the error and maximize the monitoring time of the
emitter position.
Keywords:
mobile emitter localization; Doppler effect; signal Doppler frequency (SDF); unmanned
aerial vehicle (UAV); swarm; wireless sensor network (WSN); urban area; line-of-sight (LOS) and
non-line-of-sight (NLOS) conditions
1. Introduction
A localization of radio wave sources plays an important role not only in military applications such
as electronic warfare [
1
,
2
], but also in navigation systems [
3
,
4
], internal security [
5
] and search and
rescue missions [6,7]. Most of the methods analyzed in the literature are applicable to static emission
sources. A perpetual change of emitter position significantly hinders the implementation of location
procedures. The development of unmanned aerial vehicles (UAVs), cellular [
8
,
9
], mobile ad-hoc
(MANETs) and wireless sensor networks (WSNs) contributed to developing new techniques for locating
mobile objects. Mobility and the lack of spatial restrictions in the UAV missions is a special property
that determines the use of these vehicles both to create dynamically changing network structures and
the implementation of additional communications services such as the location of emission sources.
The prospects for using the UAVs to improve the quality and scope extension of communication
services in fifth-generation (5G) mobile networks and in the localization systems of fixed emission
sources are presented in [10,11] and [12], respectively.
Time and frequency differences of arrival (TDOAs and FDOAs) measurements performed by
many sensors are some of the more commonly used techniques for estimating the position of mobile
emitters [
12
–
15
]. Target tracking techniques based on the TDOA measurements in a WSN are described,
i.a., in [
16
,
17
]. Sathyan et al. [
16
] additionally proposed the use of an extended Kalman filter (EKF).
A similar approach, but for correlated TDOA and using a Gaussian mixture (GM), was proposed by
Kim et al. [18].
The mentioned EKF is widely used in radar technology [
19
] or target tracking applications in
WSNs [
20
]. Pathirana et al. [
21
] used it for a received signal strength (RSS) to estimate the position and
Sensors 2020,20, 2575; doi:10.3390/s20092575 www.mdpi.com/journal/sensors

Sensors 2020,20, 2575 2 of 21
speed of moving MANET nodes. Schmidhammer et al. [
22
] presented a technique for tracking mobile
scatterers as secondary radio emission sources. This approach was based on the delay estimation
with the EKF and posterior Cram
é
r–Rao lower bound. The EKF also allows to reduce the location
error of the other methods, including a time of arrival (TOA) [
23
], direction of arrival (DOA) [
24
] and
TDOA–DOA [25,26].
DOA-based methods also use the GM, interacting multiple models [
24
], electronic beam
steering [
27
] and an algorithm based on the maximum entropy fuzzy clustering in a cluttered
environment [
28
]. The algorithms of maximum entropy clustering and particle swarm optimization
were used by Parvin et al. [
29
] for the energy-efficient tracking of targets in WSNs. Other examples of the
positioning of mobile emitters were presented in a survey of location methods with a mobile receiver [
30
].
Furthermore, in [31], Jing et al. presented other non-cooperative target-tracking algorithms.
The location procedures outlined above, except [
23
], were tested for the location of mobile emitters
in an open area, free space, or line-of-sight (LOS) conditions. Tracking a target moving in an urbanized
area requires more complex algorithms. This is related to multipath propagation, which results from the
presence of numerous terrain obstacles, especially buildings, vehicles and other urban infrastructure.
Hence, in urbanized environments, non-LOS (NLOS) or mixed LOS/NLOS conditions often occur.
Therefore, in such propagation environments, the estimation of received signal parameters that are the
basis of the analyzed method are constricted and burdened with a significant error.
Localization techniques for this type of propagation environment are primarily based on the
prediction and identification of LOS/NLOS conditions [
32
], followed by the application of appropriate
correction, e.g., using the EKF [
33
]. The detection of LOS or NLOS conditions may be carried out
using techniques of estimating a Rician K-factor [34,35] or an energy detector used in cognitive radio
networks to assess channel occupancy [
36
,
37
]. From the viewpoint of location accuracy, the most crucial
aspect is the correction mechanism used due to propagation conditions. It should be emphasized that
the majority of solutions available in the literature for NLOS conditions are based on the theoretical
error distributions of measured parameters, e.g., [
38
,
39
], instead of using more realistic methods of
channel modeling. In the case of mobile sensors and emitters, the time-variant channel models should
be used, e.g., [
40
,
41
]. In [
32
,
42
], this type of channel modeling was applied in relation to a signal
Doppler frequency (SDF) method.
Some of the location methods assume that LOS conditions occur for part of sensors, whereas
NLOS conditions occur for others, e.g., [
23
,
43
]. In these cases, the emitter position estimation procedure
can only be based on sensors under LOS conditions. This approach, although idealistic, provides a
much higher accuracy of location in urbanized environments. The solution proposed in this paper was
also based on this assumption and was an extension of the idea presented in [
32
]. The sensors were
located on UAVs moving above the urbanized area to make the mixed LOS/NLOS scenario realistic.
Therefore, LOS/NLOS conditions changed randomly for each sensor. To model the probabilities of the
LOS conditions depending on a UAV elevation and the type of urbanized environment, we used the
distributions presented in [
44
]. The empirical results presented in [
45
] were the basis for modeling the
radio channel between the emitter and sensors. We wanted to highlight that the use of the UAV swarm
was one of the trends in the development of location procedures, e.g., [15,46–48].
Our paper was devoted to the location of mobile emission sources in an urban environment
using the UAV swarm. Here, we focused our attention on assessing the effectiveness of the position
estimation of an emitter moving in conditions occurring in a real propagation environment. The emitter
localization considering the combined analysis of the UAV swarm, real changes in the propagation
conditions and the Doppler effect, was an innovative contribution of our paper. In the proposed
solution, the emitter location is implemented by the swarm of the sensors, in which an SDF procedure
is performed [
49
,
50
]. This procedure was based on the analytical description of the Doppler frequency
shift (DFS), which expresses the relationship between an instantaneous frequency of a received signal,
the coordinates of the emission source and the sensor [
51
]. The SDF is the only closed-form algorithm
of a frequency of arrival (FOA) [
52
]. In addition, the SDF and FOA belong to a narrow group of

Sensors 2020,20, 2575 3 of 21
methods requiring a single sensor to locate the emission source. The SDF approach allows for the
locating of the emitter based on only two current DFS measurements. The solution presented in [
32
]
showed that the UAV swarm application provided for increasing the location accuracy of the immobile
emitter. In this case, the transmitter location procedure was based on the signals received under both
the LOS and NLOS conditions. In this paper, we proposed the location of the mobile emitter based
on the signals received only under LOS conditions that have a random and limited occurrence range.
Hence, studying the impact of the environment, emitter speed and the number of sensors in the swarm
was important to assess the location efficiency. This evaluation was based on simulation tests. To solve
the analyzed problem, we presented a significant SDF extension that allowed for the location of any
velocity vectors of the sensor and emitter. In this paper, the proposed solution and the method of
modeling mixed LOS/NLOS conditions showed its innovation and originality in relation to others
presented in the literature.
The remainder of the paper is organized as follows. Firstly, the descriptions of the SDF method and
simulation test procedures are provided in Section 2. Section 3contains the assumptions, test scenario
description and simulation results. A summary and final remarks are in Section 4.
2. SDF Method and Simulation Study Procedure
2.1. SDF Method in Location
The SDF method was based on the analytical description of the relationship between the
coordinates of the emitter,
xe(t)=(xe(t),ye(t),ze(t))
, and receiver,
xs(t)=(xs(t),ys(t),zs(t))
, and the
DFS, fD(t)=fD(xe,xs,t), of the received signal [52]:
fD(t)=fc
c
vx(t)(xe(t)−xs(t)) +vy(t)(ye(t)−ys(t)) +vz(t)(ze(t)−zs(t))
q(xe(t)−xs(t))2+(ye(t)−ys(t))2+(ze(t)−zs(t))2
, (1)
where fcis a carrier frequency of the transmitted signal, v(t)=vs(t)+ve(t)=hvx(t),vy(t),vz(t)iis a
resultant velocity vector of the transmitter, ve(t), and receiver, vs(t), while cmeans the speed of light.
If the transmitter is static,
ve(t)=
0, and the receiver moves towards the OX axis at a constant
speed,
vs(t)=[vx, 0, 0]=const
. and
xs(t)=(xs(t),ys(0),zs(0))
, then Equation (1) takes the form [
51
]:
fD(t)=fc
c
vx(xe−xs(t))
q(xe−xs(t))2+(ye−ys)2+(ze−zs)2
. (2)
If the DFS measurements are made in two interception intervals,
t1
and
t2
, we can estimate
the coordinates of the emission source by transforming Equation (2). The final formulas are as
follows [49,50]:
e
xe=xs(0)+vx
t1p(t1)−t2p(t2)
p(t1)−p(t2), (3)
e
ye=ys(0)±s vx
(t2−t1)p(t1)p(t2)
p(t1)−p(t2)!2
−(e
ze−zs(0))2, (4)
where p(t)=qh(fcvx)/ce
fD(t)i2−1 and e
fD(t)is the estimated DFS.
For an assumption that
e
ze=ze
is known, Equations (3) and (4) describe the coordinates of the
localized object on the OXY plane. This assumption was the basis for the research scenarios analyzed
in the remainder of the paper. In the SDF, determining the three coordinates of the emitter position
required changing the direction of the receiver movement [53].
The method, which was based on Equations (3) and (4), had numerous limitations related to
the stability of the receiver speed and the lack of transmitter mobility. Therefore, in Section 2.6,

Sensors 2020,20, 2575 4 of 21
we presented the novel SDF extension that allowed considering the variable movement of the sensor
and emitter in any direction on the OXY plane.
Equations (3) and (4) are used to estimate the object coordinates only under LOS conditions. In the
case of a real propagation environment, the range of LOS areas is limited and random. Under these
conditions, the use of the UAV swarm, whose trajectories are varied, allows for obtaining the relatively
continuous monitoring of the emitter position. Additionally, the use of several sensors placed on UAVs
provided the opportunity to resolve an ambiguity of Equation (4) and minimize the error associated
with the adopted assumption, i.e., that e
ze=zeis known.
2.2. Diagram of Simulation Procedure
The effectiveness evaluation of the analyzed methodology for monitoring the moving emitter
position was based on the results of the simulation tests. The purpose of this research was to determine
the location accuracy and monitoring continuity as a function of the number of sensors, type of
propagation environment and the speed of the monitored object. Figure 1illustrates a spatial geometry
of the considered study scenario for a single sensor (free clipart of a Humvee is from [
54
]), while a
generalized diagram of the simulation procedure is depicted in Figure 2.
Sensors 2020, 20, x FOR PEER REVIEW 4 of 22
For an assumption that ee
zz=
 is known, Equations (3) and (4) describe the coordinates of the
localized object on the OXY plane. This assumption was the basis for the research scenarios analyzed
in the remainder of the paper. In the SDF, determining the three coordinates of the emitter position
required changing the direction of the receiver movement [53].
The method, which was based on Equations (3) and (4), had numerous limitations related to the
stability of the receiver speed and the lack of transmitter mobility. Therefore, in Section 2.6, we
presented the novel SDF extension that allowed considering the variable movement of the sensor and
emitter in any direction on the OXY plane.
Equations (3) and (4) are used to estimate the object coordinates only under LOS conditions. In
the case of a real propagation environment, the range of LOS areas is limited and random. Under
these conditions, the use of the UAV swarm, whose trajectories are varied, allows for obtaining the
relatively continuous monitoring of the emitter position. Additionally, the use of several sensors
placed on UAVs provided the opportunity to resolve an ambiguity of Equation (4) and minimize the
error associated with the adopted assumption, i.e., that ee
zz=
 is known.
2.2. Diagram of Simulation Procedure
The effectiveness evaluation of the analyzed methodology for monitoring the moving emitter
position was based on the results of the simulation tests. The purpose of this research was to
determine the location accuracy and monitoring continuity as a function of the number of sensors,
type of propagation environment and the speed of the monitored object. Figure 1 illustrates a spatial
geometry of the considered study scenario for a single sensor (free clipart of a Humvee is from [54]),
while a generalized diagram of the simulation procedure is depicted in Figure 2.
Figure 1. Spatial geometry of the simulation scenario for the selected sensor.
Figure 1. Spatial geometry of the simulation scenario for the selected sensor.

Sensors 2020,20, 2575 5 of 21
Sensors 2020, 20, x FOR PEER REVIEW 5 of 22
Figure 2. Generalized diagram of the simulation procedure.
The simulation studies were carried out as a Monte-Carlo process. In this case, for the input data,
in each Monte-Carlo run, a comprehensive process of locating the mobile emitter by the swarm was
carried out. The simulation tests for each sensor consisted of three stages:
• generation of the sensor trajectory division into sections with LOS and NLOS
conditions;
• on the route sections with LOS conditions, the DFS estimation for the resultant
velocity vector for the analyzed sensor and the mobile emitter;
• estimating the current emitter position relative to the vector of the sensor.
These steps were followed by a data fusion in the reference sensor. Based on the results obtained
in each Monte-Carlo run, the metrics to assess the effectiveness of the emitter monitoring were
determined.
2.3. Input Data for Simulation Studies
The primary input data for the simulation tests were a set  of following parameters and
characteristics:
Figure 2. Generalized diagram of the simulation procedure.
The simulation studies were carried out as a Monte-Carlo process. In this case, for the input data,
in each Monte-Carlo run, a comprehensive process of locating the mobile emitter by the swarm was
carried out. The simulation tests for each sensor consisted of three stages:
•generation of the sensor trajectory division into sections with LOS and NLOS conditions;
•
on the route sections with LOS conditions, the DFS estimation for the resultant velocity vector for
the analyzed sensor and the mobile emitter;
•estimating the current emitter position relative to the vector of the sensor.
These steps were followed by a data fusion in the reference sensor. Based on the results obtained in
each Monte-Carlo run, the metrics to assess the effectiveness of the emitter monitoring were determined.
2.3. Input Data for Simulation Studies
The primary input data for the simulation tests were a set
<
of following parameters
and characteristics:
•
the coordinates of the initial position of each sensor,
xs(0)=(xs(0),ys(0),zs(0))
, and monitored
emitter, xe(0)=(xe(0),ye(0),ze(0));

Sensors 2020,20, 2575 6 of 21
•
the velocity vectors of individual sensors,
vs(t)=hvsx(t),vs y(t),vsz(t)i
, and the emitter,
ve(t)=hvex(t),ve y(t),vez(t)i;
•
the probability
PLOS(Env,β)
of the LOS conditions occurring on the sensor trajectory as a function
of the type of propagation environment
Env
and the elevation angle
β
of the sensor relative to the
emitter position (see Figure 1);
•the carrier frequency fc, an emission type and the bandwidth Bof the transmitted signal;
•
processing parameters of the received signals such as a sampling rate
fs
and minimum acquisition
time ∆tconditioning the determination of a single DFS.
2.4. Stage 1. Generation of LOS/NLOS Sections on Sensor Trajectory
The goal of the first stage was to divide the trajectories of individual sensors into two state
sections of LOS and NLOS. We used the Poisson process to model the random occurrence of a LOS
state. This meant that the lengths of the trajectory sections, which were determined by the subsequent
moments of the appearance of the LOS state, are described by an exponential distribution:
f(d)=dfexp −d
df!, (5)
where
df
is the average length of the trajectory section determined by successive moments of the LOS
conditions,
d=dL+dN
(see Figure 1) and
dL
and
dN
are the trajectory sections of the sensor, where
LOS and NLOS conditions occur, respectively.
An analogous distribution describes the length dLof sections with LOS conditions, viz.
f(dL)=dLOS exp −dL
dLOS !, (6)
where dLOS is the average length of the trajectory section where LOS conditions occur.
To use the above distributions to generate the trajectory division of each sensor into the LOS,
{dL}
,
and NLOS,
{dN}
, sections, knowledge of
df
and
dLOS
is necessary. Based on the Erlang B formula for a
single sensor trajectory:
PLOS(Env,β)=
dLOS
df
1+dLOS
df
, (7)
thus: dLOS
df
=PLOS(Env,β)
1−PLOS(Env,β). (8)
where Env =suburban, urban, dense urban, highrise urban[44].
Equation (8) is the basis for determining
dLOS
as a function of
df
,
Env
, and
β
, which are associated
with
PLOS(Env,β)
. For each sensor in the swarm, the division of the trajectory
D
into the sections of
random length
{dL}
and
{dN}
is generated for the same parameters of the distributions (5) and (6),
considering Equation (8) and
β
determined individually for the analyzed sensor. In our research,
Figure 2in [
44
] was the basis for determining
PLOS(Env,β)
for the various propagation environments.
2.5. Stage 2. Estimation of Doppler Frequency Shift in Received Signal
In the first step of the second stage, the resultant velocity vector of the sensor and mobile emitter
is designated as
v(t)=vsj(t)+ve(t)=hvx(t),vy(t),vz(t)i=hvxs j (t)+vxe(t),vysj(t)+vye (t),vzs j (t)+vze(t)i. (9)

Sensors 2020,20, 2575 7 of 21
Then, based on the given velocity vectors and initial positions, subsequent emitter and individual
sensor positions were determined according to the relationships:



























xe,sj(t)=xe,s j (0)+
t
R0
vxe,xsj(t)dt,
ye,sj(t)=ye,s j (0)+
t
R0
vye,ysj(t)dt,
ze,sj(t)=ze,s j (0)+
t
R0
vze,zsj(t)dt.
(10)
Based on Equations (9) and (10), we determined the actual DFS according to Equation (1).
The obtained values of
fD(t)
were the basis for the generation of the received baseband signal. For jth
sensor, the signal is:
sj(t,τ)=hj(t,τ)∗a(τ)exp2πifDj(t)τ+nj(τ), (11)
where
hj(t,τ)
and
nj(τ)
represent a channel impulse response (CIR) and an baseband additive white
gaussian noise (AWGN) for the channel of the jth sensor, respectively, and
a(τ)
is a modulating function.
Considering the propagation conditions for the UAVs, the CIRs were generated according to the
methodology presented in [45].
A power spectrum density (PDS) of this signal:
sj(t,τ)=hj(t,τ)∗a(τ)exp2πifDj(t)τ+nj(τ), (12)
is the basis for estimating the DFS as an argument for which the PDS takes the maximum value:
e
fDj(t):Sjt,e
fDj=max
fSj(t,f). (13)
2.6. Stage 3. Estimation of Emitter Position by Individual Sensors
In the next stage, the current position of the emitter was estimated by individual sensors. To this
aim, the OXYZ coordinate system was transformed by shifting it by the vector
xsj(t)
and rotating to
the O’X’Y’Z’ system, as in Figure 3. As a result of the rotation, the direction of the O’X’ axis coincided
with the velocity vector vsj(t)of the jth sensor.
Sensors 2020, 20, x FOR PEER REVIEW 8 of 22
Figure 3. Transformation of the coordinate system relative to the sensor position and the direction of
its velocity vector.
Rotation angles are outlined by the following formulas:
() ()
()
() ()
() ()
22
atan ,
atan .
ysj
j
xsj
zsj
j
xsj ysj
vt
tvt
vt
t
vtvt
ϕ
θ


=



=

+

(14)
This transformation of the coordinate system was carried out relative to the velocity vector and
the current position of the individual sensors. The velocity vector of this sensor in the new coordinate
system has the form:
() () () () () () ()
222
,
,,0,0.
sj xsj ysj zsj xsj ysj zsj
t v tv tv t v t v t v t


′′′′
==++



v (15)
To simplify the further analysis, we assumed that the area where the emitter moved was flat.
Thus,
()
e
zt
was constant and equal to the height h of the transmitting antenna. In addition, if an
UAV flight altitude was
,
Hh then for ground targets we may assume 2 m,h≅ what
corresponds to the average height of the antenna for a moving human and vehicle. Then, after
transformation to the O’X’Y’Z’ system, this coordinate was equal to
()
.
e
zt hH H
′=− ≅−
 In this case,
the current coordinates of the mobile emitter estimated by the jth sensor are in the form:
() () ()
() ( )
ΔΔ
,
Δ
j
ej xsj
jj
tp t t
xt v t
pt pt t
⋅−
′′
=−−
 (16)
() () () ( )
() ( ) ()
()
2
2
ΔΔ
,
Δ
jj
ej xsj ej
jj
tp tp t t
yt v t zt
pt pt t

⋅−
′′ ′

=± −

−−


(17)
() ()
,
ej e
zt zt hH
′′
==−
 (18)
where
()
xsj
vt
′ is the average sensor speed between the interception intervals 2Δtt− and ,t and
()
j
pt
is defined as
() ()
()
()
()
21.
jcxsjDj
pt fv t cf t

′
=−


Equations (16) and (17) were the novel extension of the current version of the SDF described by
Equations (3) and (4). This extension allowed for changing the speed and direction of the sensor, as
well as considering the mobility of the emission source. We wanted to highlight that the estimation
of the current emitter position was carried out ‘locally’, i.e., based on two current DFSs estimated at
Figure 3.
Transformation of the coordinate system relative to the sensor position and the direction of
its velocity vector.

Sensors 2020,20, 2575 8 of 21
Rotation angles are outlined by the following formulas:
ϕj(t)=atanvysj (t)
vxsj (t),
θj(t)=atan
vzsj (t)
qv2
xsj (t)+v2
ysj (t).(14)
This transformation of the coordinate system was carried out relative to the velocity vector and
the current position of the individual sensors. The velocity vector of this sensor in the new coordinate
system has the form:
v0
sj(t)=hv0xs j (t),v0ys j(t),v0zsj(t)i=qv2
xsj(t)+v2
ysj(t)+v2
zsj(t), 0, 0. (15)
To simplify the further analysis, we assumed that the area where the emitter moved was flat.
Thus,
ze(t)
was constant and equal to the height
h
of the transmitting antenna. In addition, if an UAV
flight altitude was
Hh
, then for ground targets we may assume
h
2
m,
what corresponds to the
average height of the antenna for a moving human and vehicle. Then, after transformation to the
O’X’Y’Z’ system, this coordinate was equal to
e
z0e(t)=h−H−H
. In this case, the current coordinates
of the mobile emitter estimated by the jth sensor are in the form:
e
x0ej(t)=v0xs j (t)
∆t·pj(t−∆t)
pj(t)−pj(t−∆t), (16)
e
y0ej(t)=±v
t v0xsj(t)
∆t·pj(t)pj(t−∆t)
pj(t)−pj(t−∆t)!2
−e
z0ej(t)2, (17)
e
z0ej(t)=e
z0e(t)=h−H, (18)
where
v0xsj(t)
is the average sensor speed between the interception intervals
t−
2
∆t
and
t
, and
pj(t)
is
defined as pj(t)=qhfcv0xs j (t)/ce
fDj(t)i2−1.
Equations (16) and (17) were the novel extension of the current version of the SDF described by
Equations (3) and (4). This extension allowed for changing the speed and direction of the sensor, as
well as considering the mobility of the emission source. We wanted to highlight that the estimation
of the current emitter position was carried out ‘locally’, i.e., based on two current DFSs estimated
at interception intervals
t−∆t
and
t
. The use of at least two sensors moving on different trajectories
provided the opportunity to uniquely determine the coordinate sign described by Equation (17).
In the next step in the procedure, the coordinates described by Equations (16)–(18) are transformed
to the original OXYZ coordinate system:
~
xej(t)=e
xej(t)
e
yej(t)
e
zej(t)=
cos ϕj(t)−sin ϕj(t)0
sin ϕj(t)cos ϕj(t)0
0 0 1 e
x0ej(t)
e
y0ej(t)
e
z0ej(t)+
xsj(t)
ysj(t)
zsj(t). (19)
2.7. Estimation of Weighted Average Emitter Position by Swarm
Data from individual sensors were transmitted to the reference sensor. In this research, we assumed
that this sensor was stationary and located at the beginning of the adopted OXYZ coordinate system.

Sensors 2020,20, 2575 9 of 21
Each sensor transmitted the following data set
n~
xej(t),cv0xs j (t),e
fDj(t),to
, which was the basis for
determining the weighted average emitter position for the swarm:
~
xe(t)=
J
P
j=1
wj(t)~
xej(t)
J
P
j=1
wj(t)
, (20)
where
wj(t)=
1
−e
fDj(t)c/fcv0xs j (t)
or
wj(t)=
0 for LOS and NLOS conditions, respectively, and
J
represents the number of mobile sensors in the swarm.
The used weighted averaging procedure was based on a similar procedure presented in [55].
2.8. Calculation of Efficiency Metrics for Monte-Carlo Process
According to the methodology presented above, in each implementation of the simulation,
we estimated the monitored emitter coordinates based on the UAV swarm. For the ongoing effectiveness
evaluation of the proposed solution, we used the instantaneous emitter location error by individual
sensors,
∆Rj
, and the average location error for the entire swarm,
∆Rs
. These errors are defined
as follows:
∆Rs,j(t)=qkxe(t)−~
xe,ej(t)k2. (21)
The use of the Monte-Carlo method in relation to this simulation procedure provided a statistical
assessment of the effectiveness of the continuous monitoring of the current emitter position. We use a
root-mean-square error (RMSE) to evaluate the coordinate estimation error:
RMSE =v
u
t1
M
M
X
m=1
∆Ravg,m=v
u
u
u
u
u
t1
M
M
X
m=1
1
tLOS,m
tLOS,m
Z
0
∆Rs,m(t)dt, (22)
where
∆Rs,m(t)
is the error determined based on Equation (20) in the mth Monte-Carlo run,
∆Ravg,m
is
the average value of
∆Rs,m(t)
determined for a total time
tLOS,m
spent by the swarm (i.e., at least one of
the sensors) under the LOS conditions and Mis the number of the Monte-Carlo run.
In the simulation studies, we analyzed the following effectiveness measures:
•
a cumulative distribution function (CDF) of the location error,
F(∆Rs)
, obtained for the
Monte-Carlo process;
•an average percentage of flight-time under the LOS conditions for sensors in a swarm:
•an effectiveness factor (EF) of the emitter monitoring by a swarm:
τLOS =1
M
M
X
m=1
tLOS,m
T·100%, (23)
where Tis the analyzed sensor flight-time along the trajectory of length D;
EF =D
RMSE ·τLOS
100%. (24)
where
τLOS
allows for percentage-wise evaluating the emitter monitoring time by a swarm on a
mission.
EF
is a relative measure that allows a joint assessment of both monitoring time continuity
and average location error.
The application of the Monte-Carlo method in the developed simulation procedure provided a
statistical effectiveness assessment of the presented method of monitoring the mobile emitter position

Sensors 2020,20, 2575 10 of 21
using the UAV swarm. The accuracy and continuity of the location process was determined as a
function of the number of sensors, type of propagation environment, flight altitude of the sensors and
emitter speed.
3. Simulation Studies and Results
The simulation tests were carried out in the MATLAB environment in two stages. In the first
stage, we showed examples of the emitter location using the swarm consisting of
J=
5 UAVs. In this
case, we considered the determined position and velocity of the emitter. In the second stage, using
the Monte-Carlo method, we analyzed the impact of the number of sensors in the swarm, type of
urbanized environment, the sensor flight altitude, and emitter speed on the location effectiveness.
In each Monte-Carlo run, the position and motion direction of the emitter and the LOS/NLOS conditions
for each sensor were random.
3.1. Assumptions and Scenario in Simulation Tests
In the simulation studies, we used the spatial scenario presented in Figure 4.
Sensors 2020, 20, x FOR PEER REVIEW 10 of 22
,
1
1100%,
MLOS m
LOS
m
t
MT
τ
=
=⋅
 (23)
where T is the analyzed sensor flight-time along the trajectory of length ;D
.
100%
LOS
D
EF RMSE
τ
=⋅
(24)
where LOS
τ
allows for percentage-wise evaluating the emitter monitoring time by a swarm on a
mission. EF is a relative measure that allows a joint assessment of both monitoring time continuity
and average location error.
The application of the Monte-Carlo method in the developed simulation procedure provided a
statistical effectiveness assessment of the presented method of monitoring the mobile emitter position
using the UAV swarm. The accuracy and continuity of the location process was determined as a
function of the number of sensors, type of propagation environment, flight altitude of the sensors
and emitter speed.
3. Simulation Studies and Results
The simulation tests were carried out in the MATLAB environment in two stages. In the first
stage, we showed examples of the emitter location using the swarm consisting of 5
J
= UAVs. In
this case, we considered the determined position and velocity of the emitter. In the second stage,
using the Monte-Carlo method, we analyzed the impact of the number of sensors in the swarm, type
of urbanized environment, the sensor flight altitude, and emitter speed on the location effectiveness.
In each Monte-Carlo run, the position and motion direction of the emitter and the LOS/NLOS
conditions for each sensor were random.
3.1. Assumptions and Scenario in Simulation Tests
In the simulation studies, we used the spatial scenario presented in Figure 4.
Figure 4. Spatial scenario of the simulation studies.
The choice of simulation scenario parameters (i.e., swarm size, propagation conditions, emitter
speed, and UAV flight altitude) was closely related to the SDF procedure because the emitter position
relative to the UAV motion trajectory determined the accuracy of its locating. Therefore, in the
Figure 4. Spatial scenario of the simulation studies.
The choice of simulation scenario parameters (i.e., swarm size, propagation conditions, emitter
speed, and UAV flight altitude) was closely related to the SDF procedure because the emitter position
relative to the UAV motion trajectory determined the accuracy of its locating. Therefore, in the
simulation studies, we used the widest possible diversity of the UAV trajectory directions relative to
the area of occurrence of the localized object. In this scenario, we assumed that the monitored emitter
was located in an urban area that was limited by a square with dimensions
XUA ×YUA
. To simplify the
simulation procedure, the analyzed area was flat and the transmitting antenna was at the constant
height. We used a uniform distribution limited to the defined urbanized area
XUA ×YUA
to obtain
the random initial emitter position on the OXY plane,
xe(0)=(xe(0),ye(0),ze(0)) =(xe(0),ye(0),h)
.
In each Monte-Carlo simulation, we assumed that the emitter speed
ve
was constant. However, the

Sensors 2020,20, 2575 11 of 21
velocity direction,
α
, on the OXY plane was random. In this case, we also used the uniform distribution
in the range h−180◦, 180◦). Thus, the velocity vector may be described as
ve=hvex,vey,vez i=[vecos α,vesin α, 0]. (25)
The swarm command post was associated with a stationary reference sensor located west of the
urbanized area. The data from the mobile sensors were transmitted to the reference sensor, where the
data fusion and estimation of the average emitter position were implemented based on data from
the entire swarm. The reference sensor position was associated with the origin of the coordinate
system. In this coordinate system, the northwestern vertex of the urban area was located at
(XRS,YRS )
.
According to Figure 4, we adopted YRS =YUA/2 and XRS =YRS tan(ϕmax ).
The jth mobile sensor in the swarm moved at a constant speed
vs
and direction
ϕj
. The motion
directions of the sensors were determined to ensure the uniform coverage of the monitored area in
the sector limited to
−ϕmax,ϕmax 
. This meant that the angular separation
∆ϕ
between the adjacent
sensors was constant and equal to
∆ϕ=2ϕmax/(J−1)
. Thus, the movement direction of the jth sensor
is determined from the formula:
ϕj=(ϕmax −2ϕmax(j−1)/(J−1)=ϕmax −(j−1)∆ϕfor j=1, 2, . . . ,J>1,
ϕmax for j=J=1, (26)
while the sensor velocity is defined as
vsj =hvsxj ,vsy j ,vsz ji=hvscos ϕj,vssin ϕj, 0i. (27)
Additionally, we assumed that the movement analysis of each sensor began at the same time
and point located at the height
H
above the origin of the OXYZ coordinate system, i.e., at
xs(0)=
(xs(0),ys(0),zs(0)) =(0, 0, H)
. The fixed flight altitude,
H
, and the trajectory length,
D
, were the same
for each sensor.
Most simulation parameters were adopted based on the literature on other location methods or
ground-to-air channel characteristics, where UAVs were used, e.g., [
45
,
56
,
57
]. It allowed for making
the simulation tests more realistic.
Other assumptions adopted in the simulation tests were as follows:
•the dimensions of the urbanized area were XUA ×YUA =3000 m ×3000 m;
•
three types of propagation environments,
Env
, were analyzed: suburban, urban, and dense
urban; to evaluate the occurrence probability of LOS/NLOS conditions for these areas, we used
df=
500
m
as described in Section 2.4;
PLOS(Env,β)
for the analyzed
Env
and specific sensor
elevation
β
(see Figure 1) were determined based on the distributions presented in Figure 2of [
44
];
•the emitter antenna height was equal to h=2 m;
•the considered emitter speeds were ve={0, 1, 2, 5, 10}m/s;
•
the emitter transmitted a differential phase-shift keying (DPSK) signal with bandwidth
B=400 kHz and at the carrier frequency fc=5 GHz (e.g., [45,56,57]);
•an angular width of the monitored sector was 2ϕmax =90◦⇒ϕmax =45◦;
•the considered number of sensors in the swarm were 1 ≤J≤10;
•the trajectory length of each mobile sensor was equal D=3000 m;
•the speed of each mobile sensor was equal to vs=100 m/s (e.g., [16,45,56,57]);
•the flight time along the trajectory for each sensor was T=D/vs=30 s;
•
the considered flight altitudes for the mobile sensors were
H={100, 200, 500}m
(e.g., [
45
,
56
,
57
]);
•
the radio channel including attenuation, CIR and Rician factor was modeled under the methodology
described in [45];

Sensors 2020,20, 2575 12 of 21
•
the minimum signal-to-noise ratio (SNR) for the signals received by the mobile sensors was
SNRmin =3 dB (e.g., [58]);
•
the receiver parameters used in each sensor were:
Bs=
500
kHz
—the bandwidth of the received
signal,
fs=
2
Bs=
1000
kS/s
—sample rate,
Bd=
10
kHz
—a bandwidth of a decimation filter,
∆f=0.05 Hz—a spectrum resolution (i.e., the basic frequency of signal analysis);
•the estimation method of the DFS in the received signal was analogous to that presented in [59];
•the signal recording time required to determine a single DFS value was equal ∆t=0.1 s;
•the number of Monte-Carlo runs was M=200.
3.2. Sample Simulation Results for Determined Position of Emitter
In these tests, we defined additional assumptions:
•suburban or urban area;
•the initial emitter position was xe(0)=(2000, 500, 2)m;
•the emitter velocity was defined by ve=1 m/s and α=90◦;
•the number of mobile sensors in the swarm was J=5;
•the flight altitude of the mobile sensors was H=500 m.
Figures 5and 6illustrate exemplary instantaneous DFSs, location errors and the estimated emitter
position on the OXY plane obtained based on individual sensors and the swarm for suburban and
urban terrain, respectively.
Sensors 2020, 20, x FOR PEER REVIEW 13 of 22
Figure 5. Examples of instantaneous DFS, location errors and the estimated emitter position obtained
based on the individual sensors and swarm for a suburban area.
Figure 6. Examples of instantaneous DFS, location errors and the estimated emitter position obtained
based on the individual sensors and swarm for an urban area.
DFS graphs depict time intervals with LOS conditions that are the basis of the SDF-based
localization procedure. We can notice that the occurrence probability of the LOS conditions is much
higher for the suburban than the urban areas. This affects the continuous monitoring possibility of
the signal source by the swarm. This probability is also related to the sensor motion direction relative
to the emitter in the azimuth plane. (e.g., for sensors 3
j
= and 2
j
= were higher than for the
others). If more than one sensor is under LOS conditions at an interception interval, the emitter
position is weighted averaging by the swarm. In Figure 5, the graphs of the average location error for
the swarm and errors for individual sensors show that the resultant error was reduced due to this
averaging. The average estimation errors that were obtained for two different environments (see
Figures 5 and 6) assumed similar values. However, time intervals, where the emitter position was not
monitored, occurred more often in the urban environment.
Figure 5.
Examples of instantaneous DFS, location errors and the estimated emitter position obtained
based on the individual sensors and swarm for a suburban area.

Sensors 2020,20, 2575 13 of 21
Sensors 2020, 20, x FOR PEER REVIEW 13 of 22
Figure 5. Examples of instantaneous DFS, location errors and the estimated emitter position obtained
based on the individual sensors and swarm for a suburban area.
Figure 6. Examples of instantaneous DFS, location errors and the estimated emitter position obtained
based on the individual sensors and swarm for an urban area.
DFS graphs depict time intervals with LOS conditions that are the basis of the SDF-based
localization procedure. We can notice that the occurrence probability of the LOS conditions is much
higher for the suburban than the urban areas. This affects the continuous monitoring possibility of
the signal source by the swarm. This probability is also related to the sensor motion direction relative
to the emitter in the azimuth plane. (e.g., for sensors 3
j
= and 2
j
= were higher than for the
others). If more than one sensor is under LOS conditions at an interception interval, the emitter
position is weighted averaging by the swarm. In Figure 5, the graphs of the average location error for
the swarm and errors for individual sensors show that the resultant error was reduced due to this
averaging. The average estimation errors that were obtained for two different environments (see
Figures 5 and 6) assumed similar values. However, time intervals, where the emitter position was not
monitored, occurred more often in the urban environment.
Figure 6.
Examples of instantaneous DFS, location errors and the estimated emitter position obtained
based on the individual sensors and swarm for an urban area.
DFS graphs depict time intervals with LOS conditions that are the basis of the SDF-based
localization procedure. We can notice that the occurrence probability of the LOS conditions is much
higher for the suburban than the urban areas. This affects the continuous monitoring possibility of the
signal source by the swarm. This probability is also related to the sensor motion direction relative to the
emitter in the azimuth plane. (e.g., for sensors
j=
3 and
j=
2 were higher than for the others). If more
than one sensor is under LOS conditions at an interception interval, the emitter position is weighted
averaging by the swarm. In Figure 5, the graphs of the average location error for the swarm and errors
for individual sensors show that the resultant error was reduced due to this averaging. The average
estimation errors that were obtained for two different environments (see Figures 5and 6) assumed
similar values. However, time intervals, where the emitter position was not monitored, occurred more
often in the urban environment.
3.3. Impact of Swarm Size
We evaluated the effect of the number
J
of sensors on the swarm for a suburban environment,
H=
200
m,
and
ve=
1
m/s
. The obtained location accuracy in the form of the RMSE and CDF are
shown in Figures 7and 8, respectively. Additionally, the percentage of sensor flight-time under the
LOS conditions and EF are shown in Figures 9and 10, respectively.
Sensors 2020, 20, x FOR PEER REVIEW 14 of 22
3.3. Impact of Swarm Size
We evaluated the effect of the number J of sensors on the swarm for a suburban environment,
200 m,H= and 1 m s .
e
v= The obtained location accuracy in the form of the RMSE and CDF are
shown in Figures 7 and 8, respectively. Additionally, the percentage of sensor flight-time under the
LOS conditions and EF are shown in Figures 9 and 10, respectively.
Figure 7. Average location error versus the number of sensors in the swarm for a suburban area.
Figure 8. CDFs of location error versus number of sensors in swarm for suburban area.
Figure 9. Percentage of flight-time under LOS conditions versus number of sensors in swarm for
suburban area.
Figure 7. Average location error versus the number of sensors in the swarm for a suburban area.

Sensors 2020,20, 2575 14 of 21
Sensors 2020, 20, x FOR PEER REVIEW 14 of 22
3.3. Impact of Swarm Size
We evaluated the effect of the number J of sensors on the swarm for a suburban environment,
200 m,H= and 1 m s .
e
v= The obtained location accuracy in the form of the RMSE and CDF are
shown in Figures 7 and 8, respectively. Additionally, the percentage of sensor flight-time under the
LOS conditions and EF are shown in Figures 9 and 10, respectively.
Figure 7. Average location error versus the number of sensors in the swarm for a suburban area.
Figure 8. CDFs of location error versus number of sensors in swarm for suburban area.
Figure 9. Percentage of flight-time under LOS conditions versus number of sensors in swarm for
suburban area.
Figure 8. CDFs of location error versus number of sensors in swarm for suburban area.
Sensors 2020, 20, x FOR PEER REVIEW 14 of 22
3.3. Impact of Swarm Size
We evaluated the effect of the number J of sensors on the swarm for a suburban environment,
200 m,H= and 1 m s .
e
v= The obtained location accuracy in the form of the RMSE and CDF are
shown in Figures 7 and 8, respectively. Additionally, the percentage of sensor flight-time under the
LOS conditions and EF are shown in Figures 9 and 10, respectively.
Figure 7. Average location error versus the number of sensors in the swarm for a suburban area.
Figure 8. CDFs of location error versus number of sensors in swarm for suburban area.
Figure 9. Percentage of flight-time under LOS conditions versus number of sensors in swarm for
suburban area.
Figure 9.
Percentage of flight-time under LOS conditions versus number of sensors in swarm for
suburban area.
Sensors 2020, 20, x FOR PEER REVIEW 15 of 22
Figure 10. EF versus number of sensors in swarm for suburban area.
The obtained CDFs and average errors showed that the emitter location was the most accurate
for 1J= and 2.J= According to Equation (26), these sensors moved in the extreme directions
max
ϕ
± of the monitoring sector. This location of the motion trajectory relative to the possible area of
the emitter position ensured high DFS variability during the sensor movement. As a result, we
obtained an increase in location accuracy. On the other hand, Figure 9 showed that in these cases,
35%.
LOS
τ
< This meant that despite the high accuracy, the localization of the mobile emitter by a
single sensor could be realized only in selected time intervals. For 3,
J
≥ the accuracy of the method
did not significantly depend on the number of sensors in the swarm. However, the more sensors in
the swarm, the longer the monitoring time of the emitter position could be.
For suburban areas, 500 m,H= and 5,J= the swarm provides monitoring during 50 ÷ 95% of
mission time. In Figure 10, trend lines of EF show that as the sensor number increases, the
effectiveness (continuity and accuracy) of the emitter position monitoring increases.
3.4. Influence of Propagation Environment
The impact assessment of the propagation environment type is carried out for 5,J=
500 m,H= and 1 m s .
e
v= In these studies, we consider three types of urbanized areas, i.e.,
suburban, urban, and dense urban. The obtained simulation results in the form of CDFs of location
error are depicted in Figure 11, while the remaining efficiency metrics are included in Table 1.
Figure 10. EF versus number of sensors in swarm for suburban area.
The obtained CDFs and average errors showed that the emitter location was the most accurate for
J=
1 and
J=
2. According to Equation (26), these sensors moved in the extreme directions
±ϕmax
of the monitoring sector. This location of the motion trajectory relative to the possible area of the

Sensors 2020,20, 2575 15 of 21
emitter position ensured high DFS variability during the sensor movement. As a result, we obtained an
increase in location accuracy. On the other hand, Figure 9showed that in these cases,
τLOS <
35%. This
meant that despite the high accuracy, the localization of the mobile emitter by a single sensor could be
realized only in selected time intervals. For
J≥
3, the accuracy of the method did not significantly
depend on the number of sensors in the swarm. However, the more sensors in the swarm, the longer
the monitoring time of the emitter position could be.
For suburban areas,
H=
500
m,
and
J=
5, the swarm provides monitoring during 50
÷
95% of
mission time. In Figure 10, trend lines of
EF
show that as the sensor number increases, the effectiveness
(continuity and accuracy) of the emitter position monitoring increases.
3.4. Influence of Propagation Environment
The impact assessment of the propagation environment type is carried out for
J=
5,
H=
500
m,
and
ve=
1
m/s
. In these studies, we consider three types of urbanized areas, i.e., suburban, urban,
and dense urban. The obtained simulation results in the form of CDFs of location error are depicted in
Figure 11, while the remaining efficiency metrics are included in Table 1.
Sensors 2020, 20, x FOR PEER REVIEW 16 of 22
Figure 11. Cumulative distribution function (CDFs) of the location error versus the different types of
urbanized areas.
Table 1. Effectiveness metrics for the different types of urbanized areas.
Title 1 Propagation Environment Type, Env
Suburban Urban Dense urban
RMSE (m) 187 280 295
LOS
τ
(%) 96 68 43
EF (−) 15.4 7.2 4.4
A comparison of the results for the different environment types showed that the highest
accuracy was obtained for the suburban terrains. For urban and dense urban areas, the location errors
were similar. The terrain type, where the emitter is located, has a significant impact on the probability
of the LOS conditions for the UAVs (see Section 2.4), which determines the value of LOS
τ
(see Table
1). The obtained results showed that, depending on the type of propagation environment, the flight
altitude of the sensors should be appropriately selected. The impact of this parameter is shown in
Section 3.5. The results in Table 1 enable the effectiveness evaluation of the localization procedure for
the various environmental conditions. They show that along with the worsening propagation
conditions, both the location accuracy (see RMSE ) and LOS
τ
decreased. As a result, the EF, which
was a measure of the location procedure effectiveness, significantly reduced. In this case, it is possible
to offset this decline by increasing the number of sensors in the swarm.
3.5. Impact of Sensor Flight Altitude
The effect of the UAV flight altitude was tested for suburban area, 5,
J
= and 1 m s .
e
v= In
this study, three heights were considered, i.e.,
{
}
100, 200, 500 m.H= Figure 12 illustrates the CDFs
of location error for the different sensor flight altitudes. The parameters that enabled a quantitative
assessment of the monitoring process effectiveness are included in Table 2.
Figure 11.
Cumulative distribution function (CDFs) of the location error versus the different types of
urbanized areas.
Table 1. Effectiveness metrics for the different types of urbanized areas.
Title 1 Propagation Environment Type, Env
Suburban Urban Dense Urban
RMSE (m) 187 280 295
τLOS (%) 96 68 43
EF (−) 15.4 7.2 4.4
A comparison of the results for the different environment types showed that the highest accuracy
was obtained for the suburban terrains. For urban and dense urban areas, the location errors were
similar. The terrain type, where the emitter is located, has a significant impact on the probability of
the LOS conditions for the UAVs (see Section 2.4), which determines the value of
τLOS
(see Table 1).
The obtained results showed that, depending on the type of propagation environment, the flight
altitude of the sensors should be appropriately selected. The impact of this parameter is shown in
Section 3.5. The results in Table 1enable the effectiveness evaluation of the localization procedure
for the various environmental conditions. They show that along with the worsening propagation
conditions, both the location accuracy (see
RMSE
) and
τLOS
decreased. As a result, the EF, which was a

Sensors 2020,20, 2575 16 of 21
measure of the location procedure effectiveness, significantly reduced. In this case, it is possible to
offset this decline by increasing the number of sensors in the swarm.
3.5. Impact of Sensor Flight Altitude
The effect of the UAV flight altitude was tested for suburban area,
J=
5, and
ve=
1
m/s
. In this
study, three heights were considered, i.e.,
H={100, 200, 500}m
. Figure 12 illustrates the CDFs of
location error for the different sensor flight altitudes. The parameters that enabled a quantitative
assessment of the monitoring process effectiveness are included in Table 2.
Sensors 2020, 20, x FOR PEER REVIEW 17 of 22
Figure 12. CDFs of the location error versus the different flight altitudes for a suburban area.
We can see that with the increase in the flight altitude, both the location accuracy and LOS
τ
increased. As a result, we received over a tenfold increase in EF between 100 mH= and
500 m.H= This showed that we may have compensated for changes in propagation conditions
related to the environment by increasing the sensor altitude.
Table 2. Effectiveness metrics for the different flight altitudes.
Title 1 Sensor Flight Altitude, H
100 m 200 m 500 m
RMSE (m) 654 518 187
LOS
τ
(%) 31 69 96
EF (−) 1.4 4.0 15.4
3.6. Influence of Emitter Speed
The evaluation of the impact of the emitter speed on the accuracy of the proposed approach was
carried out for
{
}
0,1,2, 5,10 m s.
e
v= In assessing the effectiveness of most of the location methods,
the location estimation of the stationary object (i.e., 0
e
v=) was most often considered. 1 m s
e
v=
refers to a typical pedestrian and this is a reference value in previous studies. We also analyzed the
average speed of vehicles in urban areas, i.e., 10 m s 36 km h ,
e
v== as well as the intermediate
speeds. Depending on the legal regulations in a country, the speed limit in built-up areas is
30 70 km h .÷ Other simulation parameters were as follows, suburban area, 5,
J
= and
500 m.H= Figure 13 shows the CDFs of the location error for the different emitter speeds. In Table
3, the values of other analyzed metrics are included.
Figure 12. CDFs of the location error versus the different flight altitudes for a suburban area.
Table 2. Effectiveness metrics for the different flight altitudes.
Title 1 Sensor Flight Altitude, H
100 m 200 m 500 m
RMSE (m) 654 518 187
τLOS (%) 31 69 96
EF (−) 1.4 4.0 15.4
We can see that with the increase in the flight altitude, both the location accuracy and
τLOS
increased. As a result, we received over a tenfold increase in
EF
between
H=
100
m
and
H=
500
m
.
This showed that we may have compensated for changes in propagation conditions related to the
environment by increasing the sensor altitude.
3.6. Influence of Emitter Speed
The evaluation of the impact of the emitter speed on the accuracy of the proposed approach was
carried out for
ve={0, 1, 2, 5, 10}m/s
. In assessing the effectiveness of most of the location methods, the
location estimation of the stationary object (i.e.,
ve=
0) was most often considered.
ve=
1
m/s
refers
to a typical pedestrian and this is a reference value in previous studies. We also analyzed the average
speed of vehicles in urban areas, i.e.,
ve=
10
m/s=
36
km/h
, as well as the intermediate speeds.
Depending on the legal regulations in a country, the speed limit in built-up areas is 30
÷
70
km/h
.
Other simulation parameters were as follows, suburban area,
J=
5, and
H=
500
m
. Figure 13 shows
the CDFs of the location error for the different emitter speeds. In Table 3, the values of other analyzed
metrics are included.

Sensors 2020,20, 2575 17 of 21
Sensors 2020, 20, x FOR PEER REVIEW 18 of 22
Figure 13. CDFs of the location error versus the emitter speed for a suburban area.
Table 3. Effectiveness metrics for the different emitter speeds.
Title 1 Emitter Speed, e
v
0 1 m/s 2 m/s 5 m/s 10 m/s
RMSE (m) 142 187 252 988 2 773
LOS
τ
(%) 96
EF (–) 20.4 15.4 11.5 2.9 1.1
The results presented in Table 3 show a significant relationship between the location accuracy
and the emitter speed. An increase in the emitter speed from 1 m s to 10 m s resulted in a 15-
fold decrease in the EF. This large increase in the position estimation error was caused by the
approximation of the resultant sensor velocity relative to the emitter by the absolute value of the
sensor velocity. This approximation associated with the velocity vector was the leading cause of the
arising errors. It meant that the accuracy of the presented location procedure depended on the ratio
of sensor and emitter speed. It followed that the developed procedure required introducing an
additional prediction of the emitter velocity vector.
4. Conclusions
This paper focused on assessing the monitoring effectiveness of the mobile emitter position by
the cooperative UAV swarm in various propagation conditions. We presented the novel SDF
extension, which allowed for considering the variable motion of the sensors and the emitter in any
direction on the OXY plane. This significantly expanded the practical use of this method. The impact
analysis of the swarm size, emitter and the sensor movement parameters on the location error was
performed based on the simulation results. The choice of the mentioned simulation parameters was
closely related to the SDF procedure, where the spatial relationship between the emitter location and
the UAV flight route influenced the positioning accuracy. In the procedure of the simulation tests,
random and limited time intervals in which the mobile sensors were under LOS conditions relative
to the monitored emitter were considered. The effectiveness evaluation of utilizing the UAV swarm
was carried out based on the RMSE and the percentage of the occurrence time of the LOS conditions.
Introducing the EF provided a measure that allowed the joint assessment of the accuracy and the
continuity of the emitter position monitoring. The obtained simulation results showed that in the case
of different environmental conditions and different emitter speeds, there was a differentiation in the
effectiveness of the location procedure. To reduce these changes and ensure the expected monitoring
parameters, the appropriate selection of flight altitude or swarm size is required. Additionally, the
random way of dividing the entire sensor flight trajectory into the LOS and NLOS sections was the
Figure 13. CDFs of the location error versus the emitter speed for a suburban area.
Table 3. Effectiveness metrics for the different emitter speeds.
Title 1 Emitter Speed, ve
0 1 m/s 2 m/s 5 m/s 10 m/s
RMSE (m) 142 187 252 988 2 773
τLOS (%) 96
EF (–) 20.4 15.4 11.5 2.9 1.1
The results presented in Table 3show a significant relationship between the location accuracy
and the emitter speed. An increase in the emitter speed from 1
m/s
to 10
m/s
resulted in a 15-fold
decrease in the EF. This large increase in the position estimation error was caused by the approximation
of the resultant sensor velocity relative to the emitter by the absolute value of the sensor velocity.
This approximation associated with the velocity vector was the leading cause of the arising errors.
It meant that the accuracy of the presented location procedure depended on the ratio of sensor and
emitter speed. It followed that the developed procedure required introducing an additional prediction
of the emitter velocity vector.
4. Conclusions
This paper focused on assessing the monitoring effectiveness of the mobile emitter position by the
cooperative UAV swarm in various propagation conditions. We presented the novel SDF extension,
which allowed for considering the variable motion of the sensors and the emitter in any direction on
the OXY plane. This significantly expanded the practical use of this method. The impact analysis of
the swarm size, emitter and the sensor movement parameters on the location error was performed
based on the simulation results. The choice of the mentioned simulation parameters was closely
related to the SDF procedure, where the spatial relationship between the emitter location and the UAV
flight route influenced the positioning accuracy. In the procedure of the simulation tests, random
and limited time intervals in which the mobile sensors were under LOS conditions relative to the
monitored emitter were considered. The effectiveness evaluation of utilizing the UAV swarm was
carried out based on the RMSE and the percentage of the occurrence time of the LOS conditions.
Introducing the EF provided a measure that allowed the joint assessment of the accuracy and the
continuity of the emitter position monitoring. The obtained simulation results showed that in the case
of different environmental conditions and different emitter speeds, there was a differentiation in the
effectiveness of the location procedure. To reduce these changes and ensure the expected monitoring
parameters, the appropriate selection of flight altitude or swarm size is required. Additionally, the
random way of dividing the entire sensor flight trajectory into the LOS and NLOS sections was the

Sensors 2020,20, 2575 18 of 21
original solution used in the simulation procedure. This solution provides a method of determining
the relationship between the environment type, flight altitude and an emitter shadowing frequency.
The carried-out studies justified the need for introducing an additional procedure of the emitter speed
vector prediction into the developed location method and show the possibility of obtaining the required
location efficiency by selecting swarm parameters. The presented procedure of the simulation tests
allows for optimizing both the selection of the location system parameters and the data processing in
the SDF method. However, the impact of the additional factors related to UAV swarm management
and control requires the implementation of this procedure in dedicated simulation environments such
as [60,61].
Author Contributions:
All authors conceived the proposed method, discussed and designed the layout of this
paper, discussed the obtained results, read and approved the manuscript. J.M.K. developed the novel SDF
extension, wrote the simulation algorithm, conducted the simulation studies in the MATLAB environment, made
all figures, translated the paper to English, and formatted it according to the Sensor template. C.Z. wrote the SDF
description is Section 2.1, developed the methodology for dividing the sensor trajectory into LOS/NLOS sections,
improved the simulation procedure and article translation. All authors have read and agreed to the published
version of the manuscript.
Funding:
This work was developed partially 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.
Acknowledgments:
The authors would like to express their great appreciation to the Sensor Editors and
anonymous Reviewers for their valuable suggestions, which have improved the quality of the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).