=Paper=
{{Paper
|id=Vol-2746/paper5
|storemode=property
|title=Features of Processing Signals from Stationary Radiation Sources in Multi-Position Radio Monitoring Systems
|pdfUrl=https://ceur-ws.org/Vol-2746/paper5.pdf
|volume=Vol-2746
|authors=Volodymyr Druzhynin,Serhii Toliupa,Oleksandr Pliushch,Mikhailo Stepanov,Bohdan Zhurakovskyi
|dblpUrl=https://dblp.org/rec/conf/cpits/DruzhyninTPSZ20
}}
==Features of Processing Signals from Stationary Radiation Sources in Multi-Position Radio Monitoring Systems==
https://ceur-ws.org/Vol-2746/paper5.pdf
Features of Processing Signals from Stationary Radiation
Sources in Multi-Position Radio Monitoring Systems
Volodymyr Druzhynin1[0000-0002-5340-6237], Serhii Toliupa2[0000-0002-1919-9174],
Oleksandr Pliushch3[0000-0001-5310-0660], Mikhailo Stepanov2[0000-0001-6376-4268],
and Bohdan Zhurakovskyi1[0000-0003-3990-5205]
1 National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Ukraine
2 Taras Shevchenko National University of Kyiv, Ukraine
3 State University of Telecommunications, Ukraine
vladimirdruzhinin68@gmail.com
Abstract. This paper performs an analysis of the movement impact of radio mon-
itoring system receiving elements on this system’s functional capabilities. The
analysis is done in the context of space-time processing of the signals that arrive
from a priori unknown stationary radio-emitting sources. It is accentuated that at
present both identification of the legitimate transmitters and establishing the pres-
ence and the locations of illegitimate ones, which are paramount tasks of radio
monitoring, become more and more complicated due to the introduction of new
technologies with irregular spectrum use. A new method is proposed to determine
the coordinates of those illegitimate sources in the passive monitoring mode with
non-directional reception. For the method, a technique is designed of finding po-
sitions of signal reception points during the radio monitoring interval to unam-
biguously determine radio emissions bearings in the passive mode and radio re-
ceivers’ movement in an a priori calculated space configuration. The proposed
method and algorithms have an economic advantage over space systems with
similar tasks and can substantially improve efficiency in certain conditions.
Keywords: Radio Monitoring, Passive Monitoring Mode, Monitoring Interval,
Non-Directional Reception, Emissions’ Bearings.
1 Introduction
1.1 Analysis of Challenges in Identifying Legitimate Sources of Emissions
during Radio Monitoring Process
At present, radio frequency monitoring (RFM) is a very difficult and resource-consum-
ing task due to the density of the spectrum used by the communication systems with
multiple access, such as mobile cellular ones. Trends and features of technical deploy-
ment, which the current and prospective mobile communication technologies possess,
impose further restrictions on the RFM process. Among the main factors that hinder
RFM of the spectrum use, some are more important than others.
Copyright © 2020 for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0)
47
Firstly, it is a deployment of wideband and ultra-wideband communication channels
with a concomitant reduction in the radiation power of their transmitters. This trend
seems to be the most important feature of current and prospective technologies devel-
opment. The trend is shaped by the fact that communication systems are no longer the
systems that provide only communication services for the subscribers; rather, they show
signs of being control and monitoring elements for the complex infrastructure objects,
such as a city with its road, municipal, social and other networks for population life
activities and industrial production. In this case, communication network infrastructure
ought to reflect the features of the surrounding ones and is an organic part of the general
control and monitoring system (so-called ecosystem). In such a system, broadband
communication channels are, to a certain extent, like blood vessels (pipelines) that se-
cure transmission and reception of large volumes of information that is transferred be-
tween the general infrastructure elements. Already currently, fourth-generation mobile
networks, which use LTE-Advanced technology, have a bandwidth of 20 MHz, while
fifth-generation communication systems are expected to deploy channel bandwidths up
to 100 MHz and beyond, depending on the frequency band. Besides, the narrowband
communication systems, such as those of the second generation ones (GSM technolo-
gies), will linger on; their channels will be used for data transfer in the general topology
of promising communication networks.
Use of wideband communication channels is enabled due to the available radio fre-
quency resources (RFR) in the super-high frequency (SHF) band, such as 26 GHz, and
extremely high frequency (EHF) band, such as 40 and 70 GHz (according to СЕРТ
research). Transition to these bands implies use, among the others, of the antennas with
narrow beam directivity patterns (NBDP), which considerably complicates RFM im-
plementation.
Secondly, big challenges for RFM are created by the introduction of adaptive modes
of transmitters’ operation in both frequency-time and space domains of the emitted sig-
nals. Modern and prospective mobile communication systems use the multiple access
method based on orthogonal frequency division multiple access (OFDMA) technique
in combination with the redistribution of frequency resources between the base station
sectors, as well as the deployment of multi-antenna/multi-channel space emissions
(MIMO) for the base station and the user equipment. Adaptation to the end-users de-
mands as well as propagation media conditions is achieved at the expense of active
antenna systems (AAS) based on phased antenna arrays (PAA); this approach makes it
possible to amplify emitted signals in the required direction for a certain user. This
changing nature of the emission parameters necessitates more meticulous and pro-
longed monitoring of the transmitters’ characteristics using RFM.
Thirdly, implementation of the so-called “technological neutrality” (TN) allows the
carriers to effectively use licensed frequency band as they see fit: in mobile or fixed
modes of operation, with time-division (TTD) or frequency division duplexing (FDD)
and different multiple access technologies for the users. Thus, emission parameters
monitoring should expect changes in radiation parameters and а necessity of controlling
the operator’s compliance with the demands in the adjacent frequency bands while us-
ing those different technologies. Such requirements concern, as a rule, restrictions on
the out-of-band emissions in the transmitters (control of a block edge mask (BEM),
48
which is a transmitter spectrum mask that applies at the edge of a contiguous licensed
block of the spectrum), as well as filtration (if applicable) in adjacent receivers.
Fourthly, general changes in the electromagnetic environment in a certain location
or a city subjected to RFM are linked to multi-standard frequency use by the operators
due to deployment of promising machine type communications (МТС), which imple-
ment projects of Internet of things (ІоТ) and machine-to-machine communications
(М2М); these connections are achieved through typical technological communication
channels of the modern mobile systems in all available frequency bands and channels
including in prospective fifth-generation technologies and frequencies allocated for
them. A feature of an MTS operation is that the synchronization and the power in the
transmission channel, which, in contrast to the conventional communication channel,
are defined by a separate timetable by the tasks of an infrastructure element.
On the background of the drastic changes in the electromagnetic environment, there
will continue to operate during the transition period a lot of technological communica-
tion stations with typical radiation parameters, as well as low-powered transmitters of
wide-band internet access (WBIA), stations of radio-relay and conventional radio com-
munications, repeaters in mobile systems and so on; they will require separate detailed
radiation inspection with the aim of establishing the legality of transmitters operation
and observance of the use of RFR.
The outlined major factors that shape the electromagnetic environment of the future
create uncertainty as to transmitters’ emission parameters, which in contrast to the con-
ditions of the environment created by the previous technologies can be described as
irregular spectrum use. This irregular spectrum use substantially changes the tasks of
the RFM that are concerned with transmitters identification, and their legality of RFR
use, and radiation parameters radio monitoring. In the conditions of constant radiation
parameters variation and multi-standard spectrum use, a certain risk of en mass utiliza-
tion of the frequencies by the illegitimate network transmitters emerges; radiation pa-
rameters of those transmitters will also be variable but masked by the general back-
ground emissions of the legitimate radiations of the changeable nature, which is the
main feature of the network as a whole. A part of the whole radio resource of the trans-
mitter, which serves a certain sector of the base station, can be used in another sector,
thus making identification and assessment of transmitter parameters impossible be-
cause of the weak signal at the moment of the scheduled measurement. Similarly, emis-
sions of an illegal transmitter (for example a repeater) can be hidden in the special
schedule of the RFR exploitation, which envisions redistribution of the frequency re-
source and its multi-standard utilization. Only a detailed analysis of the whole licensed
operator’s spectrum both in the coverage area and in the immediate vicinity to the base
station permits to collect of additional information for the transmitter identification.
Thus, as the analysis indicates, the task of transmitter identification in the conditions
of introduction and development of the new technologies is topical, one of the most
difficult to deal with, and needs an urgent solution.
49
1.2 Analysis of Challenges for a Search for Interference Sources in the
Current Electromagnetic Environment
Search for sources of interference in the previously described conditions is no less dif-
ficult than the identification of the legitimate transmitters and their parameter measure-
ment. Those sources are also masked by the irregular nature of the RFR utilization. But
the interfering sources can be both illegitimate transmitters and legitimate ones that
simply do not abide by the radiation parameters specified for a certain technology, as
well as the limitations that are imposed as a result of compatibility study with the trans-
mitters in the neighboring frequency band of another operator. Transmitter identifica-
tion by the data from the network identifiers and those of certain base stations or their
sectors will permit to carry out a more detailed analysis of signal spectra in the ambient
environment of an interference location and finally reveal the interfering signal from
an illegitimate transmitter (for example, a repeater). In general, to search for the source
of interference, it is necessary to reduce general uncertainty as to the radiation param-
eters of the transmitters by the way of using additional information concerning that
interference from the complaining affected legitimate user and some preliminary meas-
urements at the site of the interference manifestation. In this case, by increasing the
power of the interference relative to the useful signal, the RFM receiver has a chance
to do a more targeted and detailed analysis of the interference spectrum and, thus, se-
cure better precision and reliability of the results of the spectrum analysis and measure-
ments.
For the described reasons, a search for an interference source in the conditions of
irregular spectrum use demands long and meticulous work and presents itself as a dif-
ficult and topical challenge.
2 Impact of the Dynamic Factors on the Operation of Airborne
Radio Monitoring Systems with One Element
2.1 The Case of Unchanging Speed and Course of the Airborne Element
It is well-known [1–4] that dynamic factors of airborne RFM systems operation have a
substantial effect on their efficiency of practical applications. This is especially so for
passive systems of RFM. Let us assume that a remotely controlled aerial vehicle
(RCAV) with an onboard radio receiving module (RRM) is moving in a fixed direction
with a constant speed 𝑉 ⃗ RRM .
At a certain time instant 𝑡𝑖 , the signal emitted from an a priori unknown radio emis-
sion source (RES) comes from a previously unknown angle α1 to the input of the RRM
antenna (Fig. 1).
50
Fig. 1. Explanation of the ambiguous bearing of the signal from the RES in the conditions of
non-directional reception.
In this case, the equation for the carrier frequency of the received signal is as follows:
𝑉
𝑓(𝑛)𝑟𝑒𝑐 = 𝑓𝑛 (1 + 𝑅𝑅𝑀 𝑐𝑜𝑠𝛼1 ) (1)
с
where fn is signal carrier frequency; с is light speed; 𝑉𝑅𝑅𝑀 is the movement speed of
RRM of RCAV [3].
If the frequency of the signal carrier 𝑓𝑛 and the traveling speed of RCAV 𝑉𝑅𝑅𝑀 are a
priori known, then, after measuring 𝑓(𝑛)𝑟𝑒𝑐 , it is possible to determine the bearing of
the radio emission source (angle 𝛼):
𝑐 𝑓(𝑛)𝑟𝑒𝑐
𝛼1 = 𝑎𝑟𝑐𝑐𝑜𝑠 [ ( − 1)]. (2)
𝐿/𝑇 𝑓𝑛
It is necessary to stress that the accuracy of the bearing for a RES depends upon the
length of L (the synthesized aperture) and the corresponding distance that is covered by
RRM during the monitoring time T.
The advantage of such systems is that they secure high accuracy of signal-bearing
measurement with the use of antennas with a small aperture. On the downside, deter-
mining the bearing is possible only if the radiation spectrum is known in advance. This
factor greatly limits the use of the monitoring systems with a synthesized aperture.
2.2 Case of Changing Speed and Course of the Airborne Element
The situation described in the previous subsection can be resolved in the case in which
the speed of the RRM movement is changed either by the absolute value or by the
direction. This causes corresponding changes in the Doppler frequency during the mon-
itoring time T.
51
If RRM moves in the fixed direction with the velocity 𝑉(𝑡) changing by module, then
the harmonic wave from the interference with the frequency 𝑓𝑛 is registered at the out-
put of the receiving element as a frequency modulated oscillation and its time function
is described by the following equation [3]:
𝑉(𝑡)
𝑓𝑟𝑒𝑐 = 𝑓𝑛 (1 + 𝑐𝑜𝑠𝛼1) (3)
с
If the speed of the receiving element 𝑉(𝑡) observes harmonic function with the fre-
quency 𝑓ℎ , then (3) can be presented as [3]:
𝑉
𝑓𝑟𝑒𝑐 = 𝑓𝑛 (1 + 0 𝑐𝑜𝑠(2𝜋𝑓ℎ 𝑡)𝑐𝑜𝑠𝛼1) (4)
с
where 𝑉0 is the amplitude of the movement speed of RRM.
The amplitude of the fluctuation of the Doppler frequency of the incoming registered
oscillations (𝐹𝐷 ) and the average frequency of these oscillations (𝑓𝑎𝑣𝑒𝑟 ) are described
as follows [3]:
𝑉
𝐹 = 𝑓𝑛 0 𝑐𝑜𝑠𝛼1
{ 𝐷 с (5)
𝑓𝑎𝑣𝑒𝑟 = 𝑓𝑛
In this case, the frequency and arrival angle of the incoming signal can be found based
on the measurements of frequency fluctuation amplitude and the average frequency of
the registered oscillations. The accuracy of the bearing of the incoming oscillation de-
pends on the amplitude of the receiving element movement.
It is necessary to stress that this phenomenon will take place as well in those cases
when changes of the RRM velocity according to the laws differing from the harmonic
one.
Let us consider the case in which RRM during the period 𝑡1 moves in the fixed di-
rection with the constant speed 𝑉1 , and then during the period 𝑡2 is in a changed fixed
direction with the constant speed 𝑉2 (Fig. 2).
52
Fig. 2. The geometrical ratio of the angles for the situation with the changes in the movement
direction for the airborne RRM.
The feature of the first two models (1) and (4) is the ambiguity in the bearings meas-
urements: signal coming from the symmetrical directions (from the angles 𝛼1 and 𝛼2 )
in Fig. 1, are indistinguishable.
In the case in question (Fig. 3), the situation is different from those above.
When the RRM moves in the first direction, the registered Doppler frequency is de-
scribed by the equation:
𝑉
𝐹𝐷1 = 𝑓𝑛 1 𝑐𝑜𝑠𝛼1 , (6)
с
and when it moves in the second direction (Fig. 2) by this one:
𝑉
𝐹𝐷2 = 𝑓𝑛 2 𝑐𝑜𝑠(𝛼1 + ∆) (7)
с
If 𝑉1, 𝑉2 and ∆ are a priori determined by the spatial configuration of the radio moni-
toring system, and 𝐹𝑟𝑒𝑐1 and 𝐹𝑟𝑒𝑐2 are the values that are measured, then the bearing of
the signal from RES and its frequency can be unambiguously determined using the
above equations (6) and (7).
In this case, the accuracy of parameters measurement from the signal of RES de-
pends upon velocity values 𝑉1 , 𝑉2 and the angle ∆.
53
3 Design of the Novel Dynamic Model of Space-Time
Processing of Signals from RES
Basing on the above-presented mathematic apparatus, this paper proposes a dynamic
model of space-time processing of signals from RES in the conditions of their space
diversity reception by the moving RRM with a priori has known space parameters on
the monitoring time interval.
Currently, mobile means of monitoring are capable to functionally complement sta-
tionary ones and secure flexible support of effective radio monitoring while carrying
out measurements of the radio emissions that are out of reach for the stationary ones by
using potential capabilities of the synthesized aperture in passive systems [5–9].
Fig.3 illustrates space locations of two signal reception points (А and В) relative to
RES. In this case, monitoring of the RES is performed by two moving RRM, which
move with velocities 𝑉1 , 𝑉2 and are located at a distance one from the other. The recep-
tion points (А and В) of the signal from the directions 𝛼1 , 𝛼2 are located within the
scope of the main lobe of the directivity pattern of the RES in both vertical and hori-
zontal planes.
Fig. 3 enables the design of an algorithm to calculate coordinates of the
RES (𝑥RES ; 𝑦RES ) in the passive mode of monitoring for non-directional reception for
the set of input data.
The input data for the algorithm are:
1. Location coordinates for RRM 1 and RRM 2 throughout RES monitoring.
2. Delay time (𝑡𝑑 ) of the RES signal arrival to the point В relative to the time of RES
signal arrival to the point А.
3. Distance (d) and interval (I) are non-changing during the monitoring time (Т) of the
RES.
4. 𝑉1 = 𝑉2 .
54
Fig. 3. The trajectory of the movement of the two RRMs by parallel courses with a specified
distance (𝑑) and interval (𝐼) between their carriers.
Algorithm of determining RES location coordinates (𝑥RES ; 𝑦RES ) in the passive mode
of monitoring can be broken down into the following steps.
Firstly, let us determine the power of the RES (P) and the angle between directions
of the movement of the receiving elements (∆= α̂ 1 − α̂ 2 ) in the horizontal plane.
Using the transmission equation of Harold Frisis, we can obtain an expression for
inclined range calculation 𝑟1incl to the RES, which looks as follows:
𝑃 1/2
𝑐𝑡𝑑 (𝑃1 )
2
𝑟1𝑖𝑛𝑐𝑙 = 𝑃1 1/2
, (8)
1−( )
𝑃2
where 𝑡𝑑 is the delay time of the signal arrival to the second receiving element relative
to the first one; 𝑃1 , 𝑃2 are powers of the signal from RES received respectively by the
antennas of RRM 1 and RRM 2.
It should be noticed that the inclined ranges to the first and the second receiving
elements are related by the equation:
r2incl r1incl ctd , (9)
55
where 𝑟1𝑖𝑛𝑐𝑙 is the inclined range to the first receiving element from the location of the
RES; 𝑟2𝑖𝑛𝑐𝑙 is the inclined range to the second receiving element from the location of
the RES; c is the speed of light.
Respectively, mathematical equations for calculating elevation angles at the recep-
tion point А and В (Fig. 3) looks as follow:
H , (10)
1 arcsin
r1incl
where H is the height of the radio receiver location at the instant of the signal received
from the RES (Fig. 1):
H . (11)
2 arcsin
r2incl
Formulas for calculating magnitudes of the projections of the inclined ranges from RES
to the points А and В on the horizontal plane according to Fig. 3 can be presented as:
2
H
H 1 (12)
H H r1incl
r1h r12incl H 2
tg 1 H H
tg arcsin
r1incl r1incl
2
H
H 1 (13)
H H r2incl
r2 h r22incl H 2
tg 2 H H
tg arcsin
r2incl r2incl .
With an account of the equations (12)–(13), the angle between directions at the signal
receiving points relative to the location point of the RES in the horizontal plane is cal-
culated as (Fig. 1):
1 2 arccos
1h 2h
r 2 r 2 I 2 d Vt 2
d (14)
2 r1h r2 h
In the given case when the parameters 𝑉1, 𝑉2 , (d, I) (distance and the interval between
the radio receivers carriers at the points А and В in Fig. 3) are a priori known, angle Δ
is calculated according to (14); as 𝑓𝑟𝑒𝑐1 і 𝑓𝑟𝑒𝑐2 are measurable, then arrival direction of
the signals and their carrier frequencies is unambiguously determined by the expres-
sions (16)–(17) based on solving the system of equation presented below:
56
V (15)
f rec1 f car 1 1 cos 1
c
f V
f car 1 2 cos 1
rec 2
c
2 1 ; V1 V2 V ,
r 2 r 2 d Vt 2 V
arccos 1h 2 h d
arccos A f rec1 1 c cos 1
2 r1h r2h
; f rec 2 1 V cos 1
c
c f rec 2 f rec1
f rec1 A cos 1 f rec1 1 A2 sin 1 f rec 2 cos 1
V
Let us designate:
r 2 r 2 d Vt 2
f rec1 A f rec1 1h 2h d
A
2 r1h r2 h
2
r 2 r 2 d Vt 2
f rec1 1 A2 f rec1 1 1h 2h h
B
2 r1h r2 h
f rec 2 C
c f rec 2 f rec1
G
V
A cos 1 B 1 cos 2 1 C cos 1 G ; cos1 t .
A C B t 2CG 2 AC 2 AG t G B 0
2 2 2 2 2 2
2CG 2 AC 2 AG 2CG 2 AC 2 AG 2 4 A2 C 2 B 2 G 2 B 2
t1,2
2 A2 C 2 B 2
Now we can introduce the restrictions: 1 t 1
0 1 .
Thus, the equations for calculating the bearing angle at RES and its carrier frequency
can be presented as:
1 arccost (16)
57
(17)
f rec1
fcar
V
1 c cos 1
Fig. 4. Block-diagram of the algorithm for bearing finding at RES (α1, α2) and its carrier fre-
quency (fcar).
Fig. 5. Movement orientation of the RRM relative to Х axis.
58
Under the condition that ОХ axis of the rectangular coordinates system ХОУ, depicted
in Fig. 5, is oriented in parallel with the movement trajectory of the receiving elements
of the radio monitoring system, with the ground site for collecting and processing of
the radiolocation information (GSCPRLI) located at its center, coordinates of the RES
location can be calculated as follows:
2 2
x c f rec1 (18)
RES x1 r1incl H 1 1
2 2
V1 f car
cf
yRES y1 r12incl H 2 rec1 1
V 1 f car
Implementation of the spatial location of the signal reception points (A and B) relative
to RES (Fig. 4) can be secured due to respective radio control of the RRM carriers and
is reduced to defining and transmitting control commands (CC) onboard the RES car-
rier with a fixed delay time relative to the CC of the leading object.
This task is characterized by the fact that the flight control is performed uninterrupt-
edly along the whole flight trajectory of the grouping of the RRM carriers. To simplify
the analysis, the above problem is considered in a single plane.
Locations of the leading and the led RRM carriers are determined in the inertial co-
ordinates system with the axis H, P, D(V ⃗ ). Leading carrier of RRM (LRRM) travels
⃗
with the speed V1 at the height H1 .
Similarly, the speed of the led RRM is ⃗V2 = ⃗V1 , and the direction of its movement
coincides with that of the leading RRM as well. From this follows that the angle of the
trajectory inclination θ̂ equals the course angle of the leading RRM. This is true in the
case when the attack angle equals zero and is illustrated by the kinematic ratios shown
in Fig. 6.
P
VT T
VT leading
d
VT
VM
VM led
1 D
VM
H
Fig. 6. Graphic interpretation of the kinematic ratios for the moving both leading and led RCAV
The viewing angle in Fig. 5 is designated as 𝛽, the distance between the leading and
the led RRM d; the projections of the speed vector of the leading and the led RRM on
the viewing line 𝑉𝛽𝑇 , 𝑉𝛽𝑀 , those on the normal to the viewing line 𝑉𝑎𝑇 , 𝑉𝑎𝑀 .
59
The role of the retaining system (RS) of the led RRM on the required trajectory is to
form such CC (for the autopilot) that would keep the led RRM in the specified position
of the grouping even when the leading one undertakes maneuvers.
Let us assume that the RS processes the incoming signal that equals (proportional)
to the angle of the viewing line 𝛽 or the viewing speed 𝛽̇ .
For such input signals, only one implementation of the control rule that can be used
to retain the leading RRM in the position is possible, which is pursuit.
In this case, the led RRM is always located behind the leading one, that is 𝜃 = 𝛽.
When any maneuver is absent, which means that the led RRM moves with the con-
stant side speed, then with the constant longitudinal speed “ideal” distance between the
two objects on the straight line is secured.
Following data in Fig. 5, kinematic ratios are as follows:
𝑉𝛽𝑇 − 𝑉𝛽𝑀 = 𝑉𝑇 𝑐𝑜𝑠(𝛽 − 𝜃𝑇 ) − 𝑉𝑀 𝑐𝑜𝑠(𝛽 − 𝜃) = 𝑑̇ (19)
𝑑 = 𝑑0 + 𝑑̇ ∆𝑡,
while the angle deviations are:
𝑉𝑎𝑇 − 𝑉𝑎𝑀 𝑉𝑇 𝑠𝑖𝑛(𝛽 − 𝜃𝑇 ) − 𝑉𝑀 𝑠𝑖𝑛(𝛽 − 𝜃)
𝛽̇ = − = −
𝑑 𝑑
𝛽 = 𝛽0 + 𝛽∆𝑡̇ (20)
The method of “clear” pursuit is characterized by the fact that neither leading nor led
RRM makes any maneuvers. Then, it is obvious that 𝑉𝑇 = 𝑐𝑜𝑛𝑠𝑡, and 𝜃𝑇 = 0, 𝜃 = 𝛽.
In this case:
𝑑(𝑑)
= 𝑉𝑇 𝑐𝑜𝑠𝛽 − 𝑉𝑀 = 𝑑̇ ;
𝑑𝑡
𝑑𝛽 𝑉 𝑠𝑖𝑛𝛽
𝛽̇ = =− 𝑇 (21)
𝑑𝑡 𝑑
For the above formulas, 𝛽̇ equals zero only if 𝛽 = 0 or 𝜋, so the pursuit is performed
exactly in “the tail.”
Solution for 𝛽 and the trajectory inclination angle 𝜃, as a function of the distance d,
looks as follows:
𝑑(𝑑) 𝑉 𝑑(𝑑)
= (−𝑐𝑡𝑔𝛽 + 𝑀 𝑐𝑜𝑠𝑒𝑐𝛽) 𝑑 → = (−𝑐𝑡𝑔𝛽 + 𝛾𝑐𝑜𝑠𝑒𝑐𝛽)𝑑𝛽, (22)
𝑑𝛽 𝑉𝑇 𝑑𝑡
𝑉𝑀
where 𝛾 = is the ratio of the speeds of the leading and the led CRRM.
𝑉𝑇
Reverse transformation of (22) can be presented as:
𝛽
𝑙𝑛𝑑 = −𝑙𝑛|𝑠𝑖𝑛𝛽| + 𝛾𝑙𝑛 |𝑡𝑔 | + 𝑐𝑜𝑛𝑠𝑡 (23)
2
60
if assumed that 0 ≤ 𝛽 < 𝜋, then
𝑑𝑠𝑖𝑛𝛽
𝑙𝑛 𝛽 𝛾
= 𝑐𝑜𝑛𝑠𝑡, (24)
𝑡𝑔( )
2
or
𝑑𝑠𝑖𝑛𝛽 𝑑0 𝑠𝑖𝑛𝛽
(𝑡𝑔𝛽/2)𝛾
= = 𝑘 = 𝜆, (25)
(𝑡𝑔𝛽0 /2)𝛾
where 𝑑0 and 𝛽0 are required values of the distance and the viewing angle of the led
CRRM relative to the leading one.
Because both the leading and the led CRRM have to be on the same line, then 𝛽
approaches zero, and 𝑘 = 𝜆 should be constant.
The exact approach “at the tail” of the leading CRRM takes place under the condi-
tion: 𝛽 = 𝜃 = 0:
𝑉 (𝑠𝑖𝑛𝛽) 2
𝛽̇ = − 𝑇 𝛾.
𝜆 (𝑡𝑔𝛽/2)
𝛽 𝛽
On the segment of the trajectory where 𝛽 ≪ 1, 𝑠𝑖𝑛𝛽 ≈ 𝛽, 𝑡𝑔 ≈ , an expression for
2 2
the angular velocity looks as follows:
𝛾
2 (𝑉𝑇 ) ̇
𝛽̇ ≈ − 𝛾.
𝜆
Implementation of the CRRM movement in parallel courses with the set interval (I) and
the distance (d) between them, on the selected monitoring time intervals, permits to
substantially increase their noise immunity due to the multi-positional reception of the
location information from the RES.
In this type of homing, for each led RRM, fixed magnitudes of the angle β and the
interval I are set; in other words, the constant advance angle is created (Fig. 7).
V1
d
I V2
Fig. 7. Projections of the trajectories of the two CRRM with the given interval (I) and the distance
(d) between them on the horizontal plane.
Fig. 8 demonstrates the probable trajectories of CRRM by the values of γ.
61
V1
V2
1 3
V3
2 2
3 1,5
Fig. 8. Probable trajectories of the CRRM by the values of γ.
When led CRRMs to move at a constant speed, they pursue without maneuvering the
leading one on a parallel course. This secures the constant nature of the trajectory, in
other words, fixed angle 𝛽𝑛 .
Thus, pursuit with a fixed angle also makes sense, as in the case of the “clear” pur-
π
suit, but for the starting conditions when β ≤ .
2
For the implementation of the pursuit with a constant angle, information about the
speed ratio of the leading CRRM to the led one is required, as well as attack angles.
If the attack angle is constant, viewing lines does not change as well, that is 𝛽̇ = 0.
It is possible in the case when the speed component 𝑉𝛼𝑇 of the led CRRM that is
located behind the normal to the viewing, the line is balanced by the normal speed
component 𝑉𝛽𝑇 of the led one. In this case angular accelerations 𝑉𝛼𝑇 ̇ and 𝑉𝛽𝑇 ̇ do not
occur and the led CRRM never overtakes the leading one.
To realize such a control method, which is similar to the parallel approach, CCs are
defined as follows:
(26)
Nevertheless, for the parallel approach method, CCs are constantly applied, while for
the method of approach with a constant angle they are used only under the condition of
acceleration, which is when θ̇ = 0, β̇ = 0.
CCs level is defined by the ratio
0 (27)
where θ0 is an initial angle of the divergence.
In this case, the CCs level can be calculated through γ:
VT
sin 0 0 sin 0 T sin 0 0 sin 0 T f
VM (28)
VM
Movement trajectory of CRRM for γ = = 2 and corresponding control commands
VT
2λ, 4λ, 6λ are shown in Fig. 9.
62
Fig. 9. Trajectories of CRRM for γ = 2 and the respective CC (2λ, 4λ, 6λ)
Implementation of the presented trajectories is possible only in the ideal control system
for any initial conditions.
To calculate reference trajectories, it is necessary to assume that the movement of
the led CRRM is performed on the time interval 𝑡𝑛 = 0 + Δ𝑡 with constant speed 𝑉𝑀
and such angles of the trajectory inclination 𝜃 that they are directed along the trajectory
of the leading CRRM.
If 𝑉𝛽𝑀 represents the speed component of the led CRRM that is directed along the
trajectory of the leading one, and the side component 𝑉𝛽𝑇 ≈ 0, then the expression for
the speed of the carrier descent can be presented as follows:
d V V const. (29)
T M
From above, the formula for the distance between the led carriers is as shown below:
d d0 VT V M t (30)
where 𝑑0 is that value of the initial distance for which approach speed is constant or
equals zero.
Delay time of the CC issuing is defined as follows:
d0 (31)
ti
VT V M
But the presence of the angular velocities of CRRM and delays in CC issuing leads to
deviation of the real trajectory from the reference one. This deviation at a certain time
instant t manifests itself by the perpendicular shift 𝑦𝑡 .
Similarly, the longitudinal location of the led CRRM is determined by the value of
the deviation 𝑦𝑚 .
Deviation of the trajectory of CRRM in time is also characterized by the velocities
𝑦̇𝑚 , which are defined by the fluctuations of the angle 𝜃.
If the trajectory of the CRRM is kept in the space angle 𝜃 ≪ 10 , then the shift speed
can be determined by the dependence:
63
ym VM cos V M
yt y0t ymt y0t ymti (32)
In practice, the realization of the pursuit with an angular shift is possible based on the
autopilot (AP) with dynamic delay.
If the operation of the AP is considered as that of a linear device, then the CC level
with the account of the errors can be expressed as follows:
ym (33)
and the distance error:
yt ym d y y
t m
(34)
d ;
yt ym
d
.
The retention error in the required angle range (DC RRM):
ym
;
V M
1o (35)
Retention of the led RRM at a respective distance is possible by deploying a radio beam
(RB) (on the viewing line).
In this case, the led CRRM move in the range of line-of-sight of the leading CRRM.
To perform the movement along the viewing line, the speed 𝑉𝛼𝑀 of the leading
CRRM has to equal the linear speed 𝑑 𝑇 𝛽̇ , where 𝑑 𝑇 is the distance from the leading
CRRM to the led one. In this case:
VT (36)
V M dT
dT
In the case when the led CRRM moves along the set trajectory (is in the range of the
radio beam) 𝑑 𝑇 ≈ 𝑐𝑜𝑛𝑠𝑡 and 𝑉𝛼𝑀 = 0, then the situation is similar to the case of the
“clear” pursuit, but with the shift.
When the led CRRM deviates from the required trajectory dT ≠ const; VαM ≠ Vαt ,
it is namely this that presents itself as a discrepancy parameter for the flight control
system (FCS) of the led CRRM.
The main advantage of the pursuit method with the shift in its simplicity. The prin-
cipal drawback of this method is the emergence of the errors when delay distance for
the led CRRM increases.
64
Dynamic error (failure) of retaining led CRRMs on the required trajectory for both the
case of the “clear” pursuit and the pursuit with the shift is as follows:
M yt (ti ) ym (ti ) (37)
where 𝑡𝑖 is the factual delay time of the CC arriving on board of the led CRRM.
Delay time of CC must not surpass the time of the complex time constant of the
control loop of the aerodynamic object Te , so t i < Te , and in an ideal case t i ≪ Te ; this
is because, in the general incident, the processing time of CC and working out control
decisions will be defined as t i + Te , hence for t i to be by order less than Te , will secure
the required quality of functioning of FCS of the led CRRM.
4 Conclusions
Mobile means of radio monitoring functionally complement the stationary ones and
provide flexible support for effective radio monitoring when radio emissions parame-
ters are measured from beyond their accessibility zone. Utilization of the mobile sys-
tems of the radio monitoring based on the mobile radio-controlled modules for per-
forming practical tasks permits to more successfully carry out radio spectrum control
and reveal unlicensed radio transmissions.
Concerning this, the problems of studying achievable potential limits of the passive
radio monitoring methods with synthesized apertures remain topical and important for
practical implementations. Radio monitoring tasks can be performed with the help of
deploying passive radiolocation systems; those systems can include not one but quite a
few spatially diversified radio-controlled receiving modules.
The necessary condition of solving the task of determining coordinates of RES by
the designed system is the deployment of at least three mobile radio receiving modules
during the monitoring time interval. In this system, the information that is received by
the separate radio locating measurers is processed together. The algorithms analyzed in
this paper permit to reveal the coordinates of the radio emission sources in the passive
mode and for non-directional reception. It should be stressed that the implementation
of the presented algorithms is economically viable in comparison to the space systems
of the radio monitoring, which perform the same technical tasks.
The efficiency of the proposed dynamic models depends not only on the parameters
of the radio reception modules but also on the characteristics of the signals from the
sources of the radio emissions. A substantial role in all this is played by the ratio be-
tween the parameters of the antenna movements of the RRM and the measured signal
coherency interval. If the phase structure of the signal does not degrade on the entire
space-time monitoring interval, then, due to taking into account a priori known infor-
mation on the movement parameters of the radio locating measurers, it is possible to
substantially increase the efficiency of the system in resolving the analyzed problem.
65
References
1. Druzhinin, V.: Forming and Processing Radar Information in Radiovision Systems (2013)
2. Druzhinin, V., et. al.: Methods and Algorithms of Information Processing and Protection in
Radar Systems with Adjustable Space Configuration (2014)
3. Gorban, I. Processing of Hydroacoustical Signals Under Complex Dynamic Conditions
(2008)
4. Karavaev, V. V., Sazonov, V. V.: Statistics Theory for Passive Location (1987)
5. Hayes, M. P., Gough, P. T.: Synthetic aperture sonar: a review of current status. IEEE J.
Ocean. Eng. 34(3): 207–224 (2009)
6. Autrey, S. W.: Passive synthetic arrays. IEEE J. Ocean. Eng. 84(2): 592–598 (1988)
7. Stergiopoulos, S.: Optimum bearing resolution for a moving towed array and extension of
its physical aperture. J. Acoust. Soc. Am. 87(5): 2128–2140 (1990)
8. Edelson, G. S., Tufts, D. W.: On the ability to estimate narrow-band signal parameters using
towed arrays. IEEE J. Ocean. Eng. 17(1): 48–61 (1992)
9. Ivanenkov, A. S., et al.: Cramer–Rao lower bound for localization of a source with partial
temporal coherence using passive synthetic aperture. 12th European Conference on Under-
water Acoustics: 564–571 (2012)