=Paper=
{{Paper
|id=Vol-2588/paper16
|storemode=property
|title=Main Threats and Solutions for Positioning by Navigational Aids Network
|pdfUrl=https://ceur-ws.org/Vol-2588/paper16.pdf
|volume=Vol-2588
|authors=Ivan Ostroumov,Nataliia Kuzmenko,Anton Petrov
|dblpUrl=https://dblp.org/rec/conf/cmigin/OstroumovKP19
}}
==Main Threats and Solutions for Positioning by Navigational Aids Network==
https://ceur-ws.org/Vol-2588/paper16.pdf
Main Threats and Solutions for Positioning by
Navigational Aids Network
Ivan Ostroumov [0000-0003-2510-9312], Nataliia Kuzmenko [0000-0002-1482-601X] and
Anton Petrov [0000-0003-3731-4276]
National Aviation University, Kyiv, Ukraine
vany@nau.edu.ua
Abstract. There are many systems on board of civil airplane for coordinates-
measurements. Global Navigation Satellite System is used as a primary posi-
tioning sensor. As a stand-by, positioning by navigational aids can be used in
case of malfunction of the primary system. Both positioning systems, except in-
ertial navigation system, are grounded on signals measurements and data trans-
ferring via communication channels. In paper we study the main threats that can
affect communication channels between different parts of navigation equipment
and analyze its potential impact into positioning performance. We discuss inter-
ference of radio waves, unintentional jamming and spoofing threats, threats of
usage not valid air navigation data and missing optimal pair of navigational aids
due too poor standard service volume model. As a result, a possible solution for
each of these threats detection and minimization of their impact is proposed,
based on improvements of data processing inside of Flight Management Sys-
tem.
Keywords: navigational aid, threat, communication, positioning, DME, VOR,
FMS, GNSS, unintentional jamming, spoofing, database.
1 Introduction
Airplane navigation is a key element of successful transport system operation that
supports the safety of aviation. Navigation function includes tasks of safe airplane
movement from one point of airspace to another by the most effective three-
dimensional trajectory. In this case, detection of airplane location or positioning in
space within predefined reference frame is important component of aviation safety. In
common case, positioning systems use direct data transmission from network of radio
beacons to airplane with further data processing. An airplane positioning system may
use Time of Arrival (ToA), Time Difference of Arrival (TDoA) [1], or angle of arri-
val (AoA) [2] methods for coordinates detection. All of these methods use radio
communication channels for navigation signals transmission. Different systems use
different radio spectrums [3]. Performance of positioning depends on quality and
continuity of navigation radio signal fixation at the receiver. Thus, all factors that can
influent communication line within navigation system degrade the accuracy of posi-
tioning significantly. Appearance of these factors has different nature and result in
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attrib-
ution 4.0 International (CC BY 4.0) CMiGIN-2019: International Workshop on Conflict Management in
Global Information Networks.
different forms [4]. Mostly it depends on communication line structure and channel
type [5]. For example, Time Division Multiple Access (TDMA) and Frequency-
Division Multiplexing (FDM) has different nature of threat influence at one of the
channels of navigation system. A simple noise at operation radio frequency of naviga-
tion system can lead to total lock in case of TDMA usage, but in case of FDM can
slightly reduce performance of positioning. Therefore, the way of threat influence on
operation of positioning system via communication line can be different, depending
on localization method used, particularities of measurement sensor structure, and
communication channel operation.
Performance of navigation detection makes Global Navigation Satellite System
(GNSS) extremely popular in a variety of civil aviation applications. But, multiple
threats [6] that can act at communication line into transmission of navigation data can
degrade performance of positioning and even can lead to positioning lock. In case of
lack of positioning performance, an Attitude Heading and Reference System (AHRS)
can be used as a stand-by equipment to continue positioning function. Unfortunately,
operation time of inertial navigation is limited by errors of positioning, which has
additive behavior and increase significantly with time. Thus, AHRS can be considered
as a solution for limited period of time. In case of error out of required performance
level, positioning by navigational aids can be initiated [7]. Both, GNSS and position-
ing by navigational aids data depend on success data transmission in communication
channel. Threats, that can affect the transmission line can reduce positioning perfor-
mance. In our research we would like to study the main threats that can affect posi-
tioning function from communication network side.
2 Treats in communication line of Global Navigation Satellite
System
GNSS is one of the most useful positioning systems in the world. Global coverage
and stable availability makes GNSS useful in various applications. Today GNSS is
realized in GPS, GLONASS, GALILEO, and Beidou with various augmentation sub-
systems. GNSS includes a set of synchronized transmitters located at Earth’s orbit.
Each satellite in constellation transmits navigation signal at specific communication
channel. The distance of communication line between transmitter and receiver in
communication channel is very significant for transmitting power. In case of GPS,
space segment is located in 20180 km from user receivers. A transmitter of satellite
for L1 supports power in 21.9 W (13.4 dBW) [8], satellite antenna gain for the worst
case of user location supports 13.4 dBW. Thus, power of navigation signal from satel-
lite is above 26.8 dBW. Radio wave propagation in free space takes 184.4 dBW. Total
atmospheric and polarization mismatch losses take 3.9 dBW. Finally, in user segment
we are getting navigation signals with power level of −158 dBW, approximately. The
power level of these signals is too small and may be easily affected by intensive noise
or interference in communication channel. Also, large spatial variation of ionosphere
delay and fluctuation of power oscillation in troposphere [9] effect power budget of
communication line and finally degrade performance of positioning by GNSS dramat-
ically.
The interference of radio waves is another important problem of GNSS. Improper
functioning equipment can be a source of noise that can affect communication line of
navigation system by means of interference. Numerous reports and papers [10, 11, 12]
are describing events all over the world with improper functioning of transmitting
equipment with the wrong settings that affect GPS positioning capability.
Continuous growing of GNSS value in positioning market makes widespread and
implementation of positioning service in different human activity and multiple com-
mercial applications. In opposite side, at the private security level, widespread GNSS
functionality creates basics to introduction and rapid world-wide spread of specific
systems for navigation signals jamming. We do not want to cover military side of this
problem where jammer is used for deliberate generation of noise at radio frequency of
communication line at predefined volume, but we would like to focus on private per-
son level. Today in global market a variety of low power jammers with an effective
operation range from a few to hundreds meters is available. Small size, low battery
supply, and low price for such kind of equipment make it popular for drivers of logis-
tical companies, taxi, and other delivery services (see Fig. 1). By the principle of
operation all of these equipment generates a simple noise at spectrum of GNSS. Us-
age spectrum of GNSS for transmission of anything including simple Gaussian noise
is a violation of radio spectrum law, that makes usage of jammers under the law.
However, low power of transmission results in 5-10 meters of effective operation
radius for positioning system lock and makes real problem for their detection with
stationary radio spectrum controller stations, make them totally undetected.
Platon
GP-50
Scorpion - GPS
G-55
USB
Fig. 1. An example of low power jammers
From another side, usage of jammers close to airport area may affect accuracy of
positioning systems used for airplane landing or take-off, navigation during taxi; op-
eration of ground services and even affect operation of different augmentation sys-
tems (LAAS, WAAS, EGNOS, GBAS). Statistic of events of such equipment usage
told us about problem of “unintentional” usage of jamming equipment. It means that
the primary reason to use this equipment is to provide locking of private user receiv-
ers and it does not directly affect aviation operation. According to numerous studies, a
problem of unintentional jamming is one of the most important threats of GNSS in
near future.
The main source of jammers' location may be highways, lanes, roars, parking lots,
and other places of possible car location. A highway can be considered as the most
unpredictable, due to limited time of appearance and continues changing the power of
transmission at point of positioning. In this case, appearance of unintentional jamming
can be considered in terms of queuing theory and a Poisson process with further con-
sideration at navigation performance level. The impact of unintentional jamming in
positioning process can be different according to variety of equipment and jammed
radio spectrum. The jammer can be oriented to transmit noise at spectrum only one of
GNSSs. However, positioning system on-board of airplane can utilize omni-
constellation principle and use navigation signals from wide vary of radio-spectrum.
In this case, loss of navigation data from one of GNSSs can reduce positioning accu-
racy, but do not lock positioning functionality at all.
One of the possible solutions for problem of interference or unintentional jam-
ming in GNSS can be found by usage of an adaptive antenna array [12]. In this case,
an antenna array can change the directional characteristics of its gain function dynam-
ic during operational mode. The operation of the adaptive antenna array follows three
main steps. At the first a presence of valuable level of noise is detected. With the help
of electronically rotated gain function of antenna, direction to the threat location can
be detected in relation to the antenna array. At the final step antenna array generates
an adaptive gain function pattern in order to minimize receiving power from threat
direction. Unfortunately, adaptive antenna systems are not popular in civil aviation,
due to economic reasons and have mostly a military application.
3 Positioning by navigational aids
Positioning by navigational aids usually is grounded on usage of data from VHF om-
nidirectional range (VOR), Distance Measuring Equipment (DME), or Automatic
Direction Finder (ADF) in order to detect airplane position [7, 13, 14]. According to
the minimum equipment list of a common civil airplane, there are two sets of each of
these sensors. Operation of these sensors usually is controlled by Flight Management
System (FMS) via Radio Management Panel (RMP) (see Fig. 2). Algorithms of posi-
tioning by navigational aids are processed in FMS. FMS includes an air navigation
database, that contains technical data about navigational aids around the world. Dur-
ing a positioning cycle, FMS analyzes the airspace around, taking into account ex-
trapolated airplane trajectory and data about ground navigational aids in order to de-
tect an optimal pair of navigational aids. At this stage, a binary integer linear pro-
gramming can be used to find a solution to the optimization problem [15]. Frequen-
cies of optimal pair of navigational aids are used by RMP for tuning sensors DME,
VOR, or ADF. Results of measured distances or angles come back to FMS for solu-
tion a system of navigation equations [14].
Flight Management System
Sensors
Solution of Air Optimal DME
navigation naviga- pair RMP VOR
equation tion selection ADF
database
Airplane position
Distances, Angles
Fig. 2. A cycle of positioning by navigational aids
According to poor accuracy of positioning by AoA method, pairs of ADF and
VOR are not used very often. But, DME/DME that utilize ToA method, and
VOR/DME (utilize AoA/ToA methods) are considered as main alternative positioning
approach in civil aviation [14, 16].
Let’s consider a sensor structure and the importance of a communication line for
measurements in VOR and DME (see Fig. 3).
On-board equipment of airplane
30 Hz FM
Communication channel reference signal
for interrogation (Fint)
DME On-board On-board VOR
DME VOR Simplex ground
ground interroga- communication
receiver channel at FVOR station
station tor
Communication channel
for reply
(Frep= Fint±63Mhz) 30 Hz AM
directional signal
a) DME communication line b) VOR communication line
Fig. 3. Communication lines of navigational aids
3.1 Distance Measuring Equipment
DME uses interrogation principle to measure distance from airplane to ground-based
navigational aid. DME operates in the UHF band between 960MHz and 1215 MHz
with1 MHz spacing that supports 252 channels [3]. On-board equipment interrogates
ground DME station at frequency of particular channel. As interrogation signal DME
uses two pulse pairs that are specified to have a Gaussian envelope and are amplitude
modulated. The time distance between pulses in pairs is different for different chan-
nels 12 μs (X channel) and 36 μs (Y channel) [17]. The time frame between pulse
pairs is unique for each interrogation and is used in system to identify own reply from
DME. The ground station of DME receives and validates interrogation signal. After
detection of valid interrogation pulses ground station generates reply signal in the 50
μs delay (for X channel) [17]. DME reply signal is the same as interrogation signal
but has a carrier frequency in 63 MHz offset. During 50 μs delay period and 10 μs
margin DME ground station is frozen for any interrogation. During measuring inter-
rogator does not know possible time of returners and have to wait up to 2.5 ms to
guarantee operational radius in 200 NM.
Slant distance in DME is calculated by measuring the time frame between sending
interrogation and receiving reply on-board of airplane and known constant speed of
radio waves propagation (c=3e8 m/s).
3.2 VHF omnidirectional range
VOR ground transmitter operates within 108-117.95 MHz frequency range in the
VHF band ( particularly 40 channels in 108-112MHz and 120 channels in 112-117.95
MHz) [3]. Navigation signal of VOR includes two sub-signals amplitude and is fre-
quency modulated. The frequency modulated reference signal (30 Hz) is Omni-
directional and produces constant phase regardless of a receiver's bearing from the
VOR. Amplitude modulated variable phase signal (30 Hz) is directional signal, creat-
ed by electronically rotated antenna pattern [17]. The on-board receiver of VOR ex-
tracts both sub-signals in amplitude and phase demodulators with further counting
phase difference. The phase difference in VOR is the same with magnetic bearing
angle from a ground station.
4 Threats of positioning by navigational aids
Both VOR and DME use communication lines in the measurement cycle (see Fig.3).
DME communication handshake requires two communication channels at different
frequencies. VOR uses only one frequency for transmitting all required for navigation
data with AM and FM separation. Thus, ground navigational aids network operation
requires some amount of VHF and UHF bands spectrum. Communication channels at
these frequencies may be simply affected by interference or jammed. Also, radio
waves at this spectrum are propagated at direct line of sight, thus communication line
can be guaranteed only within specific operational volume, constructed taking into
account technical characteristics of equipment and radio waves propagation model.
4.1 Radio Frequency Interference
In general, a thereat of Radio Frequency Interference (RFI) is caused by the presence
in the communication channel of one radio frequency another than information sig-
nals. In this case, all other signals can be considered as a noise for particular data
transmission channel. RFI can be produced by any device that conducts or radiates
radiofrequency energy. Also, source of RFI may be caused by natural phenomena,
such as lighting or solar flares. As a threat to navigational aids, RFI usually is caused
by improper functioning of radio-transmitting equipment. In some cases RFI may be a
result of multipath behavior of radio wave propagation, caused by radio waves multi-
ple reflections from high artificial constructions or natural elements of relief (such as
trees, hills, and mountains). Presence of multipath can change operational volume of
radio transmitting equipment significantly and lead to unintentional interference with
availability area of navigational aid. Computer-based simulation of radio frequency
mitigation with near-located transmitters is required to study and prevent a navigation
lost, taking into account elevation and environmental models.
4.2 Jamming and spoofing of navigation functionality
Jamming of navigational aids can be considered only as an illegal activity and can be
found in different military applications. In order to provide effective noise jammer it
is required a valuable level of transmitting power to effect airplane receiver that is
located at high altitude. National stationary radio frequency monitoring stations can
easily detect location of jammer and limit transmission power. Thus, jamming of
navigational aids is not a “real” threat for civil aviation applications according to safe-
ty statistics.
Spoofing is another important threat that may take place in case of targeting action
on airplane navigation system. Spoofing is an illegal act of influence via communica-
tion channel on some navigation system in order to replace actual transmission data
with outdated data. Usage of wrong data in navigation algorithms will result in a mal-
function of equipment. In this case spoofing is much more significant threat than
jamming, because navigation equipment can not detect historical changes in signals
and continues its operation with generation of wrong data.
VOR communication line is a simplex that makes this navigational aid sustainable
for spoofing acts. But, DME is not protected according to unencrypted data transmis-
sion in the communication channel. Also, DME uses omnidirectional antenna patterns
with high transmission power, that makes receiving and detection of airplane interro-
gation easy.
One of the most challenging tasks is to detect presence of wrong navigation signal.
In case of DME, a comparison of predicted distance and measured is the only solu-
tion. Big difference between them indicates about presence of abnormal data and
should initiate a new measurement cycle or be a cause for changing DME frequency.
For navigational aid data prediction dead reckoning method, linear extrapolation, or
different regression models can be used.
Similar to GNSS an adaptive pattern array is a possible solution in case of detected
direction of jamming/spoofing source of a radio signal that can be implemented in on-
board equipment of DME interrogator and VOR receiver.
4.3 Air navigation Data Base error
Algorithms of airplane position estimation by AoA and ToA are grounded on solv-
ing a system of linear or nonlinear navigation equation with exactly known naviga-
tional aids location [14]. Moreover, during measurement process FMS needs actual
channel or radiofrequency of DME or VOR. Coordinates and other technical data
related to each navigational aid are held inside of air navigation database in FMS
memory. The outdated database may cause a serious threat for the whole positioning
process. In common case, coordinates are changed not very often, while operational
channel may be changed. Usage of not valid data may cause spending a lot of time in
process of navigational aid pair selection, due to multiple interrogations of unused
channels and dismissing actual operation ground facility. Monthly air navigation da-
tabase updating helps to keep navigational aids data valid to support worldwide navi-
gation. Also, some FMS supports automatic database updating via wireless connec-
tion.
4.4 Threats of positioning related to availability area
Navigational aids can perform services only within their operation volume. This
volume is a result of communication line support between an airplane and ground-
based equipment. Geometry and shape of navigational aid service volume is a result
of antenna pattern, antenna gain functions, radio waves propagation models in free
space, influence of tropospheric oscillation, technical characteristics of equipment,
Earth surface and altitudinal artificial construction influence into radio waves propa-
gation.
Common FMS may use standard service volume of navigational aid in positioning
algorithms or using DME in a searching mode, sequential requesting all channels.
Standard service volume defines space inside which signals of navigational aid can be
fixed on board of airplane with enough level of signal/noise ratio for supporting
communication channel data exchange. However, results of real signal/noise study,
obtained during flight inspection of airspace, indicate two times wider service volume
in comparison with standard shape. Thus, services of navigational aid may be availa-
ble out of standard service volume, but there is no guaranty of required minimum
level of signal/noise. Positioning algorithms of FMS which uses only standard service
volume in optimal pair procedure may miss numerous pairs with potentially better
performance. Interference and jamming also affect the service volume of navigational
aid cutting a volume of acting electronic equipment. Thus, usage of not complete
volume data is another threat for positioning by navigational aids inside of FMS.
As a solution for this problem an application of advanced algorithms of naviga-
tional aids availability estimation taking into account technical characteristics of
communication equipment and influence of Earth into radio waves propagation may
be considered [18]. At least oscillation in troposphere, diffraction and refraction mod-
els should be applied. A line of sight screening within length of communication line
inside of digital elevation model data can be considered as a simple diffraction model.
More advanced diffraction models can consider individual characteristics of surface
and support bending and attenuation of radio waves due to edges. Unfortunately,
availability of navigational aids for the whole airplane trajectory can not be solved by
analytical approach, due to complexity of task. A list of available navigational aids
can be reached by applying an iterative approach [18] dividing investigation airspace
into elementary particles. In this case, dimensions of elementary particle define the
accuracy of approach. The boundary of 3D group of elements with the same charac-
teristics creates an operation volume of navigational aids.
According to regulation [16], an airplane navigation system has to follow perfor-
mance requirements within investigated airspace. Accuracy of positioning system
depends on geometry of navigational aids ground network [13, 14] that should be
taken into account at availability estimation level. Performance regulation specifies
the value of Total System Error (TSE) that should be reached. TSE includes two basic
components: Flight Technical (FTE) and Navigation System (NSE)Errors [16]. NSE
utilizes an accuracy of positioning system. Estimation of availability volume of navi-
gational aids network has to be performed taking into account required level of TSE.
The TSE value for Ukrainian controlled airspace is defined by RNP/RNAV 1 at level
of 1NM [19, 20]. Results of estimation of availability volume of positioning by na-
tional navigational aids network are represented in Fig. 4 and Fig. 5. Ukrainian navi-
gational aids consist of 12DMEs (BAH, IHA, IHR, IKI, IKV, KSN, KVR, ILO, ILV,
STB, VIN, YHT) and 8 VOR/DMEs (BRP, DNP, IVF, KHR, KVH, LIV, ODS, SLV)
[21].In computer-based simulation we use coordinates of navigational aids locations
together with their technical characteristics, Digital elevation model of relief for
frame between 23° and 40° of latitude; 43° and 52° of longitude [22].
Fig. 4. Airspace volume of DME/DME availability for positioning by optimal pair
Fig. 5. Airspace volume of VOR/DME availability for positioning by optimal pair
Also, results of navigational aids availability estimation can be represented in the
form of cutting volume at particular flight level in case of study some gaps in airspace
performance.
5 Conclusion
Operation of DME and VOR navigation equipment is grounded on successful data
transmission in radio communication channels. Threats that can affect communication
lines between ground navigational aids network and airplane reduce performance of
positioning dramatically due to reduced number of navigation parameters. We consid-
er influence of possible interference from malfunction of ground radio equipment,
unintentional jamming and spoofing problem, air navigation database error and avail-
ability area estimation model as main threats. Interference and jamming can be easily
detected by level of noise on board of airplane and switch to use another ground sta-
tion. Spoofing problem is not common according to intentional behavior in military
application, however the easiest solution to this problem can be found by simple cor-
relation estimation between actual and predicted navigation signals. Application of
more advanced simulation of radio waves propagation models and accurate technical
data reduce an error related to wrong decision of optimal pair of navigational aids for
positioning.
Obtained results indicate that protection of positioning algorithms can be applied at
software level of FMS by applying particular algorithms of threat detection and
avoiding usage of damaged navigation data in positioning process.
References
1. Mailaender, L.: Comparing geo-location bounds for TOA, TDOA, and round-trip TOA. In:
IEEE International Symposium on Personal, Indoor and Mobile Radio Communications,
pp. 1-5. IEEE, Athens(2007).
2. Yan, Q., Chen, J., Ottoy, G., Cox, B., Strycker, L.: An accurate AOA localization method
based on unreliable sensor detection. In: IEEE Sensors Applications Symposium (SAS),
pp. 1-6. IEEE (2018).
3. AC 00-31A U.S. National Aviation Standard for the Very High Frequency Omnidirection-
al Radio Range (VOR) / Distance Measuring Equipment (DME) / Tactical Air Navigation
(TACAN) Systems. FAA(1982)
4. Solomentsev, O.,Zaliskyi, M.: Correlated Failures Analysis in Navigation System. In: 5th
International Conference on Methods and Systems of Navigation and Motion Control
(MSNMC) ,pp. 41-44. IEEE, Kyiv (2018).
5. Clancy, T., Goergen, N.: Security in cognitive radio networks: Threats and mitigation. In:
3rd International Conference on Cognitive Radio Oriented Wireless Networks and Com-
munications (CrownCom 2008), pp. 1-8. IEEE (2008).
6. Lubbers, B., Mildner, S., Onincx, P., Scheele, A.: A study on the accuracy of GPS posi-
tioning during jamming. In: Navigation World Congress: IAIN International Association
of Institutes, pp. 1-6. IEEE, (2015).
7. Han,S., Gong, Z., Meng, W., Li, C., Gu, X.: Future Alternative Positioning, Navigation,
and Timing Techniques: A Survey. Wireless Communications. IEEE, 23(6), 154-
160(2016).
8. Kaplan, E., Hegarty, C..: Understanding GPS: principles and applications. 2ndedn. Artech
house, London (2005).
9. Kutsenko,O., Ilnytska,S., Konin,V.: Investigation of the residual tropospheric error influ-
ence on the coordinate determination accuracy in a satellite landing system. Aviation22(4),
156-165 (2018).
10. Narins,M., Eldredge,L., Enge,P., Harrison,M., Kenagy,R., Lo, S.: Alternative Position,
Navigation, and Timing - The Need for Robust Radionavigation. In: Global Navigation
Satellite Systems: Report of a Joint Workshop of the National Academy of Engineering
and the Chinese Academy of Engineering, pp. 119-136. The National Academies Press
(2012).
11. Aviation Safety Reporting System. Database Online,NASA,
https://asrs.arc.nasa.gov/search/database.html
12. Shvets, V., Ilnytska, S.,Kutsenko, O.: Application of Computer Modelling in Adaptive
Compensation of Interferences on Global Navigation Satellite Systems. In Shmelova,
T.,Sikirda, Y., Rizun,N.,Kucherov, D. (eds.) Cases on Modern Computer Systems in Avia-
tion pp. 339-380. IGI Global, Hershey, PA (2019).
13. Ostroumov, I.V.,Kuzmenko,N.S.: Compatibility analysis of multi signal processing in
APNT with current navigation infrastructure. Telecommunications and Radio Engineering
77(3), 211-223 (2018).
14. Kuzmenko,N.S., Ostroumov,I.V., Marais,K.: An Accuracy and Availability Estimation of
Aircraft Positioning by Navigational Aids. In: 5th International Conference Methods and
Systems of Navigation and Motion Control: MSNMC 2018, pp. 36-40.IEEE, Kyiv(2018).
15. Ostroumov, I.V.,Kuzmenko,N.S., Marais,K.:Optimal Pair of Navigational Aids Selection.
In: 5th International Conference Methods and Systems of Navigation and Motion Control:
MSNMC 2018, pp. 32–35.IEEE, Kyiv(2018).
16. Performance-Based Navigation (PBN) Manual. Doc 9613. ICAO(2008).
17. Aeronautical telecommunications. Volume 1 Radio Navigational Aids. Annex 10 to the
Convention on International Civil Aviation. ICAO (2006).
18. Kuzmenko, N.S., Ostroumov, I.V.: Performance Analysis of Positioning System by Navi-
gational Aids in Three Dimensional Space. In: 1st International Conference System Analy-
sis & Intelligent Computing: SAIC 2018, pp. 101-104. IEEE, Kyiv (2018).
19. UkSATSE'snavigation infrastructure development roadmap for 2015 to provide navigation
based on Performance. UkSATSE(2017).
20. Ostroumov, I.V., Kharchenko, V.P., Kuzmenko, N.S.: An airspace analysis according to
area navigation requirements. Aviation 23(2), 36-42 (2019).
21. Aeronautical Information Publication (AIP) of Ukraine. Ukrainian State Air Traffic Ser-
vices Enterprise (2018).
22. Shuttle Radar Topography Mission. U.S. Geological Survey's, Long Term Archive at the
National Center for Earth Resource Observations and Science, www. lta.cr.usgs.gov