603

1 INTRODUCTION

At the beginning of the 20th century, the use of radio

waves caused the genesis of the wireless

communications era. Soon after, the same radio waves

contributed to revolutionizing navigation. In this way,

the era of radio-navigation began. Its origins are

mainly hyperbolic terrestrial navigation systems

(TNSs). For this type of systems, we can include the

Decca Navigator System, Consol, Omega, Syledis,

Loran-A, Loran-C, Chayka, and Jemioluszka [1–6].

The TNSs were mainly used in sea and air transport.

In addition, ground-based augmentation systems

(GBASs) were developed mainly for aviation, e.g., the

ILS, MLS, DME, VOR, and TACAN [7].

In the late 1970s, the United States developed the

first navigation satellite system (NSS), i.e., the Transit,

also known as the Navy NSS or NAVSAT [5]. The

positioning in the Transit was based on the Doppler

effect. His successor is the GPS–NAVSTAR (Global

Positioning System – Navigation Signal Timing and

Ranging), i.e., the first global NSS (GNSS), which is

widely used in civil applications [1,8,9]. At present,

the GNSSs have dominated determining the position

and direction of objects' movement in both air, sea,

and land transport. The Russian GLONASS and

European Galileo are also counted among the GNSSs

[1,8,9]. In addition, regional NSSs (RNSSs) are

available in certain regions of the world, including the

Chinese BeiDou (BDS), Japanese QZSS, Indian

NAVIC [1,8,9]. From 2020, the BDS will gain the

status of the global system. Positioning in the GNSSs

and RNSSs is based on time of arrival (TOA)

measurements and a multilateration method,

popularly known as a time difference of arrival

(TDOA) [10]. In this case, a point localization in space

using the TDOA requires receiving a signal from at

Mobile Radio Beacons in Coastal Reserved Navigation

System for Ships

J.M. Kelner & C. Ziółkowski

Military University of Technology, Warsaw, Poland

ABSTRACT: At the turn of the 20th and 21st centuries, Global Navigation Satellite Systems (GNSSs) dominated

navigation in air, sea, and land. Then, medium-range and long-range terrestrial navigation systems (TNSs)

ceased to be developed. However, with the development of GNSS jamming and spoofing techniques, the TNSs

are being re-developed, such as the Enhanced Loran. The Polish Ministry of Defense plans to develop and

implement a medium-range backup navigation system for the Polish Navy which will operate in the Baltic

coastal zone. This plan is a part of the global trend. This paper presents the concept of a reserve TNS (RNS) that

is based on the signal Doppler frequency (SDF) location method. In 2016, the concept of the RNS, which is

based on stationary radio beacons located on coastal lighthouses, has been presented. From the military

viewpoint, the use of the mobile radio beacons, which may change their location, is more justified. Therefore,

the paper presents an idea of using the mobile beacons for this purpose. In this paper, effectiveness of the

mobile RNS is shown based on simulation studies.

http://www.transnav.eu

the

International Journal

on Marine Navigation

and Safet

y of Sea Transportation

Volume 14

Number 3

September 2020

DOI:

10.12716/1001.14.03.11

604

least four satellites of the NSS. This method is the

basis of most hyperbolic systems, including the TNSs.

Additionally, the GNSSs and RNSSs use code-

division multiple access (CDMA) technique, with the

exception of the GLONASS, which is based on

frequency-division multiple access (FDMA) [9].

Satellite-based augmentation systems (SBASs) [1,8,9]

are widely used in aviation and also in maritime [11].

To the SBASs, we may include, i.a., the American

WAAS, European EGNOS, Japanese MSAS, Indian

GAGAN, Russian SDCM, and Chinese SNAS. For

supporting systems, the French DORIS (Doppler

Orbitography and Radio-positioning Integrated by

Satellite) is also included [12]. This system based on

the Doppler effect ensures high positioning accuracy.

A space segment is an essential part of all satellite

systems. In that, the availability of the system over a

whole or major area of the Earth is assured. However,

this issue causes the costs of implementing and

maintaining such systems are very high. Most of the

GNSSs and RNSSs are military systems with the

possibility of commercial civil applications. The

Galileo and QZSS are only civilian systems. The

availability of receiving devices, coverage for the

NSSs, and high positioning precision in relation to the

TNSs caused that at the end of the 20th century, most

of the TNSs ceased to be supported and operated.

While the GBASs are still used. Currently, the eLoran

is the only operating TNS [13,14]. It consists of about

forty stations located mainly along the coasts of the

United States, the European Union, and Southeast

Asia. This provides coverage for the northern parts of

the Indian, Pacific, and Atlantic Oceans.

Over the past thirty years, we have been observing

the rapid development of the GNSSs. At the same

time, the development of mobile cellular networks

has provided access to cheap and universal GPS

receivers in smartphones. These two aspects have

resulted in the dissemination of the satellite

navigation and location-based services (LBSs) [15],

especially in civilian land traffic. On the other hand,

the widespread use of the NSSs is a secondary reason

for reducing the security of countries that do not have

their own NSS, as well as those that provide such the

system. Lowering safety results from several

premises. First, the military GNSS administrator may

cause the signal to be turned off or decreasing the

positioning accuracy for civilians in a specific area,

e.g., military operations. In this case, military users

can use code signals unavailable to civilians.

Secondly, elements of the ground control or space

segments may be destroyed by the enemy. Thirdly, at

the last time, dynamic development of jamming and

spoofing techniques dedicated to the GNSS is

observed [16–19]. In this case, the use of the satellite

navigation may be impossible or cause false results.

The second and third reasons are a serious threat to

military systems, including those countries that have

own GNSS or RNSS. On the other hand, the

aforementioned development of GNSSs resulted in

the break of the support and development of

alternative positioning methods, such as the TNSs.

In recent years, the development of the new TNSs

is again considered seriously by many countries,

especially for army needs in a period and area of

military operations. For example, in 2012, the

Armament Inspectorate of the Polish Ministry of

Defense resumed an analytical-conceptual phase in

development terms of “The medium-range radio-

navigation system for the Polish Navy” [20]. The

result of these activities is the “The medium-range

mobile radio-navigation system” developed currently

by the Research and Development Center for

Maritime Technology [21]. This system will be based

on the effects of a research team from the Gdańsk

University of Technology. This team has developed

the TDOA-based asynchronous and self-organizing

navigation system called the AEGIR [22–24]. The

work undertaken by the NATO Science & Technology

Organization (STO) and the European Defense

Agency in the area of “Navigation in GNSS denied

environment” is another premise in this direction [25–

27]. However, a monitoring system of own combat

units' location named the blue force tracking (BFT)

[28–31] belongs to the priorities of modernization of

the Polish Army. In this case, the positioning the

soldiers, equipment, and units of own forces in the

absence of the GNSS access is also considered.

In 2016, a proposal to use a coastal radio-beacon

(RB) system and the signal Doppler frequency (SDF)

location method for positioning ships in a coastal

zone was presented [20]. The SDF method [32–34],

like the previously mentioned Transit and DORIS, as

well as the COSPAS-SARSAT [35,36], a satellite

system used in search and rescue (SAR) operations,

are based on the Doppler effect. In [20], the results of

simulation studies for scenarios in the Baltic Sea are

presented. The use of the stationary RBs is a good

solution in peacetime. However, in the case of the

military operations, the reserved radio-navigation

system should base on mobile RBs. The purpose of

this paper is to present the concept of a mobile reserve

navigation system (MRNS) for ships in the coastal

zone. The effectiveness of vessel positioning using the

developed system is presented based on simulation

studies.

The remainder of the paper is organized as

follows. In Section 2, the characteristics of the

transmitting and receiving parts of the MRNS and the

SDF method are presented. Section 3 contains a

description of a scenario and assumptions for

simulation studies. The simulation results illustrating

the accuracy of the ship positioning are shown in

Section 4. The paper is finished with final remarks

and a summary.

2 MOBILE RESERVED NAVIGATION SYSTEM

2.1 System Concept

In general, the concept of the MRNS is based on the

assumptions of the stationary reserved TNS for ships,

which are presented in [20], i.e.,

− the system consists of several or dozen RBs

operating in an asynchronous broadcasting mode,

− multi-antenna and multi-frequency-channel

receiving system located on the ship enables

simultaneous analysis of signals from the several

RBs,

− the SDF is used to determine the position of the

ship, i.e., the position of a reference receiving

antenna on this ship.

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The significant differences between the stationary

and mobile versions mainly concern the transmitting

part of the system. Stationary beacons are the core of

the system presented in [20]. Their deployment was

planned in existing coastal infrastructure.

Considering propagation properties of radio waves,

we proposed using lighthouses as points located high

above sea level. In the MRNS, the RBs are placed on

vehicles that can change position. Each new position

brings changes in the transmitting signal.

A detailed description of the mobile RB is

presented in Section 2.2. The receiving part of the

system located on the ship is described in Section 2.3.

In Section 2.4, the SDF implementation method in the

receiving part of the MRNS is contained.

2.2 Transmitting part of system

The transmitting part of the MRNS consists of K

mobile RBs. The concept of the RB is depicted in

Figure 1.

Figure 1. Structure of mobile RB

The main components of the transmitting part are

identical to those in the stationary version of the RB

[20], i.e., the transmitting antenna, power amplifier,

and signal generator.

The generator should be made in the software-

defined radio (SDR) technology [37–39] in order to be

able to transmit different signal structures

(waveforms). In this case, emitting the current

position of the RB is important. In the stationary

system, the RB transmits one type of the signal

because its position is fixed. The microcomputer

connected to the SDR transmitter provides the ability

to generate the broadcasting signals with information

about the current position of the RB.

The RB devices are placed on board a wheeled

vehicle. The proposed MRNS is based on the Doppler

effect. Therefore, the frequency stability of each signal

source is very important [40]. Hence, we suggest

equipping each RB with a rubidium or cesium

frequency standard.

In order to ensure a larger operation range of the

RB, each vehicle should be equipped with a hydraulic

or pneumatic telescopic (locking) mast. These masts

allow increasing the antenna height up to 50 m.

Therefore, the vehicle should be also equipped with

hydraulic stabilizers using in technical vehicles. The

stabilizers are necessary to ensure stable operation of

the mobile RB in different weather conditions, e.g.,

strong wind, stormy weather, etc. A time of assembly

and disassembly of the antenna mast should be as

short as possible, which will allow for a quick change

of the vehicle location.

Knowing the exact position of the RB is essential

for its proper operation. Hence, the identification of

potential points on the coast, from which the RB may

transmit the signal, is required. At such points,

averaged position measurements using the GNSS

should be performed in the peacetime. In the field,

appropriate marking of these points should be

introduced, e.g., similar to geodetic reference points

(benchmarks). This point may explicitly give

geographic coordinates, e.g., on a nameplate or only a

benchmark number associated with the coordinates in

the system. This approach allows the use of the

mobile RBs in GNSS-denied conditions.

In addition, the RB should be equipped with a

GNSS receiver to operate in availability conditions of

the GNSS signal. We may imagine a scenario of using

the MRNS when the GNSS is available on land and

jamming or spoofing at a sea. In this case, the RB may

emit the signals from any unmarked point on the

coast. Then, the GNSS receiver should be connected to

the SDR generator via the microcomputer. The GNSS

receiver antenna should be placed outside the vehicle

and an application that controls the waveform

generation should provide an appropriate coordinate

conversion between the GNSS and RB antennas.

In addition to an onboard power supply of the RB

components, the vehicle should be equipped with a

backup power source, e.g., an engine generator and

uninterruptible power supply (UPS).

In [20], we assumed that individual RBs transmit

phase-shift keying (PSK) signals. The location

methodology of a PSK signal source using the SDF is

presented in [41].

2.3 Receiving part of system

The receiving part of the MRSN is not changed

compared to the stationary system presented in [20].

In Figure 2, an exemplary arrangement of the

receiving antennas (RAs) on the shipboard is

illustrated.

1 is the reference antenna to which the ship

position is determined in the MRNS. From the

viewpoint of the ship antenna system, the proposed

solution works in the multi-input-multi-output

(MIMO) or single-input-multi-output (SIMO) mode

for the vessel positioning based on multiple RBs or

only one, respectively.

The receiver in the MRSN is a multi-channel

device. On the one hand, this means that the signals

from J RAs are fed to the receiver. On the other hand,

each signal supplied from the jth RA ( j = 1, 2, ..., J )

contains the signals from K RBs that operate on K

frequency sub-bands (channels). For this reason, the

receiver is made in the SDR technology [37–39].

606

Figure 2. Exemplary arrangement of RAs on shipboard [20]

Signal processing carries out in parallel using a

multi-threaded application. The signal from each

antenna is divided into frequency sub-bands. For this

purpose, digital filtration is carried out. In each sub-

band, the information about the RB position is

decoded and a Doppler frequency shift (DFS) of the

received signal is determined. For each RB, estimated

DFS changes versus time, so-called the Doppler curve,

are the basis for determining the ship position in the

SDF method.

2.4 SDF implementation

An analytical solution of a wave equation for a

moving transmitter (Tx) in the form of relationship

between the DFS and the Tx coordinates, (x

y0, z0),

and time, t, [42]

( )

0 max

0 00

x vt

ft f

x vt y z

−

≅

− ++

(1)

is the basis of the SDF method, where f

D max = f0·v / c =

the maximum DFS; f

0 = the carrier frequency of the

transmitted signal; v = the speed of the moving object

(Tx or Rx); and c = the speed of light.

The coordinates of the emission source location

may be determined based on the transformation (1)

and assuming the DFS measurements in a few time-

moments. In a simplified two-dimensional (2D)

version of the SDF, the estimated coordinates of the

localized object,

( )

,xy



, are calculated on following

formulas [32–34]

( ) ( )

( ) ( ) (

)

( ) ( )

11 2 2

12 1 2

tAt tAt

At At

t t At At

yv z

At At

−

≅



−







−



≅± −





−







(2)

where

( )

1 Ft

−

( )

max

≅



(3)

where

(

)



and F(t) = the estimated and

normalized DFSs, respectively.

Equations (1)-(3) constitute the essence of the SDF.

In the 2D method, it was assumed that one of the

coordinates, z

0, is known. In the marine scenario, z0 is

definitely smaller (in the order of single meters) than

the other two coordinates (from several hundred

meters to several dozen kilometers). Thus, a

difference between the transmitting and receiving

antenna heights, i.e., for the analyzed RB and RA,

measured against sea level is a good approximation of

0. A three-dimensional (3D) version of the SDF is

presented in [33]. In this case, a change of the object

movement direction is required.

In a navigation application based on the SDF, in

the first step, the coordinates of the RBs are

determined in the local coordinate system associated

with Rx. In the second step, the estimated coordinates

of the RBs are referenced to the actual positions

contained in the received signal. On this basis, the Rx

(ship) position is determined.

From the technical viewpoint, two parameters, ΔT

and T

A, are significant. ΔT is the analysis time of the

received signal which is used to determine the

instantaneous DFS. Whereas, T

A is the averaging time

of the Doppler curve, which is used to estimate the

localized-object coordinates, i.e., the RB. Therefore,

estimation of the RB position is based on N discrete

instantaneous values of the DFSs,





(4)

The ship coordinates are calculated in the same

way as in [20]. For each k and j ( k = 1, 2, ..., K,

j = 1, 2, ..., J ), the set of the DFSs, f

D k,l (tn)

( n = 1, 2, ..., N ), creates the Doppler curve. For the

positioning of each RB, the SDF uses (2) and

fragments of these Doppler curves. For T

A and each

jth antenna-channel (RA) of the Rx, the position of the

kth RB is determined as follow [20]

( ) ( )

( ) ( ) ( )

( ) ( )

1, 1 1, 2

RB ,

,1 ,2

12 ,1 ,2

RB , RB ,

,1 ,2

RB , 0RB 0 RA

kj kj

kj k j

tA t tA t

At At

ttAtAt

At At

z z zz

−





−







−



=±−



−









= −−



(5)

where

( )

(

)

( )

−

( )

max

Dk j

(6)

and f

Dk max = f0k·v / c; f0k = the carrier frequency of the kth

RB.

Based on the kth RB signal, the vessel position is

obtained by averaging and transforming (5) [20]

607

( )

(

)

(

)

( )

RB , RA

RB , RA 0RB

RB , RA

RB , RA 0RB

0RB RB , RA 0

cos

sin

cos

k kj j

kj j k

k kj j

kj j k

k k kj j

x xx

yy x

y xx

yy y

zz z z z





= +











+ ++













=−+













+ ++













=− +=









∑

(7)

where α = 90° – β; and β = the direction of the ship

movement relative to the North.

If the Rx uses only the signal from a single RB,

then the current position of the ship is

(x,

y, z) = (xk, yk, zk). If the Rx receives the signals from

more than one RB, the averaging process of the ship

position is additionally executed. In this case, for K

analyzed RBs, the weighted-mean algorithm is used

[43]

( )

111

, , , ,

KKK

kk kk kk

kkk

xyz wx wy wz

= = =







∑∑∑

(8)

where

( )

k kj

w Ft

= −

∑

and

∑

(9)

The proposed averaging algorithm considers the

Doppler curve shapes and is more accurate than an

arithmetic-mean [43].

3 SCENARIO AND ASSUMPTIONS FOR

SIMULATION STUDIES

Simulation studies are carried out for the spatial

scenario shown in Figure 3. In this case, we assumed

that three RBs, marked as RB1, RB2, and RB3, are

located on a shore of the Baltic Sea in localities of

Łazy, Darłowo, and Jarosławiec, respectively. The

position coordinates in WGS 84 and UMT for these

RBs and three points, i.e., P1, P2, and P3, which

determine two measurement routes, P1→P2 and

P1→P3, are included in Table 1.

Table 1. Coordinates of RBs and points of beginning and

ending measurement routes in WGS 84 and UMT systems

(based on Google Earth Pro)

_______________________________________________

Point WGS 84 UMT

Latitude Longitude Northing Easting

(° N) (° E) (m N) (m E)

_______________________________________________

RB1 54.308662 16.201313 6018530 578160

RB2 54.432433 16.377603 6032510 589360

RB3 54.535533 16.540890 6044200 599700

P1 54.594149 16.553212 6050739 600353

P2 54.331924 16.028052 6020940 566850

P3 54.531990 15.867716 6043060 556150

_______________________________________________

Figure 3. Spatial scenario for simulation studies (based on

Google Earth Pro)

As described in Section 2.1, each RB is equipped

with the telescopic mast. In simulations, the mast

height is equal 50

m. For simplicity, we assumed that

each vehicle with the RB is located 10

m above sea

level. Hence, for all RBs, the identical antenna height

is defined, i.e., h

Tx = 60 m. Location of RAs on the

ship was assumed as in Figure 2, according to the

assumptions shown in [20]. Assuming that the height

of the lowest located RAs, i.e., for RA

5 and RA6, is

Rx =

m above sea level, then a radio horizon for

each RB is about 45

km. Therefore, line-of-sight (LOS)

conditions are provided in every point on two

analyzed measurement routes.

Other assumptions for simulation studies are

similar to shown in [20]. The RBs transmit PSK signals

with bandwidth B

= 200 kHz at frequencies

01 = 1860 MHz, f02 = 1860.3 MHz, and f03 = 1860.6 MHz,

respectively for RB1, RB2, and RB3. On the

frequencies f

0k + 0.75B, k = 1, 2, 3, the pilot signal used

in the SDF is additionally transmitted. The minimum

carrier-to-noise ratio is CNR

min = 5 dB. The basic

frequency of the spectral analysis is 1

mHz.

Additionally, we adopted ΔT

= 1 s and TA

240

s. The

speed of the ship relative to land is v

= 20 w. ≅ 10.3 m/s.

4 RESULTS OF SIMULATION STUDIES

The purpose of the carried out simulation tests is to

assess the positioning accuracy and to present several

aspects of the SDF use in the MRNS. In Section 4.1,

the comparison of the arithmetic and weighted

averaging the ship coordinates is shown. This analysis

is based on the results obtained for the measurement

route P1→P2. Section 4.2 contains a comparison of the

608

positioning results at two considered measurement

routes.

The basic measure of positioning accuracy is the

position error defined as follows [33]

( ) ( ) ( )

2 22

0 00

ΔR xx yy zz= − +− +−

(10)

where (x,

z) and (x,

z) = the estimated and real

coordinates of the vessel, respectively.

4.1 Comparison of arithmetic and weighted averaging

The simulation studies are carried out for the

measuring route P1→P2 and the assumptions

described in Section 3. Figures 4 and 5 show the ship

position at the route based on the arithmetic and

weighted averaging, respectively. Additionally,

average position errors for the entire route are

marked with dashed lines.

Figure 4. Ship position error at route P1→P2 using

arithmetic averaging

Figure 5. Ship position error at route P1→P2 using weighted

averaging

The obtained results of the measure ΔR show that

the application of the weighted average described by

(8) is more effective than the arithmetic average. In

the case of the weighted averaging, the ship position

error on the route P1→P2 does not exceed 70 m. The

average error on the entire route can be used to

compare both methods. These errors are equal to

18.9 m and 183.6 m for the weighted and arithmetic

averages, respectively.

In order to assess the qualitative positioning of the

ship using the two analyzed averaging methods, a

cumulative distribution function (CDF) is determined

for the position error, F(ΔR). These CDFs are

illustrated in Figure 6. The results obtained confirm

the greater accuracy of estimating the ship position

using the weighted average.

Figure 6. CDFs of ship position error at route P1→P2 for

two averaging methods

4.2 Comparison of ship positioning at different

measurement routes

The two measurement routes shown in Figure 3 differ

in their location relative to three analyzed RBs. This

transfers into other Doppler curves for three RBs

obtained in the ship receiver at the individual

measurement routes. Changes of the theoretical DFSs

calculated based on (1) are depicted in Figures 7 and 8

for the routes P1→P2 and P1→P3, respectively.

Figure 7. Doppler curves for route P1→P2

Figure 8. Doppler curves for route P1→P3

Based on the shown Doppler curves, we can see

that the DFSs changes are more diverse for the route

609

P1→P2. Using the weighted average in the SDF

reduces the impact of the DFS variability on the

positioning accuracy.

In Figure 9, the vessel position error along its

movement trajectory at the route P1→P3 for the

weighted average is illustrated. Analogous results for

the route P1→P2 are depicted in Figure 5.

Figure 9. Ship position error at route P1→P3 using weighted

averaging

Due to the weighted average, the results obtained

for both routes are similar. In this case, the average

error for the entire route is equal to 19.5 m. This is

also clearly visible in the CDF graphs shown in Figure

10.

Figure 10. CDFs for two analyzed routes

The obtained results confirm the effectiveness of

using the SDF method for the vessel positioning in the

coastal zone.

5 CONCLUSION

In this paper, the concept of using the mobile RBs in

the backup navigation system for the vessels in the

coastal zone was presented. Such the system may be

especially used in the denied-GNSS conditions. In the

paper, we have outlined the major differences

between the SDF-based stationery and mobile

navigation systems. The effectiveness of the MRNS

was confirmed based on the simulation studies for

two selected measurement routes and three mobile

RBs. The use of the weighted average in the SDF

method allows for decreasing the ship positioning

errors. In this case, the average position error was less

than 20 m for the analyzed measurement scenario.

The obtained results coincide with those presented for

the stationary backup system [20].

ACKNOWLEDGMENTS

This work was developed within a framework of the

Research Grant “Basic research in sensor technology field

using innovative data processing methods” no. GBMON/13-

996/2018/WAT sponsored by the Polish Ministry of Defense.

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