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Article
Study on the Positioning Accuracy of GNSS/INS Systems
Supported by DGPS and RTK Receivers for
Hydrographic Surveys
Andrzej Stateczny 1 , Cezary Specht 2 , Mariusz Specht 3,4, * , David Brčić 5 , Alen Jugović 5 ,
Szymon Widźgowski 4 , Marta Wiśniewska 4 and Oktawia Lewicka 2
1
2
3
4
5
*
Citation: Stateczny, A.; Specht, C.;
Specht, M.; Brčić, D.; Jugović, A.;
Widźgowski, S.; Wiśniewska, M.;
Lewicka, O. Study on the Positioning
Accuracy of GNSS/INS Systems
Supported by DGPS and RTK
Receivers for Hydrographic Surveys.
Energies 2021, 14, 7413. https://
doi.org/10.3390/en14217413
Academic Editor: Anibal De Almeida
Received: 10 October 2021
Accepted: 4 November 2021
Published: 7 November 2021
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affiliations.
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
Department of Geodesy, Gdańsk University of Technology, Gabriela Narutowicza 11-12,
80-233 Gdańsk, Poland; andrzej.stateczny@pg.edu.pl
Department of Geodesy and Oceanography, Gdynia Maritime University, Morska 81-87,
81-225 Gdynia, Poland; c.specht@wn.umg.edu.pl (C.S.); o.lewicka@wn.umg.edu.pl (O.L.)
Department of Transport and Logistics, Gdynia Maritime University, Morska 81-87, 81-225 Gdynia, Poland
Marine Technology Ltd., Wiktora Roszczynialskiego 4-6, 81-521 Gdynia, Poland;
s.widzgowski@marinetechnology.pl (S.W.); m.wisniewska@marinetechnology.pl (M.W.)
Faculty of Maritime Studies, University of Rijeka, Studentska ulica 2, 51000 Rijeka, Croatia;
david.brcic@pfri.uniri.hr (D.B.); alen.jugovic@pfri.uniri.hr (A.J.)
Correspondence: m.specht@wn.umg.edu.pl
Abstract: Hydrographic surveys, in accordance with the International Hydrographic Organization
(IHO) S-44 standard, can be carried out in the following five orders: Exclusive, Special, 1a, 1b and
2, for which minimum accuracy requirements for the applied positioning system have been set
out. They are as follows, respectively: 1, 2, 5, 5 and 20 m, with a confidence level of 95% in twodimensional space. The Global Navigation Satellite System (GNSS) network solutions (accuracy:
2–3 cm (p = 0.95)) and the Differential Global Positioning System (DGPS) (accuracy: 1–2 m (p = 0.95))
are now commonly used positioning methods in hydrography. Due to the fact that a new order
of hydrographic surveys has appeared in the IHO S-44 standard from 2020—Exclusive, looking at
the current positioning accuracy of the DGPS system, it is not known whether it can be used in it.
The aim of this article is to determine the usefulness of GNSS/Inertial Navigation Systems (INS) for
hydrographic surveys. During the research, the following two INSs were used: Ekinox2-U and EllipseD by the SBG Systems, which were supported by DGPS and Real Time Kinematic (RTK) receivers.
GNSS/INS measurements were carried out during the manoeuvring of the Autonomous/Unmanned
Surface Vehicle (ASV/USV) named “HydroDron” on Kłodno lake in Zawory. The acquired data were
processed using the mathematical model that allows us to assess whether any positioning system
at a given point in time meets (or not) the accuracy requirements for each IHO order. The model
was verified taking into account the historical and current test results of the DGPS and RTK systems.
Tests have confirmed that the RTK system meets the requirements of all the IHO orders, even in
situations where it is not functioning 100% properly. Moreover, it was proven that the DGPS system
does not only meet the requirements provided for the most stringent IHO order, i.e., the Exclusive
Order (horizontal position error ≤ 1 m (p = 0.95)). Statistical analyses showed that it was only a few
centimetres away from meeting this criterion. Therefore, it can be expected that soon it will be used
in all the IHO orders.
Keywords: positioning accuracy; positioning availability; Global Navigation Satellite System (GNSS);
Inertial Navigation System (INS); Differential Global Positioning System (DGPS); Real Time Kinematic
(RTK); hydrographic surveys; International Hydrographic Organization (IHO)
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1. Introduction
Hydrographic surveys are among the navigation applications that commonly use
Global Navigation Satellite Systems (GNSS). According to the International Hydrographic
Energies 2021, 14, 7413. https://doi.org/10.3390/en14217413
https://www.mdpi.com/journal/energies
Energies 2021, 14, 7413
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Organization (IHO) S-44 standard [1], they can be implemented in the following five orders:
Exclusive, Special, 1a, 1b and 2. Each of them was assigned a number of requirements,
primarily including the following two defined navigational parameters for the positioning
systems: the maximum permissible positioning accuracy and its confidence level, i.e.,
the availability of a specified position error value that is identical for all the IHO orders,
and amounts to 95%. The characteristics of the IHO orders are presented as follows in a
synthetic manner:
•
•
•
•
•
Exclusive Order—sets down the highest requirements in the field of positioning
accuracy. According to this order, hydrographic surveys are carried out on shallow
waterbodies for which the under-keel clearance is minimal, and the bottom topography
poses a potential hazard to the safety of navigation. Examples of such areas include
harbours, berthing areas and critical areas of fairways and channels. The maximum
permissible position error is 1 m with a confidence level of 95%;
Special Order—applies to the waterbodies for which the under-keel clearance is
critical. Examples of such areas include berthing areas, harbours and critical areas of
fairways and shipping channels. The maximum permissible position error is 1 m with
a confidence level of 95%;
Order 1a—applies to waterbodies with depths of less than 100 m, for which the underkeel clearance is less critical, yet there is a possibility of the occurrence of underwater
objects posing a hazard to safe navigation. The maximum permissible position error
is 5 m + 5% of depth with a confidence level of 95%;
Order 1b—applies to waterbodies with depths of less than 100 m, for which the underkeel clearance is not significant for the expected type of navigation. The maximum
permissible position error is 5 m + 5% of depth with a confidence level of 95%;
Order 2—imposes requirements on the positioning systems (and not only) used for
hydrographic surveys of waterbodies with depths of more than 100 m, where the
general depiction of the bottom is sufficient for the expected type of navigation. The
maximum permissible position error is 20 m + 5% of depth with a confidence level
of 95%.
Since the hydrographic survey orders differ in the requirements for the positioning
accuracy, it is important to know which navigation system is suitable for which IHO orders.
For the purposes of this article, we decided to determine the usefulness of GNSS/Inertial
Navigation Systems (INS) supported by Differential Global Positioning System (DGPS)
and Real Time Kinematic (RTK) for hydrographic surveys.
GNSS systems: Global Positioning System (GPS), GLObal NAvigation Satellite System
(GLONASS), BeiDou Navigation Satellite System (BDS) and Galileo, as well as Ground
Based Augmentation Systems (GBAS) and Satellite Based Augmentation Systems (SBAS) in
combination with inertial devices provided navigation solutions that, in the absence of access
to satellite signals (in tunnels, confined spaces and forested areas), enable the continuous
determination of a moving object’s position [2–4]. GNSS/INS systems can be additionally
supported by the operation of other devices, such as Light Detection And Ranging (LiDAR),
odometers or vision sensors, in order to compensate for INS errors [5–7]. Due to their extensive
capabilities, GNSS/INS systems are primarily used in navigation and transport applications.
These include tests using Unmanned Aerial Vehicles (UAV) [8–10] and Unmanned Surface
Vehicles (USV) [11,12], locating mobile phones [13], indoor [14], terrestrial [15] and space [16]
navigation, geodetic [17–19] and hydrographic surveys [20–22], operating Autonomous
Ground Vehicles (AGV) [23–25], rail transport, in particular for the purposes of High-Speed
Rail (HSR) [26,27], road transport [28–30] or preventing intentional interference [31,32].
In the early 21st century, GNSS geodetic networks became commonly launched by
the geodetic authorities of individual countries. They offered either paid or free-of-charge
real-time and post-processing services [33]. The most popular positioning methods include
the RTK technique and the increasingly common Real Time Network (RTN) technique. The
RTN measurement method consists of developing correction data based on observations
from not a single reference station, as in the case of the RTK technique, but from at least
Energies 2021, 14, 7413
3 of 19
several reference stations. Its advantage is that the position error does not increase with
the distance from the station (even up to 70–80 km) and that the results obtained are
not worse than those for RTK measurements [34]. As the name suggests, GNSS geodetic
networks are widely used in geodetic works. They can also be used in static measurements
to establish and control geodetic control networks, in satellite levelling and in geodynamic
research [35–37]. Moreover, they are used in the implementation works related to the
cadastre and the acquisition of data for the national terrain information system, in precise
engineering measurements for diagnostic and inventory purposes [38,39]. GNSS geodetic
networks are also used in navigation applications and object movement monitoring [40,41].
In addition, there is a possibility of determining the position coordinates with a high
accuracy in the event of the occurrence of unfavourable measurement conditions such as
terrain obstacles [42,43].
The second primary positioning system used in hydrography is the DGPS system. The
idea behind its operation lies in determining the error related to pseudorange observables
and is calculated by comparing the actual value computed using the GNSS receiver and
the “true” value calculated using the satellite and the reference station antenna coordinates.
This difference, referred to as a pseudorange correction, is transmitted within the frequency
range of 283.5–325 kHz to users who use a DGPS receiver and take it into account in the
positioning process [44,45]. Users can achieve accuracies in the order of 1–3 m, depending on
the correction transmission method applied under the DGPS system [46,47]. The DPGS system
enables position determination with accuracies considerably exceeding the autonomous
GPS positioning, which makes it suitable for use, e.g., in hydrography for hydroacoustic
system positioning [48–50], cartography [51], locating mobile devices [52,53], air navigation,
including the use of UAVs [54,55], marine navigation, primarily in coastal shipping and
during the Dynamic Positioning (DP) [56–58], bathymetric surveys of harbours and inland,
as well as marine waters [59], geodetic surveys of the coastal zone [60,61], the autonomous
vehicle positioning process [62–64], precision agriculture for reliable yield mapping or crop
soil variability [65] or even for studying glacier changes [66] and displacements of, e.g.,
dams [67].
Alternatively, the Precise Point Positioning (PPP) can be used, i.e., the technique of
satellite precise absolute positioning. The most important advantage of this method is
the ability to determine the position with high accuracy using only one dual-frequency
GNSS receiver, while not being connected to the regional network or a single reference
station. The PPP eliminates the need to maintain an expensive regional network of RTN
reference stations and allows measurements to be made in areas with an underdeveloped
terrestrial infrastructure. High positioning accuracy is possible with the use of precise
products provided by the International GNSS Service (IGS) [68–70]. The PPP is also used
during the performance of hydrographic surveys [71–73].
This article is structured as follows: Section 2 describes the measurement equipment
(inertial navigation systems by the SBG Systems) that was used when carrying out the
GNSS/INS surveys (including its calibration and configuration). Moreover, the section
presents the method for conducting GNSS/INS measurements and specifies how the data
recorded during the study were processed. Section 3 specifies the accuracy characteristics
of the GNSS/INS systems supported by DGPS and RTK receivers. It then discusses
whether the systems used are suitable for the purposes of hydrographic surveys. The paper
concludes with final (general) conclusions that summarise its content.
2. Materials and Methods
2.1. Measurement Equipment
As part of the INNOBAT research project [74], on 19 August 2021, hydrographic
surveys were carried out on Kłodno lake in Zawory. The aim of the study was to determine
the usefulness of an inertial navigation system for hydrographic surveys. To this end, two
GNSS/INS systems, models Ekinox2-U and Ellipse-D, by the SBG Systems, were used. The
former of the above-mentioned systems comprises the following components [75]:
2.1. Measurement Equipment
Energies 2021, 14, 7413
As part of the INNOBAT research project [74], on 19 August 2021, hydrographic surveys were carried out on Kłodno lake in Zawory. The aim of the study was to determine
the usefulness of an inertial navigation system for hydrographic surveys. To this end, two
4 of 19
GNSS/INS systems, models Ekinox2-U and Ellipse-D, by the SBG Systems, were used. The
former of the above-mentioned systems comprises the following components [75]:
•
•
••
••
••
••
••
An Inertial Measurement Unit (IMU) (SBG Systems, Carrières-sur-Seine, France)
(Figure
1a), comprised
of three
accelerometers
and three Carrières-sur-Seine,
gyroscopes, used to measAn Inertial
Measurement
Unit
(IMU) (SBG Systems,
France)
ure
accelerations
and angular
velocities
along the
pitch,
and yaw used
axes of
mov(Figure
1a), comprised
of three
accelerometers
and
threeroll
gyroscopes,
to ameasure
ing
object;
accelerations
and angular velocities along the pitch, roll and yaw axes of a moving object;
Two
AT1675-382(Apollo
(ApolloSatellite,
SatelTwoantennas:
antennas:an
anAERO
AEROGPS
GPSand
andGNSS
GNSS Survey
Survey Antenna AT1675-382
lite,
Diego,
CA,
USA)(Figure
(Figure1b)
1b)used
used to
to measure the
SanSan
Diego,
CA,
USA)
the course
courseof
ofaamoving
movingvehicle.
vehicle.
Theytrack
trackGPS,
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andGalileo
Galileosatellites;
satellites;
They
TheSplitBox
SplitBoxcomputer
computersystem
system
(SBG
Systems,
Carrières-sur-Seine,France)
France)(Figure
(Figure1c)
1c)
The
(SBG
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Carrières-sur-Seine,
usedtotoacquire
acquireand
andprocess
process data
data recorded in
used
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real-timeby
bytwo
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thethe
SplitBox
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anan
IMU
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two
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antennas;
bedded
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SplitBox
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IMU
and
two
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GNSS
antennas;
modem,enabling
enablingthe
thereception
receptionofofRTK/RTN
RTK/RTNcorrections
corrections
(KorenixTechnology,
Technology,
AAmodem,
(Korenix
New
Taipei
City,
Taiwan)
(Figure
1d)
and
providing
the
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accuracy
New Taipei City, Taiwan) (Figure 1d) and providing the positioning accuracy of a 1–of
a 1–2-centimetre
Distance
Root Mean
(DRMS)
the horizontal
and
2-centimetre
Distance
Root Mean
SquareSquare
(DRMS)
in the in
horizontal
plane plane
and 2–32–3-centimetre
Root Mean
Square
the vertical
centimetre
Root Mean
Square
(RMS)(RMS)
in thein
vertical
plane;plane;
ThesbgCenter
sbgCentersoftware
software(SBG
(SBGSystems,
Systems,Carrières-sur-Seine,
Carrières-sur-Seine,France)
France)(Figure
(Figure1e)
1e)used
used
The
setthe
theoperation
operationparameters
parametersininreal-time
real-timefor
forthe
theEkinox2-U
Ekinox2-Usystem;
system;
totoset
TheQinertia
Qinertiasoftware
software(SBG
(SBGSystems,
Systems,Carrières-sur-Seine,
Carrières-sur-Seine,France)
France)(Figure
(Figure1f)
1f)used
usedtoto
The
process
data
recorded
by
the
Ekinox2-U
system
in
the
post-processing
mode.
process data recorded by the Ekinox2-U system in the post-processing mode.
(a)
(b)
(c)
(d)
(e)
(f)
Figure
of of
thethe
GNSS/INS
system,
model
Ekinox2-U,
by the
Systems:
(a) IMU,
(b) GNSS
antennas,
(c)
Figure1.1.Components
Components
GNSS/INS
system,
model
Ekinox2-U,
by SBG
the SBG
Systems:
(a) IMU,
(b) GNSS
antennas,
SplitBox
computer
system,
(d) modem
enabling
the reception
of RTK/RTN
corrections,
(e) sbgCenter
software
and (f)
(c) SplitBox
computer
system,
(d) modem
enabling
the reception
of RTK/RTN
corrections,
(e) sbgCenter
software
and
Qinertia
software
[75].[75].
(f) Qinertia
software
Moreover,
system
has
the
following
functionalities
that
are
ofof
signifiMoreover,the
theGNSS/INS
GNSS/INS
system
has
the
following
functionalities
that
are
significance
cancefrom
fromthe
theperspective
perspectiveofofhydrographic
hydrographicsurveys
surveys[75]:
[75]:
• • The
TheEkinox2-U
Ekinox2-Usystem
systemprovides
providesoperation
operationininthe
thefollowing
followingtwo
twomodes:
modes:
o # DGPS—this
method
involves
thethe
useuse
of of
a base
station
(the
so-called
DGPS—this
method
involves
a base
station
(the
so-calledreference
reference
station),
i.e., i.e.,
a receiver
positioned
at aatprecisely
designated
point
that
station),
a receiver
positioned
a precisely
designated
point
thatdeterdetermines,
on an
basis,
differential
corrections
for all
foundfound
in thein
mines,
onongoing
an ongoing
basis,
differential
corrections
forsatellites
all satellites
the station’s field of view. The second (mobile) receiver must be able to receive
these corrections, e.g., via a satellite connection, Very High Frequency (VHF),
General Packet Radio Service (GPRS)/Wireless Local Area Network (WLAN),
which are transmitted in the Radio Technical Commission for Maritime (RTCM),
Compact Measurement Record (CMR) or another format;
#
RTK—this method involves radio transmission of L1 and L2 carrier phase
observation data or corrections from a base station of known coordinates to a
mobile receiver where a position is determined. Double differencing the mea-
corrections, e.g., via a satellite connection, Very High Frequency (VHF), General
Packet Radio Service (GPRS)/Wireless Local Area Network (WLAN), which are
transmitted in the Radio Technical Commission for Maritime (RTCM), Compact
Measurement Record (CMR) or another format;
Energies 2021, 14, 7413 o
5 of 19
RTK—this method involves radio transmission of L1 and L2 carrier phase observation data or corrections from a base station of known coordinates to a mobile receiver where a position is determined. Double differencing the measurements and resolving the integer ambiguities provide relative positioning accusurements and resolving the integer ambiguities provide relative positioning
racies at the centimetre level.
accuracies at the centimetre level.
•
The recording frequency for the data on angles, accelerations and position coordi•
The recording frequency for the data on angles, accelerations and position coordinates
nates should be as high as possible. It is recommended that the IMU’s data should be
should be as high as possible. It is recommended that the IMU’s data should be
recorded with a maximum frequency of 200 Hz.
recorded with a maximum frequency of 200 Hz.
Another GNSS/INS
system
used was
the Ellipse-D,
comprises
the following
Another
GNSS/INS
system
used waswhich
the Ellipse-D,
which
comprises the following
components [76]:
components [76]:
•
•
•
An IMU (SBG
Carrières-sur-Seine,
France) (FigureFrance)
2a), comprised
of three
An IMU (SBG
Systems, Carrières-sur-Seine,
(Figure 2a),
comprised of three
• Systems,
accelerometers accelerometers
and three gyroscopes,
used
to
measure
accelerations
and
angular
ve- and angular
and three gyroscopes, used to measure accelerations
locities along the
pitch,
roll
and
yaw
axes
of
a
moving
object;
velocities along the pitch, roll and yaw axes of a moving object;
Two TW7972
GNSS
Antennas
with L-band
(Tallysman
Wireless
Inc., Ot- Wireless Inc.,
• Triple
Two Band
TW7972
Triple
Band GNSS
Antennas
with L-band
(Tallysman
tawa, Canada) (Figure
2b)
used
to
measure
the
course
of
a
moving
vehicle.
They
track vehicle. They
Ottawa, Canada) (Figure 2b) used to measure the course of a moving
GPS, GLONASS,
BDS
and
Galileo
satellites;
track GPS, GLONASS, BDS and Galileo satellites;
The sbgCenter
(Figure
2c) used(Figure
to set the
in real-time
The sbgCenter
software
2c) operation
used to setparameters
the operation
parameters in real-time
• software
for the Ellipse-D
system.
for the Ellipse-D system.
(a)
(b)
(c)
Figure 2. Components
of the GNSS/INS
system,
model Ellipse-D,
bySystems:
the SBG (a)
Systems:
(a) GNSS
IMU, (b)
Figure 2. Components
of the GNSS/INS
system, model
Ellipse-D,
by the SBG
IMU, (b)
antennas and
GNSS
antennas
(c) sbgCenter
software
[76].and (c) sbgCenter software [76].
The of
functionalities
of the
GNSS/INS
system, model
which are of signifiThe functionalities
the GNSS/INS
system,
model Ellipse-D,
whichEllipse-D,
are of significance
from
the
perspective
of
hydrographic
surveys,
are
identical
to
those
for the Ekinox2-U
cance from the perspective of hydrographic surveys, are identical to those for the Ekinox2model.
Therefore,
they
will
not
be
provided
again.
U model. Therefore, they will not be provided again.
As regards
the accuracy of
characteristics
of systems,
the GNSS/INS
models Ekinox2-U
As regards the accuracy
characteristics
the GNSS/INS
modelssystems,
Ekinox2-U
and
Ellipse-D
are
presented
in
Table
1
[75,76].
and Ellipse-D are presented in Table 1 [75,76].
Table
1. Accuracyofcharacteristics
ofsystems,
the GNSS/INS
models
and
in the to
case
of access to and no
able 1. Accuracy
characteristics
the GNSS/INS
modelssystems,
Ekinox2-U
and Ekinox2-U
Ellipse-D in
theEllipse-D
case of access
and
access
to
a
GNSS
signal
[75,76].
o access to a GNSS signal [75,76].
Time That
Has
Elapsed
theWas
GNSS
Signal
Was Not Available
Time that Has Elapsed
since
the
GNSSSince
Signal
not
Available
0s
10 s
0s
10 s
Measurement
urement Error
Error
Ellipse-D Ellipse-D
Ekinox2-U
Ellipse-D Ellipse-D Ekinox2-U
Ekinox2-U
Ekinox2-U
DGPS
RTK
DGPS
RTK
DGPS
RTK
DGPS
RTK
DGPS
RTK
DGPS
RTK
DGPS
RTK
DGPS
RTK
σ2D (m)
1.2
0.01
1.2
0.01
3
1
2
0.35
σ2D (m)
1.2
0.01
1.2
0.01
3
1
2
0.35
σH (m)
1.5
0.02
2
0.02
3.5
1
3
0.15
σH (m)
1.5
0.02
2
0.02
3.5
1
3
0.15
σβ, σα (°)
0.1
0.05
0.05
0.05
0.1
0.05
0.1
0.1
◦
σβ, σα ( )
0.1
0.05
0.05
0.05
0.1
0.05
0.1
0.1
σδ (°)
0.8
0.2
0.1
0.05
0.8
0.2
0.15
0.1
σδ (◦ )
0.8
0.2
0.1
0.05
0.8
0.2
0.15
0.1
Where: σ2D—standard deviation of a single measurement of the 2D position of the IMU, σH—standard deviation of a single measurement
of the IMU’s height, σβ—standard deviation of a single measurement of the IMU’s pitch, σα—standard deviation of a single measurement
of the IMU’s roll, σδ—standard deviation of a single measurement of the IMU’s course.
It follows from Table 1 that the GNSS/INS system equipped with a RTK module
can be successfully used in all IHO orders. However, in the event of the loss of a GNSS
signal (up to 10 s), there is no 100% certainty that the inertial navigation system will meet
the requirements provided for the most stringent IHO order, i.e., the Exclusive Order
σβ—standard deviation of a single measurement of the IMU’s pitch,
σα—standard deviation of a single measurement of the IMU’s roll,
σδ—standard deviation of a single measurement of the IMU’s course.
It follows from Table 1 that the GNSS/INS system equipped with a RTK module can
Energies 2021, 14, 7413
6 of 19
be successfully used in all IHO orders. However, in the event of the loss of a GNSS signal
(up to 10 s), there is no 100% certainty that the inertial navigation system will meet the
requirements provided for the most stringent IHO order, i.e., the Exclusive Order (horizontal position(horizontal
error ≤ 1 mposition
(p = 0.95)).
As≤regards
DGPS
can
be used
in seerror
1 m (p =the
0.95)).
Assystem,
regardsitthe
DGPS
system,
it can be used in
lected IHO orders
(Special,
1a,
1b
and
2)
when
a
GNSS
signal
is
available.
On
the
other On the other
selected IHO orders (Special, 1a, 1b and 2) when a GNSS signal is available.
hand, in the absence
of the
access
to a satellite
GNSS/INS
systems
can only
be used
hand, in
absence
of accesssignal,
to a satellite
signal,
GNSS/INS
systems
can only be used
when carrying when
out hydrographic
in three
IHO orders,
namely
1a, 1b and
2. 1a, 1b and 2.
carrying outsurveys
hydrographic
surveys
in three
IHO orders,
namely
2.2. Configuration
Calibration of
GNSS/INS
Systems
2.2.and
Configuration
and
Calibration
of GNSS/INS Systems
Before the target
studythe
wastarget
initiated,
GNSS/INS
systems
needed tosystems
be configured.
Before
study
was initiated,
GNSS/INS
neededAs
to be configured.
As regards
the Ekinox2-U
the mast of vessel
the “HydroDron”
vessel
regards the Ekinox2-U
system,
the mast ofsystem,
the “HydroDron”
[77], on which
two[77], on which
external
GNSS
antennas
located
with a2distance
of almost
m between them,
external GNSS two
antennas
were
located
with awere
distance
of almost
m between
them, 2was
was
used
(Figure
3a). The
IMU
installed
near
symmetry (Figure
axis of the catamaran
used (Figure 3a).
The
IMU
was installed
near
thewas
symmetry
axis
of the catamaran
3b),
while thesystem
SplitBox
computer
system
and thethe
modem
enabling
3b), while the (Figure
SplitBox
computer
and
the modem
enabling
reception
of the reception
of
RTK/RTN
corrections
were
placed
in
one
of
the
hulls
of
the
hydrographic
vessel. As
RTK/RTN corrections were placed in one of the hulls of the hydrographic vessel. As reregards
secondapplied
of the systems
applied
(Ellipse-D),
installed
a similar way as
gards the second
of thethe
systems
(Ellipse-D),
it was
installed itinwas
a similar
wayinas
the Ekinox2-U
the Ekinox2-U system
(Figure system
3a,b). (Figure 3a,b).
(a)
(b)
Figure
3. The of
arrangement
of systems
the GNSS/INS
systems onSurface
the Autonomous
Surface
Vehicle
Figure 3. The
arrangement
the GNSS/INS
on the Autonomous
Vehicle (ASV)/USV
named
“HydroDron”:
(ASV)/USV
named
“HydroDron”:
(a)
view
from
the
front
of
the
vessel
and
(b)
view
on
IMUs.
(a) view from the front of the vessel and (b) view on IMUs.
After the configuration
GNSS/INS systems,
they needed
to they
be calibrated.
After theof
configuration
of GNSS/INS
systems,
needed toTo
be this
calibrated. To this
end, the “HydroDron”
was used.
Before
starting
calibration,
several
parameters
end, thevessel
“HydroDron”
vessel
was
used. the
Before
starting the
calibration,
several parameters
of the inertial
navigation
system’s
to be set.
In able
ordertotodo
bethis,
able to do this, free
of the inertial navigation
system’s
operation
hadoperation
to be set.had
In order
to be
software
needed
be used.
Among
the GNSS/INS
system’s movement
free sbgCenter sbgCenter
software needed
to be
used.toAmong
others,
theothers,
GNSS/INS
system’s moveprofile
set in it.
the character
of hydrographic
ment profile had
to behad
set to
in be
it. Given
theGiven
character
of hydrographic
surveys, itsurveys,
was de-it was decided
choose
the “Marine”
mode,
which is to
dedicated
to marine applications,
cided to choosetothe
“Marine”
mode, which
is dedicated
marine applications,
i.e., those i.e., those in
(slow) changes
and average
in the
movement
direction
and velocity occur.
in which slight which
(slow) slight
and average
in thechanges
movement
direction
and velocity
occur.
The
orientation
of
the
inertial
navigation
systems
then
needed
to
be
determined.
A leftThe orientation of the inertial navigation systems then needed to be determined. A lefthanded
orthogonal
coordinate
whose
point
wasIMU
found
on the IMU covers,
handed orthogonal
coordinate
system,
whose system,
zero point
was zero
found
on the
covers,
wasaxes
adopted.
axes of
the determined
system werein
determined
in such
a manner
that the x-axis ran
was adopted. The
of theThe
system
were
such a manner
that
the x-axis
the catamaran
front, the
wastoward
orientedthe
toward
the left catamaran
side, while
ran toward thetoward
catamaran
front, the y-axis
wasy-axis
oriented
left catamaran
side,
the z-axis ran toward the catamaran bottom. Moreover, it was necessary to determine the
geometric relationships between the GNSS antennas and the IMUs with an accuracy of no
lower than 20 cm (as recommended by the manufacturer in order to be able to perform the
calibration of the INS).
The GNSS/INS systems could then be calibrated. According to the SBG manufacturer’s recommendations for the Ekinox2-U system, calibration had to be performed in
motion, with the assumption that its duration should be at least 15 min and the velocity of
the “HydroDron” vessel’s movement should be no less than 10 km/h. Moreover, in order
to calibrate all sensors (accelerometers and gyroscopes), it is recommended that the object
should be moved in such a manner so as to constantly change the direction of movement.
Energies 2021, 14, 7413
curacy of no lower than 20 cm (as recommended by the manufacturer in order to be able
to perform the calibration of the INS).
The GNSS/INS systems could then be calibrated. According to the SBG manufacturer’s recommendations for the Ekinox2-U system, calibration had to be performed in
motion, with the assumption that its duration should be at least 15 min and the velocity
7 of 19
of the “HydroDron” vessel’s movement should be no less than 10 km/h. Moreover,
in
order to calibrate all sensors (accelerometers and gyroscopes), it is recommended that the
object should be moved in such a manner so as to constantly change the direction of movement.
Movement
in circles,
ovals
or the so-called
is recommended.
Movement
in circles,
ovals or
the so-called
“figure“figure
eights”eights”
is recommended.
After 15After
min
15
min
of
catamaran
sailing,
the
calibration
of
the
INS
was
completed.
During
calibraof catamaran sailing, the calibration of the INS was completed. During the the
calibration,
tion,
the geometric
relationships
between
the external
GNSS
antennas
IMU
were
the geometric
relationships
between
the external
GNSS
antennas
andand
the the
IMU
were
dedetermined
a precise
manner
(from
cm) (Figure
(Figure 4a).
4a). As
As regards
the latter
termined in in
a precise
manner
(from
±1±1toto±±4
4 cm)
regards the
latter of
of the
the
systems
systems applied,
applied, i.e.,
i.e., the
the Ellipse-D,
Ellipse-D, the
the magnetometer
magnetometer needed
needed to
to be calibrated in order to
compensate
for
the
effect
of
magnetic
fields
of
other
objects
(mainly
those on which it was
compensate for the effect magnetic
installed).
The
accuracy
of
the
IMU’s
course
is
calculated
by
the
quality
of the calibration
installed). The accuracy of the IMU’s course is calculated
performed.
calibration is
is not
notconducted,
conducted,the
theobject’s
object’scourse
coursemeasurement
measurement
error
performed. If calibration
error
cancan
be be
as
as
much
several
tensofofdegrees.
degrees.The
Themanufacturer
manufacturerrecommends
recommendsthat
that the
the magnetic field
much
asas
several
tens
measurements
should be
be performed
performedby
bymeans
meansofofrotating
rotatingthe
theIMU
IMUininsignificantly
significantly
differmeasurements should
different
ent
orientations.
is recommended
at least
points
should
be recorded
in 9 diforientations.
It isItrecommended
thatthat
at least
10001000
points
should
be recorded
in 9 different
orientations,
with the
assumption
that the
IMU’s
rotation
velocity
is approx.
45◦ /s.45°/s.
The
ferent
orientations,
with
the assumption
that
the IMU’s
rotation
velocity
is approx.
progress
of theofcalibration,
including,
e.g., where
how
many
points
beenhave
recorded,
The
progress
the calibration,
including,
e.g., and
where
and
how
manyhave
points
been
can be checked
the sbgCenter
in software
real-time.inAfter
performing
above steps,
recorded,
can beinchecked
in the software
sbgCenter
real-time.
After the
performing
the
e.g., standard
deviation
of adeviation
single measurement
of the IMU’s course
is obtained.
the
above
steps, e.g.,
standard
of a single measurement
of the IMU’s
courseFor
is ob◦ RMS (Figure 4b).
purposes
thispurposes
study, it of
amounted
to it
2.2amounted
tained.
Forofthe
this study,
to 2.2° RMS (Figure 4b).
(a)
(b)
Figure
Figure 4.
4. The
Thecalibration
calibration results
results of
of the
the GNSS/INS
GNSS/INSsystems,
systems,models
models(a)
(a)Ekinox2-U
Ekinox2-Uand
and(b)
(b)Ellipse-D
Ellipse-Das
asof
of19
19August
August2021.
2021.
Moreover, it was assumed
assumed that
that the
the Ekinox2-U
Ekinox2-U system
system would
would apply
apply the
the RTK
RTK method,
method,
Moreover,
while the Ellipse-D
to to
determine
thethe
vessel’s
position.
while
Ellipse-D system
systemwould
woulduse
usethe
theDGPS
DGPSmethod
method
determine
vessel’s
posiAfterAfter
saving
the above
settings,
hydrographic
surveyssurveys
proceeded
on Kłodno
lake in Zawory
tion.
saving
the above
settings,
hydrographic
proceeded
on Kłodno
lake in
in an unchanged
form. form.
Zawory
in an unchanged
2.3. GNSS/INS
GNSS/INS Measurements
Measurements
2.3.
Once the
the assembly
assembly and
and implementation
implementation works
works were
were completed,
completed, measurements
measurements were
were
Once
carried
out
in
order
to
determine
the
usefulness
of
GNSS/INS
systems
for
hydrographic
carried out in order to determine the usefulness of GNSS/INS systems for hydrographic
surveys. AAstudy
study
was
conducted
using
“HydroDron”
vessel
along
the sounding
surveys.
was
conducted
using
thethe
“HydroDron”
vessel
along
the sounding
proprofiles
designed
in
accordance
with
the
principles
provided
in
the
IHO
S-44
standard[1].
[1].
files designed in accordance with the principles provided in the IHO S-44 standard
The surveys were carried out on Kłodno lake in Zawory. Since the hydrometeorological
conditions are an important factor affecting the obtained results, the measurements were
performed in windless weather and the sea state was equal to 0, according to the Douglas
scale (no wind waves or sea currents). For the surveys, an ASV/USV equipped with
two GNSS/INS systems, models Ekinox2-U and Ellipse-D, was used to sail along the
pre-designed test routes. The sounding profiles were conducted in relation to each other in
two ways. The arrangement of both routes resembled “narrowing squares” (a spiral of)
toward the centre of the waterbody being sounded. The distance between the successive
polygons was constant and amounted to 25 m (Figure 5a) and 50 m (Figure 5b).
Energies 2021, 14, 7413
performed in windless weather and the sea state was equal to 0, according to the Douglas
scale (no wind waves or sea currents). For the surveys, an ASV/USV equipped with two
GNSS/INS systems, models Ekinox2-U and Ellipse-D, was used to sail along the pre-designed test routes. The sounding profiles were conducted in relation to each other in two
ways. The arrangement of both routes resembled “narrowing squares” (a spiral of) toward
the centre of the waterbody being sounded. The distance between the successive polygons
was constant and amounted to 25 m (Figure 5a) and 50 m (Figure 5b).
8 of 19
(a)
(b)
Figure 5. Arrangement
of the route’s
profiles—spiral
every every
(a) 25 (a)
m 25
and
Figure 5. Arrangement
of thesounding
route’s sounding
profiles—spiral
m (b)
and50
(b)m,
50 on
m, on which
which the the
ASV/USV
moved
during
the
hydrographic
surveys.
The
“HydroDron”
vessel’s
trajectory
ASV/USV moved during the hydrographic surveys. The “HydroDron” vessel’s trajectory was
was marked with a sky-blue colour.
marked with a sky-blue colour.
The routes
were
designed
using theusing
Trimble
BusinessBusiness
Center (TBC)
The
The
routes
were designed
the Trimble
Centersoftware.
(TBC) software.
The
coordinates
of
the
individual
route’s
turning
points
were
then
exported
to
two
files
in
the
coordinates of the individual route’s turning points were then exported to two files in the
*.WPT format.
These points
were recorded
as geodetic
coordinates
referenced
to to
thethe World
*.WPT format.
These points
were recorded
as geodetic
coordinates
referenced
World Geodetic
System
1984
(WGS-84)
ellipsoid
with
an
accuracy
of
nine
decimal
places.
Geodetic System 1984 (WGS-84) ellipsoid with an accuracy of nine decimal places. Later
Later on, on,
the the
datadata
created
in this
wayway
were
converted
to files
in the
*.SHP
format
dedicated
created
in this
were
converted
to files
in the
*.SHP
format
dedicated to the
to the ArduPilot
Mission
Planner
software.
This
program
is used
forfor
planning
routes
onon which
ArduPilot
Mission
Planner
software.
This
program
is used
planning
routes
which UAVs
and
USVs
can
move
inin
anan
autonomous
mode
(Figure
6).6).
The
data
prepared
UAVs
and
USVs
can
move
autonomous
mode
(Figure
The
data
prepared in this
in this manner
areare
transmitted
through
telemetry
manner
transmitted
through
telemetryfrom
fromthe
thelaptop
laptopon
onwhich
whichthe
theArduPilot
ArduPilot Mission
Planner software is installed to the autopilot (Pixhawk 2.1) mounted on the “HydroDron”.
After switching from the “Flight” mode to the “Auto” mode, the vessel starts sailing on the
pre-determined points in an autonomous mode [78].
Energies 2021, 14, x FOR PEER REVIEW
Energies 2021, 14, 7413
9 of 1
Mission Planner software is installed to the autopilot (Pixhawk 2.1) mounted
on the “Hy
9 of 19
droDron”. After switching from the “Flight” mode to the “Auto” mode, the vessel star
sailing on the pre-determined points in an autonomous mode [78].
Figure6.6.Window
Window
of the
ArduPilot
Mission
Planner
application
for the planning
and recordin
Figure
of the
ArduPilot
Mission
Planner
application
used forused
the planning
and recording
of
a
vessel’s
route.
of a vessel’s route.
Once
routes
were
uploaded
to thetoArduPilot
Mission
PlannerPlanner
software,
hydro- hydro
Oncethethe
routes
were
uploaded
the ArduPilot
Mission
software,
graphic
surveys
were
started.
The first
was covered
between
10:55:18
a.m. 10:55:1
graphic
surveys
were
started.
Theroute
first(Figure
route 5a)
(Figure
5a) was
covered
between
and 12:01:57 p.m. Universal Time Coordinated (UTC). During this period, 4000 points were
a.m. and 12:01:57 p.m. Universal Time Coordinated (UTC). During this period, 4000 poin
recorded with a sampling frequency of 1 Hz. The “HydroDron” sailed with an average
were recorded with a sampling frequency of 1 Hz. The “HydroDron” sailed with an av
velocity of 2.16 kn, and covered a distance of 4440 m. The second route (Figure 5b) was
erage velocity
of 2.16 kn,
a distance
of 4440
The second
route
(Figure 5b
covered
between 12:08:23
p.m.and
andcovered
12:46:52 p.m.
UTC. During
thism.
period,
2310 points
were
was covered
12:08:23
p.m.
12:46:52
p.m. UTC. During
thisan
period,
2310 poin
recorded
with abetween
sampling
frequency
ofand
1 Hz.
The “HydroDron”
sailed with
average
were recorded
sampling
frequency
ofm.
1 Hz. The “HydroDron” sailed with an av
velocity
of 2.12 kn,with
and a
covered
a distance
of 2525
erage velocity of 2.12 kn, and covered a distance of 2525 m.
2.4. GNSS/INS Data Processing
two passages,
data sets were acquired from two GNSS/INS systems. These
2.4. During
GNSS/INS
Data Processing
recorded measurement results (point number, measurement time, ellipsoidal coordinates,
During two passages, data sets were acquired from two GNSS/INS systems. Thes
RPY angles, course, standard deviations for a single measurement: 2D position, elevation,
recorded
measurement
results
(point
number,
time,
ellipsoidal
coordinate
pitch, roll, yaw,
course, etc.)
and saved
them
in filesmeasurement
in text form. The
Ekinox2-U
system
RPY angles,
course,
standard
deviations
a single
measurement:
2D position,
recorded
the data
applying
the RTK
method, for
while
the Ellipse-D
system used
the DGPSelevation
pitch,
roll,
yaw,
course,
etc.)
and
saved
them
in
files
in
text
form.
The
Ekinox2-U
system
method with a sampling frequency of 1 Hz.
Each route
was subjected
an identical
data and
statistical
analysis, which
willused
makethe DGP
recorded
the data
applyingtothe
RTK method,
while
the Ellipse-D
system
itmethod
possible with
to draw
general conclusions.
a sampling
frequencyThe
of 11D,
Hz.2D and 3D position errors were uploaded
into the
Mathcad
wheretoitan
was
statistically
to calculate
the position
Each
route software,
was subjected
identical
dataanalysed
and statistical
analysis,
which will mak
accuracy measures (RMS, DRMS, 2DRMS, CEP, SEP, R68 and R95), which are commonly
it possible to draw general conclusions. The 1D, 2D and 3D position errors were uploade
used in navigation. From the perspective of geodetic and navigation applications (land
into the Mathcad software, where it was statistically analysed to calculate the positio
and marine) related to the object’s movement control, the most important measures should
accuracy
measures
(RMS,characterised
DRMS, 2DRMS,
CEP,confidence
SEP, R68level
and (95.4–98.2%)
R95), which[79,80].
are commonl
be
2DRMS(2D)
and R95(2D),
by a high
used
in
navigation.
From
the
perspective
of
geodetic
and
navigation
applications
(lan
At the next stage of the analyses, the feasibility of using the DGPS and RTK systems in
and marine)
related
to To
thethisobject’s
movement model
control,
the most
important
hydrography
was
assessed.
end, a mathematical
developed
in [81]
was usedmeasure
toshould
determine
whether the requirements
setcharacterised
out in the IHOby
S-44
standard
were met
[1]. The
be 2DRMS(2D)
and R95(2D),
a high
confidence
level
(95.4–98.2%
model
was
based
on
the
theory
of
renewal
(repair)
process
reliability,
where
the
system’s
[79,80].
operation
andnext
failure
statistics
areanalyses,
referred to
as feasibility
life and failure
times the
thatDGPS
are subject
an system
At the
stage
of the
the
of using
andto
RTK
exponential distribution [82].
in hydrography was assessed. To this end, a mathematical model developed in [81] wa
Let us consider a positioning system that determines a position with the error δ
used to determine whether the requirements set out in the IHO S-44 standardnwere me
as a function of time, and for which four maximum permissible position error values,
[1]. The model
wasminimum
based onaccuracy
the theory
of renewal
process
reliability,
corresponding
to the
requirements
set (repair)
out for the
following
four IHOwhere th
system’s
operation
and
failure
statistics
are
referred
to
as
life
and
failure
times that ar
orders: Special, 1a, 1b and 2, were determined. Figure 7 (the upper diagram) shows a curve
subject to an exponential distribution [82].
Energies 2021, 14, 7413
Let us consider a positioning system that determines a position with the error δn as a
function of time, and for which four maximum permissible position error values, corre
of 19
sponding to the minimum accuracy requirements set out for the following10four
IHO or
ders: Special, 1a, 1b and 2, were determined. Figure 7 (the upper diagram) shows a curv
that presents the position error value as a function of time for any positioning system. I
that
presents
position
errorany
value
as a function
of time
any positioning
system.
It (or not
allows
us to the
assess
whether
positioning
system
atfor
a given
point in time
meets
allows
us
to
assess
whether
any
positioning
system
at
a
given
point
in
time
meets
(or
not)
the accuracy requirements for each IHO order. Initially, the position error value exceed
the
accuracy
requirements
each
IHO order.
position
error value
exceeds
20 m,
thereby
preventingforthe
system
from Initially,
meetingthe
the
requirements
of any
IHO order
20 m, thereby preventing the system from meeting the requirements of any IHO order.
After some time, this error value drops below 2 m, which results in the system meeting
After some time, this error value drops below 2 m, which results in the system meeting
therequirements
requirements
Special
Order,
etc. Below
the position
error diagram,
three
the
setset
outout
forfor
thethe
Special
Order,
etc. Below
the position
error diagram,
three
graphsare
arepresented
presented
that
show
system’s
operational
from
the perspective
o
graphs
that
show
the the
system’s
operational
status status
from the
perspective
of
meeting
the
requirements
provided
for
IHO
orders.
If
the
system
is
assigned
a
binary
meeting the requirements provided for IHO orders. If the system is assigned a binary value
of
1, this
it hasthat
a fitness
(life)
status. (life)
However,
if the
system is if
assigned
a binary
value
ofmeans
1, thisthat
means
it has
a fitness
status.
However,
the system
is assigned
value
of
0,
this
means
that
it
has
an
unfitness
(failure)
status
[82].
a binary value of 0, this means that it has an unfitness (failure) status [82].
Figure
error
as aasfunction
of time
(the upper
diagram)
and three
diagrams
correFigure7.7.The
Theposition
position
error
a function
of time
(the upper
diagram)
and
three diagrams
corre
sponding
operational
status
for the
IHO orders:
Special Special
(green colour),
(blue
spondingtotothe
the
operational
status
forfollowing
the following
IHO orders:
(green1a/1b
colour),
1a/1b (blu
colour)
colour)
[81].
colour)and
and2 2(red
(red
colour)
[81].
3. Results
3. Results
Table 2 presents the IMU position accuracy results obtained on route no. 1.
Tableon
2 presents
position that
accuracy
resultsposition
obtained
on route
no. 1.
Based
Table 2, itthe
canIMU
be concluded
the obtained
accuracy
measures
on route no. 1 are similar to those recommended by the SBG Systems. For example, the
Table 2. measure
The position
accuracy
measures
of the GNSS/INS
systems,
models Ekinox2-U
and Ellipse
R68(2D)
amounts
to 0.032
m (Ekinox2-U)
and 1.013
m (Ellipse-D).
However, the
D,
during
the
hydrographic
surveys
on
route
no.
1.
R95(2D) measure amounts to 0.383 m (Ekinox2-U) and 1.036 m (Ellipse-D). It is noteworthy
that the R95(2D) measure value for the Ekinox2-U system is considerably greater than
GNSS System
expected.
The
for Error
this is the loss of reception of RTK corrections
a period ofData
Statistics
ofreason
Position
Type offorRegistered
Ekinox2-U
Ellipse-D
approx. 7.5 min (a chainage of 1.49–2.06
km) (Figure
8).
Number of measurements
RMS(ϕ)
RMS(λ)
RMS(h)
DRMS(2D)
4000
0.093 m
0.092 m
0.062 m
0.130 m
4000
0.732 m
0.732 m
0.558 m
1.035 m
Energies 2021, 14, 7413
Figure 7. The position error as a function of time (the upper diagram) and three diagrams corresponding to the operational status for the following IHO orders: Special (green colour), 1a/1b (blue
11 of 19
colour) and 2 (red colour) [81].
3. Results
TableTable
2. The2position
accuracy
measures
of the
GNSS/INS
systems,
models
presents
the IMU
position
accuracy
results
obtained
onEkinox2-U
route no.and
1. Ellipse-D,
during the hydrographic surveys on route no. 1.
Energies 2021, 14, x FOR PEER REVIEW
11 of 18
Table 2. The position accuracy measures of the GNSS/INS systems, models Ekinox2-U and EllipseGNSS System
D,Statistics
during the
Type of Registered Data
of hydrographic
Position Errorsurveys on route no. 1.
Ekinox2-U
Ellipse-D
GNSS System
Number2DRMS(2D)
ofof
measurements
4000
4000
0.261 m
2.069 m
Statistics
Position Error
Type ofEkinox2-U
Registered Data
Ekinox2-U
Ellipse-D
RMS(φ)
0.093
m m
0.732
mm
DRMS(3D)
0.144
1.176
measurements
4000 m
4000 m
Energies 2021, 14, x FOR PEER REVIEW Number of
11 of 18
CEP(2D)
0.031
1.005
RMS(λ)
0.092
m
0.732
m
RMS(ϕ)
0.093
m
0.732
m
R68(2D)
0.032
1.013
RMS(h)
0.062
m m
0.558
mm
RMS(λ)
0.092
m
0.732
m
R95(2D)
0.383 m
1.036 m
DRMS(2D)
0.130
m m
1.035
mm
RMS(h)
0.062
0.558
2DRMS(2D)
0.261
m
2.069
Ekinox2-U
SEP(3D)
0.037 m
1.146m
m
2DRMS(2D)
0.261
m
2.069
mm
DRMS(2D)
0.130
m
1.035
DRMS(3D)
0.144
1.176
R68(3D)
0.037mm
1.157mm
Ekinox2-U
Ellipse-D
DRMS(3D)
0.144
mm
1.176
m
CEP(2D)
0.031
1.005
R95(3D)
0.418 m
1.193mm
CEP(2D)
0.031
mm
1.005
R68(2D)
0.032
1.013mm
Based
on Table 2, it can be
concluded
that
the
obtained position accuracy measures
R68(2D)
0.032
mm
1.013
mm
R95(2D)
0.383
1.036
on route no.
1
are
similar
to
those
recommended
by
SEP(3D)
0.037
1.146mm the SBG Systems. For example, the
R95(2D)
0.383
mm
1.036
R68(2D) measure
m (Ekinox2-U)
However, the
R68(3D)amounts to 0.032
0.037
1.157mand
m 1.013 m (Ellipse-D).
SEP(3D)
0.037
mm
1.146
Ellipse-D
Ellipse-D
R95(2D) measure
amounts
to
0.383
m
(Ekinox2-U)
and
1.036
m
(Ellipse-D).
It is noteworR95(3D)
0.418 m
1.193 m
R68(3D)
0.037 m
1.157 m system is considerably greater than
thy that the
R95(2D) measure value
for the Ekinox2-U
1.193 m
expected.
The
reason
forcan
this
isconcluded
themloss ofthat
reception
of RTK
corrections
for ameasures
period of
BasedR95(3D)
on Table
2, it
be0.418
the obtained
position
accuracy
approx.
7.5
min
(a
chainage
of
1.49–2.06
km)
(Figure
8).
on route no. 1 are similar to those recommended by the SBG Systems. For example, the
R68(2D) measure amounts to 0.032 m (Ekinox2-U) and 1.013 m (Ellipse-D). However, the
R95(2D) measure amounts to 0.383 m (Ekinox2-U) and 1.036 m (Ellipse-D). It is noteworthy that the R95(2D) measure value for the Ekinox2-U system is considerably greater than
expected. The reason for this is the loss of reception of RTK corrections for a period of
approx. 7.5 min (a chainage of 1.49–2.06 km) (Figure 8).
Figure8.8.Variability
Variabilityof
ofthe
the1D,
1D,2D
2Dand
and3D
3Dposition
positionerrors
errorsrecorded
recordedusing
usingthe
theEkinox2-U
Ekinox2-Usystem
systemin
in
Figure
the
RTK
mode
on
route
no.
1.
the RTK mode on route no. 1.
As regards
regardsthe
theEllipse-D
Ellipse-Dsystem,
system,ititshould
shouldbe
bestated
statedthat
thatthe
thevariability
variabilityof
ofthe
the1D,
1D,2D
2D
As
and
3D
position
errors
is
low
along
the
entirety
of
route
no.
1
(Figure
9).
They
fall
within
and 3D position errors is low along the entirety of route no. 1 (Figure 9). They fall within
the following
following ranges:
ranges: 0.482–0.657
0.482–0.657 m
m (for
(for the
the 1D
1D position
position error),
error),0.972–1.070
0.972–1.070m
m(for
(forthe
the2D
2D
the
Figure 8. Variability of the 1D, 2D and 3D position errors recorded using the Ekinox2-U system in
positionerror)
error)and
and1.093–1.236
1.093–1.236m
m(for
(forthe
the3D
3Dposition
positionerror).
error).
position
the RTK mode on route no. 1.
As regards the Ellipse-D system, it should be stated that the variability of the 1D, 2D
and 3D position errors is low along the entirety of route no. 1 (Figure 9). They fall within
the following ranges: 0.482–0.657 m (for the 1D position error), 0.972–1.070 m (for the 2D
position error) and 1.093–1.236 m (for the 3D position error).
Figure 8. Variability of the 1D, 2D and 3D position errors recorded using the Ekinox2-U system in
the RTK mode on route no. 1.
Energies 2021, 14, 7413
As regards the Ellipse-D system, it should be stated that the variability of the 1D, 2D
and 3D position errors is low along the entirety of route no. 1 (Figure 9). They fall12
within
of 19
the following ranges: 0.482–0.657 m (for the 1D position error), 0.972–1.070 m (for the 2D
position error) and 1.093–1.236 m (for the 3D position error).
Energies 2021, 14, x FOR PEER REVIEW
12 of 18
Figure 9. Variability of the 1D, 2D and 3D position errors recorded using the Ellipse-D system in the
DGPS mode on route no. 1.
Figure 9. Variability of the 1D, 2D and 3D position errors recorded using the Ellipse-D system in the
DGPSIn
mode
on to
route
no. 1.the reliability of the results obtaining during the performance of
order
assess
hydrographic surveys on route no. 1, it was decided to analyse the results of GNSS/INS
In order toon
assess
of the results obtaining during the performance of
measurements
routethe
no.reliability
2 (Table 3).
hydrographic surveys on route no. 1, it was decided to analyse the results of GNSS/INS
measurements
on route
no. measures
2 (Table 3).
Table 3. The position
accuracy
of the GNSS/INS systems, models Ekinox2-U and Ellipse-D,
during the hydrographic surveys on route no. 2.
Table 3. The position accuracy measures of the GNSS/INS systems, models Ekinox2-U and EllipseD, during the hydrographic surveys onGNSS
route no.
2.
System
Type of Registered Data
Statistics of Position Error
Ekinox2-U
Ellipse-D
GNSS System
Type of Registered Data
2310
Ekinox2-U Ellipse-D
m
0.864 m
Number RMS(φ)
of measurements 0.023
2310
2310
Energies 2021, 14, x FOR PEER REVIEW
11 of 18
RMS(λ)
0.022
mm
0.865
RMS(ϕ)
0.023
0.864mm
RMS(h)
0.019
mm
0.582
RMS(λ)
0.022
0.865mm
RMS(h)
0.019
0.582mm
DRMS(2D)
0.032
mm
1.222
2DRMS(2D)
0.261
m
2.069 m
m
Ekinox2-U
DRMS(2D)
0.032
1.222
2DRMS(2D)
0.064
mm
2.444
m
DRMS(3D)
0.144 m
m
1.176 m
m
Ekinox2-U
2DRMS(2D)
0.064
2.444
Ekinox2-U
DRMS(3D)
0.037
m
1.353
m
CEP(2D)
0.031
m
1.005
m
DRMS(3D)
0.037 m
1.353 m
CEP(2D)
0.032
mm
1.022
R68(2D)
0.032
1.013mm
m
CEP(2D)
0.032
m
1.022
R68(2D)
0.032
mm
1.032
mm
R95(2D)
0.383
1.036
R68(2D)
0.032 m
1.032 m
R95(2D)
0.034
mm
1.065
SEP(3D)
0.037
1.146mm
m
R95(2D)
0.034
m
1.065
R68(3D)
0.037
m
1.157
m
SEP(3D)
0.037
mm
1.164
Ellipse-D
SEP(3D)
0.037
1.164mm
Ellipse-D
R95(3D)
0.418
m
1.193
m
R68(3D)
0.037
mm
1.180
R68(3D)
0.037
1.180mm
Ellipse-D
R95(3D)
0.039
1.230mm
R95(3D)
0.039
mm
1.230
Based on Table 2, it can be concluded that the obtained position accuracy measures
on route no. 1 are similar to those recommended by the SBG Systems. For example, the
Based on Table 3, it can be concluded that the obtained position accuracy measured
Based
on Table
3, it cantobe0.032
concluded
that the obtained
position
accuracyHowever,
measuredthe
on
R68(2D)
measure
amounts
m (Ekinox2-U)
and 1.013
m (Ellipse-D).
on
route
no.
2 are
very
similar
to those
recommended
by the
SBG
Systems.
For
example,
route
no.
2
are
very
similar
to
those
recommended
by
the
SBG
Systems.
For
example,
the
R95(2D) measure amounts to 0.383 m (Ekinox2-U) and 1.036 m (Ellipse-D). It is noteworthe
R68(2D)
measure
amounts
to 0.032
m (Ekinox2-U)
and
1.032
m (Ellipse-D).
However,
R68(2D)
measure
amounts
tovalue
0.032
m (Ekinox2-U)
and
1.032
m
(Ellipse-D).
However,
the
thy
that the
R95(2D)
measure
for
the Ekinox2-U
system
is considerably
greater than
the
R95(2D)
measure
amounts
to 0.034
m (Ekinox2-U)
and 1.065
m (Ellipse-D).
It is noteR95(2D)
measure
amounts
to 0.034
(Ekinox2-U)
and of
1.065
m corrections
(Ellipse-D).
It
expected.
The reason
for this
is themloss
of reception
RTK
foris anoteworthy
period of
worthy
the individual
position
accuracy measures
are almost
identical
to those
obthat thethat
individual
position
are8).almost
identical
to those
obtained
approx.
7.5
min (a chainage
ofaccuracy
1.49–2.06measures
km) (Figure
tained
during
the
hydrographic
surveys
on
route
no.
1.
The
exception
is
the
R95(2D)
measduring the hydrographic surveys on route no. 1. The exception is the R95(2D) measure
ure
value
for the
Ekinox2-U
system,
which
differs
the R68(2D)
measure
2
value
for the
Ekinox2-U
system,
which
onlyonly
differs
fromfrom
the R68(2D)
measure
by 2by
mm.
mm.
This
is
due
to
the
fact
that
during
the
performance
of
hydrographic
surveys,
there
This is due to the fact that during the performance of hydrographic surveys, there was no
was
lossreception
in the reception
RTK corrections,
which helped
obtain
the expected
measloss no
in the
of RTK of
corrections,
which helped
obtain the
expected
measurement
urement
results
(Figure
10).
results (Figure 10).
Statistics
Position Error
Number ofofmeasurements
2310
the R95(2D) measure amounts to 0.034 m (Ekinox2-U) and 1.065 m (Ellipse-D). It is noteworthy that the individual position accuracy measures are almost identical to those obtained during the hydrographic surveys on route no. 1. The exception is the R95(2D) measure value for the Ekinox2-U system, which only differs from the R68(2D) measure by 2
mm. This is due to the fact that during the performance of hydrographic surveys, there
Energies 2021, 14, 7413
was no loss in the reception of RTK corrections, which helped obtain the expected measurement results (Figure 10).
2021, 14, x FOR PEER REVIEW
13 of 19
13 of 18
10. Variability
1D,3D
2Dposition
and 3D errors
position
errors recorded
the Ekinox2-U
system
in mode on
Figure 10. Figure
Variability
of the 1D, of
2Dthe
and
recorded
using theusing
Ekinox2-U
system in
the RTK
the RTK mode on route no. 2.
route no. 2.
regardssystem,
the Ellipse-D
system,
it should
be variability
stated that of
thethe
variability
As regards the As
Ellipse-D
it should
be stated
that the
1D, 2D of the 1D, 2D
and
3D
position
errors
is
low
along
the
entirety
of
route
no.
2
and
is
almost
and 3D position errors is low along the entirety of route no. 2 and is almost as low as
that as low as that
on
route
no.
1
(Figure
11).
They
fall
within
the
following
ranges:
0.478–0.804
m (for the
on route no. 1 (Figure 11). They fall within the following ranges: 0.478–0.804 m (for the 1D
1D
position
error),
0.976–1.210
m
(for
the
2D
position
error)
and
1.094–1.402
m
(for
the 3D
position error), 0.976–1.210 m (for the 2D position error) and 1.094–1.402 m (for the 3D
position
error).
position error).
11. Variability
and 3Derrors
position
errors using
recorded
the Ellipse-D
in mode on
Figure 11. Figure
Variability
of the 1D, of
2Dthe
and1D,
3D2D
position
recorded
the using
Ellipse-D
system insystem
the DGPS
the
DGPS
mode
on
route
no.
2.
route no. 2.
to use the model
mathematical
model
presented
in [81]. Statistical
Further on, weFurther
decidedon,
to we
use decided
the mathematical
presented
in [81].
Statistical
analyses
and
calculations
were
carried
out
for
the
data
recorded
using
analyses and calculations were carried out for the data recorded using the GNSS/INS sys-the GNSS/INS
systems.
In data
addition,
from the DGPS
measurements,
conducted
during the
tems. In addition,
archival
from archival
the DGPSdata
measurements,
conducted
during the
“Tu“Tucana”
buoy
tender’s
manoeuvring
in
the
Gda
ńsk
Bay
on
20
June
2017,
were
used.
Those
cana” buoy tender’s manoeuvring in the Gdańsk Bay on 20 June 2017, were used. Those
surveys used a Simrad MXB5 receiver [83]. For each IHO order, characterised by different
surveys used a Simrad MXB5 receiver [83]. For each IHO order, characterised by different
permissible position errors, the availability factor value was calculated (Table 4).
permissible position errors, the availability factor value was calculated (Table 4).
able 4. The availability factor values determined for the GNSS/INS systems in the context of minimum positioning reuirements, set for all IHO orders.
sitioning System
ox2-U (Route no. 1)
ox2-U (Route no. 2)
pse-D (Route no. 1)
pse-D (Route no. 2)
Positioning Availability (%)
Exclusive Order Special Order 1a/1b Orders Order 2
100
100
100
100
100
100
100
100
38.48
99.55
100
100
15.54
100
100
100
Positioning Accuracy (m)
R95(2D)
0.383
0.034
1.036
1.085
Energies 2021, 14, 7413
14 of 19
Table 4. The availability factor values determined for the GNSS/INS systems in the context of minimum positioning
requirements, set for all IHO orders.
Positioning System
Positioning Availability (%)
Positioning Accuracy (m)
Exclusive Order
Special Order
1a/1b Orders
Order 2
R95(2D)
Ekinox2-U (Route no. 1)
100
100
100
100
0.383
Ekinox2-U (Route no. 2)
100
100
100
100
0.034
Ellipse-D (Route no. 1)
38.48
99.55
100
100
1.036
Ellipse-D (Route no. 2)
15.54
100
100
100
1.085
DGPS 2017
87.57
98.09
100
100
1.424
4. Discussion
The analysis of the RTK results clearly proves that the system meets the positioning
requirements provided for all the IHO orders, even in situations where it does not operate
100% correctly, e.g., due to the loss of reception of RTK corrections on route no. 1 (Figure 8).
Hence, it can be applied during the implementation of hydrographic works, irrespective of
Energies 2021, 14, x FOR PEER REVIEWthe IHO order.
14 of 18
As regards the DGPS system, it must be pointed out that it easily meets the positioning
requirements provided for four IHO orders (Special, 1a, 1b and 2). The availability factor
value amounts to 100% almost every time. However, it should be noted that the DGPS
DGPS system has not once reached the positioning availability required for the Exclusive
system has not once reached the positioning availability required for the Exclusive Order,
Order, i.e., 38.48% (Ellipse-D (Route no. 1)), 15.54% (Ellipse-D (Route no. 2)) and 87.57%
i.e., 38.48% (Ellipse-D (Route no. 1)), 15.54% (Ellipse-D (Route no. 2)) and 87.57% (DGPS
(DGPS 2017). Figure 12 shows graphs of the availability of individual positioning solu2017). Figure 12 shows graphs of the availability of individual positioning solutions broken
tions broken down into the following two IHO orders: Exclusive and Special. The three
down into the following two IHO orders: Exclusive and Special. The three other orders
other orders (1a, 1b and 2) require no separate analysis, as the interpretation of the results
(1a, 1b and 2) require no separate analysis, as the interpretation of the results from Table 4
from Table 4 raises no doubts whatsoever.
raises no doubts whatsoever.
Figure
The
availability
factor
values
determined
the
GNSS/INS
systems
context
Figure
12.12.
The
availability
factor
values
determined
forfor
the
GNSS/INS
systems
in in
thethe
context
of of
minimum
positioning
requirements,
two
most
stringent
IHO
orders.
minimum
positioning
requirements,
setset
forfor
thethe
two
most
stringent
IHO
orders.
Since
DGPS
system
fails
meet
requirements
provided
most
stringent
Since
thethe
DGPS
system
fails
to to
meet
thethe
requirements
provided
forfor
thethe
most
stringent
IHO
order,
i.e.,
the
Exclusive
Order,
we
decided
to
calculate
the
2D
position
error
value
IHO order, i.e., the Exclusive Order, we decided to calculate the 2D position error value
for which the confidence level will be 95%. To this end, the R95(2D) measure was deterfor which the confidence level will be 95%. To this end, the R95(2D) measure was determined based on the data recorded during the performance of hydrographic surveys using
mined based on the data recorded during the performance of hydrographic surveys using
GNSS/INS systems and tests for the DGPS system from 2017 (Figure 13).
GNSS/INS systems and tests for the DGPS system from 2017 (Figure 13).
minimum positioning requirements, set for the two most stringent IHO orders.
Energies 2021, 14, 7413
Since the DGPS system fails to meet the requirements provided for the most stringent
IHO order, i.e., the Exclusive Order, we decided to calculate the 2D position error value
for which the confidence level will be 95%. To this end, the R95(2D) measure was deter15 of 19
mined based on the data recorded during the performance of hydrographic surveys using
GNSS/INS systems and tests for the DGPS system from 2017 (Figure 13).
Figure
R95(2D)
measure
values
GNSS/INS
systems
individual
routes,
and
Figure
13.13.
TheThe
R95(2D)
measure
values
forfor
thethe
GNSS/INS
systems
on on
individual
routes,
and
forfor
thethe
DGPS
system
from
2017.
DGPS
system
from
2017.
Based
Figure
it can
concluded
that
DGPS
system
permanently
improves
Based
onon
Figure
13,13,
it can
be be
concluded
that
thethe
DGPS
system
permanently
improves
positioning
characteristics,
hence
hydrography
will
soon
possible
positioning
characteristics,
hence
itsits
useuse
in in
hydrography
will
soon
bebe
possible
forfor
allall
thethe
IHO
orders.
R95(2D)
measure
for Ellipse-D
the Ellipse-D
system
amounts
to 1.036
m (Route
IHO
orders.
TheThe
R95(2D)
measure
for the
system
amounts
to 1.036
m (Route
no.
andm
1.085
m (Route
i.e., it exceeds
the maximum
permissible
2D position
1) no.
and 1)
1.085
(Route
no. 2), no.
i.e., 2),
it exceeds
the maximum
permissible
2D position
error
error
provided
for
the
Exclusive
Order
by
only
a
few
centimetres.
However,
the
R95(2D)
provided for the Exclusive Order by only a few centimetres. However, the R95(2D) measfor thesystem
DGPS system
from
is noticeably
and amounts
to almost
uremeasure
for the DGPS
from 2017
is 2017
noticeably
higher higher
and amounts
to almost
1.5 m. 1.5 m.
5. Conclusions
5. Conclusions
The study demonstrated that the GNSS/INS systems, which are additionally supported with RTK receivers, can be successfully used to carry out hydrographic surveys
in any IHO order (Exclusive, Special, 1a, 1b and 2), even in situations where they do not
operate 100% correctly, e.g., due to the loss of reception of RTK corrections on route no. 1
(Figure 8). However, the DGPS system fails to meet only the requirements provided for
the most stringent IHO order, i.e., the Exclusive Order (horizontal position error ≤ 1 m
(p = 0.95)). Statistical analyses showed that it only lacked 3.6 and 8.5 cm to meet this
criterion (Figure 13). The above conclusions could be drawn due to the application of the
mathematical model developed in [81]. It enables the determination of whether any positioning system, at a given point in time, meets (or does not meet) the accuracy requirements
provided for individual IHO orders. A particular feature of the model is the possibility for
an assessment based on the actual measurements and analyses of a positioning system’s
operation and failure times.
The 1D, 2D and 3D position error values obtained using the GNSS/INS systems,
models Ekinox2-U and Ellipse-D, are similar to the accuracy characteristics recommended
by the SBG Systems. For example, the R68(2D) measure amounts to 0.032 m (Ekinox2-U)
and 1.013–1.032 m (Ellipse-D). However, the R95(2D) measure amounts to 0.034–0.383 m
(Ekinox2-U) and 1.036–1.065 m (Ellipse-D). It is noteworthy that almost all the position
accuracy measures are identical during the performance of GNSS/INS measurements on
both routes. The differences between the individual measures for the Ekinox2-U system
are of an order of a few millimetres, while for the Ellipse-D system, they amount to a
few centimetres.
Author Contributions: Conceptualisation, A.S., C.S. and M.S.; data curation, M.S., S.W., M.W. and
O.L.; formal analysis, M.S., D.B. and A.J.; investigation, A.S., M.S., S.W., M.W. and O.L.; methodology,
D.B. and A.J.; supervision, A.S. and C.S.; validation, C.S., D.B. and A.J.; visualisation, M.S., S.W., M.W.
and O.L.; writing—original draft, A.S., C.S. and M.S.; writing—review and editing, D.B. and A.J. All
authors have read and agreed to the published version of the manuscript.
Energies 2021, 14, 7413
16 of 19
Funding: This research was funded by the National Centre for Research and Development in Poland,
grant number LIDER/10/0030/L-11/19/NCBR/2020. Moreover, this research was funded by the
National Science Centre in Poland, grant number 2020/04/X/ST10/01777.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
IHO. IHO Standards for Hydrographic Surveys, 6th ed.; Special Publication No. 44; IHO: Monaco, Monaco, 2020.
Li, W.; Liu, G.; Cui, X.; Lu, M. Feature-aided RTK/LiDAR/INS Integrated Positioning System with Parallel Filters in the
Ambiguity-position-joint Domain for Urban Environments. Remote Sens. 2021, 13, 2013. [CrossRef]
Won, D.H.; Lee, E.; Heo, M.; Lee, S.-W.; Lee, J.; Kim, J.; Sung, S.; Jae, Y. Selective Integration of GNSS, Vision Sensor, and INS
Using Weighted DOP Under GNSS-challenged Environments. IEEE Trans. Instrum. Meas. 2014, 63, 2288–2298. [CrossRef]
Yan, P.; Jiang, J.; Tang, Y.; Zhang, F.; Xie, D.; Wu, J.; Liu, J.; Liu, J. Dynamic Adaptive Low Power Adjustment Scheme for
Single-frequency GNSS/MEMS-IMU/Odometer Integrated Navigation in the Complex Urban Environment. Remote Sens. 2021,
13, 3236. [CrossRef]
Broumandan, A.; Lachapelle, G. Spoofing Detection Using GNSS/INS/Odometer Coupling for Vehicular Navigation. Sensors
2018, 18, 1305. [CrossRef] [PubMed]
Vagle, N.; Broumandan, A.; Lachapelle, G. Multi-antenna GNSS and Inertial Sensors/Odometer Coupling for Robust Vehicular
Navigation. IEEE Internet Things J. 2018, 5, 4816–4828. [CrossRef]
Yang, L.; Li, Y.; Wu, Y.; Rizos, C. An Enhanced MEMS-INS/GNSS Integrated System with Fault Detection and Exclusion
Capability for Land Vehicle Navigation in Urban Areas. GPS Solutions 2014, 18, 593–603. [CrossRef]
Brazeal, R.G.; Wilkinson, B.E.; Benjamin, A.R. Investigating Practical Impacts of Using Single-antenna and Dual-antenna
GNSS/INS Sensors in UAS-Lidar Applications. Sensors 2021, 21, 5382. [CrossRef] [PubMed]
Mwenegoha, H.A.; Moore, T.; Pinchin, J.; Jabbal, M. A Model-based Tightly Coupled Architecture for Low-cost Unmanned Aerial
Vehicles for Real-time Applications. IEEE Access 2020, 1–20. [CrossRef]
Naus, K.; Szymak, P.; Piskur, P.; Niedziela, M.; Nowak, A. Methodology for the Correction of the Spatial Orientation Angles of
the Unmanned Aerial Vehicle Using Real Time GNSS, a Shoreline Image and an Electronic Navigational Chart. Energies 2021,
14, 2810. [CrossRef]
Wang, Q.; Cui, X.; Li, Y.; Ye, F. Performance Enhancement of a USV INS/CNS/DVL Integration Navigation System Based on an
Adaptive Information Sharing Factor Federated Filter. Sensors 2017, 17, 239. [CrossRef] [PubMed]
Xia, G.; Wang, G. INS/GNSS Tightly-Coupled Integration Using Quaternion-based AUPF for USV. Sensors 2016, 16, 1215.
[CrossRef]
Yan, W.; Zhang, Q.; Zhang, Y.; Wang, A.; Zhao, C. The Validation and Performance Assessment of the Android Smartphone
Based GNSS/INS Coupled Navigation System. In Proceedings of the 12th China Satellite Navigation Conference (CSNC 2021),
Nanchang, China, 22–25 May 2021.
Li, N.; Guan, L.; Gao, Y.; Du, S.; Wu, M.; Guang, X.; Cong, X. Indoor and Outdoor Low-cost Seamless Integrated Navigation
System Based on the Integration of INS/GNSS/LIDAR System. Remote Sens. 2020, 12, 3271. [CrossRef]
Zhuang, Y.; Lan, H.; Li, Y.; El-Sheimy, N. PDR/INS/WiFi Integration Based on Handheld Devices for Indoor Pedestrian
Navigation. Micromachines 2015, 6, 793–812. [CrossRef]
Jing, S.; Zhan, X.; Liu, B.; Chen, M. Weak and Dynamic GNSS Signal Tracking Strategies for Flight Missions in the Space Service
Volume. Sensors 2016, 16, 1412. [CrossRef] [PubMed]
Barzaghi, R.; Carrion, D.; Pepe, M.; Prezioso, G. Computing the Deflection of the Vertical for Improving Aerial Surveys: A
Comparison between EGM2008 and ITALGEO05 Estimates. Sensors 2016, 16, 1168. [CrossRef] [PubMed]
Pytka, J.; Budzyński, P.; Józwik, J.; Michałowska, J.; Tofil, A.; Łyszczyk, T.; Błażejczak, D. Application of GNSS/INS and an Optical
Sensor for Determining Airplane Takeoff and Landing Performance on a Grassy Airfield. Sensors 2019, 19, 5492. [CrossRef]
[PubMed]
Qian, C.; Liu, H.; Tang, J.; Chen, Y.; Kaartinen, H.; Kukko, A.; Zhu, L.; Liang, X.; Chen, L.; Hyyppä, J. An Integrated
GNSS/INS/LiDAR-SLAM Positioning Method for Highly Accurate Forest Stem Mapping. Remote Sens. 2017, 9, 3. [CrossRef]
El-Diasty, M. Development of Real-time PPP-based GPS/INS Integration System Using IGS Real-time Service for Hydrographic
Surveys. J. Surv. Eng. 2016, 142, 05015005. [CrossRef]
El-Diasty, M. Evaluation of KSACORS-based Network GNSS-INS Integrated System for Saudi Coastal Hydrographic Surveys.
Geomat. Nat. Hazards Risk 2020, 11, 1426–1446. [CrossRef]
Scheider, A.; Wirth, H.; Breitenfeld, M.; Schwieger, V. HydrOs—An Integrated Hydrographic Positioning System for Surveying
Vessels. In Proceedings of the XXV FIG Congress 2014, Kuala Lumpur, Malaysia, 16–21 June 2014.
Energies 2021, 14, 7413
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
17 of 19
Bedkowski, J.; Nowak, H.; Kubiak, B.; Studzinski, W.; Janeczek, M.; Karas, S.; Kopaczewski, A.; Makosiej, P.; Koszuk, J.; Pec,
M.; et al. A Novel Approach to Global Positioning System Accuracy Assessment, Verified on LiDAR Alignment of One Million
Kilometers at a Continent Scale, as a Foundation for Autonomous DRIVING Safety Analysis. Sensors 2021, 21, 5691. [CrossRef]
Elsheikh, M.; Abdelfatah, W.; Noureldin, A.; Iqbal, U.; Korenberg, M. Low-cost Real-time PPP/INS Integration for Automated
Land Vehicles. Sensors 2019, 19, 4896. [CrossRef]
Zhu, F.; Shen, Y.; Wang, Y.; Jia, J.; Zhang, X. Fusing GNSS/INS/Vision with a Priori Feature Map for High-precision and
Continuous Navigation. IEEE Sens. J. 2021, 21, 23370–23381. [CrossRef]
Sun, Z.; Tang, K.; Wang, X.; Wu, M.; Guo, Y. High-speed Train Tunnel Navigation Method Based on Integrated MIMU/ODO/MC
Navigation. Appl. Sci. 2021, 11, 3680. [CrossRef]
Sun, Z.; Tang, K.; Wu, M.; Guo, Y.; Wang, X. High-speed Train Positioning Method Based on Motion Constraints Suppressing INS
Error in Tunnel. J. Northwest. Polytech. Univ. 2021, 39, 624–632. [CrossRef]
Chen, K.; Chang, G.; Chen, C. GINav: A MATLAB-based Software for the Data Processing and Analysis of a GNSS/INS Integrated
Navigation System. GPS Solutions 2021, 25, 108. [CrossRef]
Du, S.; Zhang, S.; Gan, X. A Hybrid Fusion Strategy for the Land Vehicle Navigation Using MEMS INS, Odometer and GNSS.
IEEE Access 2020, 8, 152512–152522. [CrossRef]
Elmezayen, A.; El-Rabbany, A. Ultra-low-cost Tightly Coupled Triple-constellation GNSS PPP/MEMS-based INS Integration for
Land Vehicular Applications. Geomatics 2021, 1, 258–286. [CrossRef]
Dong, P.; Cheng, J.; Liu, L. A Novel Anti-jamming Technique for INS/GNSS Integration Based on Black Box Variational Inference.
Appl. Sci. 2021, 11, 3664. [CrossRef]
Kujur, B.; Khanafseh, S.; Pervan, B. Detecting GNSS Spoofing of ADS-B Equipped Aircraft Using INS. In Proceedings of the 2020
IEEE/ION Position, Location and Navigation Symposium (PLANS 2020), Portland, OR, USA, 20–23 April 2020.
Specht, C.; Specht, M.; Dabrowski,
˛
P. Comparative Analysis of Active Geodetic Networks in Poland. In Proceedings of the 17th
International Multidisciplinary Scientific GeoConference (SGEM 2017), Albena, Bulgaria, 27 June–6 July 2017.
Mora, O.E.; Langford, M.; Mislang, R.; Josenhans, R.; Jorge Chen, J. Precision Performance Evaluation of RTK and RTN Solutions:
A Case Study. J. Spat. Sci. 2020, 1–14. [CrossRef]
Bakuła, M. Study of Reliable Rapid and Ultrarapid Static GNSS Surveying for Determination of the Coordinates of Control Points
in Obstructed Conditions. J. Surv. Eng. 2013, 139, 188–193. [CrossRef]
Bogusz, J.; Figurski, M.; Kontny, B.; Grzempowski, P. Horizontal Velocity Field Derived from EPN and ASG-EUPOS Satellite Data
on the Example of South-western Part of Poland. Acta Geodyn. Geomater. 2012, 9, 349–357.
St˛epniak, K.; Baryła, R.; Wielgosz, P.; Kurpiński, G. Optimal Data Processing Strategy in Precise GPS Levelling Networks. Acta
Geodyn. Geomater. 2013, 10, 443–452. [CrossRef]
Ćwiakała,
˛
P.; Gabryszuk, J.; Krawczyk, K.; Krzyżek, R.; Leń, P.; Oleniacz, G.; Puchniach, E.; Siejka, Z.; Wójcik-Leń, J. GNSS
Technology and Its Application in Setting out Surveys and Monitoring; Rzeszów School of Engineering and Economics Publishing
House: Rzeszów, Poland, 2015. (In Polish)
Przestrzelski, P.; Bakuła, M. Performance of Real-time Network Code DGPS Services of ASG-EUPOS in North-Eastern Poland.
Tech. Sci. 2014, 17, 191–207.
Specht, C.; Rudnicki, J. A Method for the Assessing of Reliability Characteristics Relevant to an Assumed Position-fixing Accuracy
in Navigational Positioning Systems. Pol. Marit. Res. 2016, 23, 20–27. [CrossRef]
Visconti, P.; Iaia, F.; De Fazio, R.; Giannoccaro, N.I. A Stake-out Prototype System Based on GNSS-RTK Technology for Implementing Accurate Vehicle Reliability and Performance Tests. Energies 2021, 14, 4885. [CrossRef]
Bakuła, M.; Pelc-Mieczkowska, R.; Walawski, M. Reliable and Redundant RTK Positioning for Applications in Hard Observational
Conditions. Artif. Satell. 2012, 47, 23–33. [CrossRef]
Janos, D.; Kuras, P. Evaluation of Low-cost GNSS Receiver under Demanding Conditions in RTK Network Mode. Sensors 2021,
21, 5552. [CrossRef] [PubMed]
IALA. IALA Recommendation R-121 on the Performance and Monitoring of DGNSS Services in the Frequency Band 283.5–325 kHz,
2.0 ed.; IALA: Saint-Germain-en-Laye, France, 2015.
Specht, C.; Weintrit, A.; Specht, M. A History of Maritime Radio-navigation Positioning Systems Used in Poland. J. Navig. 2016,
69, 468–480. [CrossRef]
Dziewicki, M.; Specht, C. Position Accuracy Evaluation of the Modernized Polish DGPS. Pol. Marit. Res. 2009, 16, 57–61.
[CrossRef]
Kim, J.; Song, J.; No, H.; Han, D.; Kim, D.; Park, B.; Kee, C. Accuracy Improvement of DGPS for Low-cost Single-frequency
Receiver Using Modified Flachen Korrektur Parameter Correction. ISPRS Int. J. Geo-Inf. 2017, 6, 222. [CrossRef]
Lubis, M.Z.; Anggraini, K.; Kausarian, H.; Pujiyati, S. Review: Marine Seismic and Side-scan Sonar Investigations for Seabed
Identification with Sonar System. J. Geosci. Eng. Environ. Technol. 2017, 2, 166–170. [CrossRef]
Ratheesh, R.; Ritesh, A.; Remya, P.G.; Nagakumar, K.C.V.; Demudu, G.; Rajawat, A.S.; Nair, B.; Nageswara Rao, K. Modelling
Coastal Erosion: A Case Study of Yarada Beach Near Visakhapatnam, East Coast of India. Ocean. Coast. Manag. 2018, 156, 239–248.
Ward, R.D.; Burnside, N.G.; Joyce, C.B.; Sepp, K.; Teasdale, P.A. Improved Modelling of the Impacts of Sea Level Rise on Coastal
Wetland Plant Communities. Hydrobiologia 2016, 774, 203–216. [CrossRef]
Energies 2021, 14, 7413
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
18 of 19
Honarmand, M.; Shahriari, H. Geological Mapping Using Drone-based Photogrammetry: An Application for Exploration of
Vein-type Cu Mineralization. Minerals 2021, 11, 585. [CrossRef]
Ji, S.; Gao, Z.; Wang, W. M-DGPS: Mobile Devices Supported Differential Global Positioning System Algorithm. Arab. J. Geosci.
2015, 8, 6667–6675. [CrossRef]
Yoon, D.; Kee, C.; Seo, J.; Park, B. Position Accuracy Improvement by Implementing the DGNSS-CP Algorithm in Smartphones.
Sensors 2016, 16, 910. [CrossRef] [PubMed]
Krasuski, K.; Popielarczyk, D.; Ciećko, A.; Ćwiklak, J. A New Strategy for Improving the Accuracy of Aircraft Positioning Using
DGPS Technique in Aerial Navigation. Energies 2021, 14, 4431. [CrossRef]
Yoon, H.; Seok, H.; Lim, C.; Park, B. An Online SBAS Service to Improve Drone Navigation Performance in High-elevation
Masked Areas. Sensors 2020, 20, 3047. [CrossRef]
Chen, H.; Moan, T.; Verhoeven, H. Effect of DGPS Failures on Dynamic Positioning of Mobile Drilling Units in the North Sea.
Accid. Anal. Prev. 2009, 41, 1164–1171. [CrossRef]
Kim, Y.W. DGPS Service Analysis in the Korean Coastal Ferry Route. J. Korea Inst. Inf. Commun. Eng. 2014, 18, 2073–2078. [CrossRef]
Moore, T.; Hill, C.; Monteiro, L. Is DGPS Still a Good Option for Mariners? J. Navig. 2001, 54, 437–446. [CrossRef]
Ibrahim, P.O.; Sternberg, H. Bathymetric Survey for Enhancing the Volumetric Capacity of Tagwai Dam in Nigeria via Leapfrogging Approach. Geomatics 2021, 1, 246–257. [CrossRef]
Bini, M.; Casarosa, N.; Luppichini, M. Exploring the Relationship between River Discharge and Coastal Erosion: An Integrated
Approach Applied to the Pisa Coastal Plain (Italy). Remote Sens. 2021, 13, 226. [CrossRef]
Frati, G.; Launeau, P.; Robin, M.; Giraud, M.; Juigner, M.; Debaine, F.; Michon, C. Coastal Sand Dunes Monitoring by Low
Vegetation Cover Classification and Digital Elevation Model Improvement Using Synchronized Hyperspectral and Full-waveform
LiDAR Remote Sensing. Remote Sens. 2021, 13, 29. [CrossRef]
Rathour, S.S.; Boyali, A.; Zheming, L.; Mita, S.; John, V. A Map-based Lateral and Longitudinal DGPS/DR Bias Estimation Method
for Autonomous Driving. Int. J. Mach. Learn. Comput. 2017, 7, 67–71. [CrossRef]
Ssebazza, L.; Pan, Y.J. DGPS-based Localization and Path Following Approach for Outdoor Wheeled Mobile Robots. Int. J. Robot.
Autom. 2015, 30, 13–25. [CrossRef]
Vetrella, A.R.; Fasano, G.; Accardo, D.; Moccia, A. Differential GNSS and Vision-based Tracking to Improve Navigation
Performance in Cooperative Multi-UAV Systems. Sensors 2016, 16, 2164. [CrossRef] [PubMed]
Liu, J.; Wang, L.; Teng, F.; Li, D.; Wang, X.; Cao, H. Crop Area Ground Sample Survey Using Google Earth Image-aided. Trans.
Chin. Soc. Agric. Eng. 2015, 31, 149–154.
Muhammad, S.; Tian, L. Hunza, Gilgit and Astore Valley Glacier Elevation Changes During 2003 to 2014 Using ICESat and DGPS
Data. In Proceedings of the International Symposium on Glaciology in High-mountain Asia, Kathmandu, Nepal, 1–6 March 2015.
Galan-Martin, D.; Marchamalo-Sacristan, M.; Martinez-Marin, R.; Sanchez-Sobrino, J.A. Geomatics Applied to Dam Safety DGPS
Real Time Monitoring. Int. J. Civ. Eng. 2013, 11, 134–141.
Malinowski, M. Precise Point Positioning (PPP) Accuracy Using Online Web Services. J. Civil. Eng. Environ. Archit. 2017, 64,
297–313.
Zhang, B.; Chen, Y.; Yuan, Y. PPP-RTK Based on Undifferenced and Uncombined Observations: Theoretical and Practical Aspects.
J. Geod. 2019, 93, 1011–1024. [CrossRef]
Zhang, B.; Hou, P.; Zha, J.; Liu, T. Integer-estimable FDMA Model as an Enabler of GLONASS PPP-RTK. J. Geod. 2021, 95, 91.
[CrossRef]
Akpınar, B.; Aykut, N.O. Determining the Coordinates of Control Points in Hydrographic Surveying by the Precise Point
Positioning Method. J. Navig. 2017, 70, 1241–1252. [CrossRef]
Erol, S.; Alkan, R.M.; Ozulu, İ.M.; İlçi, V. Performance Analysis of Real-time and Post-mission Kinematic Precise Point Positioning
in Marine Environments. Geod. Geodyn. 2020, 11, 401–410. [CrossRef]
Seonghyeon, Y.; Hungkyu, L.; Yunsoo, C.; Geonwoo, H. Potential Accuracy of GNSS PPP- and PPK-derived Heights for
Ellipsoidally Referenced Hydrographic Surveys: Experimental Assessment and Results. J. Position. Navig. Timing 2017, 6, 211–221.
Specht, M.; Stateczny, A.; Specht, C.; Widźgowski, S.; Lewicka, O.; Wiśniewska, M. Concept of an Innovative Autonomous
Unmanned System for Bathymetric Monitoring of Shallow Waterbodies (INNOBAT System). Energies 2021, 14, 5370. [CrossRef]
SBG Systems. Ekinox Series. Available online: https://www.sbg-systems.com/products/ekinox-series/ (accessed on 5 November 2021).
SBG Systems. Ellipse Series. Available online: https://www.sbg-systems.com/products/ellipse-series/ (accessed on 5 November 2021).
Stateczny, A.; Kazimierski, W.; Burdziakowski, P.; Motyl, W.; Wisniewska, M. Shore Construction Detection by Automotive Radar
for the Needs of Autonomous Surface Vehicle Navigation. ISPRS Int. J. Geo-Inf. 2019, 8, 80. [CrossRef]
Specht, M.; Specht, C.; Lasota, H.; Cywiński, P. Assessment of the Steering Precision of a Hydrographic Unmanned Surface Vessel
(USV) along Sounding Profiles Using a Low-cost Multi-Global Navigation Satellite System (GNSS) Receiver Supported Autopilot.
Sensors 2019, 19, 3939. [CrossRef]
Specht, M.; Specht, C.; Dabrowski,
˛
P.; Czaplewski, K.; Smolarek, L.; Lewicka, O. Road Tests of the Positioning Accuracy of
INS/GNSS Systems Based on MEMS Technology for Navigating Railway Vehicles. Energies 2020, 13, 4463. [CrossRef]
Szot, T.; Specht, C.; Specht, M.; Dabrowski, P.S. Comparative Analysis of Positioning Accuracy of Samsung Galaxy Smartphones
in Stationary Measurements. PLoS ONE 2019, 14, e0215562. [CrossRef] [PubMed]
Energies 2021, 14, 7413
81.
82.
83.
19 of 19
Specht, M. Method of Evaluating the Positioning System Capability for Complying with the Minimum Accuracy Requirements
for the International Hydrographic Organization Orders. Sensors 2019, 19, 3860. [CrossRef] [PubMed]
Specht, C. Availability, Reliability and Continuity Model of Differential GPS Transmission. Annu. Navig. 2003, 5, 1–85.
Specht, C.; Pawelski, J.; Smolarek, L.; Specht, M.; Dabrowski,
˛
P. Assessment of the Positioning Accuracy of DGPS and EGNOS
Systems in the Bay of Gdansk Using Maritime Dynamic Measurements. J. Navig. 2019, 72, 575–587. [CrossRef]