energies 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 2 of 19 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, GPS,GLONASS GLONASSand andGalileo Galileosatellites; satellites; They TheSplitBox SplitBoxcomputer computersystem system (SBG Systems, Carrières-sur-Seine,France) France)(Figure (Figure1c) 1c) The (SBG Systems, Carrières-sur-Seine, usedtotoacquire acquireand andprocess process data data recorded in used in real-time real-timeby bytwo twoGNSS GNSSreceivers receivers(embed(emded inside thethe SplitBox system), anan IMU and two external GNSS antennas; bedded inside SplitBox system), IMU and two external GNSS antennas; modem,enabling enablingthe thereception receptionofofRTK/RTN RTK/RTNcorrections corrections (KorenixTechnology, Technology, AAmodem, (Korenix New Taipei City, Taiwan) (Figure 1d) and providing the positioning 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. 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