Development of a Digital Twin of the Harbour Waters and Surrounding Infrastructure Based on Spatial Data Acquired with Multimodal and Multi-Sensor Mapping Systems

Abstract

Digital twin is an attractive technology for the representation of objects due to its ability to produce precise measurements and their geovisualisation. Of special interest is the application and fusion of various remote sensing techniques for shallow river and inland water areas, commonly measured using conventional surveying or multimodal photogrammetry. The construction of spatial digital twins of river areas requires the use of multi-platform and multi-sensor measurements to obtain reliable data of the river environment. Due to the high dynamics of river changes, the cost of measurements and the difficult-to-access measurement area, the mapping should be large-scale and simultaneous. To address these challenges, the authors performed an experiment using three measurement platforms (boat, plane, UAV) and multiple sensors to acquire both cloud and image spatial data, which were integrated temporally and spatially. The integration methods improved the accuracy of the resulting digital model by approximately 20 percent.

1. Introduction

The management of water bodies, such as rivers, lakes, inland water, and seaports, and the infrastructure in their surroundings is a key task in order to keep these areas safe and operational. Reliable geospatial information greatly enhances this process. The most difficult aspect of acquiring spatial data in water areas is environmental constraints affecting the difficult measurement accessibility of mapped areas as well as sublime measurement techniques requiring multimodal measurement platforms. To improve accuracy and reduce the duration of measurement sessions, for years, the measurement community has been working on the broadest possible integration of different measurement techniques, i.e., acoustic, optical, and satellite, which require different techniques of positioning and orientation in space [1,2,3,4,5,6,7]. In addition, they have varying degrees of measurement uncertainty, resolution, and area coverage. The speed of the sensor platforms used, e.g., aeroplanes, autonomous underwater vehicles (AUVs), and boats, is also a challenge.

This publication describes a research experiment and the process of developing a spatial digital twin of rivers and inland navigation areas using multiple measurement technologies. The main objective of the research is to develop a method for integrating data from multiple sensors and different platforms while maintaining the measurement accuracy characteristic of bathymetric data (0.1 m). The authors hypothesise that a digital twin accuracy of 0.1 m can be achieved through temporal integration of data from different sensors and by increasing the accuracy of determining the offsets of the measuring devices mounted on the boat and by applying modified Q-ST (Quasi-Similarity Transformation) to the integration of data from different measuring platforms. Finding answers to the main research problem, formulated below in the form of questions, will make it possible to realise the aim of research.

• How can we use a time server to integrate measurement data?
• Will using modified Q-ST transformation to integrate data from different measurement platforms improve the accuracy of data fusion?
• How do we measure the offsets of survey equipment on a hydrographic boat to ensure high accuracy of their determination (within a few millimetres)?

An accurate spatial model of water bodies and the surrounding infrastructure was gained by integrating in time and spatial manner the geospatial data from multiple sensors:

• ALS—Airborne Laser Scanning.
• ALB—Airborne Laser Bathymetry.
• MSLS—Mobile Surface Laser Scanning onboard.
• MLS—Mobile Laser Scanning on Land.
• MBES—multibeam echosounder.
• SBP—Sub-Bottom Profiler.
• S—Side Scan Sonar.
• Measurements of DGNSS—Differential Global Navigation Satellite System.
• Airborne aerial photogrammetry and UAV.

The main criterion for integration was to reduce the duration of measurement sessions and their number. To time-match the data, an acquisition system was developed, the central element of which is a time server. After fitting in the time domain of the data, an integrated method of measuring device offsets and a modified Q-ST (Quasi-Similarity Transformation) algorithm [8] of adjustment points were used for their spatial integration.

The concept of a digital twin has been defined by the Digital Twin Consortium as a “virtual” representation of real-world entities and processes synchronised at a specified frequency and fidelity [9]. Digital twin technology, as discussed, represents a transformative approach by creating real-time digital replicas of physical systems, allowing for dynamic monitoring, prediction, and optimisation of water systems. These digital frameworks, coupled with data from the Internet of Things (IoT) and advanced analytics, have demonstrated their potential to revolutionise water conservancy through more precise forecasting and better resource allocation [10,11,12]. However, the successful deployment of digital twins in water management still faces technical and infrastructure-related challenges, particularly in integrating legacy systems and ensuring data accuracy and consistency [13,14,15,16]. In parallel, the application of remote sensing technology in water management has expanded significantly. Refs. [1,6] provide a comprehensive review of how remote sensing techniques are being utilised to monitor river corridors, assess water quality, and track hydrological changes over time. The ability to collect spatial and temporal data at various scales offers water managers unparalleled insights into watershed behaviour, which, when combined with other digital tools, enhances the predictive capabilities of water management systems [13,16]. Digital twins enable testing in a virtual environment, providing valuable information on performance, safety, and environmental impact before resources are expended and potentially wasted [17,18,19,20,21,22,23]. Digital twins are classified into five levels of development (Figure 1). Digital twin development levels include integration of geospatial data (stage 1), integration of measurement sensors (stage 2), real-time analysis, including prediction (stage 3), simulation of various scenarios, including optimisation and remote diagnostics (stage 4), and autonomous digital twin capable of learning and decision making (stage 5) [24,25,26]. The use of geospatial data and digital object models takes place at all levels of digital twin development and is a key element in its construction [17,27].

Spatial models of cities and area objects are commonly created using laser scanning and digital photogrammetry [28,29]. For areas of rivers and reservoirs, the use of a green laser beam (532 nm) for imaging the topography of the bottom is of particular importance, which is made possible by the use of Airborne Laser Bathymetry (ALB) lidar [30,31]. This is important for shallow and non-navigable areas, where bathymetric lidar is an alternative to traditional low-density GNSS or Total Station surveys [32]. Automated mapping of bathymetry and coastal areas, including precise underwater positioning, is the subject of much research and focuses on the use of various remote sensing methods, including underwater, surface, aerial, and satellite measurements [33,34,35]. The fusion of bathymetric lidar data and hyperspectral imagery (HY) and bathymetric lidar and multibeam echosounder (MBES) or Side Scan Sonar have a special place in these studies [36,37,38,39,40]. Data fusion is possible, among others, through the use of special algorithms related to the study of the waveform of the laser scanner (FWF—full-waveform), the analysis of the neighbourhood of cloud points, or the study of the features of the extracted elements of the previously built spatial model [32,36,41,42,43]. Multi-source spatial data, including imagery and sensor-based observations, were processed through machine learning algorithms to enhance data reliability and provide comprehensive spatial coverage. Artificial intelligence methods, including machine learning [44,45,46], are also used in bottom research, mainly related to its classification. This fusion process was essential in overcoming the challenges posed by the heterogeneous nature of spatial datasets collected from different sources [10]. Ref. [13] discussed the use of multi-agent systems (MAS) for optimising the use of spatial data in water resource management. MAS facilitated the automated processing of spatial data, allowing for real-time decision making based on environmental conditions, resource availability, and consumption patterns. These methods, with regard to data fusion, generally involve two types of sensors (e.g., MBE and ALB or HY and BLS), and they make it possible to develop a point cloud in shallow-water areas, classify the bottom, or define morphological changes. Despite significant advancements, several challenges in integrating spatial data were highlighted, including inconsistencies in data formats, the need for high computational resources for real-time data processing, and the lack of standardised methodologies for integrating heterogeneous data sources. These barriers continue to impede the seamless integration of spatial data into water management systems, but ongoing research is addressing these gaps [10].

The paper is organised as follows. In the Introduction section, arguments to support the need for solutions to integrate spatial data in the process of building digital twins of rivers and fairways were presented. Based on the literature, research problems not yet solved effectively were detailed. Next, the method of data integration to improve the accuracy of the models created is proposed.

The materials and methodology section presents the testbed, the research techniques, and methods used to achieve the research objectives. The results of the research are then presented based on processed data from the multi modal and multi-senor platforms. They are discussed, and conclusions are drawn.

2. Materials and Methods

2.1. Study Area

The study was conducted in eight test areas located in northwestern Poland (Figure 2, Table 1):

a.

Trzebież (waterway—open area of the Szczecin Lagoon)—body of sea water;

b.

Brdowski Bridge—body of sea water located in Szczecin;

c.

Szczecin centre—Chrobry Embankment area—a body of water connecting sea and inland waters;

d.

Cłowy and Dębska Struga Bridges—inland water body;

e.

Stepnica—waterway, turntable, port—sea water area;

f.

Orli Przesmyk—sea and inland water area;

g.

Western Oder—inland water area in Szczecin;

h.

Siecino Lake (West Pomeranian Voivodeship—coordinates: 53.6246884, 16.0145501).

Figure 2. Research test areas a–g.

Figure 2. Research test areas a–g.

Table 1. Data collected using different measurement systems.

Area	Measurement System
	Airborne Laser Scanning	Airborne Laser Bathymetry	Mobile Laser Scanning on Land	Unmanned Aerial Vehicle	Mobile Surface Laser Scanning Onboard	Multibeam Echosounder	Sub-Bottom Profiler	Side Scan Sonar
a	+	+				+	+	+
b	+	+	+	+	+	+		+
c	+	+	+	+	+	+		+
d	+	+		+		+		+
e	+	+		+	+	+		+
f	+	+		+	+	+		+
g	+	+				+		+
h	+	+		+		+	+	+

Table 1. Data collected using different measurement systems.

Area	Measurement System
	Airborne Laser Scanning	Airborne Laser Bathymetry	Mobile Laser Scanning on Land	Unmanned Aerial Vehicle	Mobile Surface Laser Scanning Onboard	Multibeam Echosounder	Sub-Bottom Profiler	Side Scan Sonar
a	+	+				+	+	+
b	+	+	+	+	+	+		+
c	+	+	+	+	+	+		+
d	+	+		+		+		+
e	+	+		+	+	+		+
f	+	+		+	+	+		+
g	+	+				+		+
h	+	+		+		+	+	+

Data were collected in inland areas, river areas (including shallow water), a lake (test area a, Szczecin Lagoon), and internal marine waters that administratively extend to the centre of the city of Szczecin (test area c). In test areas c and b, data were also collected using MLS on land. The types of data collected for each test area are shown in Table 1.

In this study, in eight test areas, labelled in Table 1 from a to g, aerial data (ALS and ALB) were collected from all areas. MLS data were collected mainly from urbanised areas, where access by car was possible (areas b and c). In these areas, data were also collected using laser scanning from a survey boat (MSLS). In all aquatic areas, data were also collected using sonar and echosounder, while SBP was used to measure on lakes.

2.2. Materials

In this study, data were acquired from the air (from high and low altitude from aircraft and UAV), from the water surface, underwater, and from the ground surface, shown schematically in Figure 3.

Two boats were used for hydrographic data acquisition: Hydrograf XXI (Maritime University in Szczecin) and HYDROMAPPER (from Gispro).

The hydrographic measurements were divided into two stages. The first stage was preliminary and served as preparation and validation of hardware and software configurations. The second stage was the main stage of measurement, during which data were collected in the test areas. During the first stage of measurements, a single-head bathymetric system installed on the Hydrograf XXI survey boat was used for hydrographic data acquisition, which included the following:

• Multibeam echosounder: R2Sonic 2024 (R2Sonic LLC, Austin, TX, USA).
• Positioning system INS: I2NS™ Type I (Applanix, Oswestry, UK).
• SVS and SVP: Valeport water speed of sound sensors (Valeport, Devon, UK).

In stage two, the equipment was mobilised on a HYDROMAPPER floating measurement unit. The unit was adapted for integrated measurements. The measurement system used in stage two was expanded with more hydrographic sensors, which mainly included a second R2Sonic 2024 multibeam echosounder head, including the following:

• Side-scan sonar Edgetech 4125 (EdgeTech, West Wareham, MA, USA);
• Parametric sonar Subbottom profiler (SBP) Innomar SES-2000 (Innomar Technologie GmbH, Rostock, Germany);
• Underwater positioning system USBL Easy Track (Aae Technologies, Great Yarmouth, UK;
• Heading Sensor iXblue (iXblue Inc., Denver, CO, USA).

Aerial data collection was performed using aircraft and UAVs owned by GISPRO. (GISPRO SA, Szczecin, Poland) The aircraft was equipped with a Riegl VQ-880-G II (RIEGL Laser Measurement Systems GmbH, Horn, Austria) laser scanner with simultaneous green (ALB) beam measurement at 532 nm and infrared (topographic-ALS) beam measurement at 1064 nm and a medium-format camera. The Unmanned Aerial Vehicle was equipped with a hybrid combustion–electric engine and was developed specifically for this project [47]. The use of such engines allowed us to extend the flight time to two hours, and it was equipped with sensors: a laser scanner Riegl VUX-120 (RIEGL Laser Measurement Systems GmbH, Horn, Austria), INS APX-20, a Sony A7R IV camera, and a multispectral Parrot Sequoia+ (Parrot Drones, Paris, France) camera. Mobile laser scanning (MLS) and water surface laser scanning (MSLS) data were collected using a Riegl VMQ-1HA device and VMZ-400i (RIEGL Laser Measurement Systems GmbH, Horn, Austria).

2.3. Methodology

This publication proposes a method for creating a digital spatial twin of rivers and inland areas, the novelty of which involves the following:

• Use of a wide variety of platforms and measurement systems: aerial, surface, terrestrial, and underwater;
• Determination of offsets of measuring devices on hydrographic boats using a new measurement and calculation method;
• Time synchronisation of measurements by using a Time Tagging Unit time server;
• Use of a modified Q-ST transformation to combine point clouds by changing the sequence of calculations and applying a robustness criterion based on the lengths of homologous vectors while reducing the number of these vectors to the vectors with the highest confidence level.

The data fusion algorithm is shown in Figure 4.

The first step in developing the twin is to prepare the systems and measurement platforms for operation. To this end, installation of equipment and measurement systems on measurement platforms, calibration of sensors, and determination of offsets of measurement equipment are performed. In the next step, test measurements are made, on the basis of which the configuration of equipment and the correctness of data collection are tested.

Lidar sensor data collection can be described by the general equations of point cloud measurement in the local system of the device (BF—Body Frame) (1):

$$x_P=r·\cos \beta ·\cos \alpha$$

$$y_P=r·\cos \beta ·\sin \alpha$$

$$x_P=r·\sin \beta$$

(1)

where

r—distance of the measured point from the sensor;

α—horizontal angle (measured in the horizontal plane of the sensor);

β—vertical angle (measured in the vertical plane containing the axis of rotation of the sensor).

The laser scanner used in land mobile measurements (MLS) and above-water measurements (MSLS) has the manufacturer’s offsets of the scanner’s own local coordinate system (SOCS) (Fig. relative to the BF (Body Frame) system reference point). The laser scanner takes measurements in its own system, so measurements (1) are referenced to the SOCS point, which is the local origin of the coordinate system to which the measurements are referenced.

Because the system associated with the IMU (BF—Body Frame) is a NED (North–East–Down) system and given the offsets of the SOCS relative to the BF (the manufacturer’s data), the coordinates from the scanner’s own system (SOCS) to the BF system are converted according to the following Formula (2):

$$\left[\begin{array}{c}{X}_L^{IMU}\\ Y_L^{IMU}\\ Z_L^{IMU}\end{array}\right]=\left[\begin{array}{ccc}-1& 0& 0\\ 0& 1& 0\\ 0& 0& -1\end{array}\right]\times \left[\begin{array}{c}{X}_{SOCS}\\ Y_{SOCS}\\ Z_{SOCS}\end{array}\right]+\left[\begin{array}{c}-0.0100\\ -0.0011\\ -0.2761\end{array}\right]$$

(2)

A number of factors influence the accuracy of point measurement through mobile laser scanning. The main ones are those related to the elements of the system itself, i.e., the measurement accuracy of the scanner, the GNSS positioning system, and the IMU, and the accuracy of the whole system is the result of the fusion of data from these elements. In the literature, the relationship between these systems is described by the following formula:

$$\left[\begin{array}{c}{x}_p\\ y_p\\ z_p\end{array}\right]=R_{LH}^W\left(t\right)R_{IMU}^{LH}\left(t\right)\left[k_L^{IMU}{R}_L^{IMU}\left[\begin{array}{c}{x}_L\\ y_L\\ z_L\end{array}\right]+\left[\begin{array}{c}{x}_L^{IMU}\\ y_L^{IMU}\\ z_L^{IMU}\end{array}\right] \right]+\left[\begin{array}{c}{x}_{LH}^W\left(t\right)\\ y_{LH}^W\left(t\right)\\ z_{LH}^W\left(t\right)\end{array}\right]$$

(3)

where

$x_p, y_p, z_p$—coordinates of a point in the global coordinate system (WGS-84);

$R_{LH}^W\left(t\right)$—transformation matrix from the local coordinate system to the WGS-84 system;

$R_{IMU}^{LH}\left(t\right)$—transformation matrix from the IMU system to the local coordinate system;

$k_L^{IMU}$—scale factor between the scanner coordinate system and the IMU coordinate system;

$R_L^{IMU}$—transformation matrix from the laser scanner coordinate system to the IMU coordinate system;

$x_L, y_L, z_L$—coordinates of a point in the scanner’s coordinate system;

$x_L^{IMU}, y_L^{IMU}, z_L^{IMU}$—centre of the scanner in the IMU coordinate system;

$x_{LH}^W, y_{LH}^W, z_{LH}^W$—shift between the local coordinate system and the WGS-84 coordinate system.

The collection of hydrographic sensor data using an echosounder can be described by the following general Equation (4) [47]:

$$M_N=P_n+R_{bI}^n(\phi , \theta , \psi )·(R_{bs}^{bI}·r_{bs}+{LA}_{{GNSS}_{bI}}^{MBES})$$

(4)

where

$M_N$—position in the Local Navigation Frame (LNF) (approximated using the Local Geodetic Frame (LGF));

$P_n={[N_P E_P D]}^T$—position of the phase centre of the GNSS antenna in the local navigation system;

$R_{bI}^n$—transformation (rotation matrix by Euler angles: $\phi , \theta , \psi$) from IMU (bI) to LGF (LNF);

$R_{bs}^{bI}$—transformation from the echo sounder system (MBES frame) from the IMU system (bI);

$r_{bs}$—position (position vector) of a point in the echosounder system (MBES frame);

${LA}_{{GNSS}_{bI}}^{MBES}$—offset of the beginning of an echosounder system (MBES frame) relative to the phase centre of an IMU GNSS receiver (bI).

Measurement data from individual sensors installed on the hydrographic boat (MSLM, MBES, SBP, SSS) are integrated in the first step on the basis of the DGNSS time and the PPS signal in the time server ATTU (EivaTime Tagging Unit), which maintains timestamps and distributed dataflows (Figure 5).

The remaining unit, based on the provided information from the DGNSS system, processes the data connected via RS-232 signal cables, combining them with the time, and it sends them further to the workstation via an Ethernet connection. In this way, measurement data from platforms with a DGNSS timestamp are integrated, including aerial data from aircrafts (ALS, BLS), on UAV (photogrammetric camera, ALS), and the ground (MLS). Time integration of data is performed first within the measurement platforms (aircraft, UAV, hydrographic boat, measurement vehicle (MLS)), and then time integration is performed within the whole system. Time synchronisation of data is performed every 200–600 ms. A diagram of the hardware configuration for time synchronisation of measurements is shown in Figure 5. For this purpose, a modified Q-ST (Quasi-Similarity Transformation) algorithm was used, which in its original version was presented in another paper [35]. The modified version, used in the present study, is described by the following relationship (5):

$$X_{RPC}=R·\left[\lambda \left(X_{TPC}-X_{CTPC}\right)\right]+X_{CRPC}$$

(5)

where

$X_{RPC}$—coordinates in the reference point cloud (RPC);

$R$—3D rotation matrix;

$\lambda$—adjusted scale factor;

$X_{TPC}$—coordinates in the transformed point cloud (TPC);

$X_{CTPC}$—coordinates of the centre of gravity in the transformed point cloud (CTPC);

$X_{CRPC}$—coordinates of the centre of gravity in the reference point cloud (CRPC).

In the first step of transformation (5), the two point clouds are translated to their own centres of gravity (centroids—geometric centres). This creates an auxiliary computational space in which the lengths of homologous vectors built from points identified on the two point clouds are compared. The average error for all lengths of homologous vectors is then calculated, and 5% (statistically exceeding twice the average error) of the vectors are rejected. In subsequent steps, more vectors built on homologous points are iteratively discarded, until vectors built on the basis of 16 points (2 in each quadrant for positive and negative Z-coordinate values) are left. Then, scaling is performed in the auxiliary space according to the method of least squares (6), which can be written in the form of Equation (7)

$$X={\left(A^T·A\right)}^{-1}·A^T·L$$

(6)

where

• X—vector of unknown parameters;
• A—matrix of coefficients (partial derivatives —Jacobian transformation);
• L—constants vector.

$$\lambda ={\left({D_{TPC}}^T·D_{TPC}\right)}^{-1}·{D_{TPC}}^T·D_{RPC}$$

(7)

where

D_i—length of the homologous vector in both point clouds—reference and transformed.

In the next step, the quasi-rotation matrix is determined in the auxiliary space using Equations (5) and (7).

$$\left[\begin{array}{c}{X}_{rpc1}\\ Y_{rpc1}\\ \begin{array}{c}{Z}_{rpc1}\\ X_{rpc2}\\ \begin{array}{c}{Y}_{rpc2}\\ Z_{rpc2}\\ \begin{array}{c}\dots \\ X_{rpcN}\\ \begin{array}{c}{X}_{rpcN}\\ X_{rpcN}\end{array}\end{array}\end{array}\end{array}\end{array}\right]=\left[\begin{array}{c}\begin{array}{ccc}{X}_{pc1}& Y_{pc1}& \begin{array}{ccc}{Z}_{pc1}& 0& \begin{array}{ccc}0& 0& \begin{array}{ccc}0& 0& 0\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{ccc}0& 0& \begin{array}{ccc}0& X_{pc1}& \begin{array}{ccc}{Y}_{pc1}& Z_{pc1}& \begin{array}{ccc}0& 0& 0\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{ccc}0& 0& \begin{array}{ccc}0& 0& \begin{array}{ccc}0& 0& \begin{array}{ccc}{X}_{pc1}& Y_{pc1}& Z_{pc1}\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{ccc}{X}_{pc2}& Y_{pc2}& \begin{array}{ccc}{Z}_{pc2}& 0& \begin{array}{ccc}0& 0& \begin{array}{ccc}0& 0& 0\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{ccc}0& 0& \begin{array}{ccc}0& X_{ipc2}& \begin{array}{ccc}{Y}_{pc2}& Z_{pc2}& \begin{array}{ccc}0& 0& 0\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{ccc}0& 0& \begin{array}{ccc}0& 0& \begin{array}{ccc}0& 0& \begin{array}{ccc}{X}_{pc2}& Y_{pc2}& Z_{pc2}\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{c}\dots \\ \begin{array}{ccc}{X}_{pcN}& Y_{pcN}& \begin{array}{ccc}{Z}_{pcN}& 0& \begin{array}{ccc}0& 0& \begin{array}{ccc}0& 0& 0\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{ccc}0& 0& \begin{array}{ccc}0& X_{pcN}& \begin{array}{ccc}{Y}_{pcN}& Z_{pcN}& \begin{array}{ccc}0& 0& 0\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{ccc}0& 0& \begin{array}{ccc}0& 0& \begin{array}{ccc}0& 0& \begin{array}{ccc}{X}_{pcN}& Y_{pcN}& Z_{pcN}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right]·\left[\begin{array}{c}{m}_{11}\\ m_{12}\\ \begin{array}{c}{m}_{13}\\ m_{21}\\ \begin{array}{c}{m}_{22}\\ m_{23}\\ \begin{array}{c}{m}_{31}\\ m_{32}\\ m_{33}\end{array}\end{array}\end{array}\end{array}\right]$$

(8)

where

${rpc}_i, {pc}_i—$indexes of the coordinates refer to subspace, with the centroid (centre of gravity) as the origin of the coordinate system.

In the last step of the transformation, a return translation is performed from the auxiliary space to the real (measurement) space of the reference point cloud, which is written through the last component of the sum in Equation (5).

Post-transformation deviations are calculated using relationship (9), and average errors m are calculated using deviations (9) and covariance matrix Q, using the Formula (10)

$$V=A·X-L$$

(9)

$$Q={\left(A^T·A\right)}^{-1}$$

(10)

with

$$m_0=\pm \sqrt{{\displaystyle \frac{V^T·V}{n-k}}}$$

(11)

$$m_X=m_0·\sqrt{Q_{XX}}$$

(12)

$$m_Y=m_0·\sqrt{Q_{YY}}$$

(13)

$$m_Z=m_0·\sqrt{Q_{ZZ}}$$

(14)

The point cloud fusion is validated on the field control points, and accuracy is assessed by the mean deviation errors of the transformed points relative to the reference control points. The field control points in the form of targets were measured using Total Station and in the form of ground points using the DGNSS RTK technique.

3. Results

3.1. Offsets Measurement

Dimensional control of the survey boat and the offsets of measuring equipment on hydrographic boats was carried out in two stages. In the first stage, offsets were measured on the Hydrograf XXI boat, during which the Total Station–Terrestrial Laser Scanning (TLS) integrated survey method was tested. This method was tested due to the small size of the hydrographic boat, which meant that there was limited opportunity to select measurement stands for Total Station. In addition, Total Stations are generally limited in their ability to measure close points (less than 1 m) due to the problem of aiming and focusing on such a close target. Dual-purpose measurement targets were used to integrate Total Station measurement data with the point cloud from TLS (Figure 5).

Tachymetric measurements were used as a reference for all measurements, to which laser scanning measurements were referenced. Tachymetric measurements were made using the technology of a (completely) free station—Total Free Station (TFS) [48,49]. TFS measurements were made from two stations, each time without levelling the instrument (Total Station). The measurements were taken as random local datums and then combined into a sparse point cloud using transformation (5). The accuracy of the point clouds is shown in

Table 2. Transformation of coordinates between TLS and Total Station point clouds (accuracy estimation).

Accuracy Estimation	Coordinates’ Accuracy After Transformation [m]
	Calculated for Total Station Point Cloud	Calculated for TLS Point Cloud
Mean error	$1.4\times {10}^{-3}$	$4.5\times {10}^{-3}$
Total error (of point)	$1.4\times {10}^{-3}$	$4.7\times {10}^{-3}$

.

Table 2 shows the point cloud accuracies after measuring offsets using the combined Total Station (TS) and TLS methods. The accuracy of the transformation of the tachymetric measurements to the combined point cloud was 1.4 mm, and the accuracy of the transformation of the TLS point cloud relative to the TS point cloud was 4.5 mm. This gives a total TLS cloud error of 4.7 mm, which is at the level of the point cloud density from terrestrial laser scanning. Taking this into account, the result of the transformation and the accuracy of the determination of offsets at the level of no worse than 5 mm was considered satisfactory. This type of survey on larger boats and ships does not impose restrictions on the use of Total Station, which occurs on small survey boats (instrument distance to measured point less than 1 m). It is therefore not necessary to supplement the measurements with additional TLS measurements and thus to combine data of different accuracies. In our study, this was necessary, and to increase the accuracy we used a coordinate transformation algorithm so that the combined point cloud from the Total Station and TLS measurements was at the level of accuracy of the Total Station measurement. This is especially true for points that are impossible to measure with Total Station. The next stage of the work involved dimensioning and measuring the offsets of the HYDROMAPPER boat.

An electronic Total Station, Trimble SPS 930 (Trimble, Westminster, CO, USA), and two terrestrial laser scanners, Faro Focus 3D (FARO Technologies, Lake Mary, FL, USA) and Riegl ZF 5016 (RIEGL Laser Measurement Systems GmbH, Horn, Austria), were used for the measurements. A photogrammetric–geodetic (dual-function) warp was established to check the correctness and accuracy of the fit of the scans, which consisted of measurement discs that were measured with Total Station (Figure 2). The discs were visible on the scans and were used to orient the scans and check the accuracy of their fit. The coordinates of the control points are summarised in

Table 3. Coordinates of geodetic–photogrammetric control points.

Accuracy Estimation	Coordinates’ Accuracy After Transformation [m]
	Calculated for Total Station Point Cloud	Calculated for TLS Point Cloud
Mean error	$1.4\times {10}^{-3}$	$4.5\times {10}^{-3}$
Total error (of point)	$1.4\times {10}^{-3}$	$4.7\times {10}^{-3}$

. The control points were measured in the local coordinate system, levelled with the measuring instrument (Total Station).

Table 3 shows the coordinates of the control points measured by Total Station after their transformation to a single coordinate system. These points were the reference for measured point clouds using terrestrial laser scanning. The accuracy of the control points was 2.4 mm, while the individual scans in the area including the boat (Figure 6) fitted in with an accuracy within 3–10 mm, which was within the limits of the point cloud density, with a distance of the scanned points from the scanner up to 20 m. This result was considered satisfactory. Based on the point cloud processed in this way, the coordinates of the DGNSS receivers and the offsets of the measuring devices were determined on it with an average error of 6 mm (Figure 6). The approach used is satisfactory compared to traditionally used Total Station survey methods. In the approach presented here, as well as the measuring offsets, a TLS point cloud was used while maintaining the accuracy characteristic of tachymetric measurements of 1–10 mm.

3.2. Hydrographic Surveys

Conducting data acquisition in designated areas (see Figure 2, Table 1), the measuring system on the hydrographic boats was configured to acquire all kinds of hydrographic and topographic data from the installed lidar systems at one time. The dual head of the multibeam echosounder provided information on bathymetry—the shape of the bottom, backscatter—data on the intensity of acoustic signal reflection, used for bottom classification, and water column data. The solution used, compared to the preparatory work (the first stage in Figure 4) with a single head, has the advantage of wider coverage of the bottom with data in a similar measurement time. This was made possible by using two heads and angular inclination of the sonar heads by ±20 degrees outwards.

Figure 7 compares data from the same area for one and two measuring heads. The use of two heads, at depths of 7–8 m, increased the range twice: from 26 m to 54 m (Figure 7).

With this configuration, improvements in scanning underwater vertical surfaces, i.e., quay walls, bridge pylons, are also apparent. The heads are physically tilted, so their point cloud collection capability is close to the water surface, which, in conjunction with laser scanning, results in an integral situational model (Figure 8).

The hydrographic data underwent processing consisting of alignment of navigation data, removal of outliers, and cleaning of depth measurement interference. This was performed using manual and automatic techniques implemented in the hydrographic software (Kuda Processing 4.8.1). Finally, processing quality control was performed by comparing the mapped areas to the requirements of the IHO special category S-44.

Table 4. Evaluation of compliance of bathymetric data with the s-44 standard.

Area (See Figure 2, Table 1)	QC Statistics
Area “Most Clowy”	Survey Accuracy: Standard = Exclusive Order, a = 0.150, b = 0.004 Footprints conform with survey accuracy: 25,016,768 (96.59%)
Area “Stepnica”	Survey Accuracy: Standard = Exclusive Order, a = 0.150, b = 0.004 Footprints conform with survey accuracy: 39,566,095 (98.93%)
Area “Orli Przesmyk”	Survey Accuracy: Standard = IHO Special Order, a = 0.250, b = 0.007 Footprints conform with survey accuracy: 17,577,633 (98.77%)
Area “Trzebież”	Survey Accuracy: Standard = Exclusive Order, a = 0.150, b = 0.004 Footprints conform with survey accuracy: 21,263,698 (98.27%)

shows the percentage of mapped areas that meet the IHO accuracy criteria for area type: Exclusive and Special. The green colour indicates achievement of accuracy in accordance with the standard.

EIVA NaviModel Producer and NaviEdit software (4.8.1)were used to process bathymetric data. For each area, a point cloud was exported in *.las format. Then, a GRID model was generated from the point cloud with a resolution of 0.25 m. Using the “show difference” tool, new layers with difference models were created. Transverse and longitudinal profiles generated from the resulting terrain (bathymetric) model were also analysed in the comparison (Figure 9).

Analysing the differential model (Figure 9) from the two measurement stages (equipment setup and data acquisition), it is clear that the configured bathymetric system has repeatability in the same area. Cross-sectional profiles on the bathymetric surface from the two stages showed slight deviations within the measurement error. The models were created one year apart, where bottom migration of the material has an influence. Subsequent models in designated areas confirm the repeatability of the system at intervals of several days. The occurrence of larger differences is within the limits of error.

Figure 10 shows graphs for the accuracy of TVU (Total Vertical Uncertainty) and THU (Total Horizontal Uncertainty), which are part of the Total Propagated Uncertainty (TPU).

The input data for the calculations were the measurement uncertainties of the individual sensors at a confidence level of 68% included in the MBES R2Sonic dual-head measurement system. TVU and THU were determined for a depth of 12 m at a confidence level of 95%. Both TVU and THU over the entire beam angle range meet the requirements of the IHO S-44 standard [50] for the “special” class. As expected, the accuracy of the measurements decreased upon increasing the beam angle from nadir. The Apriori Multibeam Uncertainty Simulation Tool, TU Delft, was used in the calculations.

For the mathematical model of the total measurement uncertainty TPU (Total Propagated Error), it was assumed that the magnitudes of the unmeasured measurement uncertainties of some sensors are within acceptable ranges, and such values were introduced into the stochastic model. This mainly concerns systematic uncertainties (calibration of sensors, including misalignment of the motion sensor, misalignment of the gyrocompass, information on changes in the height of the water surface or tides, time delay, uncertainties of sensor coordinates in the local reference system of the measuring platform).

3.3. Data Integration and Cross-Validation

Integration of data from multiple measurement platforms and sensors has a temporal and spatial dimension. Integration is performed first within the measurement platforms: aerial (aircraft, UAV), terrestrial (measurement vehicle with MLS), and surface (measurement boat). Integration of data collected using these platforms is performed after their mutual calibration and time synchronisation. In the first stage, data integration was performed through the time server (Figure 11). As a result of the time integration, a uniform DGNSS timestamp was assigned to all measurements, making it possible to determine the coordinates of the measured points in the local systems associated with the measurement platforms. In the next step, geospatial data from all measurement platforms are fused (Figure 3 and Figure 11). For spatial integration of the data (the next steps after Time Alignment in Data Fusion Algorithm—Figure 4), a modified Q-ST algorithm was used along with a homology point selection algorithm, which is resistant to perturbations in the data, for point cloud transformation. Coordinate transformation was performed based on Formulas (5)–(8), and uncertainties were determined based on Formulas (9) and (10).

Geospatial data fusion shown in Figure 11 is performed based on checkpoints: GCP (Ground Control Points) and ICP (Independent Control Point—checkpoint). Nomenclature familiar from photogrammetry and geodesy was adopted for these points. GCP points participated in the Q-ST transformation for calculating the parameters of this transformation, while ICP points were used to check the accuracy of the transformation. GCP and ICP points were measured using GNSS RTK and Total Station measurements. In addition, very high-resolution orthophotos (0.02–0.05 m) were developed from the data acquired from the aerial ceiling, aircraft, and UAVs, which were then used to acquire further control points (ICPs), except that they were 2D. This resulted in a dataset of 3D and 2D control points, which were used for geospatial fusion of the data and evaluation of the accuracy.

For the acquired images and compiled data in the form of orthophotos from the area around the Stepnica Port (study area e), the Orli Przesmyk (study area f), and the Cłowy and Dębska Struga Bridge (study area d), an accuracy analysis was carried out. For this purpose, 27 control points were measured. The average pixel size of the orthophotos compiled from UAV images was 0.03 m. The accuracies obtained using the control points are shown in

Table 5. Accuracy estimation of control points.

GSD [m]	Mean Errors [m]
	GCP	ICP
$3\times {10}^{-2}$	$2.1\times {10}^{-2}$	$3.5\times {10}^{-2}$

. The accuracies were approximately within pixel size (GSD), and for the GCP, the average error was 0.7 GSD. For the ICP, the average error was 1.1 GSD, which confirms the accuracy correctness of the orthophoto processing.

Table 5 shows the mean errors averaged for all study areas. Orthophoto development accuracies within 1 pixel are difficult to achieve in practice but possible for studies of flat areas.

For the acquired and compiled data into a point cloud from the area near the Stepnica Port (study area e), Orli Przesmyk (study area f), Szczecin Venice, and Wały Chrobrego (study area c), 28 control points were measured and used to develop and evaluate the accuracy of MLS and MSLS. Field checkpoints to develop and evaluate the accuracy of MLS and MSLS were (a) the study area Szczecin centre and (b) Brdowski Bridge. The accuracies are collected in

Table 6. Accuracy of MLS and MSLS.

Mean Errors of Control Points
MLS [m]			MSLS [m]
X	Y	Z	X	Y	Z
0.034	0.048	0.059	0.046	0.044	0.056
Accuracy of point
$m_0=8.35\times {10}^{-2}$			$m_0=8.53\times {10}^{-2}$

.

The accuracies shown in Table 6 are at a similar level for both MLS and MSLS. The accuracy of the X and Y coordinates is slightly higher than that of the Z coordinate, which is influenced by the accuracy of DGNSS measurements of control points, which is lower for the Z coordinate. The accuracy (mean error) of the position of MLS and MSLS points relative to the DGNSS matrix is within 0.08–0.09 m relative to the matrix, which was measured with a mean error of 0.03 m. This result is within the measurement accuracy of both systems, confirming the validity of the measurements taken.

The accuracy of the MLS measurements was also verified on the Brdowski Bridge (study area b), where tachymetric measurements were made to the targets (Figure 12). Lengths were compared between homologous points measured with Total Station and the point cloud developed with MLS. The mean error of the MLS relative to the Total Station measurements (vector length error) was determined as m₀ = 0.025 m, which was defined as a satisfactory result.

Aerial data via ALS and ALB were integrated into an aerial platform (aircraft) that was used to plan a synchronous mission.

After the integration of the data, based on algorithm (5), the accuracy of their fit was checked. This was realised in two ways, through cross-sectional analysis and error analysis of adjustment points. Examples of point cloud integration are shown in Figure 13 and Figure 14.

The achieved accuracies of temporal–spatial integration of point clouds are shown in

Table 7. Accuracy of time and spatial data integration.

Mean Errors [m]
Q-ST (Adopted)			Similarity Transformation (Traditional Approach)
X	Y	Z	X	Y	Z
0.084	0.092	0.123	0.113	0.213	0.301
Accuracy of point
$m_0=1.33\times {10}^{-2}$			$m_0=1.94\times {10}^{-2}$

.

Figure 15 shows the validation of ALB measurements against geodetic measurements on water and land. The achieved accuracies show conformity to a normal distribution with a standard deviation of 0.1 m. The top graphs (Figure 15) show the magnitudes of uncertainty in the (from left) XY, XZ, and YZ planes. In each of the cases shown, a random distribution of errors can be seen both in magnitude and position. The histograms of the uncertainties in the X and Y coordinates are further illustrated in the bottom row of the graphs. These histograms show that the distribution of errors is normal.

In fact, the data in both cases (for water and land) are similar and within a mean error of about 0.07 m. At the same time, a comparison of the height of the point cloud against classical hydrographic measurements (Figure 15f) shows that the differences are even smaller, as the average error does not exceed the value of 0.05 m.

4. Discussion

The findings of this study contribute significantly to the ongoing development of spatial digital twins, particularly in integrating diverse spatial datasets for water and land-based systems. Through the use of data from aerial laser scanning (ALS), mobile laser scanning (MLS), and multi-beam echo sounders (MBES), the study achieved a precision improvement of 0.1 to 0.2 m in bathymetric measurements, a more than 20% enhancement compared to traditional methods. This was made possible by implementing a combination of time synchronisation and spatial alignment algorithms, underscoring the value of precise temporal–spatial integration. Such levels of accuracy are essential for tasks like flood prevention, navigation safety, and infrastructure maintenance, particularly in dynamic inland waterways.

Temporal integration, where timestamps were harmonised across different platforms, emerged as a key innovation, significantly enhancing the initial data fusion accuracy from several centimetres to just a few millimetres. Similarly, spatial integration ensured point cloud consistency within a margin of 0.1 m. The Q-ST transformation algorithm proved superior to traditional Helmert transformations, reducing the number of required points for accurate alignment and optimising computational resources without sacrificing precision. Validation exercises confirmed these improvements, with field control points showing a mean deviation error of just 0.1 m.

These advancements align with existing research on digital twins where spatial data forms the foundational building block. For example, studies have used LiDAR data to create digital twins of bridges for virtual-reality-based inspections [51], to assess geometric quality in building facades [52], and to monitor large-scale structures like wind turbines [53]. Each of these applications emphasises the importance of regular updates to reflect the current physical state of assets and their environmental context. Similarly, urban-scale digital twins, such as those in [54,55,56], rely on LiDAR and other geospatial data sources for modeling city objects and ensuring real-time monitoring.

Our study distinguishes itself by integrating geospatial data not as an end but as a means to enrich behavioural and contextual understandings of cyber–physical systems (CPS). Unlike approaches focusing solely on static geospatial information [51,52,55], our methodology highlights system behaviours over time captured and structured to support lifecycle perspectives and stakeholder-specific business processes. For example, studies like [57,58] have shown the potential of integrating LiDAR data with other datasets for dynamic applications like power line inspections and vegetation management. Our work extends these principles by combining temporal, spatial, and semantic dimensions, thus advancing towards intelligent, behaviour-centred digital twins.

Despite these successes, challenges remain. Processing large datasets requires substantial computational power, and discrepancies between horizontal and vertical resolutions persist, especially in shallow water areas. Future research should address these limitations by refining algorithms for dataset alignment and exploring more efficient data fusion techniques. Methodologies like those proposed in [59,60,61,62,63,64] offer valuable insights for addressing these challenges. For instance, automated deployment methods [62] and life-cycle-oriented design models [64] could enhance our approach, particularly for continuous updates and real-time monitoring.

5. Conclusions

The study conducted on the development of spatial digital twin of rivers and inland areas showed that with the approach used, the achievable accuracy of integration of ALS, ALB, MLS, MSLS, and MBES point clouds is at the level of 0.1 m.

The proposed method, thanks to the temporal integration of measurements through a time server and spatial integration through a modified Q-ST algorithm, made it possible to increase the accuracy of developing a digital twin of inland rivers by more than 20% compared to mapping methods used without sensor integration. In addition, it has been shown that aerial bathymetric scanning is comparable in accuracy to classical measurement methods using echosounders and is a valuable source of elevation data acquisition.

The transformation used in this research is an optimised approach in terms of cloud point selection to a small number of points, where the advantages of the Q-ST transformation over the traditional approach of transformation by similarity (Helmert) become apparent.

Various platforms and measurement systems were used to create a geometric digital twin of rivers and inland areas: aerial, surface, terrestrial, and underwater. At the same time, a new approach was used to determine the offsets of measuring devices on hydrographic boats using integrated Total Station–TLS measurements and a modified Q-ST transformation. Time synchronisation of the measurements through a time server made it possible to reduce the uncertainty of the determined coordinates of points obtained in the fusion of MBES and MSLS data. The robustness criterion used led to the creation of a data fusion algorithm with improved accuracy. According to the authors, this is a step toward increasing the accuracy of autonomous navigation on rivers and inland areas. It can also be an important step towards the construction and development of Smart Digital Reality, by means of which the combined digital world with the real world will create a single, frequently updated, data-enriched, and machine-learning-model-enhanced reality of the future. This work was performed under the project “Research and development work on the creation of a complete, multimodal mapping system for the needs of inland and sea waterways and exploitation areas”. The results will enable further research into the development of dynamic digital models of water areas and the synchronisation of the obtained data with public database systems to design technological and systemic solutions for the management and control of retention on surface waters for the development and availability of marine and inland navigation through the use of available hydrotechnical facilities, including junctions and water stages, wharves, and bridges while ensuring the required level of flood protection.