## 2 Materials and Methods
### Methodology
where  
\(x_{p},\,y_{p},\,z_{p}\)--coordinates of a point in the global coordinate system (WGS-84);  
\(R_{LH}^{W}(t)\)--transformation matrix from the local coordinate system to the WGS-84 system;  
\(R_{IMU}^{LH}(t)\)--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]:  
\[M_{N}=P_{n}+R_{bl}^{n}(\varphi,\,\theta,\,\psi)\cdot\left(R_{bs}^{bl}\cdot r_{bs }+LA_{GNSS_{hl}}^{MES}\right) \tag{4}\]  
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;  
\(R_{bl}^{n}\)--transformation (rotation matrix by Euler angles: \(\varphi,\,\theta,\,\psi\)) from IMU (bI) to LGF (LNF);  
\(R_{bs}^{bl}\)--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);  
\(LA_{GNSS_{hl}}^{MES}\)--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  
Figure 5: Scheme of time-server-based synchronisation of measurements. 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):  
\[X_{RPC}=R\cdot[\lambda(X_{TPC}-X_{CTPC})]+X_{CRPC} \tag{5}\]  
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.