## 2 Materials and Methods  
### Research Methodology  
To achieve the aims enunciated in Section 1.2, the research was divided into three phases. In the first phase an electronic system was implemented to synchronise the Deeper Smart Sonar CHIRP+ or Pro+ 2 and an external GNSS receiver (SimpleRTK2B) via smartphone, the system was called GNSS \(>\) Sonar \(>\) Phone System (G \(>\) S \(>\) P Sys). The idea behind the implementation of the G \(>\) S \(>\) P Sys was to create a network for data exchange, using the smartphone as a platform for input and output data management between the external GNSS receiver and the sonar. The final aim of the System was to send real-time SPP positioning data from the external GNSS receiver to the Deeper Smart Sonar. The System improves sonar geolocation during the bathymetric survey and simultaneously records the raw data from the external GNSS receiver for post-processing in PPK, to additionally improve the sonar GNSS positioning in post-processing. The real-time correction of sonar geolocation via an external GNSS receiver was possible due to the \"mock location\" function present in Android smartphones. Using this function, an app connected to an external GNSS receiver can correct the geolocation of other apps on the smartphone. In the second phase, through some specific tests, several datasets were built to study the performance of the Deeper Smart Sonar and G \(>\) S \(>\) P Sys. A preliminary test was performed to evaluate the performance in static GNSS positioning of the Deeper Smart Sonar (CHIRP+ and Pro+ 2) and the G \(>\) S \(>\) P Sys. Subsequently, two tests were performed under dynamic conditions to evaluate the performance of the Deeper Smart Sonars and the G \(>\) S \(>\) P Sys in kinematic positioning. To study the accuracy and precision of the Deeper Smart Sonars in measuring water depth, a test under controlled conditions in a swimming pool and a test under real conditions in the sea were performed. In order to apply the PPK correction method of sonar geolocation and test the pipeline for 3D modelling of the data obtained from the G \(>\) S \(>\) P Sys, the complete survey of a swimming pool and the survey of a portion of the seabed was performed. Based on the pool survey, a dataset was created to test the 3D modelling of artificial structures, while based on the sea survey, a dataset was created to test the 3D modelling of natural surfaces. In addition, the purpose of the sea test was also to analyse the devices under real operating conditions. Both tests were performed using the Deeper Smart Sonar CHIRP+. In the third research phase, a pipeline was created for the 3D modelling of natural surfaces and artificial structures. The 3D modelling method used can be classified in the macro-group of data-driven modelling [18]. The pipeline developed for modelling natural surfaces consists of three steps: synchronisation, interpolation and 3D modelling. In the synchronisation step, the GNSS positions recorded by the external receiver and corrected in PPK were synchronised with the depth values recorded by the sonar; the sonar GNSS position was corrected during the survey. The proposed method is spatio-temporal as it is performed by synchronising the data produced by the System first based on latitude and longitude coordinates and then on the GPS Time (GPST). This step is possible because, through the electronic synchronisation in real-time of the devices via smartphone, the external GNSS receiver previously transmitted its coordinates to the sonar. The operation allows synchronisation to a one thousandth of a second (\({}^{1}/_{1000}\)). The interpolation step was performed in order to transform isolated data into continuous data in a grid format. To generate the bathymetric grid, an innovative interpolation method based on Machine Learning (ML) was used. In particular, the Forest-based Classification and Regression algorithm implemented in ArcGIS PRO software (ESRI, Redlands, CA, USA) was applied.