## 2 Materials and Methods
### GNSS RTK Corrections and Field Data Acquisition  
A Trimble Ag25 dual-frequency GNSS receiver with a Trimble CFX-750 GNSS controller (Trimble, Sunnyvale, CA, USA) using GPS and GLONASS satellite data were used for GNSS observations (Figure 2). The GNSS positioning and navigation system was equipped on the agricultural tractor Case IH CS 105 PRO (Case IH, Racine, WI, USA), while the Trimble EZ-steer system (Trimble, Sunnyvale, CA, USA) ensured assisted guidance of the vehicle. The same assisted guidance solution minimized subjective steering errors by the operator, with the GNSS receiver dominantly producing positioning errors with a major variability in a previous study [11]. While inferior to the more expensive fully integrated autosteering solution, its practical effectiveness and consistency combined with RTK corrections in a similar application were noted [8]. EZ-steer was integrated and compatible with all evaluated GNSS corrections, applied for both straight and curved sections of the trajectory. The movement speed of the agricultural tractor was constantly 4 km h\({}^{-1}\) for all repetitions, simulating the tractor movement speed during the agrotechnical operations, such as sowing and planting [22]. Figure 1: Study area and the trajectory for the accuracy assessment of GNSS RTK corrections. Figure 2: The equipment used for the research: (**a**) Case IH CS 105 PRO agricultural tractor, (**b**) Trimble Ag25 GNSS receiver with the CFX-750 controller. Three GNSS corrections and an absolute positioning method with the smartphone receiving GPS, GLONASS, and Beidou signals were used in the research. All GNSS observations representing the actual trajectory of the agricultural tractor were performed in one epoch, simulating the actual use of GNSS positioning and navigation during agotechnical operations. Each positioning variant was performed in two repetitions to ensure repeatability of the proposed method, the lower effect of the operator's subjective assessment, and lower effect of a particular constellation of GNSS satellites [23; 24]. Previous studies successfully addressed these conditions either by performing fieldwork in a similar duration to this study under varying satellite constellations [4] or by applying few shorter consecutive repetitions [9]. The three GNSS corrections used included CROPOS, base station, and SBAS. CROPOS with High-Precision Positioning Service (VPPS) was used for RTK observation with the declared horizontal accuracy of 2 cm and vertical accuracy of 4 cm [7]. The GNSS positioning was performed using the 33 permanent base stations in Croatia, distributing mobile RTK corrections in RTCM 3.1 format. Base station variant represented GNSS positioning using the single base station, distributing radio RTK corrections [25]. A commercial solution by the major local agricultural company was used, being 18 km away from the study area. Similar solutions implemented in previous studies achieved a horizontal positioning accuracy up to 2 cm, while a relatively large distance from the base station to the rover is expected to produce a slightly lower accuracy [26]. SBAS is arguably the most widely implemented GNSS solution for agricultural machinery in Croatia due to its low cost, allowing horizontal precision accuracy in the range of 15-25 cm [27]. The European Geostationary Navigation Overlay Service (EGNOS) (European Space Agency, Paris, France) corrections were used in this study, while SBAS solutions are widely available worldwide depending on the location by similar services [28]. Mobile device GNSS positioning using the absolute positioning method was the last variant, as the most widely available method requiring only a smartphone and a free Android tracking app. It was used as a reference for the comparison to other GNSS corrections, with a declared positioning accuracy of more than 3 m [29].