## 1 Introduction
A PID controller is a commonly used feedback controller, which is popular because of its simplicity in design and robustness in performance. In a PID controller, which is sometimes called a three-term controller, three separate constants work together to minimise the error between the desired commands and the actual system response [27]. The distinguishing feature of the PID controller is the ability to use the three control terms of proportional, integral, and derivative influence on the controller output to apply accurate and optimal control of the USV's course between the points located on the sounding profile. The PID controller continuously calculates an error value, e(t), as the difference between the calculated course between the (start and end) points of the sounding profile, r(t), and the current course calculated between the current USV's position from the Global Positioning System (GPS) and the turning point on the profile, y(t). On this basis, the autopilot calculates the control signal, u(t), as a weighted sum of the outputs of three PID control terms (Figure 3) and feeds it to the vessel steering system. The K\({}_{\text{p}}\), K\({}_{\text{i}}\), and K\({}_{\text{d}}\) coefficients are values for determining the effect of particular terms on the automatic process control. Their values are determined in the autopilot tuning process. The values of variables r(t) and y(t) presented in Figure 3 are, in navigation terms, two angles. The former is the sounding profile azimuth (the angle between the line connecting the beginning and the end of the profile and the geographic north), while the latter is the current USV course, i.e., the angle between the instantaneous course line and the direction of geographic north (Figure 4). Figure 3: USV autopilot steering process. Own study based on [28]. Figure 2: Applications used to plan sounding work, such as AutoDron (**a**) [26] and QINSy (**b**). In automatic mode, the USV autopilot should control in such a manner so that, based on the course y(t) being continuously determined, the rudder angle could be changed to obtain the end point of the profile along the shortest route. This is only possible provided that the current vessel's position is determined using GNSS systems. Hence, the accuracy of USV positioning using a GNSS system is crucial due to the control accuracy. On the other hand, the referenced study proposed that the measure of steering precision should be the value of the transverse, lateral deviation from the course (cross track error--XTE). It should be minimised, i.e., the vessel ought to be located as close as possible to the sounding profile. For calculating XTE, the discrete location samples representing the vehicle's path must be represented in a local Cartesian (x, y) coordinate system. While some location recording equipment may directly provide this information, others (such as that used in this work) provide output in the form of latitude and longitude coordinates. These were simply transformed using formulas and methods described in International Organization for Standardization (ISO) 12188-2:2012 standard [29]. This provided input to the XTE calculation procedure that consisted of a list of points in Cartesian coordinates for both the outbound and return paths [30]. In Figure 4, the XTE parameter, i.e., the lateral distance (transverse to the course) between the USV's position and the sounding profile, is added. In view of the fact that contemporary USVs use various GNSS system solutions (with various positioning accuracies) for the positioning, it is reasonable to ask: what GNSS solutions should be applied to ensure a positioning accuracy that is acceptable from the steering accuracy perspective? This study attempted to assess the accuracy of controlling a small automatic hydrographic vessel using an autopilot with a low-cost multi-GNSS receiver that is typical of recreational and Unmanned Aerial Vehicles (UAV).