## 2 Materials and Methods
### MRA Reference Trajectory
If, hypothetically, one of the sides of the trolley was raised to a height of 20 mm, this would mean a horizontal error (acting in the direction of the trajectory) less than 0.2 mm. * The possible error caused by the torsion of the trolley and the deflection drawbar in the yaw direction was reduced by the tilting of the driven wheels in the direction of the tangent to the trajectory. This resulted in the elimination of wheel skidding and reduction of the centrifugal force. By placing the driven wheels and most of the weight (construction of the trolley and its components) at the end of the freely rotating lever, the possible deflection of the drawbar was eliminated. Another aspect minimising this possible deviation was the even distribution of the component weights on the trolley. * The possible error caused by the torsion of the trolley frame and the deflection of the drawbar in the roll direction was minimised by the robust joint at the height of the trolley centroid. Since the test track had a suitable tilt of the surface (less than 0.01 m to a radius of 3 m with respect to the circle created by the trolley wheels), the error according to the horizontal surface in the calculations of the location determination deviation was less than 0.02 mm. Figure 2: Drawing of the absolute alignment of MRA trajectory of two reference points, the placement of four evaluated RTK receivers, the instruments of MRA represented by blocks and the placement of the GNSS antennas. The absolute angles were obtained based on the recorded times of microprocessor hours from the incoming leading edge of the three sensors: incremental encoder, a Hall probe and clock synchronisation signal Pulse per second (PPS) from the built-in MRA GNSS. Each signal was assigned a UTC time stamp in seconds per day in a microsecond resolution, as verified in the previous study of the authors of reference [45]. In contrast to the methodology used in the previous study, only one signal from the incremental encoder was used (the second signal was used only to determine the arm rotation direction). This decreased the MRA resolution from 5000 pulses to 2500 pulses related to one turn. The incremental encoder signal validity was algorithmically processed with the maximal set tolerance of \(\pm 3\) redundant or missing pulses per turn. Measurement sections (turns bounded by two pulses from the Hall probe) failing to meet this condition were excluded. This ensured the accuracy of the angle distance (potential distance error in the direction of motion along the MRA reference trajectory) of 22.6 mm in relation to the MRA trajectory. The obtained signal was further resampled using linear interpolation of the time-synchronous signal, corresponding to the clock of the given each RTK receiver. These samples were assigned corresponding coordinates in the ENU coordinate system with the same origin as the reference trajectory by subtracting the GNSS antenna angle offset (\(\delta\)) of size \(18^{\circ}\). Using the obtained data pairs, the values of instantaneous angular speed \(v_{r}\) and instantaneous angular acceleration \(a_{r}\) in relation to the trolley were calculated. Due to the high noise levels, these waveforms had to be smoothed out by a convolution filter with a core size equal to 7 for the instantaneous angular speed \(v_{f}\) and 33 for the instantaneous angular acceleration \(a_{f}\). On each measurement day, six sets of tests were performed, and the approximate angle speed of the arm (antenna of the RTK receivers) was set at the following values: 2 m s\({}^{-1}\), 3.5 m s\({}^{-1}\), 5 m s\({}^{-1}\), 6.5 m s\({}^{-1}\), 8 m s\({}^{-1}\) and 9.5 m s\({}^{-1}\). This represented the range of speeds used in agriculture, from soil tillage to transport. Each set of a concrete angle speed comprised three parts, forming the following scenario (Figure 8b): a gradual start from zero to the speed with the required value, even movements during the speed with the required value for 40 or 60 s approximately and breaking.