## 2 Materials and Methods
### MRA Reference Trajectory  
In a previous study [46], the development of a MRA reference platform was finalised, and the method for the measurements of RTK dynamic properties was verified. This methodology determined the process of data collection and data evaluation, aiming to obtain a precise reference trajectory. Following the previous study, it was possible to compare the reference trajectory to the measured trajectories of four selected RTK receivers and deliver, based on this comparison, specific values determining the properties of RTK receivers. The measurements were performed in an outside test track of the development centre (Figure 1), which met the suitable conditions for measuring purposes. This place was selected based on its surface quality, necessary equipment and the possibility to perform recurring measurements at the same place during three measurement days. The measurements were performed on three days: 4 July 2019, 2 August 2019 and 28 August 2019. The MRA was installed in a precisely marked location before each measurement day. This location was defined after the first day of measurement by accurately surveying the two reference points (Figure 2). For this surveying, Receiver A was used, which was the most credible. The catalogue accuracy of this device stated by the manufacturer was 0.01 m + 1 ppm. The static measurement, which was part of this study, then showed \(RMS_{err}=0.009\) m (Evaluation 5). Both reference points were determined by the averaging of fixed positions with the same correction signal as the one used for the measurement. The first point defined the absolute location of the centre of the circular reference trajectory (\(P_{C}\)), and the second point defined the initial absolute angle (azimuth) of this circular reference trajectory (\(P_{A}\)). A beam of laser rangefinder Leica DISTO D810 representing a straight line came out from a tripod placed on \(P_{A}\), was aimed at the axis of rotation placed on \(P_{C}\) and passed through the trolley peephole where the signal from the Hall sensor was detected. The distance between points \(P_{C}\) and \(P_{A}\) was 34 m.  
Figure 1: Recording the measurements from four RTK receivers in movement while performing evaluations based on the MRA method. The equipment performing the circular movement (**a**) was located on the horizontal surface near the building, trees, walls and personal vehicles (**b**). These obstacles obscuring the orbits were measured by an approximate method (**c**). The red circle determines the approximate trajectory of the MRA. The MRA was constructed with emphasis on the stiffness of the frame and designed so that the linkages allowed the smoothest and most stable movement of the trolley in the direction of a circular trajectory with a radius of 3 m. The following measures were taken to reduce the reference trajectory error due to the torsion of the structure:  
* The robust construction of the rotation axis of the MRA was firmly anchored with screws and concrete blocks to the concrete surface in order to prevent possible deflection of the axis. Tilting the driven wheels in the direction of the tangent to the trajectory resulted in a reduction of the centrifugal force. The deflection of the rotation axis at the bearing height was measured in two perpendicular directions with a Hoteche HT284610 dial indicator located between the rotation axis rod wall below the bearing and the structure attached to concrete blocks at the maximum angle speed. These deflections were less than 2 mm in both directions. * The vibration and possible tilting of the trolley in the pitch direction were eliminated by using sufficiently inflated tires with a wheelbase of 1.2 m and a very smooth and flat surface panelled with oriented strand board. Another aspect of reducing the trajectory error in this direction was the smooth acceleration (a\({}_{\text{max}}\) = 0.7 m s\({}^{-2}\)) during the scenarios and the installation of the brake on the rear of the trolley.