## 2 Methods
### Step 1
#### 2.3.2 Method Comparison  
In order to compare the GNSS-based trajectories with the reference trajectory, the GNSS coordinates in the global (WGS84) coordinate system were transformed into the local coordinate system (LCS). Five points (tachymeter position, two GNSS base stations and two reference points) surrounding the area (see Figure 3) were periodically measured with the tachymeter (LCS) and differential GNSS and were used for matching. The transformation was accomplished using a least square resection method ([PERSON], 1995) and the software Leica Geo Office (Leica Geosystems, Heerbrugg, Switzerland). The matching of the coordinate system was conducted before and after the motion capture period on all four days. The drift over time between the two measurements was accounted for by distribution of the differences between the solution before and the solution after the motion capture period by time interpolation. The mean difference of the resection at a reference point was below 13 mm in the vertical component and below 9 mm in the horizontal component, with standard deviations of 4 mm and 3 mm, respectively. The z-axis of the LCS pointed in the opposite direction to gravity, the x-axis was parallel to the vector from gate 7 to gate 9 and the y-axis was orthogonal to the x and y axis.  
The GNSS antenna trajectory solutions \(\mathbf{A}\)-\(\mathbf{E}\) were compared to \(\mathbf{P_{REF}}\) every 0.02 s within turn 7 using GPS time as reference time. \(\mathbf{P_{REF}}\) was time interpolated to the GPS time points to allow spatial comparison at the corresponding point in time. The spatial differences between \(\mathbf{P_{REF}}\) and the GNSS position solutions were expressed as vector norms (XYZ) and decomposed in the z-direction (Z) and the horizontal component (XY). For the double difference methods (integer fixed and real number float ambiguity), the differences were computed for all fixed solutions and all float solutions separately but also for the combination of fixed and float solutions. For the latter, fixed solutions were used when these could be computed, while float solutions were used when the system was unable to fix ineger ambiguities. The differences of the combination of fixed and float solutions was computed as a measure for the overallperformance of the system, while the comparison of only fixed or only float solutions were computed to give more detailed insight in the system's performance. For each run the mean difference, standard deviation (SD) of the difference, the median of the difference and the maximal difference (maximum) were calculated. Subsequent to the analysis of each trajectory, these measures were averaged across the 12 runs for each component. To express the results for the methods _A-E_ in a histogram, the difference of each epoch to the reference system was assigned to accuracy categories and expressed as fractions of the total time the skier skied through the reference turn. The timespans in which the methods were unable to compute solutions were marked as NaN, along with the spatial differences for fixed and float solutions. In addition the number of runs for which a fixed solution was computed at least once was computed. In addition, the timespan when fixed, float or no solutions that were computed were expressed as % of total time the skier skied through the reference turn.