## 3 Results  
### Analysis of Heading Precision Estimates for Flight A  
The slow horizontal velocity experienced by the APX-18 sensor during flight A allowed for the best analysis of the impact of using a single versus dual-antenna GNSS/INS sensor to estimate heading. As the horizontal velocity of the UAS was the slowest of all the flights, the differences between the single-antenna and dual-antenna heading precisions would be maximized. Figure 8 illustrates the reported heading precisions during flight A for the single-antenna and dual-antenna trajectories, along with the experienced horizontal velocities and total accelerations. In the figure, note that the software-reported heading precisions based on using a single-antenna and dual-antenna GNSS/INS are shown as the top and bottom plotted lines, respectively, and reference the primary vertical axis. The total accelerations with the horizontal velocities overlaid are shown in the middle of the plot and reference the secondary vertical axis. As illustrated in Figure 7, each mission began in the north-west corner of the project area and the first flight line was flown in the south direction. Based on this information, Figure 8 indicates that the APX-18 experienced higher accelerations while flying in the south direction, relative to the accelerations experienced while flying in the north direction. The distinguishable'spikes' in the acceleration plot are the result of the UAS quickly starting and abruptly stopping at the beginning and end of each flight line, respectively. It  
Figure 8: Single and dual-antenna GNSS/INS heading precisions, horizontal velocities, and total accelerations for flight A of the experiment. is speculated that higher accelerations experienced while flying south are the result of a 2-3 m/s headwind (see Table 3) causing increased vibrations within the UAS. Although the Alta X UAS utilizes a payload vibration dampening mechanism, increased vibrations were still experienced by the APX-18. An inspection of Figure 8 indicates varying correlations between the accelerations and the single-antenna and dual-antenna heading precisions. The single-antenna heading precisions for every flight line flown in the south direction are larger at the end of the flight line relative to the start of the flight line, except for the first flight line which was likely collected before the INS had properly initialized. Conversely, the single-antenna heading precisions for the north-flown flight lines are smaller at the end of the flight line relative to the start of the flight line. These results are believed to be attributed to the different accelerations experienced during the north and south-flown flight lines caused by wind. Figure 8 also indicates that the single-antenna heading precisions quickly improved at the end of a N-S flight line (abrupt deceleration) and then quickly worsened at the start of a N-S flight line (quick acceleration followed by zero acceleration). The dual-antenna heading precisions respond in the opposite manner and illustrate a'smooth' response to the experienced accelerations. This is suspected to be a result of the GNSS compass producing a consistent, high-precision heading estimate that is given more observational weight within the proprietary navigation filter. Based on the theoretical GNSS compass model presented in Section 2.2, the expected heading precision for a GNSS compass with a baseline length of 1.525 m is between 0.08\({}^{\circ}\) and 0.38\({}^{\circ}\) (see Equation (3) and Figure 3), which coincides with the results of flight A. The heading precisions for the single-antenna GNSS/INS trajectory varied between 0.28\({}^{\circ}\) and 0.45\({}^{\circ}\) with a mean of 0.369\({}^{\circ}\), and the heading precisions for the dual-antenna GNSS/INS trajectory varied between 0.07\({}^{\circ}\) and 0.11\({}^{\circ}\) with a mean of 0.082\({}^{\circ}\).