## 3 Results
### Analysis of Heading Precision Estimates for All Flights  
The different horizontal velocities experienced within the flights allowed for an analysis of the impact of increasing velocity on estimating heading using a single-antenna and dual-antenna GNSS/INS sensor. Figure 9 illustrates the reported heading precisions for the single and dual-antenna GNSS/INS trajectories for all flights. In the figure, note that the legend information indicates the single and dual-antenna GNSS/INS trajectory with a suffix of 1 and 2, respectively. The heading precisions for flight A are shown as dotted lines to emphasize the link between Figures 8 and 9. An inspection of Figure 9 indicates a negative correlation between horizontal velocity and heading precisions for single-antenna GNSS/INS sensors. The single-antenna heading precisions for flights B, C, and D all improve as the associated horizontal velocities increase. However, the dual-antenna heading precisions are practically unaffected by the increase in horizontal velocity and exhibit a consistent heading precision regardless of the horizontal velocity. Although the single-antenna heading precisions begin to approach the consistent level of precision of the dual-antenna trajectories as horizontal velocity increases (e.g., flight D-1), the lack of GNSS compass heading observations limits the achievable precision of the single-antenna trajectories. Table 4 presents quantitative measures for the single-antenna and dual-antenna heading precisions across the horizontal velocities tested within the experiment. The single-antenna heading precisions of flight B improve in response to the experienced accelerations, similar to the relationship of the single-antenna heading precisions shown in Figure 8. Conversely, the single-antenna heading precisions of flight C and D worsened in response to the accelerations, similar to the relationship of the dual-antenna heading precisions shown in Figure 8. This suggests that a horizontal velocity threshold may exist between 5 m/s and 10 m/s, in which the beneficial influences of the accelerations on heading precision become a detrimental influence. For each flight, the mean horizontal velocity of the APX-18 during the longer north-south flight lines was calculated. The shorter east-west flight lines were excluded as the APX-18 was moving at a considerably lower velocity during these flight lines, which introduced a bias within the mean velocity measures. The mean horizontal velocities and associated mean single-antenna heading precisions were then considered as observations produced by a theoretical GNSS velocity model (see Section 2.2, Equation (6)) and were used to estimate the model's GNSS-derived horizontal velocity precision (\(\sigma_{\text{r}th}\)) and heading precision achievable limit (\(\sigma_{\text{c}}\)) parameters via a general least-squares adjustment. The resulting estimates were 0.015 m/s for \(\sigma_{\text{r}th}\), which agrees with the manufacturer's velocity error performance specification for the APX-18 sensor shown in Table 2, and 0.148\({}^{\circ}\) for \(\sigma_{\text{c}}\). These results suggest that the GNSS velocity model may be a reasonable estimator of the expected heading precision for a single-antenna GNSS/INS sensor based on horizontal velocity. They also suggest that a point of diminishing returns for the improvement of heading precisions exists at a horizontal velocity of approximately 15 m/s for single-antenna GNSS/INS sensors. Figure 10 illustrates the GNSS velocity model that best fits the mean velocity and single-antenna heading precision estimates from the experiment.