## 4 Discussion and Conclusions  
Due to the wide adoption of smaller, lower-cost MEMS-based IMUs within GNSS/INS solutions, hardware sensors that are suitable for UAS applications now exist. However, the ability to accurately determine heading with such sensors is often challenging, especially at the lower velocities often experienced during UAS operations. By utilizing two GNSS antennas, a real-time differential GNSS solution leveraging the millimeter precise carrier phase observable to determine heading is possible. Though widely employed in ground-based and sea-based applications, dual-antenna GNSS/INS sensors are not commonly used onboard UAS due to the increased cost, weight, and complexity of installing the dual GNSS antennas with an adequate separation onboard the airframe of the UAS. The principal objective of this study was to assess and understand the impacts of using either a single  
Figure 16: Vertical position differences between the single and dual-antenna generated point clouds for the five regions of points of flight A. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Region**} & \multicolumn{3}{c}{**Vertical Position Differences**} \\ \cline{2-4}  & **Minimum** & **Maximum** & **Mean** \\ \hline Top Edge Points & \(-\)0.004 m & 0.037 m & 0.015 m \\ Bottom Edge Points & \(-\)0.039 m & 0.005 m & \(-\)0.013 m \\ Left Edge Points & \(-\)0.034 m & 0.025 m & 0.002 m \\ Right Edge Points & \(-\)0.035 m & 0.023 m & \(-\)0.001 m \\ Middle Points & \(-\)0.028m & 0.013 m & 0.001 m \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Quantitative measures for the vertical position differences of points within the five regions of interest for flight A.  
antenna or a dual-antenna GNSS/INS sensor for UAS-lidar applications by collecting and analyzing field-collected data from a typical UAS-lidar mapping system. The positioning and navigation principles involved within GNSS and inertial-based systems were presented with a specific focus on heading determination. The theoretical relationship between a GNSS compass and heading precision was discussed, for which the results of this study supported the theory and provided compelling arguments that heading precision can be improved by up to a factor of five when a dual-antenna GNSS/INS sensor is used. Additionally, the theoretical relationship between the horizontal velocity of a GNSS/INS sensor and the heading precision was discussed and validated through the results of the four UAS-lidar flights conducted within this study. At higher horizontal velocities, a single-antenna GNSS/INS sensor can estimate heading to a level of precision that approaches that of a dual-antenna GNSS/INS sensor, but even at 15 m/s, the single-antenna heading estimates are still less precise than the dual-antenna estimates by a factor of 1.5. Additionally, a downside of collecting lidar observations while flying at higher horizontal velocities concerns a decrease in the point density of the generated point cloud. Interpolating between the experimental results of the test flights, an argument can be made that a balance between improving heading precision and maintaining point cloud density exists at a horizontal velocity between 5 m/s and 10 m/s for single-antenna GNSS/INS sensors. Dual-antenna GNSS/INS sensors are practically unaffected by horizontal velocity and maintain the ability to provide higher-precision heading estimates given adequate satellite visibility and a low multipath environment. The results of this study also indicated that the precisions of the remaining roll, pitch, and positional GNSS/INS trajectory estimates were negligibly impacted by using a single-antenna versus a dual-antenna or by changes in the horizontal velocity.