## 3 Methodology  
### LiDAR Workflow  
The use of airborne LiDAR has received significant research attention and operational use as a source of information for forest scientist since its introduction in the mid-1990s. This has allowed a well defined best practice data collection and processing workflow to be established by data providers. The  
\begin{table}
\begin{tabular}{l c c} \hline \hline  & **Gyroscopes** & **Accelerometers** \\ \hline Range & \(50^{\circ}\)/s & \(1.7\)g \\ Non-linearity & \(0.2\%\) & \(0.2\%\) \\ Bias Stability & \(0.2^{\circ}\)/s & \(0.003\)g \\ \hline \hline \end{tabular}
\end{table}
Table 1: Properties of the MEMS based Microstrain 3 DM-GX3 35 IMU.  
end product of this workflow is a spatially accurate point cloud with each point given an appropriate classification. The processing of LiDAR data captured using a UAV follows a similar workflow as shown in Figure 2. However, considerations need to be given to the miniaturised sensors, reduced flying height and time, as well as the increased point density during each of the stages of processing. For example, during the data collection phase consideration needs to be given to the limited flight time of a UAV and optimal mapping strategies need to be determined. An advantage of the platform used in this study is the on-board autopilot allowing maximum coverage of the targeted area during each flight.  
Similarly, modifications need to be made within the trajectory determination and point cloud generation stages due to the use of miniaturised sensors. The underlying requirement of these stages is the determination of all the variables within the direct georeferencing LiDAR equation at the instance of each pulse, given as follows:  
\[\begin{bmatrix}x\\ y\\ z\end{bmatrix}=p_{t}+R_{b}^{m}[R_{s}^{b}r^{s}+a^{b}] \tag{1}\]  
The determination of aircraft trajectory, including position, \(p_{t}=\left[X\;Y\;Z\right]^{T}\), and the orientation matrix, \(R_{b}^{m}\), are crucial to the final spatial accuracy of the position of each measured LiDAR point \(\left[x\;y\;z\right]^{T}\) measured in the mapping frame (North, East, Up). System calibration to determine the boresight matrix \(R_{s}^{b}\) and lever arm \(a^{b}\) is performed separately, as the reduced accuracy of the laser scanner means traditional techniques such as strip adjustment are not feasible. Further discussion on these issue is  
Figure 2: The modified LiDAR workflow to be used in producing a point cloud from the UAV system. Significant modifications are highlighted in red to account for the miniaturised sensors and increased resolution when using this workflow to produce a point cloud from data captured from on-board a mini-UAV.  
provided in Sections 3.2 and 3.3. Furthermore, the four layer off-nadir scanning properties of the Ibeo LUX laser scanner require the laser scanner observation matrix (\(r^{s}\)) to be modified giving Equation (2).  
\[r^{s}=\begin{bmatrix}\cos\Theta_{L}&-\sin\Theta_{L}\sin\Theta_{E}&-\sin\Theta_{L }\cos\Theta_{E}\\ 0&\cos\Theta_{E}&-\sin\Theta_{E}\\ \sin\Theta_{L}&-\cos\Theta_{L}\sin\Theta_{E}&\cos\Theta_{L}\cos\Theta_{E}\\ \end{bmatrix}\begin{bmatrix}0\\ 0\\ r\end{bmatrix} \tag{2}\]  
This observation matrix includes the addition of a layer angle, \(\Theta_{L}\), as well as the range \(r\) and the encoder angle, \(\Theta_{E}\), used within the common LiDAR equation.