## 2 Prototype System and Methods
### Sensor Georeferencing  
In a sensor network, point clouds acquired by the individual sensors have to be transformed into a common reference frame that could be local or global. When rigidly connected sensors are used together, then the coordinate system of one of the sensors is considered as a local frame, and the relative translation and rotation of the other sensors are estimated. This procedure is called point cloud co-registration. There are many co-registration approaches and most of these methods require a measurable overlap between point clouds that may not be feasible in the proposed system configuration here. Therefore, in contrast to co-registration, the coordinates and rotations of the sensors are independently estimated in a global system. This procedure is generally referred to as sensor georeferencing.  
Sensor georeferencing includes the determination of the position and orientation in a reference frame. The coordinates of the LiDAR sensor location are measured with conventional land surveying technique using total station. The sensor orientation is usually indirectly estimated by using object space targets. In our case for estimating the three attitude angles, a 1.8 m x 1.2 m calibration board is used as a target (see Figure 2). This smooth and flat calibration board is large enough to provide a sufficient number of points obtained from it. Prisms attached to the four corners of the board were used to measure their global coordinates with a total station. The board was observed at various locations and orientations in the field of view of the sensors (see Figure 2).  
The boresight estimation is based on comparing the total station measured target locations and orientations to the same parameters, estimated from the point clouds of the targets. Obviously, there is no chance that the prism locations are measured by the point cloud, but fitting a plane the orientation of the board surface can be estimated. Consequently, the norm vectors of the board in the sensor and global system can be calculated from the LiDAR points and the corner measurements, respectively. Using the two results, finding the unknown orientation parameters can be formulated as a least squares estimation problem:  
\[\text{minimize }(\text{w.r.t }\alpha,\beta,\gamma)\ \sum_{i=1}^{n}\left| \left|\mathbf{R}(\alpha,\beta,\gamma)\mathbf{n}_{i}^{\text{S}}-\mathbf{n}_{i} ^{\text{G}}\right|\right|_{2}^{2}, \tag{1}\]  
where \(\mathbf{n}_{i}^{\text{G}}\in\mathbb{R}^{3}\) is the norm vector of the board in the global system at the \(i\)th position, \(\mathbf{n}_{i}^{\text{S}}\in\mathbb{R}^{3}\) is the norm vector of the board in the sensor coordinate system at the \(i\)th position, \(n\) is the  
Figure 2: Sensor georeferencing: calibration board with surveying prism (upper left corner) measured with total station and sensor station.  
number of board positions, and \(\mathbf{R}(\alpha,\beta,\gamma)\in SO(3)\) is the rotation matrix as the function of the \(\alpha,\beta,\gamma\in[0,\,2\pi]\) orientation parameters; for detailed notations and definitions see Appendix A. The Levenberg-Marquardt method is used to solve Equation (1). The positions and orientations of the sensors along with the time synchronization allow for transforming all points captured at different epochs to the same global coordinate system.