## 3 Ultra-Long-Range Scanning and Acquisition Technology
### Initial Pointing  
The initial pointing is a crucial factor in determining the scanning strategy of the scanning terminal. The residual error after the initial pointing defines the uncertain range of the system's scanning area, which needs to be fully covered by the beacon light. This ensures the scanning capture probability [17; 18]. To increase the scanning capture probability, the initial pointing accuracy must be maximized. To achieve high-precision initial alignment, the geodetic coordinates of the two terminals obtained from Global Navigation Satellite System (GNSS) must be converted into the azimuth, and elevation angles are required to \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Value** & **Remarks** \\ \hline Transmit Power & 40 dBm/1544 nm & 10 W \\ Transmit Optical Loss & \(-\)2.22 dB & \\ Transmit Optical Gain & 95.78 dB & 65 \(\upmu\)rad divergence (60 mm) \\ Aiming Loss & \(-\)1 dB & 5 \(\upmu\)rad \\ Space Loss & \(-\)238.26 dB & 100 km line-of-sight \\ Receive Optical Gain & 104.20 dB & \\ Receive Optical Loss & \(-\)2.22 dB & \\ Beam Splitter Loss & \(-\)0.45 dB & 1:9 ratio \\ Fiber Coupling Loss & \(-\)10 dB & 10\% (cross-lake, 3500 m \\ altitude) \\ Atmospheric Absorption & \(-\)15 dB & 0.15 dB/km (Qinghai Lake) \\ Received Power & \(-\)29.17 dBm & \\ Receiver Sensitivity & \(-\)40.00 dBm & 100 Gbps (with coding gain) \\ Link Margin & 10.83 dB & \\ \hline \end{tabular}
\end{table} 
Table 2: Communication link budget. Figure 2: Key parameters of beacon laser and communication laser in laser communication links. point at each other. After obtaining the azimuth and elevation angles, the PAT terminal must rotate precisely according to these angles. Otherwise, significant initial pointing errors will be introduced due to the misalignment between the optical axis and the PAT terminal control system [19]. First, the geodetic coordinates of the terminals are converted into Cartesian coordinates, as shown in Equation (1):  
\[ \begin{pmatrix}x\\ y\\ z\end{pmatrix} = \begin{pmatrix}(N+H)\cos B\cos L\\ (N+H)\cos B\sin L\\ \left(N\left(1-e^{2}\right)+H\right)\sin B\end{pmatrix}  \tag{1}\]  
where \(N=\frac{a}{\sqrt{1-e^{2}\sin^{2}B}}\), \(a=6,378,137\) m, \(e^{2}=0.006694379995\) and \(B\), \(L\), \(H\) denote latitude, longitude, and altitude. The vector pointing to the target in the World Geodetic System 1984 (WGS84) coordinate system is denoted as \(\left( \begin{bmatrix}x_{t}\\ y_{t}\\ z_{t}\end{bmatrix} - \begin{bmatrix}x\\ y\\ z\end{bmatrix} \right)\) Based on the attitude information of the laser terminal's installation on the ground, the observed vector of the target relative to the PAT terminal is transformed into the PAT terminal's initial coordinate system (East north up (ENU)), resulting in  
\[\mathbf{v}_{0}= \begin{bmatrix}v_{x}\\ v_{y}\\ v_{z}\end{bmatrix} =\mathbf{A}^{-1}\left( \begin{bmatrix}x_{t}\\ y_{t}\\ z_{t}\end{bmatrix} - \begin{bmatrix}x\\ y\\ z\end{bmatrix} \right) \tag{2}\]  
where  
\[\mathbf{A}^{-1}=\left( \begin{array}{ccc}-\sin L&\cos L&0\\ -\sin B\cos L&-\sin B\sin L&\cos B\\ \cos B\cos L&\cos B\sin L&\sin B\end{array} \right) \tag{3}\]  
At this point, \(\mathbf{v}_{0}\) represents the direction of the PAT terminal's initial coordinate system (ENU). If the initial azimuth of the PAT terminal is \(0^{\circ}\) and the elevation is \(0^{\circ}\), with the PAT terminal initially pointing true north, it is conventionally agreed that a clockwise rotation of the PAT terminal azimuth is considered positive. To make the PAT terminal point the target, the azimuth and elevation angles the PAT terminal needs to rotate are given by Equations (4) and (5). \[Az=\arcsin\left(\frac{v_{x}}{\sqrt{v_{x}^{2}+v_{y}^{2}}}\right) \tag{4}\]  
\[El=\arcsin\left(\frac{v_{z}}{\sqrt{v_{x}^{2}+v_{y}^{2}+v_{z}^{2}}}\right) \tag{5}\]  
In practice, it is not possible to directly measure the absolute azimuth and elevation angles of the PAT terminal in the Cartesian coordinate system.