## 5 Conclusions  
While LSPSs employing laser transmitter stations have been employed in engineering practice, the introduction of an LSPS into an existing industrial manufacturing setting must first solve the problems of docking with existing control points and external parameter calibration. However, calibrating the external parameters of a measurement system is very difficult under extreme and complicated working conditions due to the limited visibility of transmitter stations and the measurement distances involved. This problem was addressed here by proposing a single transmitter station calibration method based on a photoelectric scanning multi-angle resection positioning model that combines photoelectric scanning angle measurements and spatial resection in conjunction with an external receiver array. Positioning information is then obtained by solving the unknown parameters of \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Point Name** & **Method** & \(\mathbf{X}\) & \(\mathbf{Y}\) & \(\mathbf{Z}\) & \(\mathbf{DX}\) & \(\mathbf{DY}\) & \(\mathbf{DZ}\) & \(\mathbf{\Delta L}\) \\ \hline \multirow{3}{*}{1} & RTS & 106,367.8 & 103,597.0 & 10,061.9 & \multirow{3}{*}{0.8} & \multirow{3}{*}{1.5} & \multirow{3}{*}{–1.6} & \multirow{3}{*}{2.3} \\  & RASS & 106,367.0 & 103,595.5 & 10,063.5 & & & & \\  & RTS & 106,166.7 & 105,443.3 & 10,060.8 & \multirow{3}{*}{–1.5} & \multirow{3}{*}{1.9} & \multirow{3}{*}{1.6} & \multirow{3}{*}{2.9} \\
2 & RASS & 106,168.2 & 105,441.4 & 10,059.2 & & & & \\  & RTS & 106,156.3 & 106,285.1 & 10,071.0 & \multirow{3}{*}{–0.7} & \multirow{3}{*}{1.5} & \multirow{3}{*}{–2.1} & \multirow{3}{*}{2.7} \\  & RASS & 106,157.0 & 106,283.6 & 10,073.1 & & & & \\  & RTS & 108,045.9 & 108,595.1 & 10,092.2 & \multirow{3}{*}{2.0} & \multirow{3}{*}{1.9} & \multirow{3}{*}{3.7} \\
4 & RASS & 108,043.9 & 108,592.6 & 10,090.3 & & & & \\  & RTS & 109,667.7 & 107,222.4 & 10,097.9 & & & & \\  & RASS & 109,666.8 & 107,225.2 & 10,098.8 & & & & \\  & RTS & 108,026.8 & 105,480.6 & 10,086.4 & \multirow{3}{*}{–0.6} & \multirow{3}{*}{1.6} & \multirow{3}{*}{–2.0} & \multirow{3}{*}{2.6} \\
6 & RASS & 108,027.4 & 105,479.0 & 10,088.4 & & & & \\  & RTS & 112,321.8 & 104,221.2 & 10,079.4 & & & & \\  & RASS & 112,323.1 & 104,220.1 & 10,081.2 & \multirow{3}{*}{–1.3} & \multirow{3}{*}{1.1} & \multirow{3}{*}{–1.8} & \multirow{3}{*}{2.5} \\  & RTS & 122,829.8 & 93,402.2 & 10,026.6 & & & & \\  & RASS & 122,829.8 & 93,401.4 & 10,025.6 & & & & \\  & RTS & 126,278.7 & 96,203.8 & 10,097.0 & & & & \\  & RASS & 126,276.8 & 96,201.4 & 10,099.4 & & & & \\  & RTS & 110,704.1 & 102,478.5 & 10,061.2 & & & & \\
10 & RASS & 110,702.4 & 102,477.9 & 10,059.4 & & & & \\  & RTS & 110,464.1 & 105,179.0 & 10,084.5 & & & & \\  & RASS & 110,462.9 & 105,180.7 & 10,085.7 & 1.2 & & & \\  & Average & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Coordinate differences of verification points from (RTS) and (RASS) (mm), where \(DX\), \(DY\), and \(DZ\) are the differences of coordinates. Here, \(\Delta L=\sqrt{(\Delta X^{2}+\Delta Y^{2}+\Delta Z^{2})}\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter** & \(\mathbf{\Delta X}\) & \(\mathbf{\Delta Y}\) & \(\mathbf{\Delta Z}\) & \(\mathbf{\Delta\alpha}\) & \(\mathbf{\Delta\beta}\) & \(\mathbf{\Delta\gamma}\) & \(\mathbf{K}\) \\ \hline Value & 113,526.6 & 97,152.5 & 8704.9 & \(-0.0240148\) & \(-0.028201\) & \(0.889006\) & \(0.99880\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Conversion parameters from the receiver array single station system (RASS) coordinate system to the total station (RTS) coordinate system, where \(\Delta X\), \(\Delta Y\), and \(\Delta Z\) are translation parameters, and \(\Delta\alpha\), \(\Delta\beta\), and \(\Delta\gamma\) are rotation parameters; \(K\) is a scale factor. the model according to a nonlinear optimization approach using the Levenberg-Marquardt least-squares fitting algorithm. Two approaches were used to verify the feasibility and measurement accuracy of the positioning method.