## 4 Verification Experiments
### Estimation and Analysis of the Experimental Data
#### 4.2.2 Accuracy Verification Experiment  
A Leica TCL1201+ electronic total station (with the accuracy of angle measurement of \(\pm 1\) and that of distance measurement of \(\pm\) (1 mm + \(1.5\times 10^{-6}\)\(D\))) were installed to verify the measured data. Two sets of data were obtained by measuring 14 control points in the test site with total station (RTS) and receiver array single station system (RASS). Three points were selected to obtain the transformation parameters (see Table 5) from the coordinate system of the launching station to that of the total station. The other 11 points measured by the single transmitting station were changed to the coordinate system of the total station as the verification points by transforming the parameters.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Posture** & \(X\) & \(Y\) & \(Z\) & \(\Delta X\) & \(\Delta Y\) & \(\Delta Z\) & \(\Delta L\) \\ \hline
1 & 9556.1 & 1473.6 & \(-1126.2\) & \(-2.5\) & \(-0.4\) & \(0.3\) & \(2.6\) \\
2 & 9560.5 & 1474.2 & \(-1126.9\) & \(1.7\) & \(0.3\) & \(-0.5\) & \(1.8\) \\
3 & 9558.4 & 1473.7 & \(-1126.3\) & \(-0.1\) & \(-0.3\) & \(0.2\) & \(0.4\) \\
4 & 9559.5 & 1474.4 & \(-1126.6\) & \(0.9\) & \(0.5\) & \(-0.1\) & \(1.0\) \\ Average & 9558.6 & 1474.0 & \(-1126.5\) & \(1.3\) & \(0.4\) & \(0.3\) & \(1.5\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Measured \(X\), \(Y\), and \(Z\) coordinate values (unit: mm) and their deviations from the true values with the external receiver array held in four different postures. Here, \(\Delta L=\sqrt{(\Delta X^{2}+\Delta Y^{2}+\Delta Z^{2})}\).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Posture** & **1** & **2** & **3** & **4** \\ \hline \(r_{1}\) & \(-0.87051125\) & \(-0.79116910\) & \(-0.77006598\) & \(-0.71680738\) \\ \(r_{2}\) & \(0.45422411\) & \(0.45022282\) & \(0.51670999\) & \(0.58164049\) \\ \(r_{3}\) & \(0.18944815\) & \(0.41394549\) & \(-0.37417830\) & \(-0.38455397\) \\ \(r_{4}\) & \(0.32510523\) & \(0.535991181\) & \(0.61074966\) & \(0.68063671\) \\ \(r_{5}\) & \(0.81972864\) & \(0.8368869\) & \(0.76657725\) & \(0.70342008\) \\ \(r_{6}\) & \(-0.47154174\) & \(0.11474707\) & \(-0.1985402\) & \(-0.20477787\) \\ \(r_{7}\) & \(-0.36948175\) & \(-0.29455764\) & \(0.18434507\) & \(0.15139587\) \\ \(r_{8}\) & \(-0.34889166\) & \(0.31265615\) & \(-0.38127457\) & \(-0.40852700\) \\ \(r_{9}\) & \(-0.86125362\) & \(-0.90304030\) & \(-0.90589527\) & \(-0.90010200\) \\ \(t_{1}\) & \(78627.2\) & \(7366.73\) & \(6177.68\) & \(5561.38\) \\ \(t_{2}\) & \(-48457.74\) & \(-6228.05\) & \(-7190.85\) & \(-7774.33\) \\ \(t_{3}\) & \(3074.98\) & \(1337.52\) & \(-2220.50\) & \(-1858.96\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Conversion parameters for transforming between the o-xyz frame and the \(O\)-\(XYZ\) frame with the shaped receiver array held in four different postures.  
Comparison results are shown in Table 6, where \(DX\), \(DY\), and \(DZ\) are the differences of coordinates, \(\Delta L\) denotes the location difference, and \(\Delta L=\sqrt{\Delta X^{2}+\Delta Y^{2}+\Delta Z^{2}}\) represents the average value of absolute value of each difference. It can be seen from the Table 6 that the single transmitter station system using the external receiver array generally obtained a greater error at points 4 and 9, both of which are farthest from the launch site, and the maximum error obtained was \(-2.8\) mm, while \(\Delta L\) was not greater than 3.9 mm. That means, with increasing distance from the target to the launch station, the accuracy of the receiver array single station system becomes lower. This is consistent with the measurement error distribution of wMPS.  
Therefore, the experimental results clearly demonstrate that the single station calibration method based on the receiver array proposed in this paper is entirely feasible, and the proposed solution method of the measurement model is correct and effective.