# Adjustment Algorithm for Free Station Control Network of Ultra-Large Deepwater Jacket
## 3 Results and Discussion
### Comparison of Different Adjustment Schemes
#### 3.2.2 Adjustment Results via Traditional Method  
Constrain the coordinates of the S7 and S8 points in Table 1, and then implement adjustment for the second-phase observations, and calculate the coordinates of each point and their difference with the first coordinates as shown in Table 2 (the newly deployed S9 and S10 points are not involved in the comparison because there are no first coordinates, so they are not included in the table), in which dx and dy represent the deviation of the x and y directions, respectively, \(dp=\sqrt{dx^{2}+dy^{2}}\) represents the deviation of the point position, and \(mdp=\sqrt{mp_{1}^{2}+mp_{2}^{2}}\) is the RMSE of the dp.  
From the above table, it can be seen that except for the two starting points, S7 and S8, the coordinate deviations of the remaining five control points are a minimum of 0.9 cm (S3, S5) and a maximum of 1.5 cm (S6), with an average value of 1.1 cm. Their point deviations are greater than twice their mean square error, which can be considered a significant displacement.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Point Name** & **x (m)** & **y (m)** & **mx (mm)** & **my (mm)** & **mp (mm)** \\ \hline S1 & 553.915 & 1090.548 & 0.8 & 1.3 & 1.5 \\ S2 & 564.461 & 970.895 & 0.5 & 1.0 & 1.1 \\ S3 & 600.744 & 759.503 & 0.8 & 1.2 & 1.4 \\ S4 & 679.336 & 748.647 & 1.0 & 1.1 & 1.5 \\ S5 & 661.115 & 898.152 & 0.8 & 1.1 & 1.4 \\ S6 & 655.618 & 1095.404 & 0.9 & 1.2 & 1.6 \\ S7 & 500.000 & 1074.986 & 0.0 & 1.1 & 1.1 \\ S8 & 500.000 & 800.000 & 0.0 & 0.0 & 0.0 \\ \hline \end{tabular}
\end{table}
Table 1: The adjustment coordinates and RMSEs of the first phase.  
Figure 5: A schematic diagram of the second phase of free station observations. STA# indicates the station’s location, # represents the station number, and different colors distinguish the observation values of different stations.  
In addition, we also compared the adjustment effect of constraining different control points. Figure 6 shows the point deviation of the coordinates of the points obtained when constraining S8 and any remaining control point (represented by S8 + S# in the figure, where # represents the station number) compared with the first-phase results. The RMSE of each point deviation is also plotted as error bars. To avoid overlapping between different error bars at the same point, we adjusted the ratio of the error bars to 30% of their original values.  
Table 3 lists the statistical information on the point deviation of the various scenarios. It can be seen that the results vary considerably when different starting points are chosen for the constraints, making it challenging to determine which points are stable or unstable.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Point Name** & **x (m)** & **y (m)** & **dx (cm)** & **dy (cm)** & **dp (cm)** & **mdp (cm)** \\ \hline S1 & 553.905 & 1090.550 & \(-1.0\) & 0.2 & 1.0 & 0.3 \\ S3 & 600.749 & 759.511 & 0.5 & 0.8 & 0.9 & 0.4 \\ S4 & 679.343 & 748.655 & 0.7 & 0.8 & 1.1 & 0.5 \\ S5 & 661.112 & 898.160 & \(-0.3\) & 0.8 & 0.9 & 0.4 \\ S6 & 655.606 & 1095.413 & \(-1.2\) & 0.9 & 1.5 & 0.4 \\ S7 & 500.000 & 1074.986 & 0.0 & 0.0 & 0.0 & 0.1 \\ S8 & 500.000 & 800.000 & 0.0 & 0.0 & 0.0 & 0.0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The adjustment coordinates (constraints S8 and S7) and their differences compared to the first results.  
Figure 6: The point deviation of different constraint adjustment schemes compared to the first phase.