## 4 Results and Discussion
The best network configuration obtained based on the optimal position of the control point is shown in Figure 4. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Maximum External Reliability (mm)** & **Maximum External Reliability (mm)** \\ \cline{2-3}
**Control Point** & **Observations with Same Variance** & **Observations with Different Variances** \\ \hline A & \(\pm 3.97\) & \(\pm 5.70\) \\ B & \(\pm 3.97\) & \(\pm 5.70\) \\ C & \(-3.97\) & \(-5.70\) \\ D & \(+3.97\) & \(+5.70\) \\ E & \(-3.97\) & \(-5.70\) \\ F & \(+3.97\) & \(+5.70\) \\ G & \(\pm 3.28\) & \(\pm 3.94\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum external reliability for a single control point for both observations with equal variances and with different variances. Figure 3: MDB (\(\sigma\)) for a single control point—minimally constrained scenario (a)—for the cases of observations with same variances and different variances. In the second case, we consider the closed levelling network in Figure 2 over-constrained with two control stations, totalling 21 possible combinations of control points. For example, taking A and B as fixed, we have \(u=5\) unknown heights (C, D, E, F, G), \(n=12\) observations and \(n-u=7\) redundant observations. In that case, the design matrix \(A\) has dimension \(12\times 5\) and the covariance matrix of observations \(Q_{e}\) has dimension \(12\times 12\). On the other hand, we have \(u=5\) unknown heights (B, D, E, F, G), \(n=11\) observations and \(n-u=16\) redundant observations in the case of selecting control points a and C. In that case, when the control points are adjacent, the respective levelling line are not observed and, therefore, the design matrix \(A\) has dimension \(11\times 5\) and the covariance matrix of observations \(Q_{e}\) has dimension \(11\times 11\). Figure 5 shows an example when the control points are adjacent. For the second case, we produce and analyse 21 graphs showing the MDB values. Due to the large number of graphs, we show here a table with a summary of the results. Table 3 shows the overall statistics of the MDBs (average, maximum, minimum, and standard-deviation) for each possible combination, two by two, of control points and for each scenario of variance. For the case of same variances, it can be noted that when the points A and B were taken as control points (AB), the observations presented a good level of homogeneity (homogeneous redundancy), i.e., all of them had the same internal reliability. It means that, in the presence of an outlier, all observations have the same ability to detect it. This fact is expected and due to the complete symmetry of the network design and the variances of observations. The search for homogeneous redundancy in all the observations has already been investigated in [14; 15]. Figure 6 shows the maximum external reliability for the over-constrained network. The maximum external reliability of the network for combinations of control points AB, AG, BG, CD, CF, DE and EF had positive and negative signals. This is represented by the \(\pm\) sign in Figure 6. It means that the maximum influence of an outlier on the network occurs in two directions. It can be noted that both cases of observations with same variances and different variances, the smallest value of the maximum influence of an MDB on the heights occurred when the stations A and B were fixed as control, with \(\max{(\
abla{\mathbf{X}})}=2.3 mm\). In general, the inflation of the variances in the network amplified the maximum external reliability, i.e., it increased the maximum influence of a possible  
Figure 4: Optimum Configuration of the network for a single control point—minimally constrained scenario (a). Figure 5: Example of the network configuration for adjacent control points a and C.  
outlier on the network. The optimum configuration of the network according to our algorithm is shown in Figure 7.