# Robust Estimators in Geodetic Networks Based on a New Metaheuristic: Independent Vortices Search
## 5 Results and Discussion
### Results in Network Adjustments
#### 5.3.3 Large Magnitude Outliers  
In contrast to the experiments with small outliers, all REs showed greater ease in detecting larger outliers. Most the results were classified as \"A\" or \"B\", and rarely as \"E\" or \"F\" (see the classifications of the solutions in Figure 17). In this case, LS presented solutions with false positives, \"B\" and \"D\" types, resembling the other tested estimators. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline  & \multicolumn{2}{c}{**LS**} & \multicolumn{2}{c}{**LS**} & \multicolumn{2}{c}{**LTS-RC**} & \multicolumn{2}{c}{**SRLS**} & \multicolumn{2}{c}{**IRLS**} & \multicolumn{2}{c}{**LTS-RC-N2**} & \multicolumn{2}{c}{**LMS-N2**} & \multicolumn{2}{c}{**LTS-N2**} & \multicolumn{2}{c}{**LTA**} \\  & **(No Outliers)** & **LS** & **LMS** & **LTS** & **LTS-RC** & **SRLS** & **IRLS** & **LTS-RC-N2** & **LMS-N2** & **LTS-N2** & **LTA** \\ \hline
1 outlier & 0.014 & 0.017 & 0.023 & 0.024 & 0.024 & 0.026 & 0.024 & 0.021 & 0.023 & 0.024 & 0.029 \\
2 outliers & 0.014 & 0.020 & 0.025 & 0.027 & 0.027 & 0.028 & 0.027 & 0.026 & 0.025 & 0.027 & 0.032 \\
3 outliers & 0.014 & 0.022 & 0.027 & 0.027 & 0.027 & 0.030 & 0.025 & 0.027 & 0.028 & 0.028 & 0.035 \\
4 outliers & 0.014 & 0.025 & 0.029 & 0.029 & 0.030 & 0.031 & 0.024 & 0.030 & 0.029 & 0.031 & 0.036 \\ \hline \end{tabular}
\end{table} 
Table 2: Mean distance of the solutions for each estimator, organized in the scenarios of 1-4 concurrent small outliers. Figure 17: Solution classifications, from “A” to “F”, for the 400 scenarios containing 1-4 outliers of larger magnitude, organized by estimator. For classifications \"A\"and \"B\" (i.e., all outliers were identified), the estimators presented similar results, around 90%. By counting the detected false positives and undetected outliers, all estimators pointed out most of the blunders, as can we see from Figure 18. For 1000 outliers, the values ranged from 906-962 for detection. As the detection of outliers is almost optimal, it remains to compare the amount of false positives, where IRLS, LS, LMS, and LTS-RC-N2 had the lowest false positive values, ranging from 489-587. Table 3 presents the mean distance of solutions from the original co-ordinates. LS presented an unsatisfactory estimate for large outliers. The solution deteriorated, even with only one outlier of great magnitude. As we added more blunders to the scenarios, LS became one of the worst solutions for direct parameter estimation. LTA and SRLS also showed bad estimates, whereas most estimators presented similar, more satisfactory results, proving greater insensitivity to the outliers. In general, for outlier identification, the LS, IRLS, LMS, or LTS-RC-N2 methods had better detection. Regarding the computational cost of these solutions, LS is the best choice because it has its own iterative method. However, for the final estimate of the co-ordinates, the REs presented more satisfactory estimates. This shows the sensitivity of LS to outliers of great magnitude and the strength of robust methods. Table 4 presents the best estimator, concerning the application and scenario of errors. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**LS**} & \multirow{2}{*}{**LS**} & \multirow{2}{*}{**LTS**} & \multirow{2}{*}{**LTS-RC**} & \multirow{2}{*}{**SRLS**} & \multirow{2}{*}{**IRLS**} & \multirow{2}{*}{**LTS-RC-N2**} & \multirow{2}{*}{**LTS-N2**} & \multirow{2}{*}{**LTS-N2**} & \multirow{2}{*}{**LTA**} \\  & & & & & & & & & & & \\
1 outlier & 0.014 & 0.023 & 0.022 & 0.023 & 0.023 & 0.030 & 0.023 & 0.023 & 0.025 & 0.025 & 0.037 \\
2 outliers & 0.014 & 0.031 & 0.025 & 0.027 & 0.027 & 0.036 & 0.026 & 0.027 & 0.025 & 0.028 & 0.039 \\
3 outliers & 0.014 & 0.037 & 0.024 & 0.028 & 0.028 & 0.040 & 0.028 & 0.028 & 0.029 & 0.031 & 0.044 \\
4 outliers & 0.014 & 0.045 & 0.036 & 0.031 & 0.031 & 0.043 & 0.032 & 0.031 & 0.034 & 0.036 & 0.051 \\ \hline Mean & 0.014 & 0.034 & 0.027 & 0.027 & 0.027 & 0.037 & 0.027 & 0.027 & 0.028 & 0.030 & 0.043 \\ \hline \hline \end{tabular}
\end{table}