# Robust Estimators in Geodetic Networks Based on a New Metaheuristic: Independent Vortices Search
## 5 Results and Discussion
### Results in Network Adjustments
#### 5.3.2 Small Magnitude Outliers  
Starting with the outlier detection, Figure 15 gives the solution classifications for each RE in the 400 scenarios. LS presents its results concentrated in the 'no false positives' classifications (\"A\", \"C\" and \"E\"). This shows a resistance for pointing out false positives in the residuals vector by LS solutions. The IRLS got the highest number of solutions classified as \"A\", overcoming the other estimators. By checking the results for classifications that identified all outliers (\"A\" + \"B\"), the LMS, LTS, and LTS-RC-N2 had the best identification ability.  
Figure 14: Scenarios without outliers organized by estimator. Each point represents the average absolute distance from the estimated co-ordinates of each scenario, compared to the official values of the stations in the network.  
Although the LTA presented many classifications of type \"B\", this estimator had the lowest number of solutions classified as type \"A\", similar to SRLS. In Figure 16, we see that LTA presented 1303 false positives in the residuals vector, over the 400 scenarios. It also confirms LS as the estimator with the least amount of false positives (43). In contrast, LS missed most of the blunders, not detecting 572 out of 1000 inserted outliers. Among the REs where IVS was applied, the LMS identified a good part of the outliers without an exaggerated quantity of false positives, missing less than IRLS and LS.  
Analyzing the estimator solutions for parameter estimation, Table 2 shows the mean distance of solutions from the official co-ordinates. It also adds the LS result without outliers, to compare the influence of the random errors.  
Figure 16: Number of identified false positives and undetected outliers for each estimator in the 400 scenarios with outliers of smaller magnitude.  
Figure 15: Solution classifications, from “A” to “F”, for the 400 scenarios containing 1–4 outliers of smaller magnitude, organized by estimator.  
LS presented the smallest deviations, being the best estimate of the parameters in the case of adopting the solution, without eliminating contaminated observations and making new adjustments. Even in scenarios with four outliers, the LS showed a better result than the REs, although the difference became smaller. The IRLS presented low variation in the solutions, even with an increase of blunders. Whereas most RE presented similar solutions, LTA, in contrast, had the worst estimates.  
For an application where outliers should be identified, the LS method is not the best. In these cases, according to the results of the experiments, it is recommended to work with IRLS, or, for a better identification with a higher cost in false positives, LMS, LTS, and LTS-RC-N2 obtained more satisfying results.  
By analyzing the estimates, LS presented a more solid estimate, even with the lowest detection of blunders. This shows that the outliers which were not detected by LS did not exert great distortion in the estimation. For both scenarios without outliers or schemes that present blunders of small magnitude, LS remains as the best estimator for the parameters. The good redundancy of the network probably contributed to this result. In networks with poorer geometry, the LS will not be as robust to small outliers.