# Indoor Localization System Using Fingerprinting and Novelty Detection for Evaluation of Confidence
## 4 Performance Evaluation
### Evaluation of Confidence Using the Hybrid Approach  
In this section, we show and discuss the results of our third, hybrid approach to evaluate the confidence of the estimated positions. As mentioned in Section 3.3, it combines the previous two approaches in order to improve accuracy while reducing the number of discarded estimations.  
Figure 11: Cumulative distribution function of the localization error using novelty detection with thresholds \(\alpha=25\%\), \(45\%\), and \(75\%\): a higher percentage of the position estimations resulted in lower errors.  
Figure 10: Results for the evaluation of confidence using novelty detection: relationship among the value of the threshold \(\alpha\) (\(x\)-axis), the percentage of accepted estimations (in blue), and (**a**) the final accuracy of the accepted classifications, (**b**) the average localization error, and (**c**) the room accuracy. Compared to the previous results, the localization accuracy is improved, but at the cost of reducing the number of accepted estimations.  
It was observed in the previous sections that the lower the probability threshold, the higher the localization error. Thus, in this hybrid solution, we use the prediction probability for higher values of \(\alpha\) as a first, initial filter. Then, we use a lower probability threshold \(\beta\) to get possibly wrong estimations and apply the stricter, novelty detection test, to confirm their predictions. Thus, we expect to mitigate the loss of predictions in the highest probabilities and, thus, have some lost estimations only in the predictions with lower probabilities.  
As in the previous sections, Figure 12 shows our results when using the hybrid approach for the evaluation of confidence. In the case of Figure 12a, we can notice that the localization accuracy is very close to the ones obtained by the novelty detection approach (as shown in Section 4.3). On the other hand, the number of accepted predictions is closely similar to the ones obtained by the probability prediction approach (as shown in Section 4.2). For instance, for the threshold \(\alpha=40\), the accuracy is 42%, close to the second approach and, in terms of accepted predictions, it increased from 64% to 70%, similar to the first approach. These results show that this hybrid approach can reach a compromise, improving the localization while decreasing only slightly the number of discarded estimations.  
The same can be observed for the average localization error, shown in Figure 12b. Finally, in the case of room accuracy, shown in Figure 12c, the hybrid approach was also able to improve this accuracy while having almost the same number of accepted samples when compared to the prediction probability.  
Figure 13 shows the cumulative distribution function of the localization error using our three approaches for the evaluation of confidence in three different threshold configurations. As we can see, the hybrid approach has an error curve almost equal to or better than the more restrictive technique but, as seen in the previous results, it has a higher number of accepted estimations.