## 5 Results and Discussion
### Performance Evaluation against Metric-Based Detector  
In this section, there are four metrics to be tested, namely **Qe**, **Qs**, **Qh**, and **Qo**. Similar to our proposed approach, these metrics are _local_, i.e., it depends only on two consecutive time instances by comparing the scans obtained by the sensor as given in (5) to (8). The performance of these metrics against QS-2 DDTW without and with relocalization are shown in Figures 8 and 9, respectively. Figure 8: Performance result of metric-based detectors against QS-2 DDTW (**bottom**) without relocalization. Black pixels indicate \(\eta\leq 0\). Figure 7: Performance result of MCW (**top**), ME (**middle**), and proposed QS-2 DDTW (**bottom**) with relocalization. Black pixels indicate \(\eta\leq 0\). From the presented results in Figures 8 and 9, the small changes in metrics-based detectors between the first test (without relocalization) and second test (with relocalization) indicate a low dependency towards relocalization, thus the detection accuracy is very less likely affected by the success rate in the relocalization process. Among the five detectors, however, QS-2 DDTW once again outperforms others in terms of accuracy for kidnapping across all time instances. It can successfully distinguish normal conditions around kidnapping points from the kidnapping event at the kidnapping points itself better than other methods used as benchmarks. A low dependency towards relocalization also ensures that the accuracy is maintained no matter how successfully the relocalization can be achieved. Different experiments were set up to evaluate the effectiveness as well as demonstrate the performance of proposed QS-2 DDTW in real static and featureless indoor environments as shown in Figure 10. The map of the environment treated as a ground truth with several room dividers and walkway exists in this environment. In Figure 10a, the robot is performing a 2D area mapping while Figure 10b shows the map generated in ROS visualization (RViz) from those indoor environments. An experimental analysis was then performed in several kidnapping and nonkidnapping situations under Metric-Based Detector and the proposed QS-2 DDTW. The classical statistical analysis was carried out to examine the difference in the distribution of variables between the presence and absence of kidnapping. Nominal variables (kidnapping time, distance between the start and the end points of the kidnapping event and robot orientation) were independently important  
Figure 9: Performance result of metric-based detectors against QS-2 DDTW (**bottom**) with relocalization. Black pixels indicate \(\eta\leq 0\). between presence and absence of kidnapping. Using the independent predictors, we used LR technique with a stepwise variable selection and receiver operating characteristics (ROC) curve to visualize the probability of presence of kidnapping. Note that the ROC curve is based on the true positive rate that represents a fraction of the detected kidnapping out of the total number of actual kidnapping events as well as the false positive rate that is the fraction of the incorrectly detected nonkidnapping out of the total number of actual nonkidnapping events. In the initial experiment, we evaluated the detection method under a nonkidnapping situation where there is some possibility of false alarm. A case study of a nonkidnapping situation with Gmapping in this environment as shown in Figure 11 also helps to ensure the smoothness of robot navigation (collision free) as well as validate the recorded coordinates (its starting and ending points). The second experimental case study involves a robot kidnapping situation as shown in Figure 12. From the mapping result created by Gmapping, Figure 12 depicts the starting  
Figure 11: Experimental case study of mapping result of a nonkidnapping situation. Figure 10: The mapping process and result of experimental testbed. (**a**) Mapping process using Turtlebot, (**b**) mapping result. and ending locations of the kidnapping event.