# Robust Visual Localization with Dynamic Uncertainty Management in Omnidirectional SLAM
## 5 Results
### Omnidirectional SLAM Results  
In this subsection, a number of tests is performed to evaluate the overall omnidirectional SLAM system, with the robust localization embedded. Notice that the redesign of the observation model, \(z_{t,n}\), in Equation (15), now implements the proposed robust localization. In this sense, Figure 14 shows real data results for such omnidirectional SLAM approach, using Dataset 2. In particular, Figure 14a confirms the suitability of the approach to produce a reliable estimation under a real application operation. Moreover, it is demonstrated to outperform the accuracy of a general SLAM approach, with standard localization, as presented in previous works [33]. This confirms the robustness of the estimation, which remains stable, whereas the estimation of the standard model tends to diverge in the presence of subtle error drifts on the localization. In addition to this, Figure 14b presents the average RMS results for the computed error, when the number of matchings is modified. Likewise, Figure 14c  
Figure 13: Omnidirectional localization results. (**a**) % matched points and time consumption with total number of matched points; (**b**) localization error in angular terms; (**c**) Root Mean Square Error (RMSE) and time consumption with the number of feature points in a localization experiment; (**d**) localization results for a sample path in Dataset 1.  
presents the same results for the standard localization. Again, these results confirm that a tradeoff setup with a low number of matching points still produces a well-balanced and feasible estimation.  
Next, Figure 15 presents more real data results regarding the error-time implications, which refer to the experiment shown in Figure 14. Figure 15a,b shows the behavior of the error on the estimated pose with the time step. In particular, Figure 15a expresses the evolution on the error for each coordinate in the omnidirectional SLAM approach, with the robust localization proposal embedded. Likewise, Figure 15b presents the error for the standard SLAM system, with the standard localization technique. It may be observed that the presented proposal outperforms the standard one.  
Figure 14: Omnidirectional Simultaneous Localization and Mapping (SLAM) results in Dataset 2. (a) SLAM estimation with the proposed localization approach (green), standard (red) and ground truth (black); (b) RMSE (m) with the number of matchings for the localization proposal; (c) RMSE (m) with the number of matchings for the standard localization.  
Having tested the validity and suitability of the approach in terms of the estimation accuracy, then it is worth evaluating the behavior of the uncertainty. To that end, Figure 15c assesses the evolution of the current uncertainty of the system at each time step. As described in Section 3, a dynamic uncertanty management was devised, together with Bayesian regression. According to this, the same experimental parameters for the weighting coefficients in the advanced matching, as defined in Equation (13), are here considered. Then, Figure 15c proves that the implemented approach provides a robust and feasible management of the uncertainty, which is significantly improved in contrast to that obtained by the standard SLAM system. The uncertainty metric is computed from the covariance matrix \(P_{t}\), as presented in Table 1:  
\[\sigma_{experiment}^{2}=trace[P_{t}\cdot P_{t}^{T}] \tag{16}\]  
Figure 15: Omnidirectional SLAM error results in Dataset 2: (**a**) error in the SLAM estimation for the robot’s pose along each time step with the proposed localization approach (\(X\), \(Y\) and \(\theta\)); (**b**) error in the standard SLAM approach with standard localization; (**c**) uncertainty evolution (m) at each time step: proposed SLAM approach with robust localization (green); standard SLAM approach (red).