# Vehicular Localization Enhancement via Consensus
## 5 Evaluation
Nonetheless, a longer communication range increases the IF, suggesting that the benefit of the availability of more estimates overcomes the possible inflow of more erroneous data. In addition, the loss of the accuracy caused by short communication range is overcome by the increased number of the iteration of the updates; Local information that is too far from a vehicle to be reached with a single hop is ultimately delivered via multi-hop transmission. Under the same communication range, higher IF is achieved by allowing more iteration. While Figure 5 shows the changes in the efficiency of the proposed strategy under various circumstances, Figure 6 shows whether the distributed implementation indeed grants more accuracy than simply employing a centralized management. For detailed comparison, situations where vehicles may be temporarily unavailable due to communication error are simulated. For the distributed protocol, when the anchor fails to communicate with others, an alternative vehicle temporarily acts  
Figure 5: Changes of improvement factor (IF) of the proposed strategy under varying circumstances. as an anchor. The substitute for the anchor is chosen by \(\sigma_{self}^{2}\), the noise level of the sensory devices that pertain to the self-localization. To represent accuracy differences among the vehicles, 20 different choices of \(\sigma_{self}\) are set to 1 m, 2 m..., 20 m. In such configurations, when the vehicle with \(\sigma_{self}^{2}=1\) m\({}^{2}\) fails to communicate, another available vehicle with the lowest \(\sigma_{self}^{2}\) temporarily acts as an anchor. On the other hand, for the centralized implementation, only the central manager can serve as an anchor. When the central manager fails to communicate, all vehicles in the network are thus unable to perform the update, leaving with the unchanged initial estimates. The IF of both the distributed and the centralized approaches are presented according to the node failure probability ranging from 0 to 1. In both cases, zero node failure probability indicates that all vehicles stay available for the respective protocols. Since both implementations proceed in the same steps when no node failure occurs, both curves start at the same IF. As the node failure probability increases, the distributed protocol has a high IF over the centralized protocol. This suggests that as communication error occur more often, the distributed implementation successfully adapts to temporary setbacks while the centralized implementation cannot. However, When the node failure probability exceeds 0.8, both distributed and centralized implementations result in IF below 0, suggesting that the vehicles' initial self-localization results are more accurate than the results that utilize poorly exchanged data. In addition, the distributed implementation shows far worse performance than the centralized implementation when the node failure probability is between 0.8 and 1. This observation is made since, when most vehicles become unavailable during the exchange, the distributed protocol may send out the compensation based on the vehicle of very poor accuracy, thus degrading the quality of all estimates in the network. Finally, if the node failure probability equals 1, no exchange is carried out and both IFs equal 0 at this point. The comprehensive observation thus suggests that the distributed implementation outperforms the centralized one for reasonable range of the node failure probability and that utilization of the proposed strategy may be undesirable when the communication is severely impeded. Figure 7 illustrates cumulative distribution functions (CDF) of the localization errors under different qualities of the anchor. The CDFs for multiple set of measurement noise levels are shown for both the distributed and the centralized modes. For the distributed mode, the measurement noise level of the anchor is denoted as \(\sigma_{A}^{2}\), where that of the central manager is denoted as \(\sigma_{\text{CM}}^{2}\).