# Vehicular Localization Enhancement via Consensus
## 5 Evaluation  
The experiment on specific setup of the previous section poses questions regarding how changes in the system setup affects the performance of the localization strategy. For comprehensive comparison of the effect of the proposed strategy under diverse circumstances, the improvement factor (IF) is introduced as  
\[IF=\frac{\text{initial average localization error}-\text{final average localization error}}{\text{initial average localization error}}. \tag{16}\]  
Under this definition, \(IF=1\) if the proposed strategy completely removes the localization error. Also, \(IF=0\) if it does not change the localization at all, and \(IF<0\) if it degrades the localization and the proposed strategy should rather not be used. Figure 5 shows the changes of IF under multiple varying system parameters such as measurement noises and connection statuses between the vehicles. It is noted that the noise level of the pairwise AoA measurement has little to no direct impact on the performance and thus is fixed to \(3^{\circ}\). Such an observation is made since, when the directional information are averaged during the consensus-based updates, the magnitude of the resulting AoA does not hold any significant information and does not affect the preciseness of the localization. Figure 4: Measurement errors at each step. Figure 4(a) shows how IF changes with respect to the noise level of self-localization, denoted by \(\sigma_{\text{self, anchor}}\). The change is observed under different settings of the agents' self-localization noise levels, similarly denoted as \(\sigma_{\text{self, agent}}\). The increase of the self-localization error has a negative linear effect on IF since the trend of IF according to the noise level can be approximated to a straight line. For each line, the point where \(IF=0\) is reached when \(\sigma_{\text{self, anchor}}=\sigma_{\text{self, agent}}\). For example, when \(\sigma_{d}\) of the agents equal 5 m, the corresponding red line crosses the point where \(IF=0\) when \(\sigma_{d}\) of the anchor equals 5 m. This suggests that the presence of an anchor that is superior to the agents in terms of the self-localization guarantees the improvement in the localization performance of all vehicles in the network. In other words, as long as the vehicle of the best localization accuracy can be properly determined, the proposed strategy enhances the localization accuracy of all vehicles. On the other hand, when \(\sigma_{d}\) of the agents are sufficiently low, IF does not reach 1 regardless of the precision of the self-localization of the anchor. This does not necessarily indicate that the estimates are less accurate when agent vehicles are capable of sufficiently precise localization; with lesser amount of noise is initially present, the proportion of the remaining noise is larger in such cases, thus preventing the IF from reaching 1. Figure 4(b) shows the change of IF upon varying communication ranges. With insufficient communication range, not all neighboring vehicles may be able to directly communicate with each other. This prevents thorough delivery of all local information within the network. Since the consensus protocol takes advantage of abundant local data, the lack of the full information leads to degradation of the accuracy. However, the receipt of estimates from long distances may also deteriorate the accuracy somehow. The measurement error becomes larger when two vehicles are farther from each other since the same AoA measurement error can cause larger positional error at greater distances. Furthermore, signals tend to degrade over longer ranges and thus aggravates this issues. While the expansion in the communication range results in the availability of more local information, additional information are therefore relatively inaccurate and may be undesirable. These suggest a possible trade-off between the quantity and the quality of the measurement.