# Vehicular Localization Enhancement via Consensus
## 4 Experiment  
To evaluate the performance of the proposed strategy in details, a 1300 m\(\times\)750 m vehicular network consisting of 20 vehicles is simulated. The vehicles perform self-localization under additive Gaussian noise of \(\sigma=25\) m. Note that the noise level of the self-localization of the agent vehicles have no direct effect on the performance of the proposed strategy. Thus, a rather large setup of \(\sigma=25\) m is for the purpose of lucid observation of the changes of the location estimates. On the other hand, one of the 20 vehicles has the most accurate means of self-localization and thus serves as the anchor. The self-localization performance of the anchor is decisive to the effectiveness of the proposed strategy. The location of the anchor is assumed to be deterministic in this case for the purpose of clear illustration of the strategy. Such a deterministic location of the anchor can be achieved when a road-side unit (RSU) [24] with measurement and communication capabilities is available. General cases where the measurement of the anchor is not very accurate are discussed in the subsequent section. While using mmWave-based technologies, additive zero-mean Gaussian noises with \(\sigma=1\) m and \(\sigma=3^{\circ}\) occur during measurements of pair-wise distance and AoA, respectively. For the tested network size, the propagation delay can extend up to 5.00 ms if the communication distance is not limited. To achieve at least three message exchanges within 10 ms, the maximum communication distance is set to 900 m in the simulations unless specified otherwise. General choices of all simulation parameters follow the configuration of the urban scenario specified in 3 GPP TR 37.885, while the performances under different circumstances are discussed briefly. Figure 3 illustrates changes of the location estimates during the overall execution of the proposed strategy. Unlike the practical implementation discussed in Section 3.3, the compensation step is illustrated separately in order to clarify its role. The effect of adopting the practical implementation is subsequently discussed. The comparison is made between the ground truth locations and the estimates at three different stages--the initial estimation, the halt of the consensus-based updates, and the compensation. Each pair of the real and the estimated locations is connected by a line for the  
unambiguity. The estimate and the ground truth location of the anchor are indicated by a surrounding circle. Figure 2(a) shows the initial stage of the strategy, where no update has been applied on the estimates. Self-localization errors misplace the estimates randomly with respect to each corresponding ground truth locations. Since the self-localization of the anchor is noiseless in this particular case, the estimate made by the anchor is correctly placed onto the ground truth location. On the other hand, the immediate purpose of the iteration of the update is the delivery of the messages to as many neighbors as possible, rather than the convergence to an accurate value. To meet this purpose, the exact value of the threshold is chosen so that enough number of multi-hop can occur for the farthest pair of neighbors in the network can exchange messages. For the proposed test case, the threshold of \(C_{h}=0.5\) m suffices for the longest possible inter-vehicular length of 1500 m. Under such a halt condition, four updates are iterated before the halt. The result of the consensus-based updates are shown in Figure 2(b). The updated estimates are all similarly misplaced slightly downwards and to the left with respect to each corresponding real location. This shows that the updated estimates of all vehicles carry similar magnitudes and orientations of the error. Figure 2(c) depicts the location estimates after the compensation is applied. As indicated by the estimates placed onto the ground truths, much accurate estimates are achieved after the compensation.