7.2.1 Simulation Settings
Using the SUMO traffic simulator, 10 vehicles’ trajectories have been extracted from a wide-scale urban simulation scenario calibrated for the city of Bologna, Italy. A restricted geographic area has been considered, including several pathological cases (including 1 por-tion of urban canyon), simulating for 200 seconds (see Figure 7.1). This test environment enables to show:
• The sensitivity to GNSS quality variations as a function of local environmental conditions (e.g., road width and buildings height) (see Table 7.1);
• The sensitivity to erratic mobility while crossing several intersections (e.g., possibly causing harmful mismatch between the mobility models assumed for prediction and actual mobility patterns).
• The sensitivity to the relative topology (and number) of cooperating vehicles.
In the cooperating fleet, each vehicle is alternatively viewed as the “ego” vehicle under testing, whereas the other(s) are viewed as assisting neighbors (or “virtual anchors”).
At each vehicle, the fusion engine relies on a PF with 1000 particles. Prediction is based on the bicycle model, using inputs from WSS (i.e., speed) and IMU (i.e., heading). As for data synchronization, “ego” prediction and neighboring prediction are slightly different.
Since we cannot instantly access the neighbors’ WSS and IMU measurements to perform the corresponding prediction at the “ego”, we artificially add extra uncertainties (say, 10% of maximum speed of 15 m/s and 10% of typical heading change of 20◦) to the speed and heading values contained in the latest CAMs received from these neighbors. In the correction step, GNSS positions and IR-UWB ranges with respect to the neighbors with informed positions (i.e., for which a CAM has been received) are used to update the
Figure 7.1: Focused geographic area of Bologna city used in calibrated SUMO simulations, with mixed urban environments.
predicted values in our CLoc solution. On the contrary, non-CLoc refers to the data fusion of GNSS position, WSS speed, and IMU heading (i.e., using only local information).
The GNSS model and accuracy depend on both the portion of trajectory and the arbi-trarily assigned GNSS kind/class (see tables 7.1 and 7.2), while the WSS and IMU models are similar to that used in Chapter 6 (see Table 6.1). Besides, based on statistics reported in [8, 136] in a urban environment and in systematic LOS, as well as experimental illus-trations based on integrated IR-UWB modules taken from [133], the standard deviation of V2V range measurements is assumed to be 0.122 m, whereas the bias has a mean of 0.21 m. Finally, we assume no packet loss for simplicity but still account for non-visibility configurations caused by static building obstructions at intersections. In this case, some ranging measurements become harmful for the fusion and are rejected.
7.2.2 Results
Figure 7.2 and Figure 7.3 show the localization performance of each individual vehicle and over 10 vehicles in terms of empirical CDFs. Figure 7.2(a) shows that non-CLoc yields rather good performance even when the vehicles are equipped with only GNSS SPS receivers (i.e., about 0.8 m in median errors at vehicles 1, 5 and 9). Obviously, with better GNSS receivers like SBAS, DGNSS, and RTK, the performance gets better as
Table 7.1: GNSS quality associated to each portion of road of the Bologna scenario in Figure 7.1.
Street Environment GNSS quality
Via Tolmino open urban environment, large road with 3 by 3 lanes, sparse and medium-size buildings
nominal→1σ Via Sabotino intermediary urban environment, narrow road,
3 lanes, sparse and medium-size buildings
slightly degraded→2σ Strada Statale Porrettana,
Viale Giovanni Vicini
open urban environment, large road with 3 by 3 lanes, sparse and medium-size buildings
nominal→1σ Viale Antonio Silvani Intermediary urban environment, large road
with 3 by 3 lanes, tall buildings
slightly degraded→2σ Via S. Felice (outer) urban canyon (close to intersections),
ultra-narrow road with 2 lanes, very dense and tall buildings
severely degraded→5σ
Via S. Felice (inner) urban canyon (inner part), ultra-narrow road with 2 lanes, very dense and tall buildings
lost→N/A
Table 7.2: GNSS device kinds assigned to simulated vehicles in the city of Bologna.
GNSS device kind IDs of simulated vehicles
SPS 1, 5, 9
SBAS 2, 6, 10
DGNSS 3, 7
RTK 4, 8
depicted in Figures 7.2 (b), (c), and (d) respectively. Then, CLoc boosts further accuracy.
Particularly, for SPS vehicles (i.e., vehicles 1, 5, and 9), the gains are very impressive (about 50% in median errors). For SBAS vehicles (i.e., vehicles 2, 6, and 10) and DGNSS vehicle (i.e., vehicle 3), the gains are less significant but still high in the range 30–40% in terms of median errors. For RTK vehicles (i.e., vehicles 4 and 8), the gains are more modest because RTK is already extremely accurate. Note that we still observe an improvement at vehicle 4 in its high error regime (CDF at 95%) because it goes through the urban canyon with no GNSS signal at all during several seconds at the end of the simulation (see Figure 7.1), so that accuracy is improved through cooperation in this pathological case.
A closer look at Figure 7.2 reveals that except RTK vehicles like 4 and 8, other vehicles have rather different performance levels. It may due to the GNSS quality but via coop-erative message exchanges, it is expected that they achieve approximately homogeneous accuracy. One reason lies in the actual connectivity of the vehicles. Although we assume perfect packet reception rate, as already mentioned, we still account for non-visibility con-figurations. One tangible example is illustrated in Figure 7.4. When the vehicles change their direction and turn from Via Sabotino to Viale Giovanni Vicini (see again Figure 7.1), vehicle 2 is stopped and left behind due to traffic lights so it temporally loses connections
0 0.5 1 1.5 2
Figure 7.2: Empirical CDFs of localization errors of each vehicle in case of CLoc (GNSS+WSS+IMU+UWB) and non-CLoc (GNSS+WSS+IMU) for the Bologna scenario.
0 0.5 1 1.5 2 2.5 3
Figure 7.3: Empirical CDFs of aggregated localization errors over all 10 vehicles in case of CLoc (GNSS+WSS+IMU+UWB) and non-CLoc (GNSS+WSS+IMU) for the Bologna scenario.
with respect to other vehicles belonging to the same cooperating group (see Figure 7.4).
Therefore, vehicle 2 has poorer accuracy in comparison with for example, vehicles 6 and 10 (see Figure 7.2(b)). In addition, regardless of their nominal GNSS capabilities, pe-ripheral vehicles such as 2 and 7 are likely more penalized by poorer GDOP conditions in comparison with vehicles in the convex hull formed by the piconet’s relative topology. In realistic operating conditions however, each vehicle would benefit from cooperation with
1300 1350 1400 1450
Figure 7.4: Relative geometry of the 10 simulated vehicles at t = 130 s and t = 145 s for the Bologna scenario.
respect to vehicles belonging to different so-called piconet (including vehicles driving in the opposite directions, even for a short period of time), unlike in our restrictive scenario.
Figure 7.3 shows the overall performance (i.e., over the 10 vehicles and over their respective trajectories). It can be seen that CLoc yields rather good performance with a median error of 0.18 m and a sub-meter worst-case accuracy at 95% of the empirical CDF.
Thus far, simulations show that CLoc could reach the required 25 cm accuracy. Note that within the worst-case setup, we still achieve 18 cm accuracy with a probability of 50%.
Because we only exploit 10 mobility traces from SUMO, we are forced into cooperating with the provided set of neighbors. However, in practice, each vehicle would select in a dynamic -and thus, more optimal- way more optimal sets of neighbors as “virtual anchors”
over time, considering the relative problem geometry, as already discussed in Chapter 3.