Scenario Evaluation

Homogeneous GNSS (S1)

Figure 3.6 shows the RMSEs of the position estimates of all vehicles as a function of time.

Note that the 15 vehicles need approximately 8 s to completely enter/leave the different areas (due to its length of 60×4 = 240 m and speed of about 30 m/s) causing some tran-sitions in GNSS precision levels, as depicted on the same figure. As expected, the CLoc outperforms the non-CLoc (i.e., stand-alone filtered GNSS) in terms of accuracy and ser-vice continuity (i.e., preventing the error from flourishing in harsh/lost conditions). In favorable GNSS conditions, the gains yielded by CLoc over non-CLoc are modest

(rela-30 m/s

vehicle with high-class GNSS receiver (𝜎 = 1 m) vehicle with normal GNSS receiver (𝜎 = 5 m) vehicle with low-class GNSS receiver (𝜎 = 10 m) (a) Scenario 1 (S1)

Figure 3.5: Topology of the evaluated VANET and associated configurations for S1 (urban canyon) and S2 (different classes of GNSS receiver) for the evaluation of links selection algorithms.

RMSE [m] normal GNSS harsh GNSS lost GNSS harsh GNSS

5 10 15 20 25

SD of GNSS residual errors [m]

filtered GNSS

Figure 3.6: Localization RMSEs (over vehicles) as a function of time for non-CLoc, CLoc with exhaustive fusion, and CLoc with selective fusion when GNSS quality varies depend-ing on the geographic area (S1).

tive drop in RMSE of about 9% by exhaustive CLoc and no drop by selective approaches) whereas in harsh or lost GNSS environments, huge improvements in accuracy are observed.

In particular, in comparison with non-CLoc, a relative fall in RMSE of 33% is experienced by exhaustive CLoc and of about 21% by both selective schemes in harsh areas whereas in GNSS-denied periods, relative drops of 30% and of 21% are reported respectively. The reason can be understood as follows: in comparison with the GNSS position, RSSI mea-surements to “virtual anchors” can contribute to the positioning performance but in a modest way due to the non-linear relationship between received power and state (derived from the distance to the known “virtual anchors”), the uncertainties of “virtual anchors”

exhaus. CRLB BCRLB fusion scheme

0 40 50 100 140 150

no. of required packets [packets/s/vehicle] ₀

0.5 1 1.5

RMSE [m]

normal GNSS harsh GNSS lost GNSS

Figure 3.7: Trade-off between the number of required packets for CLoc and the localization RMSE (over vehicles and time) with or without selective cooperation in different GNSS conditions (S1).

and the GDOP, the extrapolated/approximate RSSI values at fusion time, the RSSI shad-owing dispersion, etc. In other words, when the accuracy of the filtered GNSS remains high enough, there is little room for improvement by fusing with ITS-G5 as a source of range-dependent information through RSSI and vice versa, when GNSS performance is degraded, the accuracy gain through ITS-G5 is more noticeable.

Quantitatively, both CRLB and BCRLB-based selective fusion schemes are quasi equivalent, and suffer both from a RMSE increase of 10%, 18%, and 14% in normal, harsh, and lost GNSS respectively in comparison with exhaustive CLoc due to the infor-mation loss. Note that in our scenario, the positioning error in harsh GNSS conditions is superior than that in lost GNSS. This is not really contradictory since the “harsh”

zone is composed of 2 distinct areas (see again Figure 3.5) and the latter (i.e., that after the “lost” period) is more severe due to errors accumulation during the “lost” interval (i.e., reflecting the memory effect pointed out in [65]). From the communication point of view, selective CLoc dramatically reduces the number of required packets (more than 70% shown in Figure 3.7) considering an error increase of 14–18% in worst cases and of 10% in normal cases. Last but not least, from the processing and fusion points of view, the complexity of the particle-based core engine is mainly related to the weights update (see line 4 in Algorithm 1). Particularly, the complexity scales asO(P|S_→i,k|) where the number of particles P can be large (typically 500–5000). In our scenario, without link selection,|S_→i,k|= 14, whereas with link selection |S_→i,k| ≤4.

vehicle index

8 7 9 5 11 4 6 10 12 1 2 3 13 14 15

RMSE [m]

0 0.2 0.4 0.6 0.8 1

full/degraded class partial/degraded class full/clear class partial/clear class unclassified vehicles

exhaustive fusion CRLB-based selective fusion BCRLB-based selective fusion

Figure 3.8: Localization RMSEs (over the full trajectory) for different fusion schemes with and without selective cooperation at each vehicle (S2).

In summary, link selection is critical to significantly reduce the computational com-plexity and also network traffic (if coupled with Tx censorship mechanisms) without losing significant accuracy. In this specific scenario, BCRLB based selection (i.e., by design more adapted to heterogeneous GNSS conditions) can just match the selection scheme based on classical CRLB, as expected. In other words, all the vehicles experience approximately the same GNSS error regime so that the injected prior uncertainty information regarding their estimated positions is quite neutral from a selection perspective.

Heterogeneous GNSS (S2)

While matching the classic CRLB in scenarios considering homogeneous neighboring ve-hicles uncertainties (as in scenario S1), the BCRLB criterion shows its efficiency when considering more realistic heterogeneous large dispersion of neighboring vehicles uncer-tainties. Considering our illustrative example, one can classify vehicles into four classes of dispersion: (i) full topology (i.e., cars fully surrounded by neighbors) versus partial topol-ogy (i.e., cars on outside lanes); and (ii) clear GNSS (i.e., cars whose nearest neighbors have good GNSS/estimates) versus degraded GNSS (i.e., cars whose closest neighbors have poor GNSS/estimates), as reported in Table 3.3 (the remaining are not classified due to strong border effects).

Figure 3.8 shows the positioning performance in terms of RMSE (over the full trajec-tory) for each vehicle whereas Figure 3.9 exhibits the empirical CDFs for one representative vehicle of each class. Both confirm that in 2 degraded classes, when the nearest neighbors

error [m]

Figure 3.9: Empirical CDFs of localization errors for different fusion schemes with and without selective cooperation at 4 representative vehicles with distinct GNSS quality classes (S2).

Table 3.3: Classification of vehicles in Figure 3.5(b) with respect to the uncertainty dis-persion.

Criterion Full topology Partial topology

Clear GNSS 5, 11 4, 6, 10, 12

Degraded GNSS 8 7, 9

experience poor GNSS positions or estimates, the classic CRLB criterion neglecting the anchor uncertainties fails to capture the optimal set of neighbors (See the two top sub plots in Figure 3.9). In other words, the strong dependency of RSSI measurements onto distances to the neighbors in the FIM tricks the CRLB to choose among a small subset of the nearest candidates, regardless of their dispersion. As expected, in the 2 clear classes when the nearest neighbors have good GNSS or estimates, the selections are likely to be very similar leading to equivalent performance (See the two bottom sub plots in Fig. 3.9).

In brief, the second scenario accounts for more realistic heterogeneous conditions (at a smaller scale), where the proposed BCRLB solution would be definitely more helpful.

Note that we can also assume some vehicles with more advanced sensor package (e.g., lidar, camera, etc.) leading to more accurate estimated positions, thus contributing to achieve even better heterogeneous localization accuracy among vehicles. However, since

we have considered only the fusion of GNSS and V2V information at this stage of the study in this chapter, we simply manipulate the GNSS capabilities.

Preliminary Cooperative Application Impact

Although a larger application evaluation is left to future work, we confront here the link selection performance with tangible application needs. Considering the Highway Capacity Manual (HCM) recommendation of a 2-second time between two successive vehicle in free flow traffic, a typical cooperative traffic safety application would need to have a clear position awareness corresponding to at least the distance between two successive vehicles.

This translates to about 30 m and 60 m inter-distance considering a speed of 50 km/h in urban and 100 km/h on highways respectively. In the worst case, exhaustive CLoc yields an error of about 0.85 m (see Figure 3.6). Even while loosing 14–18% of accuracy through selective fusion, one would still get relative longitudinal error of 1.6% (respectively 3%) at 60 m (respectively 30 m)¹¹, and a fully acceptable increased error of 0.2% between an exhaustive and selective fusion.