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Uneven surfaces All

GPS

10 9

Turns Stops

Uneven surfaces All

GPS

Average estimation error (mph)

Average estimation error (mph)

Average estimation error (mph)

7 6 5 4 3 2 1 0 ring Inner time peak ring Innerak time e off-p r ring Outek time pea r ring Oute ak time e off-p

7 6 5 4 3 2 1 0 ring Inner time peak ring Innerak time e off-p r ring Outek time pea r ring Oute ak time e off-p

7 6 5 4 3 2 1 0 n ntow Dow k time pea n ntow Doweak time off-p wn Upto time peak wn Upto k time ea off-p

Average estimation error (mph)

8

8

8

8 7 6 5 4 3 2 1 0 n ntow Dow k time pea n ntow Doweak time off-p wn Upto time peak wn Upto k time ea off-p

Area and Time

Area and Time

Area and Time

Area and Time

(a) Local road, Shanghai, Offline
10 9 Turns Stops Uneven surfaces All GPS

ring Inner time peak ring Innerak time e off-p r ring Outek time pea r ring Oute ak time e off-p

7 6 5 4 3 2 1 0 n ntow Dow k time pea n ntow Doweak time off-p wn Upto time peak wn Upto k time ea off-p

Average estimation error (mph)

8

8

8

8 7 6 5 4 3 2 1 0 n ntow Dow k time pea n ntow Doweak time off-p wn Upto time peak wn Upto k time ea off-p

Area and Time

Area and Time

Area and Time

Area and Time

(e) Local road, Shanghai, Online

(f) Elevated road, Shanghai, Online

(g) Local road, Manhattan, Online

(h) Highway, Manhattan, Online

Fig. 14.

The average estimation error of the vehicle speed in Shanghai and Manhattan.

sample from GPS is unknown, the online estimation using GPS has lower accuracy). Further, we find that the offline estimation is slightly better than that of the online estimation, and this is because the value of acceleration error is not exactly accurate due to the lack of the next reference point information. Accuracy v.s. Reference Points: We next evaluate the estimation accuracy of our system by using only one type of reference points. We find that the average estimation error on local road is still lower than of GPS even if only one type of reference points is used in both cities. However, the speed estimation using turns or stops is worse than that of GPS under elevated road and highways due to the fact that there are less turns and stops can be used as reference points. Still, we find that by using uneven road surfaces only, we can achieve comparable or better accuracy when comparing with GPS under all types driving roads. Accuracy v.s. Type of Roads: Fig.14 shows the road type affects the speed estimation accuracy. In particular, the average speed estimation errors on the elevated road or highway are higher than that on the local road (e.g. in Shanghai, the average error of the offline and online speed estimation is 0.67mph and 1.23mph respectively on local roads, but it is up to 1.7mph and 2.5mph respectively on the elevated road). This is because there are less reference points on the elevated road and highway than those on local road. However, the average estimation error on elevated road and highway is still lower than that of GPS. Further, for GPS, we can observe the average estimation error on local road is higher than the error on highway due to the urban canyon environment (i.e., local road) causes lower GPS availability and accuracy. Finally, we find that the period of day and various districts slightly affect the estimation accuracy. The average estimation error at the peak time in financial district is slightly lower than at the off-peak time in living district respectively. It is 8

the heavy traffic that causes more stops and further increases the density of stops. Since only the density of stops is affected by traffic, overall performance of SenSpeed is not affected evidently by various districts and the period of day. E. Impact of Reference Points To further evaluate the accuracy and robustness of SenSpeed, we analyze the speed estimation errors using different percentages of reference points and compare the estimated speed with the ground truth collected from an OBD-II adapter. Fig.15 shows the CDF of the speed estimation errors using different percentages (i.e., 25%, 50%, 75% and 100%) of reference points. As we have seen, we can always get high accurate speed estimations for the offline speed estimation regardless how many percent of reference points are used. For example, 80% of estimation errors are lower than 1.2mph if all reference points are used for the offline speed estimation, and the accuracy shows no obvious change when reference points are reduced from 100% to 25%. For the online speed estimation, 80% of estimation errors are lower than 2.3mph if all reference points are used, and also the accuracy shows no obvious change when reference points are reduced from 100% to 50%. Even if the reference points are reduced to 25%, 65% of estimation errors are still lower than 2.3mph. Thus, the proposed online speed estimation is highly accurate and robust to different densities of reference points in urban environments. Although the accuracy of SenSpeed is affected by the density of reference points, excessive reference points do not contribute much to the estimation accuracy. For example, in the online speed estimation, the speed estimation errors using 50% reference points are very close to the estimation errors using 100% reference points. Thus, SenSpeed is robust when facing a decline of reference point density in urban environments, and has potential to be employed in rural area.

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