Simulation Results - Simulation Results and Analysis

Chapter 5 Simulation Results and Analysis

5.2. Simulation Results

In our experiments, we evaluate the error of estimation position by comparing with the true position of vehicles. The performance metric used is root-mean-square error (RMSE) [26] , which is expressed in our experiments as follows:

(4)

RMSE is the common metric used for evaluating the accuracy of positioning. We define the real position of vehicle V_i is P_i^* (x_i^*,y_i^*) and estimated position of V_i is P^_i ( , x y_i _i) in our experiments, and the RMSE represents as the average distance between P_i^* and ^P_i with n samples.

First, we show the lane discrimination between GPS lane and video lane in Figure 5.2.

With the GPS error of 5 and 10 meters, this figure has shown the value of |GL – VL| = 0 of vehicles exceeded half of vehicles which are less position error than others, the result represent that half of vehicle with low error can help other vehicles to correct their position.

Figure 5-2 : Comparison the lane discrimination with GPS lane and video lane

Figure 5.3(a) shows the RMSE of the estimated positions with all vehicles are fully equipped and the sensing range is set to 50m and 150m respectively. When sensing range is 50m, the results show the position error can be reduced 25 to 30 percent (around 3.6m).

When sensing range is set to 150m and scaling factor α = 1, GPS error of 5m, the position error is under 3.3m. When α larger than 4, the error can less than 3m. But we found that when α > 6 the error could get larger in some cases. So, we set α = 5 as the default value of our system. The Figure 5.4 has shown the value of α is 4~6 and the weight is less than 1/5 with |GL – VL| = 1, that shows |GL – VL| = 1 can improve some accuracy. This figure also shows the helpless when |GL – VL| > 2. In the Figure 5.3(b) shows the RMSE when GPS error is 10m and sensing range is 150m, which can reduce the position error to 5.8m with the value of σ was 4~6. The improvement rate of VIP with different value of α and GPS error σ is shown in Figure 5.5. It shows the equal improving ability of VIP in different GPS errors and sensing ranges, and the accuracy by factor of 30 and 40 percent improvement respectively when α > 4.

(a) With GPS error of 5m (b) With GPS error of 10m Figure 5-3 : RMSE with different values of the scaling factor and GPS error

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Figure 5-4 : Distribution of position validation under different scaling factor

Figure 5-5 : Improvement rate with scaling factor and GPS error

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We also evaluate the accuracy with different ratio of fully equipped vehicles in Figure 5.6. With increasing the ratio of fully equipped vehicles the improvement of positioning accuracy also arises. When the ratio of fully equipped vehicles is less than 30 percent, the average number of neighbor vehicles is not enough, it makes the improvement of estimations results not obviously. The number of neighbor vehicles is around 7 vehicles with the all vehicles are fully equipped and sensing range is 150m, it can provide the best correction result in VIP system. In the Figure 5.7 we can see when the ratio of fully equipped vehicles more than 50 percent, the ratio of estimated vehicle is over 70 and 90 percent in different sensing ranges. It shows VIP system can improve the accuracy of positioning did not require that all vehicles need to equipped with a driving video logger.

(a) With GPS error of 5m (b) With GPS error of 10m

Figure 5-6 : RMSE with different ratio of fully equipped vehicles

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

VIP Error (sensing range = 150m, total vehicles) VIP Error (sensing range = 50m, total vehicles) VIP Error (sensing range = 150m, correction vehicles) VIP Error (sensing range = 50m, correction vehicles)

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

(a) With sensing range of 50m (b) With sensing range of 150m Figure 5-7 : Measure the ratio of correction vehicle with different ratio of fully equipped

vehicles

Figure 5.8 measure the accuracy with different vehicle flow rates. With the rate of 1,200 vehicles/hour, it shows the improvement of positioning lower than 1,800 vehicles/hour, because the former’s number of neighbor vehicles is less than the later that the reference vehicles is not enough for providing good correction. The vehicle flow rate of 2,400 vehicles/hour is better than 1,800 vehicles/hour, and when ratio of fully equipped vehicles less than 90 percent and sensing range is 150m that the RMSE of estimation position is less than 3m.

Figure 5-8 : RMSE with vehicle flow rates

The comparisons of the accuracy with different video sensing range and angle have shown in Figure 5.9 and Figure 5.10. In these results, we change the video sensing range from 50m to 150m. The result shows the larger sensing range may provide more number of neighbor vehicles, and then get better positioning. The sensing angle may have not any effect of positioning accuracy. Because these angles can coverage most of vehicles, the effect of number of neighbor vehicle is very low.

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

1200 Vehicles / Hour, Sensing range = 150m 1800 Vehicles / Hour, Sensing range = 150m 2400 Vehicles / Hour, Sensing range = 150m 1200 Vehicles / Hour, Sensing range = 50m 1800 Vehicles / Hour, Sensing range = 50m 2400 Vehicles / Hour, Sensing range = 50m

Figure 5-9 : RMSE with sensing ranges

Figure 5-10 : RMSE with sensing angles

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Sensing angle = 150°, Sensing range = 150m Sensing angle = 120°, Sensing range = 150m Sensing angle = 90°, Sensing range = 150m Sensing angle = 150°, Sensing range = 50m Sensing angle = 120°, Sensing range = 50m Sensing angle = 90°, Sensing range = 50m

We also evaluate the VIP system with 2, 3 and 4 lanes. The result has shown in Figure 5-11, the improvement rate of 2 and 3 lanes are similar, and the best result is 21 percent.

When all of vehicles are fully equipped vehicles and sensing range is 50m, the improvement rate is around 13 percent (4.3m), and the rate of 4 lanes is 2 times greater than 2 and 3 lanes.

It means our system is working better on 4 lanes.

Figure 5-11 : RMSE with different number of lanes

Finally, we assume the relative positions obtained by video sensing have error. We add 1~5% distance error in the relative positions. As shown in Figure 5-12, when the sensing range is 50m, the distance error is from 0.5m to 2.5m, the result has shown the error will reduce the accuracy of positioning. When the ratio of fully equipped vehicles is less than 30 percent, the RMSE of VIP is higher than GPS error. If all vehicles are fully equipped, the improvement rate is 12 percent (4.35m).

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

2 Lanes, Sensing range = 50m 2 Lanes, Sensing range = 150m 3 Lanes, Sensing range = 50m 3 Lanes, Sensing range = 150m 4 Lanes, Sensing range = 50m 4 Lanes, Sensing range = 150m

Figure 5-12 : RMSE with video sensing error

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Ratio of fully equipped vehicles

RMSE (meter)

VIP Error (σ = 5)

VIP Error (σ = 5, video error)

在文檔中影像輔助之協同式車輛定位系統 (頁 35-44)