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Investigation of driver lane keeping behavior in normal driving based on Naturalistic Driving Study data.

ABSTRACT

Lane departure warning (LDW) systems can detect an impending road departure and deliver an alert to allow the driver to steer back to the lane. LDW has great potential to reduce the number of road departure crashes, but the effectiveness is highly dependent upon driver acceptance. If the driver perceives there is little danger after receiving an alert, the driver may become annoyed and deactivate the system. Most current LDW systems rely heavily upon distance to lane boundary (DTLB) in the decision to deliver an alert. There is early evidence that in normal driving DTLB may be only one of a host of other cues which drivers use in lane keeping and in their perception of lane departure risk. A more effective threshold for LDW could potentially be delivered if there was a better understanding of this normal lane keeping behavior. The objective of this paper is to investigate the lane keeping behavior of drivers in normal driving. The study will be based upon data extracted from the Integrated Vehicle-Based Safety Systems (IVBSS) Naturalistic Driving Study conducted by University of Michigan Transportation Research Institute (UMTRI). The study first presents the distributions of DTLB and lateral velocity during normal lane keeping and then examines the relationship between DTLB and lateral velocity as a function of lane width and radius of curvature.

CITATION: Johnson, T., Chen, R., Sherony, R., and Gabler, H., "Investigation of Driver Lane Keeping Behavior in Normal Driving based on Naturalistic Driving Study Data," SAE Int. J. Trans. Safety 4(2):2016, doi: 10.4271/2016-01-1449.

INTRODUCTION

Road departure crashes are one of the most dangerous crash modes in the United States. When a vehicle departs a roadway, there is a higher potential of impacting less compliant roadside objects, such as trees, poles, as well as other vehicles. In the U.S., road departure crashes account for 10% of all crashes, but are responsible for over 30% of all vehicle occupant fatalities [4]. Lane departure warning (LDW) systems are becoming increasingly common in the U.S. vehicle fleet to help reduce the number of road departures, or at least mitigate the severity of these departures [2]. Previous studies estimate between 11% and 23% of drift out of lane departure crashes could be prevented with these systems if implemented in the entire U.S. vehicle fleet [2]. LDW systems are designed to detect when road departures are imminent. The system can provide the driver with a visual, tactile, or audible warning so they may react and steer the vehicle back into the lane of travel. However, sometimes the LDW system may provide warnings when the driver feels there is no risk of departure. The concern is that drivers may become annoyed by these false-positive warnings and disable the system.

One promising strategy to increase driver acceptance of LDW is to tailor the alert to driver behavior and the driving environment. Naturalistic driving studies provide a foundation for determining driver behavior during lane keeping. By using naturalistic driving behavior data, the influence of road characteristics, such as lane width and road curvature, on driver behavior can be investigated as additional factors to optimize warning delivery time.

Although production LDW systems are proprietary and the algorithms governing warning intervention timing are not publically available, we believe these systems rely on a combination of the lateral distance between the vehicle's leading wheel and the lane edge, or the distance to lane boundary (DTLB), and lateral velocity to determine when a warning should be delivered. These two quantities are defined in Figure 1.

The National Highway Traffic Safety Administration (NHTSA) New Car Assessment Program (NCAP) has a component that tests the performance of LDW systems. The NHTSA procedure is structured as follows [5]:

* A constant forward speed of 72 kph (45 mph)

* A target lateral velocity of 0.5 m/s

* Two departure directions: left and right

* Three roadway markings: continuous white lines, discontinuous yellow lines, and discontinuous raised pavement markers

* Each combination of test conditions are repeated five times

Each test is performed by a driver who induces a lane departure event by steering the test vehicle towards the lane boundary. Prior to crossing the lane line, the driver releases the steering wheel and the DTLB is recorded when the LDW is received. This procedure is illustrated in Figure 2. The NCAP criteria for a successful test is when a warning is delivered to the driver with a DTLB between -0.3 m and 0.75 m, where positive distance represents a vehicle still in the lane of travel [5].

Fujishiro and Takahashi (2015) hypothesized lateral velocity may be a better metric than the NCAP DTLB criteria for determining thresholds for the LDW system to deliver a warning to the driver. The NHTSA method for evaluating LDW systems does not take into account varying lateral departure rates. Fujishiro and Takahashi (2015) studied naturalistic driving behavior in Japan and determined that in general, drivers have higher lateral velocities when they are near the center of the lane and lower lateral velocities as they approach the lane boundaries. The study also found that departures tended to occur as drivers entered narrower and sharper curved roads. They showed that lateral velocity and these other factors may be a better predictor of when departures may occur. Adjusting LDW thresholds and warning times to better fit natural driving habits could reduce the number of false-positive warnings and increase driver acceptance [1].

The objective of this study was to investigate the lane keeping behavior of drivers in normal driving. The study particularly focused on the distribution of lateral velocity and DTLB and the influence of lane width and radius of curvature upon these two metrics.

APPROACH

This study utilized data extracted from the Integrated Vehicle-Based Safety Systems (IVBSS) Naturalistic Driving Study (NDS) conducted by the University of Michigan Transportation Research Institute (UMTRI) [3]. The aim of the IVBSS Naturalistic Driving Study was to assess the effectiveness of integrated crash safety systems while also monitoring driver behavior. IVBSS evaluated a number of active safety systems including forward collision warning (FCW), lane change/merge (LCM) warning, blind spot monitoring (BSM), curve speed warning (CSW), and lane departure warning (LDW) [3].

The IVBSS-NDS randomly selected a sample of 108 drivers. Each driver was given a 2006 or 2007 model year Honda Accord equipped with a LDW system and instrumented for data collection. The drivers were instructed to drive as they normally would for 40 days. The first 12 days were a baseline period in which data was collected, but the LDW system was disabled and provided no warnings to the driver.

The remaining 28 days were a treatment period where the LDW system was enabled and provided the driver with warnings when a possible lane departure was detected. Data was collected for a total of 147,389 km, in which 12,760 unintentional drift out of lane departure events were recorded. Data was recorded at 10 Hz for the duration of every trip using the following instrumentation [3]:

* Forward facing camera and radar for lane detection, vehicle position, and other roadway characteristics such as lane marking type

* Yaw rate sensor to measure angular velocity

* Tri-axial accelerometer to measure longitudinal and lateral accelerations

* Differential GPS to measure latitude, longitude, and speed

Time series data was provided by UMTRI including the duration of the departure event, plus 30 seconds of normal driving before and 30 seconds after the event occurred. Data elements included key variables such as distance past lane edge, maximum excursion, and lane width for the 12,760 unintentional lane departure events.

UMTRI provided a subset of the IVBSS data which contained unintentional lane departure events. The constraints applied to select the data subset included [3]:

* Lane boundary type known and real (not virtual)

* Maximum lane tracking software confidence level 100%

* Lane tracker enabled

* No braking, lane changes, or turn-signal use during lane

departure events

* Buffer time of 5 seconds before and after any intentional

maneuver

* Vehicle returned to lane in less than 20 seconds (plus buffer)

* Speed above 40.2 kph (25 mph)

* Valid trip and driver

Note that the restrictions on braking, turn-signal use, and lane changes were only applied to the lane departure event. Some trips had intentional lane changes in the 30 seconds before or after the unintentional departure event. Some of the data also had less than 100% lane tracking confidence or virtual lane boundaries outside of the departure event and buffer window. Additional data quality checks were implemented to verify the data used for this study met the IVBSS criteria at all time points.

For our study, we wanted to focus on purely naturalistic driving behavior without the influence of LDW. We found the ratio of departure events per day for the treatment period was about half the ratio of departure events per day during the baseline period. This shows a significant impact of LDW on driver behavior. The system likely kept drivers out of potential departure situations or encouraged more cautious driving behavior. Therefore, only data collected during the baseline period was used in our analysis. This resulted in a subset of 5,833 lane departure events with no LDW intervention.

The IVBSS-NDS variables used in this study are illustrated in Figure 3. A lane departure event is defined by the instant the leading wheel crosses the lane boundary. The end of a lane departure event is defined by the instant the leading wheel fully returns to the lane [3].

The variable DistancePastEdge is defined as the distance between the leading wheel and the lane boundary. Note that the sign convention for DistancePastEdge is positive out of the lane.

Lateral Velocity

One of the main objectives of this study was to characterize natural driving behavior in terms of lateral velocity and DTLB. Vehicles in the IVBSS Naturalistic Driving Study were equipped with forward facing cameras used to track and record the position of the vehicle with respect to the lane. Specifically, the lateral distance the leading wheel traveled past the lane edge was recorded as illustrated in Figure 3. Our study used a simple time derivative estimate to calculate the lateral velocity as shown in Equation 1. The IVBSS Naturalistic Driving Study variable was called DistancePastEdge. The sign convention was positive distance outside the lane of travel. This convention resulted in positive lateral velocities when the vehicle was traveling away from the center of the lane, regardless of departure side.

Lateral Velocity = d(DistancePastEdge)/d(Time) (1)

The sign convention for DTLB, on the other hand, is for distances outside the lane of travel to be negative. In our study, we flipped the polarity of the DistancePastEdge variable when plotting the lateral velocity - DTLB distribution to be consistent with DTLB convention. The lateral velocity calculation was performed for the entire subset of baseline period events.

Artifacts of Machine Vision

After plotting the normal driving distribution, we found a small subset of the data contained high magnitude lateral velocities (above 5 m/s). These were artifacts of the machine vision and our differentiation method. These unrealistically high lateral velocities occurred when there were large measured changes in lateral DTLB for a single time step of 0.1 seconds. After manually reviewing a sample of these cases, these large DTLB steps were typically found to occur when there were obstacles hindering the lane tracking equipment. Some examples included camera washout from passing under an overpass, changes in pavement contrast, or poor lane markings, especially entering or exiting construction zones. However, the more prominent artifacts were generated when drivers made lane changes, passed through intersections, or approached a highway on or off ramp outside of the unintentional lane departure event window.

Although these high magnitude lateral velocities accounted for less than 0.1% of the time series data and did not significantly skew our results, many of them were removed from our dataset to focus on lane keeping behavior rather than changes in road demographics. Figure 4 illustrates the method used to remove artifacts that could be characterized by a steep spike.

Peaks were identified within each departure event, and any peaks found past the maximum excursion were flagged for removal. Most of the steep spikes like the two shown in Figure 4 were the result of an intentional lane change. Toledo and Zohar (2015) conducted a study on lane change duration. They found drivers may take between 1.0 and 13.3 seconds, with an average of 4.6 seconds, to complete a lane change [7]. A sample of plots using the IVBSS data similar to Figure 4 showed agreement with these reported ranges. Each sample peak duration was calculated by taking the difference of the two lower points, resulting in an upper limit of around 10 seconds and an average peak width lasting between 5 and 6 seconds. Therefore, a conservative 10 second window was used to remove any data associated with the intentional lane change spike.

Lane Width and Road Curvature

In order to extend the lateral velocity and DTLB relationship, our study also explored the effect of lane width and road curvature on these metrics. The forward facing cameras installed in the test vehicles recorded several key road characteristics including lane width, lane marking type, and offset from the center of the lane. Inertial sensors in the vehicle also measured vehicle kinematics such as yaw rate and lateral acceleration. A differential GPS tracked the position and forward speed of the vehicle.

To calculate the road curvature, we approximated each curve as a segment of a circular arc and used the angular rate and tangential velocity to compute the radius of curvature. The instantaneous tangential velocity was calculated using Equation 2. Given the speed and yaw rate of the vehicle, the radius of curvature was calculated by dividing the velocity by the yaw rate, as seen in Equation 3.

Velocity = Yaw Rate * Radius (2)

Radius = Velocity/Yaw Rate (3)

Following the approach of Fujishiro and Takahashi (2015), the radius of curvature was converted to a centripetal acceleration term, Curve G, defined by the vehicle velocity squared divided by the radius of curvature (Equation 4).

Curve G = [Velocity.sup.2]/Radius = Velocity * Yaw Rate (4)

The vehicles in the IVBSS database had small lateral departure distances and low lateral velocities. The departures were considered very minor. Because the events were minor, the roadway curvature characteristics were assumed to be very similar to the vehicle curvature characteristics. The Curve G and lane width were then merged with the time series data and calculated lateral velocity.

Data Visualization

To help visualize the large dataset generated in the IVBSS Naturalistic Driving Study, scatter density plots were used to show areas of high frequency in the lateral velocity - DTLB distributions [6]. This method was useful for determining trends in normal driving behavior.

The second method used to help visualize the distributions and incorporate the effect of other factors was to fit an ellipsoidal distribution to the data, following the approach of Fujishiro and Takahashi (2015). Equation 5 shows the probability density function of the 2D normal distribution in terms of lateral velocity and DTLB. In this equation, LV is the lateral velocity, DTLB is the distance to lane boundary, and [mu] and [sigma] represent the mean and standard deviation, respectively, of each variable.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Integrating Equation 5 over the region of an ellipsoid (S) gives the probability of data falling within this ellipsoidal isopleth area as seen in Equation 6, where the exponential portion of Equation 5 is set equal to -[c.sup.2]/2.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

In order to capture as much normal driving data as possible in these ellipses, a probability of 99% was selected for P. This represents the majority of all driving behavior in our sample population. Solving Equation 6 for -[c.sup.2]/2 and setting the solution equal to the exponential in Equation 5 gives the following distribution to be plotted as a function of lateral velocity and DTLB (Equation 7).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

In Equation 7, the variables LV and DTLB along with their respective means and standard deviations are based on the selected data road characteristics subset. When considering the effect of lane width on the distribution, the data was subset by Curve G first and then by lane width within each Curve G. When considering the effect of Curve G on normal driving, the data was subset first by lane width and then by Curve G within each lane width. The following groupings were used to generate data subsets:

* Lane width groupings: up to 3.25 m, 3.25 m to 3.50 m, and above 3.50 m

* Curve G groupings: up to 0.5 m/[s.sup.2], 0.5 m/[s.sup.2] to 1.5 m/[s.sup.2], and 1.5 m/[s.sup.2] to 2.5 m/[s.sup.2]

RESULTS

The following section displays the results of applying this approach to the IVBSS dataset.

Lane Departure and Road Characteristics

Figure 5 shows the cumulative frequency distribution of vehicle speed recorded throughout all time points in the subset of IVBSS Naturalistic Driving Study data. The median vehicle speed was 113.6 kph (70.6 mph). The number of time points used in each of the following figures is given by N.

Figure 6 shows the cumulative frequency distribution of the roadway lane width. Most of the data fell within a 1 m range between 3 m and 4 m, with the median lane width found to be approximately 3.4 m. This distribution was used to determine the appropriate lane width subsets previously described.

Figure 7 shows the cumulative frequency distribution of the maximum lateral distance traveled out of the lane with respect to the leading wheel. The median maximum distance past edge was approximately 0.1 m. Less than 2% of the departures exceeded 0.5 m out of the lane.

Figure 8 shows the cumulative frequency distribution of the calculated Curve G. Nearly all of the data (99.5%) fell between 0 m/[s.sup.2] (straight road) and 2.5 m/[s.sup.2] (moderate to sharp curved road), with a median of 0.2 m/[s.sup.2]. As with the lane width distribution in Figure 6. this distribution was used to select groupings for the Curve G subsets previously described.

Lateral Velocity - DTLB Distribution

Figure 9 displays the density scatter plot of the measured DTLB as a function of the calculated lateral velocity at every time point for the baseline period. The dark blue shows areas of low frequency occurrences, while the lighter, warmer colors up to yellow show areas of higher frequencies, or more common driving modes. The peak frequencies centers around a lateral velocity of 0 m/s and DTLB just below 0.5 m. This means that under normal driving conditions, drivers tend to remain straight, with zero lateral velocity with respect to the lane, when the leading wheel is about 0.5 m from the lane boundary-a distance that places the vehicle close to being centered in the lane.

Note that there are still a small percent (less than 0.01%) of data with high magnitude lateral velocities (above 5 m/s). The lane change spikes were removed, but there were still some artifacts from the machine vision that were difficult to remove for the large dataset. These were likely single point jumps that did not create the prominent peaks shown in Figure 4. However, since the outliers account for such a small portion of the data, they did not impact the density plot or ellipsoidal distributions when looking for effects of road characteristics on driver behavior.

Figure 10 isolates a window of the data displayed in Figure 9. Due to the sign convention established, negative lateral velocities represent recovery velocities as drivers move back towards the lane centerline. The selected window shows only positive lateral velocities in order to focus on how drivers behave as they approach the lane boundary.

The distribution in Figure 10 was then estimated by an ellipsoidal isopleth described by Equation 7. This ellipsoidal distribution approach provides a much cleaner visualization and analysis method for comparing trends. The distribution predicts the region of expected normal driving behavior, and in our study captures 99% of all driving behavior in the sample population. The ellipsoid for the baseline period data is illustrated in Figure 11. and primarily captures the yellow to green areas of the density plots shown in Figure 10.

There are three main components in the ellipsoidal isopleth version of the lateral velocity - DTLB distribution that we focused on to formulate conclusions. The lower boundary, or minimum DTLB, represents the furthest possible departure distance predicted for the driving population. The right hand boundary, or maximum lateral velocity, is the maximum lateral velocity predicted for the driving population. The intersection of the isopleth with the lane boundary represents the maximum lateral velocity predicted as drivers cross the lane line.

The method used to illustrate the overall ellipsoidal distribution was extended to help visualize other factors such as lane width and road curvature. Figure 12 and Figure 13 show the resulting distributions for our subset of the IVBSS-NDS data.

Figure 12 shows the effect of lane width on driving behavior within the sample population. The data was first split by the three Curve G groups, and then by the three lane width groups within each Curve G group. Within each Curve G group, we see the lane width ellipsoids converging to the same maximum departure distances. We also see similar maximum lateral velocities for each group. The only main difference is the DTLB within the lane, which is intuitive. If lanes are wider, drivers have larger driving regions and can move further from the lane boundary while maintaining their lane.

Figure 13 shows the effect of road curvature on normal driving behavior within the sample population. The data was first split by the three lane widths, and then by the three Curve G groups within each lane width group. We found that within each lane width group, as Curve G increases, or roads curvature becomes sharper, the ellipses increase in size. As the ellipsoid distributions grow, the function shows higher maximum lateral velocities and lower DTLB. This means that as Curve G increases and roads become more sharply curved, drivers tend to have higher lateral velocities and depart further from the lane of travel. If we look at the intersection of the lane boundary and ellipses, we also notice that as drivers approach the lane line from a positive DTLB (within the lane), the lateral velocity decreases.

Significance Testing

Table 1 quantifies the ellipsoid distribution lower limits illustrated in Figure 12 and Figure 13. The ellipse distributions estimate 99% of normal driving behavior, so this lower limit represents the maximum possible lateral distance traveled out of lane predicted for the sample driving population. The lower limit for both groupings were calculated for comparision. Table 1 can be used to illustrate the effect of lane width and road curvature on driving behavior and departure distances.

A one-way analysis of variance (ANOVA) was performed on both groupings. The ANOVA on lane width resulted a p-value of 0.84, confirming there is no significant impact of lane width on the normal driving distribution for this population. The lane width analysis is shown in Figure 14.

The ANOVA on Curve G resulted in a p-value of 0.0009. This was below [alpha] = 0.05, so we confirm that road curvature does have a significant impact on driving behavior. The Curve G analysis is shown in Figure 15.

Tukey's Honestly Significant Difference multiple comparison test was then performed for Curve G to determine which levels were significant. Comparisons between all three groups returned p-values below 0.05. Therefore, we conclude that the low, medium, and high levels of Curve G are significantly different from one another. This conclusion validates the visual inferences drawn from Figure 13 that maximum departure distance depends on road curvature.

DISCUSSION

The trends seen in Figure 12 and Figure 13 show some interesting characteristics about how lane width and road curvature affect normal driving behaviors. Fujishiro and Takahashi (2015) presented data supporting the hypothesis that under normal driving conditions, drivers tend to have lower lateral velocities as they approach lane boundaries. We also saw a reduction of lateral velocity near the lane line in the U.S. data, but the lateral velocities in general tended to be higher than the lateral velocities in the Japanese data.

Fujishiro and Takahashi (2015) found that drivers tend to depart more from the lane as the Curve G became sharper and lanes became narrower [1]. Our study using the U.S. data also showed this trend in Curve G. However, the IVBSS data does not show lateral departure distance varies in the same way with lane width. The lower limit of the ellipses did increase with increasing Curve G for all lane width groups, showing further lateral departure distances as the road curvature becomes sharper, as seen in Table 1. However, the lane width factor did not show narrower lanes resulting in higher departure distances. All lane width groups in each of the three Curve G subsets converged to roughly the same lower limit. This shows that lane width is not a significant factor and does not affect normal driving behavior for this particular sample population.

The findings from this study are important in understanding how drivers behave as they approach the lane boundary. One of the main reasons LDW systems currently have lower than expected acceptance rates in the U.S. is that drivers feel the systems are too sensitive, providing warnings when they feel in control with no threat of a lane departure. Many systems have sensitivity options or the ability to completely disable the warnings. However, reducing the sensitivity or completely disabling the system reduces the potential benefits if an actual departure was to occur. If the analysis from this study was performed on individual drivers over time, a scatter density plot could be generated for each driver. These personalized driver distributions could be used to set LDW thresholds for each individual based on when they deviate from their typical driving ellipse.

Our study is somewhat limited by the small amount of driving diversity and road demographics found in the IVBSS-NDS dataset. The majority of these minor drift out of lane events were detected when drivers were on the main highways surrounding the Ann Arbor, Michigan area. Future work may apply this analysis to other naturalistic driving studies to compare sample driving populations and road demographics. It would also be interesting to extend the study to include other roadway factors such as lane boundary marking type and lane side proximity, especially in terms of drivers approaching lane boundaries of opposite traffic flow. Another improvement to this study may include refining the methods for detecting and filtering machine vision artifacts.

CONCLUSIONS

This study investigated naturalistic driving behavior and the influence of lane width and road curvature on the distribution of lateral velocity and distance to lane boundary. The following conclusions were drawn for this population:

* Normal driving tends to center around driving straight about 0.5 m from the lane boundary.

* Lane width is not a significant factor in the normal driving distribution.

* Drivers depart further from the lane as road curvature becomes sharper.

* Drivers tend to have higher lateral velocities further from the lane boundary, and lower lateral velocities as they approach the lane boundary.

The methods and results from this study can be used to better understand natural driving characteristics and what factors are most impactful in the occurrence of unintentional lane departures. The analysis can easily be applied to other databases to look at general driving distributions, and could even be applied to individual drivers to study differences in personal lane keeping profiles. The results can aid in the development of LDW systems to better determine intervention timing and improve driver acceptance.

REFERENCES

[1.] Fujishiro, R., Takahashi, H. (2015). Research on Driver Acceptance of LDA (Lane Departure Alert) System. Enhanced Safety of Vehicles (ESV), Gothenburg, Sweden. Paper No. 15-0222.

[2.] Kusano, K. D., and Gabler, H. C. "Comparison of Expected Crash and Injury Reduction from Production Forward Collision and Lane Departure Warning Systems." Traffic injury prevention 16, no. sup2 (2015):S109-S114.

[3.] Sayer, I., Buonarosa, M., Bao, S., Bogard, S., LeBlanc, D., Blankespoor, A., Funkhouser, D., and Winkler, C. (2010) Integrated Vehicle-Based Safety Systems Light-Vehicle Field Operational Test Methodology and Results Report. UMTRI-2010-30. Ann Arbor, MI: The University of Michigan Transportation Research Institute.

[4.] Scanlon, J.M., Kusano, K.D., Gabler, H.C. (2015) The Influence of Roadway Characteristics on Potential Safety Benefits of Lane Departure Warning and Prevention Systems in the U.S. Vehicle Fleet. Proceedings of the 3rd International Symposium on Future Active Safety Technology Towards Zero Traffic Accidents. Gothenburg, Sweden.

[5.] Lane Departure Warning System Confirmation Test and Lane Keeping Support Performance Documentation. Washington, DC: NHTSA; 2013.

[6.] Henson, Robert (2005). Flow Cytometry Data Reader and Visualization. MATLAB Central File Exchange. Retrieved October 9, 2015.

[7.] Toledo, T., & Zohar, D. (2015). Modeling duration of lane changes. Transportation Research Record: Journal of the Transportation Research Board.

Contact Information

Taylor Johnson's email address is tj916@vt.edu

Rong Chen's email address is rjchen@vt.edu

H. Clay Gabler's email address is gabier@vt.edu

Acknowledgments

The research team would like to thank the Toyota Collaborative Safety Research Center (CSRC) and Toyota Motor Corporation for funding this study. The authors would also like to thank UMTRI for providing the IVBSS Naturalistic Driving Study data.

Taylor Johnson and Rong Chen Virginia Tech.

Rini Sherony TEMA

Hampton C. Gabler Virginia Tech.

Table 1. Ellipse distribution lower DTLB limit for baseline period

Minimum DTLB [m]                      Lane Width [m]
Minimum DTLB [m]           From 3.50  3.25 to 3.50    Up to 3.25

Curve G        Up to 0.5   -0.3407    -0.3266         -0.3846
[m/[s.sup.2]]  0.5 to 1.5  -0.3949    -0.3881         -0.4116
               1.5 to 2.5  -0.4648    -0.4642         -0.4670
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Author:Johnson, Taylor; Chen, Rong; Sherony, Rini; Gabler, Hampton C.
Publication:SAE International Journal of Transportation Safety
Article Type:Report
Date:Jul 1, 2016
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