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.
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 .
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.
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).
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.
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.
There are three main components in the ellipsoidal isopleth version of the lateral velocity - DTLB distribution that we focused on to formulate conclusions.
The only main difference is the DTLB within the lane, which is intuitive.