A couple of questions about your original paper.

[Harvey]

1. Why isn't vehicle dynamics assumed to be x_{t+1} = x_{t} + v_{t} \Delta t + 1/2 a (\Delta t)^2?
2. The standard deviation of x_{t+1} should be \sigma_{IDM} \Delta t^2 / 2 instead of \sigma_{IDM} \Delta t^2 indicated in the paper.